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•

r.

A tandem Paul-Penning trap

mass measurement system

for radionuclides

A thesi:; submined to the Faculty of Graduate

Studies and Research in p~r!hl fulfillment

of the Tl'.quirements for fhe degree of

Doetor of Philosophy

Submined

by

Gary Rouleau

Physics Depanmem

McGiII University, Montreal

©July 1992

••• Nationallibraryof Canada

Bibliolhèque nationaledu Canada

Acquisilions and Direction des acquiSitions elBibliographie Services Branch des services bibliographiques

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L'auteur conserve la propriété dudroit d'auteur qui protège sathèse. Ni la thèse ni des extraitssubstantif:ls de celle·ci nedoivent être imprimés ouautrement reproduits sans sonautorisation.

ISBN 0-315-80265-0

Canada

Abstract

A new high-precision atomic mass measurement technique based on a tandem Penning

trap system is described. Data from the mass measurements of l'Ubidium and strontium are

analyzed to reveal what infonnation desirable for nuc1ear physics can be extracted and to

indicate the limitations in the presently employed set up at the ISOLDE facility at CERN. The

possibility of substantially improving the Penning trap collection efficiency through the use

of a Paul (radio-frequency quadrupole) ion trap as a collection device for preparing the

radionuclides hefore the measurement system is then presented. Results from engineering

tests on the perfonnance of the Paul trap at the ISOLDE facility are discussed. The work

concludes with suggestions for the design of feasible system to capture 100% of weak

ISOLDE heams. This new system is to he incorporated into the Penning trap set up at the

newly constructed ISOLDE-BOOSTER facility.

Résumé

Une nouvelle technique de haute précision pour la mesure des masses atomiques basée

sur un ensemble de deux pièges Penning est décrite. Les données des mesures de masse du

rubidium et du strontium sont analysées de façon à révéler la quar.titée d'information

pertinente à la physique nucléaire qui peut être extraite et à déterminer les limites du montage

expérimental présentement utilisé à ISOLDE au CERN. La possibilité d'améliorer de façon

significative l'éfficacité de collection du piège Penning en l'utilisant un piège à ion de Paul

(quadrupôle radio fréquence) pour accumuler et préparer les noyaux radioactifs

préabablement au systéme de mesure est ensuite présentée. Les résultats de test d'ingénierie

du componement du piége à ion Paul à ISOLDE sont discutés. Cet ouvrage se conclut par

des suggestions pour la conception d un systéme réalisable pour capturer 100% des faibles

faiseau d'ISOLDE. Ce nouveau systéme sera incorporé au montage de pi.ége Penning du

"ISOLDE-BOOSTER" nouvellement consouit.

-.

Acknowledgements

There are many people who have conttibuted to the success of this project. The author

wishes to express his deepest thanks to Or. R.B. Moore (the Master) for his encouragement

and support, to H.-} Kluge, G. Savard, G. Bollen, T. OllO, H. Stolzenberg and St. Becker

of the University of Mainz in Germany and to H. Haas, K. Gase and the ISOLDE

collaboration. Thanks are given to Leo Nikkinen and Steve Kecani of the Foster Radiation

Laboratory for technical support and allthe people of the Foster Laboratory. Finally, 1 want

to thank everyone who made this project a success and whom 1 have forgollen to mention

above.

r am gratefulto McGilI University for the financial support given to me during this work

and the opportunity to slUdy al CERN, Switzerland. And to the University of Mainz for

financial assistance during my stay al Mainz and CERN.

Thanks 10 Roger Lacasse for translating the absttacl.

,,

(

Original Contribution to Knowledge

A new mclhod for atomic mass measurements is dcscribed in which two masses 78· 79Sr

have been measured for the first time. A precision of several keV was achieved.

Measuremcnls include two long isotopic chains, 75· 89Rb and 78·83, 87sr, leading to new,

more accurate, values for sorne of these masses. With the high precision obtainable from the

system, the tirst mass resolution of a ground and isomeric state was achicved, the particular

case being 84 . 84mRb.

The experimental work also achieved a successful deceleration of a 60 keV ISOLDE

beam at CERN to 30 eV, resulting in the first in-flight capture of a high velocity ion beam

into an electromagnetic (paul) trap. A capture efficiency of 0.2% was achieved for 132Xe

ions. Based on the knowledge gained from the experimental testing, a new system capable of

collecting up to 100% of the ISOLDE beam is suggested for the new ISOLDE-BOOSTER

facility.

TABLE OF CONTENTS

Introduction .

Chapter 1: Direct nuclear mass measurements using a Penning trap...... 5

1.1 The Penning trap........................ 6

1.2 The mass measurement system................................................... Il

1.3 Determination of the cyclotron frequency....................................... 16

1.4 Performance of the system...................... 19

1.5 Data evaluation and sources of error............................................ 20

1.6 Comparison with previous results........ 22

Chapter 2: Measurement of nuclear masses of Rb & Sr radioisotopes... 25

2.1

2.2

2.3

2.3./

2.3.2

2.3.3

2.4

2.5

2.6

The nuclear region of the Rb & Sr radioisotopes.............................. 25

Experimental methods and results............................................... 30

Discussion of results.............................................................. 31

Mass excesses..................................................................... 31

Two neutron separation energies............................................... 34

Nue/ear deformotion at N, Z = 38.............................................. 36

The direct observation of nuclear isomers...................................... 39

Limitations of the system......................................................... 43

A suggested improvement to the system........................................ 46

3.1

3././

3./.2

3./.3

3./.4

3.2

3.2./

• 3.2.2

Chapter 3: The Paul trap as a collection device for a Penning trap.. ..... 49

The dynamics of ions in a Paul trap............................................. 49

The Equations of Motion in a Pure RFQ Paul Trap........................... 52

Solutions of the Equations of Motion in a Pure RFQ Paul Trap............. 53

Energy of the beta oscillation..................................................... 58

Energy of the micromotion................................................... ...... 59

Phase space considerations of trap injection................................... 62

Phase space and Liouvi//e's theorem........................................... 62

Phase space of an ion beam...................................................... 63

r

3.2.3 Phase space volume of a partide trap........................................... 65

3.2.4 Adapting the phase space ofa beam ta that ofa partide trap................. 66

3.3 The deceleration of ions into a Paul trap........................................ 68

3.4 Properties of the extracted beam from a Paul trap 70

Chapler 4: Apparatlls and results..................................................... 73

4.1 The Paul trap....................................................................... 73

4.2 Vacuum system.................................................................... 76

4.3 Faraday cages. 77

4.4 High-voltage system.............................................................. 77

4.5 Electronic system. 79

4.5.1 Ejection pulse...................................................................... 79

4.5.2 Radio frequency generation 79

4.6 Ion source.......................................................................... 81

4.6.1 Off-line source 81

4.6.2 On-Une ISOLDE sources......................................................... 81

4.7 The ion observation system and calibration.................................... 84

4.8 Experimental procedure for efficiency measurements........................ 86

4.9 Experimental results............................................................... 90

4.10 Interpretation of results........................................................... 92

4.11 Testing of extracted pulse delivery to the mass measurement system....... 94

Chapler 5: Conclusion.................................................................. 99

Appendix:

The injection of high velocity particles into an electromagnetic trap.................... 103

References......... 108

Table of figures•

Figure 1.1 Penning trap electrode consisting of a central ring and end

caps with complementary hyperbolic surfaces. 6

Figure 1.2 Ion motioil in a Penning trap. 9

Figure 1.3 The tand;,;m Penning trap mass measurement spectrometer. 12

Figure lA The Penning trap transfer section. 13

Figure 1.5 The electrode configuration that produces an rf field which

couples the magnetron and c:;clotron motions. 14

Figure 1.6 The result of numerical integ,ration of the equations of

motion for a particle in a Pe\ming trap with an applied

azimuthal quadrupole eleco.ic field of frequency equ.ù to

the sum of the cyclotron ancJ magnetron frequencÏC'•. 15

Figure 1.7 A time of fIight spectra showing ions oif and in resonan';e 18

Figure 1.8 A typical time-of-flight resonance for 120Cs (TIro! = 64 s)with a resolving power of 1,500,000. 19

Figure 1.9 Shifts in the cyclotron frequency of a stable isotope ion(85Rb) over 3. 3.5 day period. 21

Figure 1.10 Mass comparison of the cesium isotopes. 23

Figure 2.1 A Nilsson diagram of the N, Z =38 region. 26

Figure 2.2 Mass excesses in the N, Z =38 region. 28

Figure 2.3 Differences beIWeen the theoretical pr:dictions and the

experimenial mass .~xcesses values for :he rubidium

isotopes. 32

Figure 204 Differences beIWeen the theoretical predictions and the

experimenial mass excesses values for the strontium

isotopes. 33

Figure 2.5 Deviation beIWeen the IWO neutron separation values from

the models and the experimenial values rubidium. 34

Figure 2.6 Deviation beIWeen the IWO neutron separation values from

the models and the experimenial values for strontium. 35.•

Figure 2.7 Shell energies plotted against the neutron number for Rb.

Sr. Kr. and Y isotopes. 37

Figure 2.8 The cyclotron resonances for 84j{b and 84mRb. The mass

difference is detennined to 463(10) keV.The measuremenlS

were perfor.1led a) shonly after the collection and b) with a

delay of several half lives of the isomeric state. 40

Figure 2.9 Cyclotron frequencies of the ground and isomeric state of

84Rb as a function of the delay time between collection of

the ions and the measurement 42

Figure 2.10 ISOLDE productionb yields for rubidium and strontium

radionuclides. 45

Figure 3.1 A membrane analogy to the Paul trap. 50

Figure 3.2 Lens an:ùogy to a Paul trap. 51.

Figure 3.3 Representative solutions to the Mathieu equation for the

axial motion of a 133Cs ion in an idea1 Paul trap of Zo ~ 14

mm operated al an RF of 250 kHz. 54

Figure 3.4 The beta oscillation frequencies (as a ratio of the drive

frequency) versus qz in a Paul trap. 55

Figure 3.5 The beta oscillation frequencies (as a ratio of the drive

frequency) versus Oz in a Pual trap. 56

Figure 3.6 The Mathieu stabilily diagram showing beta oscillationfrequencies v, and v, (as ratios of the drive frequency)

versus qz and Oz in a Puai trap. 57

Figure 3.7 The instantaneous kinetic energy for typical ion motion in

a Puai trap. The upper graph shows the axial displacemenl

versus lime. 60

Fifure 3.8 The two-dimensionai phase space diagrann for a collection

of particles undergoing simple hannonic motion in a trap. 65

Figure 3.9 The deceleration and injection system. 69

Figure 4.1 The configuration of the Paul trap collection system as

installed on the ISOLDE 3 beamIine. 74

f

Figure 4.2 A sectional view of the Paul trap collection system as., installed at the ISOLDE 3 facility. 75

Figure 4.3 Schematic of the electronic layout. 80

Figure 4.4 The test off-lïne ion source. 83

Figure 4.5 The extraction system. 85

Figure 4.6 Currents det~cted on the deceleration ground electrode at

various pedestal pOlentials. 88

Figure 4.7 Overall collection efficiency as a function of rf amplitude. 91

Figure 4.8 Collection efficiency as a function of ':le pedestal voltage. 92

Figure 4.9 Expectt:IÏ collection efficiency as a function of trar phase

space volume. 93

Figure 4.10 The configuration of the transmission test at the ISOLDE 2

facility. 94

Figw-e 4.11 Transmission tests of the current measured at the Penning

trap as a function of the bias voltage on the ion source 3.5

meters away. 96

Figure 4.12 Pulse shapes of the cum:nt in an ejected ion cloud from the

Paul trap detected a) just above the trap and b) at the

Penning trap, a distance of approximately 3.5 meters

further downstream. 97

Figure 5.1 The configuration of the. new mass measurement system to

he installed on the new ISOLDE facility at the CERN

booster accelerator. 100

Figure Al Cyclotron and magnetron motion in a Penning trap. 105

".

.'

r1

INTRODUCTION

Because the forces of the surrounding electrons on an atomic nucleus are so weak

compared to the nuclear forces within the nucleus itself, the properties of the nucleus at rest

at the center of an atom are determined almost completely by the nuclear forces themselves.

Measurements of the intrinsic ground state properties of the nucleus and how they change

with neutron-proton composition of the nucleus :L"e therefore ba~ic to understanding these

forces and how they fOTm the suucture of the nucleus. One of the earliest examples of this

was the discovery that the size of various nuclei showed that they had approximately the

same density, indicating that the nuclear force was of the shon-range saturable variety that

wOllld lead to the nucleus behaving like a very dense Iiquid drop.

Another basic propeny that was found early to he of great significance was the nuclear

mass. This is because the nuclear forces are so great that the resulting binding energy

makes a discernable difference in the mass of the nucleus compared to the sum of the

masses of its constituent protons and neutrons. This was fust realized with the publication

of F. W. Aston's "packing fraction" curve in 1927 [As27], showing essentially the average

binding energy per nucleon in various nuclei. This revealed one of the most imponant

propenies of the atomic nuclei; the binding energy with which the nucleons are bound

together. A study of this binding energy leads to one of the most imponant facts relating to

how our universe is puttogether; that the most stable fOTm of nuclear matter is the nucleus

of the iron awm.

Measurements of other nuclear ground state properties such as spin and electric and

magnetic moments have also been basic to understanding the interactions hetween nucleons

within the nucleus. In particular, such measurements have lead to the "shell" model of the

nucleus in which the whole nucleus takes on properties which ar" strongly determined by

only a few nucleons, in sorne cases only one, which seem to be uncouplcd from the

remainder of the nucleons which themselves seem to fonn a set of closed shells.

New measurements of nuclear masses have remained one of the most basic sources of

lInderstanding of the nuclear force. This is because the nuc1ear ground state mass is

determined not only by the strength and range of the nuclear force and also by such

mllltipanicle interactions as the pairing of particles which leads to the shell effects. It is

therefore a major parameter to he duplicatt'd by a nuclear mode!.

- 1 -

Presenùy there are three main interests for measuring ground state masses to very high

accuracy:

1. The testing of specifie theories, such as the conserved vector current hypothesis

[N079] in the 0+ - 0+ superallowed beta-decay; the isobaric multiplet mass equation

(IMME) [Ka79] with charge dependence, and coulomb energies [C088,Th50]. At

present, precise measurements of these effects are available for only very few nuclei.

2. The observation of systematic effects in long isotopie chains extending far from the

valley of beta stability. Studies restricted to nuelei at or close to the valley of stability

would miss many important features of the nucleus. Exact measurements of nuelei far

from stability would offer the possibilities of studying nuclear deforrnation and shell

effects, filling in the gaps in the differential mass measurements [Au89], and correlation

of nuclear masses with nuclear structure data such as nuclear charge radii.

The shell ~odel of the nucleus has had a great deal of success in accounting for

sorne of the structural features of the nucleus. Nuclear masses reveal shell structure

effects through systematic effects on the nuclear binding energy. The observed effects

are independent of theory and appear in the plots of two-neutron separation energies.

Discontinuities in these plots signal the presence of closed shells and the possible

location of sub-shells [Ze65].

Nuclear binding energies have also shown that the shell strengths for protons and

neutrons are correlated, giving a maximum strength at doubly magic nuclei. In the case

of neutrons the strength decreases with increased number of valence prolons or proton

holes. Similar effects are also found for protons.

Nuclear structure can he studied systematically by irregularities in the nuclear mass

surface [Au89]. The mass surface divides into four sub-sheets (even N - even Z),

(even N - odd Z), (odd N - even Z) and (odd N - odd Z) nuclei. The mass differences

between these sheets reflects the pairing energies of the neutrons and protons and

interactions of a c10sed shell nucleus with an odd neutron or an odd proton.

The nuclear mass surface can also reveal the shape of nuclei. Nuclear deforrnalion

is observed from the systematic behavior of double proton or neutron separation

energies as a function of Z or N. A sudden change in the two particle separation energy

signifies the crossing of a magic number or closed shell. Deforrned nuclei are secn as

graduai changes in slope, creating a broad hump in the two-neutron separation energy

(S2n) plots. In the case of sodium isotopes [Th75] a change occurs at N =20, and is

explained in terrns of the onset of prolate deforrnation [Ca75].

- 2 -

3. The testing of mass for.nulae 50 as to refine the input parameters. These would

lead to betler predictions of unknown masses, betler predictions of the existence or

non-existence of exotic nuclei, and a belter estimate of the limit of nuclear stability.

Measurements of ground state masses serve as important test of the predictions of

nuclear mass fonnulae. This importance is very evident for nuclei far from the valley

of beta stability where systematic comparisons of experimental values to values

calculated from present fonnulae reveal differences that can be significantly large. More

mass measurements farther from the valley of stability would lead to better predictive

power for stability against nuclear emission, islands of long lived superheavy elements,

or the possible existence or non-existence of exotic nuclei at the neutron drip line where

extreme neutron-proton imbalances can be found.

Better mass fonnulae would also provide a basis for nuclear level density

systematics [Ca65) which are critical parameters for the determination of neutron

capture and beta decay rates essential in the astrophysical r-processes, and for the

natural abundance of elements in the universe. Such mass fonnulae are particularly

needed in the case of the nucleosynthesis r-process. which proceeds along narrow

paths among the very neutron rich nuclei where the mass and half-lives are unknown

and perhaps may never be known due to an inability to produce them on eanh.

The masses of the nuclei of stable isotopes are now generally known to within an

accuracy of a few keV. These have been determined by classical mass spectrometric

methods using static electric and magnetic fields. The nuclear masses of unstable nuclei

were first obtained indirectly from the total beta decay energy (Q{3) to a nuclei of known

mass. This Q{3 was determined from beta-gamma coincidence by summing the energies of

a beta decay to a particular state in the daughter nucleus with the energies of any gamma

rays emitled in the decay of that state to the ground state. The mass of a nucleus was then

detennined by adding the Q~ values to the known mass of the daughter ground State.

However, for unstable isotopes away from the valley of beta-stability the error grows

rapidly. This is because of the summing of errors in the many mass differences linking the

mass of an unknown isotope to that of a wel1 known mass. and from the laek of detailed

knowledge in the level schemes. For example the errors in the work of Decker et al. (DeSl)

on the nuclear masses of the neutron rich cesium radionuclides rises from 5keV for 139Cs

to 900 keV for 146Cs. Mass measurements from beta-endpoint energies with the use of

intrinsic germanium spectrometers have recently becn developed and have obtained better

accuracies (~40 keV) for high energy heta decay studies yet difficulties remain in the

deterrnination of the decay scheme of nuclei emitting such energetic beta particles.

-3-

T1

Other more direct methods for detennining the nuclear masses of unstable nuclei are

based on measuring the total energy involved in a decay or on detennining the energy

balance in particle reactions wè.ich lead to a specific radionuclide as a product and in which

the energies of ail the outgoing particles can be accurately detemlined. These methods can

have eITors in the range of 20 to 100 keV but depend on the existence of an a decay or a

suitable combination of accelerated particle and target nucleus.

Until recently, direct mass determinations of radionuclides, i.e. detenninations

requiring no prior knowledge of neighboring isotopes or level schemes, nor of reaclion

kinematics leading to their production, were limite<! to nuclei close to stability so that their

life-times pennitted the same spectrometric methods as were applied to the stable nuclei.

The f1l'St extensive direct rneasurements of the masses of short-lived radioactive nuclei were

made in the 1970's with a Mattauch-Herzog spectrometer instal1ed on-line to an isotope

separator at CERN [Th75]. This spectrometer consists of a radial electric field energy filter

followed by a unifonn magnetic field momentum filter, where the energy filter is used as a

collirnator with velocity dispersion. The fmt measurement of a long isotopic chain of alkali

elements was accomplished with such a spectrometer by the Orsay group [Au86] at

ISOLDE at CERN, achieving a resolution of 10 000 and a precision of 10 to 100 keV.

These results clearly showed the value of direct nuclear mass measurements and

prompted the application of other more powerful techniques to such measurements. One of

these techniques is the determination of the ion cyclotron frequency in a Penning trap. In

principle, this can be determined 10 extremely high predsion and related very accuralely to

the mass of the ion with only & single ion in the trap at any one time. This accuracy and

sensitivity make the technique very attractive for direct detennination of the mass of the

very rare and very unstable radionuclei.

This thesis describes such a new high-precision mass measurement system at the

ISOLDE facility at CERN and results obtained with that system. These results show that

the system can yield the son of information desired for nuclear physics in a broad range of

radionuclides. The power of the method used in the system is demonstrated in the first

successful mass-spectrometric resolution of a nuclear isomer and its ground state.

The thesis also presents the limitations of the method as it is presently employed. The

possibility of substantial improvements to the technique by the use of a Paul (radio­

frequency quadrupole) ion trap as a col1ection device for preparing the radionuclides for the

measurement system is then presented, with results of tests on the performance of such a

system at the ISOLDE facility. It will conclude with a suggestion of a feasible system ta be

installed at the new ISOLDE facility being construeted at the CERN proton booster.

-4-

CHAPTER 1

DIRECT NUCLEAR MASS MEASUREMENTS

USING A PENNING TRAP

Ion cyclotron resonance was discovered with the invention of the cyclotron by E.O.

Lawrence at Berkeley in 1932. However, the first application of cyclotron resonance to

accurate mass measurements on heavy ions (A> 4) was in the invention of the Omegatron

by Sommer, Thomas and Hippie in 1951 [SoSl]. This device usoo collinear e1ectric and

magnetic fields, very much as use<! by Penning in the mid-1930's to investigate gaseous

discharges, to hold low energy ions in stable trajectories i:, a high magnetic field for long

enough 10 get accurate measurements of their cyclotron frequencies. The application of the

Fourier transform technique to such a device by Comisarow and Marshall [Co75] has 100 to

its very extensive use in mass spectroscopy, where modem forms of the device are usually

referrOO to as "Penning trap mass spectrometers". Mass resolving powers of over l()6 for

each mass in a single collection of ions with a wide mass range have been routinely

achievOO in a wide variety of applications, particularly in organic chemistry.

Recently there have been major developments in the art of cyclotron resonance in

Pc::nning traps. For example, using very stab:e operating conditions over a long period of

lime, Wanczek [Wa89] has achieved resolutions of over 4 x 108 for 40Ar ions.

Furthermore, by using high-precision techniques of trap construction, operation and

analysis, very high accuracy has been demonstrated as being possible. Van Dyck,

Schwinberg and Dehmelt [Dy84] were the fITst to dramatically demonstrate the possibilities

by their work on a single electron in a Penning trap (which they have callOO "Geonium").

The accuracy of their measurement of the magnetic moment of the electron, 4 parts in 1012,

is about 900 times better than previous measurements by other techniques. Recently, very

high accuracy has also been extendOO to mass measurements of light ions. Comell et al

[C089] have demonstratOO an accuracy of 4 x 10-10 for the mass ratio of CO to N2 and Van

Dyck et al [Dy89] have achievOO similar accuracies in the comparison of the masses of

protons, deuterons and 3He+ ions with that of 12e. Wineland et al [Wi83] have predicted

that accuracies of mass measurements near 1 part in 1013 should be possible.

The theory of the Penning trap as it applies to nuclear mass measurements is presentOO

by Bollen et al. [B090] and in the thesis of Bollen [B089]. A description of a working

system for such measurements is presented by Schnatz et al. [Sc86]. This thesis will

present only a summary of the important points conceming such an application with an

- S -

emphasis on applying the technique to a broader range of measurements then has presently

been possible,

1.1 The Penning Trap:

A "Penning trap" has come to mean any device that uses two repelling electrodes

mounted on the axis of a magnetic field solenoid to conlain the motion of charged particles

collected between the electrodes. An "ideal" Penning trap is one in which an attractive ring

electrode is mounted centraily between the two repelling (end) electrodes and the electrodes

have complementary hyperboloidal surfaces as shown in figure 1.1. The electric field

necessary to confine the particles axially is achieved by the application of a voltage (V0) on

the end electrodes relative to the ring electrode.

z tB

1-- -"

Zo

ro r

,2 z2Electrode contours defined bY"2 -"2 = ±1

'0 Zo(+ for ring, - for end electrodes, '0 ="Zzo)

-1"'"

Figure 1.1 Penning trap e1ectrodes consisting of !! centrai ring and end e1ectrodes

with complementary hyperbolic surfaces.'.

-6-

( ln slich an declfode configurJtion the trapping electric field is a pure quadrupole. 1 The

radial and axial clectric field components, for positive ion confinement, are therefore

aEr = :2 r ; Ez =-az. (I.I )

whcre rand z are the radial and axial coordinates in a cylindrical system and the

proportionality factor a is related to the applied voltage and the electrode separation through

(1.2)

The axially restoring force confines the ions to an axial oscillation of angular frequency

Wz given by

(j)Z2 = a !L .m

(1.3)

(

where q and mare, respectively, the charge and mass of the particle.

The rudial electric field in itself would produce radia!!]' un:;table motion. Stable radial

motion is achieved by the superimposed magnetic field along the axial direction. In such a

magnetic field with no electric field a charged particle would undergo simple cyclotron at an

orbit frequency % = 'i..n B. However, the electric field perturbs this motion resulting in

two new stable solutions for the orbit. This can be most easily seen by noting that the

ccnlripetal force to keep a charged particle in a circular orbit is provided by the net radial

force after subtracting the electric force from the magnetic force;

V2m - = qvB -qErr (lA)

Motion which is stable in r (i.e r constant) may be described by a constant angular

velocity ro relmed to the velocity by

v = ror . (1.5)

(

1This assumes thalthe electrode surfaces extend 10 inlinity. ln practise they are truncated at a distanee l'rom

the trap center of abouttwice the radius of the ring electrode. This introduccs higher order multipoles which

make lhe lt:lp "noll-ideal". However, by using correction eleetrodes in the gap, the strength of the electric

Iïdd l'mm lhese higher order multipoles can he reduced 10 insignilicance over the usable volume of the uap(BolleIlIBo90J).

- 7 -

•Rewriting (lA) with this substitution eliminates the dependence on r;

ma9- = qWB-q~ (1.6)

and substituting B and a by their expressions in terms of Wc and Wz yields a simple

quadratic equation for ~

(1.7)

The !wo solutions of this equation are

(1.8)

1

The solution with the plus sign in front of the square root is often referred to as the

actual cyclotron frequency W+. This "cyclotron" motion can be thought of as a

perturbation of the cyclotron motion in no elecoic field in which the orbit frequency is

reduced by a cancellation of a part of the Lorentz force by the elecoic field. (Note that both

the Lorentz force and the elecoic force are proportional to the radius and so the electric field

can masquerade as a perturbation of the magnetic field.) Typically for heavy ions in a

Penning trap the cyclotron frequency will be perturbed downward by about 0.5%.

The solution with the minus sign (W. ) is known as the magnetron or precessional

frequency. A pure magnetron motion is a slow circular orbit in which the Lorentz force

and the elecoic force are almost balanced because of the very small cenoipetal acceleration

on the slow orbi!. By noting that the sum of the two solutions in (l.8) is just the

unperturbed cyclotron frequency ClIo, the magnetron frequency is seen to be just the

perturbation of the cyclotron frequency. or about 0.5% in a typical trap.

It is to be noted that these !wo solutions are not only purely circular about the elecoic

field axis but are also independent solutions of linear differential equations describing the

motion. Thus any combination of the two types, at independent phases and amplitudes, is

also a solution for the motion of a charged particle. Combining these motions with the

axial motion gives, in general, three independent motions for a charged particle. The

typical motion of a charged particle in a Penning trap is therefore as shown in Fig. 1.2

·8-

-----------L\f\; ;;~~-~---- J -------.-.y\ ........./ Cyclotron

!, 1'-"\ motion r\':iJ···.~... \'. ~\f' ~~i~n " ; ; ; /; ......\ / ~;\ ";.-._-- ----~. \ - - - - - - - - - - - - - - - - - Ma~netron

Path of center of \ . monon

cyclotron molion r V

Figure 1.2 Ion motion in a Penning trap.

There is a set of very simple equations relating these three uncoupled angular

frequencies;

(1.9)

(LlO)

(1.11 )

Thus it can be quickly calculated that if in a typical Penning trap the magnetron

frequency is about 0.5% of the cyclotron frequency, then the axial motion frequency will

he about 10% of the cyclotron frequency.

The most direct detennination of the mass of an ion in a Penning trap would he through

an observation of the unpenurbed cyclotron frequency COo since this depends only on the

magnetic field. which can be made very unifonn and stable, and not on the electric field

which is much more difficult to detennine with high accuracy. However, it is seen from

-9-

•

.'

the above equations that there is no motion at this frequency in an ideal Penning trap (Le.

one with a unifonn magnetic field along the axis of a pure electric quadrupole field).

However, (1.9) shows that in such a trap, the sum frequency W+ + W_ is equal to the

unperturbed frequency and an observation of it would therefore give Wo. Essentially, it

would eliminate the need for detennining the electric field except, of course, to establish

that il is indeed purely quadrupolar.

Very high precision observation of resonance at the unperturbed cyclotron frequency of

ions in a Penning trap using ejection of ions from the trap was fust demonstrated by Grl!ff

et al. [GrSO). Although the nature of the coupling of the cyclotron and magnetron motions

that led to the observation of such a "resonance" was not understood at the time, the

possibility of directly observing the unperturbed cyclotron frequency made the technique

very attractive for nllclear mass measurements on very rare radioisolopes since the detection

by 00serving the ejected ions themselves allowed the technique, in principle, to be used

wilh only a few ions (~ 100) in the trap at any one time. A program to exploit this

technique was therefore initiated by a Mainz-McGiIl collaboration and put forward at the

Mont-Gabriel workshop [DaS4).

One of the fust things to be realized in an application of high-precision Penning trap

mass spectrometry ro short-Iived radionuclides is that it is necessary to be able to inject ions

into the trap from an outside source. This is because such nuclides are only produced at

large accelerator facilities in very Iimited quantities and in the presence of much more

numerous longer Iived material. They are only available in the purity required for high

accuracy measurements as high velocity ion beams from an on-Iine mass separator such as

ISOLDE at CERN. Collecting a reasonable fraction of such ion bearns in a trap will involve

apparatus which, if incorporated in the trap itself, would severely compromise the trap as a

high precision instrument. It is therefore necessary to collect the ions extemally and to then

carefnlly inject them into the trap.

The method chosen to accomplish this was implantation of the original ion beam into a

foil followed by desorption and re-ionization for collection in a Penning trap specifically

designed for this purpose. The collected ions were then delivered to the precision Penning

trap for the mass determinations. This system is referred to as a tandem Penning trap mass

spectrometer, and will be described in the following section.

-10 -

1.2 The Mass Measurement System:

The tandem Penning trap mass spectrometer as installed at ISOLDE 2, CERN is shown

in ligure 1.3. The first trap (trap#I),located in the pole gap of an electromagnet having a

0.7 Tesla lield and a homogeneity of 10-3 gauss/cm3, is used as a collection device for the

continuous ISOLDE ion beam. Since a trap can only accept a pulsed low energy (= leV)

beam this trap perfonns the function of decelerating and bunching the initial ISOLDE beam.

ln order to deline the energy more precisely the ions are then cooled to remove any residual

kinetic energy from the ion creation process. The second (trap#2), used for the high

precision measurements, is placed in a stable (decay rate of 1O-8/hr) and homogeneous

(variation of less than 10-7over 1 cm3) 5.8 Tesla field of a superconducting magnet. The

traps are connected by a transfer section, a series of drift tubes, diaphragms and

electrostatic lenses to guide the ion bunch into the fringe field of the superconducting

magnetic in a manner which prevents the radial energy from increasing (figure 1.4). Anultra-high vacuum (:S:l0-9mbars) is essential in the high-precision trap in order to minimize

ion collisions with residual gas molecules which can cause broadening ?nd shifts in the

resonant frequency. Efficiencies of 70% have been achieved for the transfer ofions from

trap#1 to trap#2.

The capture of the raàlonuclide ions delivered by ISOLDE is achieved in trap#l by

implanting about 108of the 60 keV ions into a rhenium foillocated in the lower end

electrode of the trap. The foil is then tumed to face the interior of the trap and heated by a

pulse of D.C. current. Neutral atoms are released and ionized by the hot rhenium surface

before leaving il. A fraction of these ions (= 100) intemct sufficiently with helium gas

deliberately introduced into this trap so as to achieve stable orbits in the trap. The helium

gas then cools the ion motions until the collected ions sit at or near the boltom of the

potential weil at the trap center.

The method by which this is accomplished is described by Savard et al. [Sa91]. The

buffer gas cools the axial and cyclotron motions by a viscous drag on the ions. However,

this wouId nonnally result in the ions mlgrating down the sides of the electric potential

saddle towards the ring electrode. This is due :0 the inherent instability of the magnetron

motion; a decrease in magnetron energy results in a increased magnetron radius. Thus the

energy removed from the magnetron motion by collisions with a background of buffer gas

causes the ions to migrate oUlWard from the center of the trap.

To reduce the magnetron radii, and thereby center the ion cloud in the trap, energy has

to be actually added to the magnetron motion. As described in Bollen et al [Bo90], this cao

• 11 -

. transtersec~ion

transter of pulsedlkeV ion beam

•

1050mm

I=i"'.-I----L. channel platC2 dC2teetqrr mcasuremcnt ot lime of night

r- ni drift tubeJII~ 1transtormation ot radial ta axial .ncrgy

,. TRAP 2fi:':,l''II~ dee<l erelion and traooing

indueuon al cyclotron fr.qu.ney Wc

l' j LJ inerease of rodiel energy'- l': d .1::. pulse ejcetion

Il==:====R===:3m~~T~~;=CR====YO:P==UHP~~III :! ~.-:-J

""""""~""" ""'"

h2 m:==~

~~2~;:~1",,\'\~~,f\"""""'1~'r ~; .,-" dl rURsoi- TCAP 1:I~ l, . 1 W-- . "

: ~~~lr• .;gr- ~~r~~~~~:;no~~=ns1 =~~.~.\~. 1 pulm '!"::on

1 - ;:5; '-'-'-'1 1 ~=-....:..

'~l. WHI~7-;---7--7--;-,---- I:OLDEL-.-J bC2cm linC2

f =

SO ke'l ion bocm

'.

Figure 1.3 The tandem Penning trap mass measurement spectrometer.

- 12·

1 11 1 L~

Il15 mm-i 1-

i Figure 1.4 The Penning trap transfer section.

- 13-

be accomplished by applying a weak radiofrequency azimuthal quadrupole electric field

(i.e. a field which has an electric potential which varies as sin40P where oP is the azimuthal

angle) at the sum frequency of the cyclotron and magnetron motions. In that work it was

shown that such a field, which is produced by splitting the ring electrode into four

quadrants and applying the radiofrequency voltage between the electrodes as shown in

figure 1.5, couples the cyclotron and magnetron motions.

Figure 1.5 The electrode configuration that produces an rf field which couples the

magnetron and cyclotron motions

Bollen et al showed that if the radiofrequency of the weak applied azimuthal quadrupole

field is the sum of the cyclotron and magnetron frequencies then the coupling of these

motions that it induces will result in a slow beating between the magnetron and cyclotron

motions in which a purely magnetron motion will be transformed into a purely cyclotron

motion and back, the period during which this occurs being determined by the strength of

the applied field (see fig. 1.6). Since the buffer gas cooling removes most of the cyclotron

motion, the coupling by the applied field only has the magnetron motion upon which to

work and so it transforms that motion into cyclotron motion. Since the cyclotron motion is

continually being removed by the buffer gas, the magnetron motion itself is continuously

reduced until the ions are centered in the trap.

This cooling scheme is also mass selective, since the coupling of the cyclotron and

magnetron motion is achieved only when the applied resonance frequency is the sum of the

cyclotron and magnetron frequencies and it was shown above that in an ideal Penning trap

- 14-

3

2

4

r

Figure 1.6 The result of numerical integration of the equations of motion for a

particle in a Penning trap with an applied azimuthal quadrupo1e e1ectric field of

frequency equal to the sum of the cyclotron and magnetron frequencies. The center

of the trap is indicated by a cross. The initial motion was chosen to he completely

magnetron and the quadrupole field strength was chosen to cause a transition to

completely cyclotron motion in about 60 cyclotron orbi:s. Frame 1 shows the fust

32 orbits whereupon the cyclotron and the magnetron radius have become equal.

Here, as in frame 4, :he trace for an undisturbed magnetron orbit is shown for

reference. Frame 2 shows the orbits leading to completely cyclotron motion while 3

and 4 show the progression back to completely magnetron motion.

- 15 -

1

this is just the unperturbed cyclotron frequency of the selected ion. To further favour the

selected ions of a given mass, unwanted ions of a different mass can be purged from the

trap by applying a radiofrequency dipole field at their cyclotron frequency to directly ex:cile

them into cyclotron motion.

The remaining, i.e. selec:ed, ions are then ejected from the trap as a single bunch by

applying a pulse to the ring and lower ene; dectrode. The ion bunch is accelerated to 1 keV

and guided to the second trap while keeping the enclosure of the ion cloud, i.e the transfer

section, biased to a -1 kV potential.

At trap#2 the ions are decelerated to a few electron volts before entering and are then

captured in-flight in the trap (ScS6]. This technique requires swilching the potential of the

lower end cap to that of the ring. Once the ions of interest have entered the trap, the

potential is raised and the ions are trapped. Captured in trap#2 in this way. confinement

times of the order of tens of minutes have been achieved in that trap.

1.3 Determination of the Cyclotron Frequency:

The cyclotron frequency is determined by the resonar.ce-time of flight detection

technique developed by Grllff et al. (GrSO]. The basis of this technique is that charged

particles which have acquired cylclotron motion while in the trap will transform the energy

of this cyclotron motion into ax:ial energy when they are pulied out of the trap into a low

magnetic field. This is a consequence of adiabatic ex:pansion of the cyclotron orbits, a

process in which the orbiting particle continues to encircle the same set of magnetic flux:

lines as it moves from a high to a low magnetic field and which ocurrs when there is a

gradual change of magnetic field strength within the orbit, as is the case in gentle ax:ial

ex:traction of a charged particle from a Penning trap. Perhaps the simplest way to

understand this process is to regard the cyclotron motion of a charged particle as resulting

in a magnetic dipole which has a rnagnetic potential energy while in the high rnagnetic field.

It is this rnagnetic potential energy which is transformed into axial kinetic energy upon exit

from the trap. In truely adiabatic expansion, the kinetic energy rernaining in the cyclotron

orbit will be proportional to the magnetic field causing that orbit. This means that when an

extracted particle n:aches a region of low magnetic field essentially ail of the kinetic energy

of its cyclotron motion while it was in the trap will be transformed into ax:ial kinetic energy.

If the initial ejection from the trap is gentle enough then the kinetic energy gained from

the magnetic potential energy can cause a significant increase in the ax:ial velocity of the

- 16-

!

extracted ions. This increase can be detected as a marked reduction in thc time-of-flight of

the extracled ions to the channel plate dete~:tor on the magnetic field axis.

For precise measurements of the ion mass it remains to be able to excite the cyclotron

motion by a resonance at the unperturbed cyclotron frequency. This is accomplished by

the same mechanism as used in the cooling Penning trap; the transformation of magnetron

motion into cyclotron motion by an applied azimuthal quadrupole field at the sum frequency

of the cyclotron and magnetron motions. In this case an initial nearly pure magnetron

motion is obtained by guiding the ions into the trap gently along magnetic field lines which

lead to a point off-axis by several millimeters. This results in magnetron motion of radius

equal to that distance. The azimuthal quadrupole field, again achieved by splitting the ring

electrode into quadrants and applying a potential as in figure 1.5, is adjusted in strength 50

that the conversion from magnetron to purely cyclotron motion is completed in a desired

time interval, usually about one second. (In this case there is no buffer gas cooling to

impede the growth of the cyclotron motion.)

This conversion process is markedly frequency sensitive. If the applied azimuthal

quadrupole field is not at the sum frequency of the magnetron and cyclotron motion, there

will be sorne initial transformation of the magnetron motion into cyclotron motion but

before the transformation is complete, the phase of the a;;plied field will be such that this

transformation will be undone. The result of loading the trap, applying the azimuthal field

and observing the time-of-flight of the extracted ions and repeating this sequence for

azimuthal field frequencies which scan over the sum frequency of the magnetron and

cyclotron motions is therefore a sort of resonance curve which dips sharply at that sum

frequency. BoUen et al. [Bo90] showed that in an ideal Penning trap, i.e one with

insignificant higher order dectric field components, the "re5Onance" curve was symmetrical

and has a FWHM very nearly equal to that of the Fourier transform of a radiofrequency

applied for the same time interval as the azimuthal quadrupole field.

Of course, in a practical system it is impossible to place all of the incoming ions at

precisely the same location in the Penning trap and with no initial cyclotrr'i energy. There

will therefore he a spread of final cyclotron energies resulting from the coupling of the

magnetron and cyclotron motions. Typical time-of-fIight records of a collection of cesium

ions (A = 133) with the applied field "off-resonance" and "on-resonance" is shown in

figure 1.7. It can be seen that there is a marked reduction in the time-of-arrival of the bulk

of the ions when the field is applied in-resonance. The shifts shown at the peak of the ion

intensity correspond to gains in kinetic energy of the ions of about 20 eV and to reductions

in the time-of-flight of about 40%.

- 17 -

Figure 1.7 A rime of f1ight spectra showing ions off and on resonance.

A typical resonance curve obtained by plotting the centroid of time-of-fIight data as

shown in figure 1.7 for different frequencies of applied azimuthal fields is shown in figure

1.8. This spectrum was obtained for the radionuclide 120Cs which has a half-life of 64

seconds. A FWHM of 0.5 Hz was obtained by applying the azimuthal field for about 2

seconds. At the unpeI1urbed cyclotron frequency of 759160.7 Hz this gave a mass

resolution of about 1 500 000.

- 18 -

i'; seo

~~ iI)l\, ,l''I!:.

1560

1 Il Il IlIl} l'II Il Il Ilf-:r:~5"O...Ju..

520u..C;

w500 l..,~ ~ F1IHH • 0.5 [HzJ-f-.80

;r

, ' .! •

·2 ·1 0 2

u - 759160.7 [H:: J

Figure 1.8 A typical time-of-flight resonance. The'data shown are for 120Cs

(T1/2 = 64 s) with a resolving power of 1,500,000.

1.4 Performance of the System:

Sïnce the mass system has come on-line in 1986,65 isotopes have been investigated of

which six were measured for the f1I'St lime (sec table 1.1).

Isotope

K

Rb

Sr

Cs

Ba

Fr

Ra

Ma5s Number

39

75,76,77,78,78m,80,81,82m,83,84,84m,85,86,87

78,79,80,81,82,83,87

118,119,120,121,122+122m,122m,123,124,125,126,127,128,129,130131,132,133,134,135,136,137,138,139,140

124,126,138,139,140,141,143,144

209,210,211,212,221,222

226,230

Table 1.1 Isotopes for which the cyclotron resonances have been determined with the

Penning trap mass spectrometer. The bold faced isotopes represent masses measured for

the fust time.

- 19-

A mass resolving power of over 2 million has been achieved for stable cesium ions (Le.

A = 133) but is deliberately reduced to about a million for aClual mass measurements of

radionuclides. This is done by raising the level of the resonating azimuthal quadrupole field

and reducing the duration of its application, thereby increasing the frequency width of the

Fourier transform of the signal. Since at these resolutions the accuracy of the

measurements is determined primarily by other factors (see below), the increased speed

with which the measurements can be carried out actually results in increased accuracy at

these lower resolutions.

With the present èetection system the measurement technique has been shown to he

useful down to about 50 stored ions. The overall efficiency (ratio of the number of

implanted ions to the number of ions detected by the multichannel plaIes) is = 5 li 10-5 with

a transfer efficiency between the two traps of 70%. A typical spectrum, such as that of

figure 1.8, can be achieved in 30 minutes. Accuracies achieved are typically 1 part in 107•

1.5 Data Evaluation and Sources of Error:

To achieve the high accuracies that are possible with this system many aspects of it

have to be taken into account. These include trap imperfections, system stabilities etc. and

have been detailed in the thesis of G. Bollen [B089] and by Becker et al. [Be90]. The

present work will concentrate more upon the overall performance, details of the data

evaluation, the handling of isomers, and a comparison of the results with previous results

[Au84] in an anempt to reveal the problems that are involved.

Although high resolution is important in separating two very similar masses, it does not

necessarily imply a high accuracy ta the measurement because of possible systematic erron

in the measurement process. In the Penning trap system, these errors arise in relating theratio of the resonance frequencies of an unknown and a known mass to their actual mass

ratio. To obtain these resonance frequencies time of flight (TOF) data are accumulated for

several frequency scans and summed to obtain TOF spectra for each frequency that is

applied. The centroid of every TOF spectrum is then obtained and plotted against

frequency, yielding a resonance curve as shown in figure 1.8. The analysis by Bollen et

al. [Bo90] has shown that the shape of this resonance curve is symmetrical and very similar

to that of a gaussian. A gaussian was therefore used a a fitting function to the data. The

resultant fit determines the center of the resonance to about 1/20th of the fullline-width at

half maximum or typically 0.5 Hz. This is the adopted value for the accuracy of the

- 20-

,•

cyclotron frequency (uc) determination and is regarded as the statistical accuracy of the

measurement.

In relating this observation of the cyclotron frequency to the mass of the ion, reference

scans are performed periodically during a run using the stable isotopes 85Rb. 87Rb and

133Cs. The quality of the data can be seen in a typical plot of the cyclotron frequency for

such a stable isotope versus time (figure 1.9). This plot shows a 24 hr variation due to

structural changes in the experimental hall with temperature variation but it also c1early

shows an average decay rate in the magnetic field of 10-8 gauss/hr. The observed cyclotron

frcquencies can easily be corrected by a straight line fit to the reference measurements.

Oct 18

l' •

•h..! ••

+ .: t_ f

• •t.. t.-• • •.-.

11f

t

1 ..

1072 119.62 l--J...u..lI•.1.l.J..I.u.u.IJ.J'1.1.l.J..'p..u.1 •.1.l.J..'u.''.u..w'1J.J..1.''u.u.'.LJJ.JI.'t'-'-l ".l..L.I.LJJ.J''LU.J.'.LJJ.JI •..L.LJ.."u.'1.1...L1-j'..L.LJ..•.LJJ.JI.J.JIl 'u.u.'I.LJJ.J'1.1.l.J..'u.J..Lt'1. 1

Oclt 14 Oci 15 oc~ 17

1072120.24 - t

~·I~

·f

Figure 1.9 Shifts in the cyclotron frequency of a stable isotope ion (85Rb) over a

3.5 day period. The frequency span of the vertical of the plot is about

0.6 Hz with a center frequency of 1.07 MHz.

After correcting for the frequency shift due to the magnetic field decay. masses are

calculated by the isotopie mass ratio

,If"~

VxR =--=Vrej

MrefMx (1.12)

- 21 -

...

where x denotes the unknown isotope and M is the isotopie mass. The calculated error is

derived from the statistics of the measured and reference set. Averaging over the values of

R obtained from different runs leads to a systematîc error in the frequency shifts of less

than 10-7 of the center frequency. The systematic error is added in quadrature to the

statistical error yielding the final value of Rand its error. Atomic mass·excesses can then

00 calculated from the isotopie ratio.

1.6 Comparison with previous results:

In the very first run of the system on a set of radionuclides of cesium in the late 1989,

the masses of 20 isotopes spanning 118.137Cs were measured with an accuracy of OOlter

than 1 pan in 107, equivalentto about 10 keV, in less than 48 hours by StolzenOOrg et al.

[St90]. Even though analysis is still OOing perforrned on this data for a redefinition of the

cesium masses, the significance of the results is easily seen from a simple comparison with

previous data. Figure 1.10 shows a comparison of the oost previously available mass data,

that of Orsay [Au86], and that of the new Penning trap data with a preliminary least square

fitto ail of the data that is presently available for the cesium isotopes, including that of the

Penning trap measurements2. The most sniking feature of the Penning trap data compared

to the previous data is the uniformly low errer of the trap measurements, no malter how far

the nuclei are from stability. The excellent agreement of the Penning trap results with thenew adjusted values shows how thcir very low errers compared to those of the other data

causes then to dominate in the determ:nation of these values.

2Each measurcment is assigned a weighting faclOr according ta the accuracy of Ihe experimenlal value. Thil

is the approach taken by Wapsua who has published new mass values roughly eyecy nye years as new and

accurale measurements become possible. The last preyjous publication of such yalues was in 1988.

- 22-

140130120

(a)

••l :!: '"

i:i

1· • t ~ - 1:1 .... '" .. '". .

!l!, •

100

200

o

CIl

~ ·100::; 110

140130120

(bl

~ ï i ï 2Q2 9 2 r2 2~ 22 m m-2!FI

, 1·200110

·100

o

CIl

~ 100::;

...,'C

« 200

Mass Number

Figure 1.10 Mass data of the cesium isotopes. The zero line is the result of an adjustment

of all data available including the Penning trap mass measurements. The deviations from

these values are plotted for (a) Orsay data [Au86], and (b) the data of the present work by

the Penning trap mass measurement system with 133Cs as the reference mass.

- 23-

(This page left blank intentionally.)

- 24-

CHAPTER 2

MEASUREMENTS OF NUCLEAR MASSES OF RB & SRRADIOISOTOPES

il was shown in Chapter 1 that a significant advantage of the tandem Penning trap mass

spectrometer over previous methods used to measure the masses of radionuclides is the

ability to measure with unifonnly high accuracy a long c~ain of isotopes leading far from

beta stability. Because the development and testing of the Penning trap nuclear mass

measurement system centered on the use of a surface ionization source of the naturallymonoisotopic t33Cs, the flfst long chain of nuclear masses to be measured were those of

the radioisotopes of cesium as reponed in Chapter 1.

This thesis presents the flfst attempt to broaden the range of measurements to other

radionuclides. The primary purpose of this work was, of course, to extend knowledge of

nuclear masses but an imponant secondary purpose was to further probe the usefulness of

the system and its limitations. One limitation of the system as it is presently constructed is

that it can only deal with elements that can be easily ionized by contact with a hot surface.

This Iimits the system to the alkali metals and the alkaline earth metals.

The panicular examples chosen for the work of this thesis were rubidium and

strontium. The case of rubidium was particularly attractive since it has nuclear isomers of

excitation energies and half-lives appropriate for demonstrating the power of the system to

resolve a nuclear isomer from its ground state for the flfst time by a mass spectrometric

method.

2.1 The Nuclear Region of the Rb & Sr Radioisotopes

The neutron numbers of the rubidium and strontium radioisotopes straddle the N = 50

closed shell while the proton numbers (Z =37,38) are about half-way between the Z =28

and Z =50 closed shells and are at a possible sub-shell closure of the fSf1 state at Z =38

(see the Nilsson diagram in Fig. 2.1). Such a sub-shell closure could reduce the

deformation nonnally associated with nuclei in a transition region between major shell

closures and possibly be detected in binding energies detennined from nuclear mass

measurements. Even though this interesting region has already been explored quite

thoroughly, the high accuracy obtainable with the Penning trap mass measurement system

gives a closer look at iL

- 25-

•

Neutrons ( 8o Br levels)

", •...........

50

--

36

-_._--

-5 r=. ...--

....................

-1 0 t======·=~~.~~~g~9~12~~~ : :::::::::.:.......... '........... 40 -......::::~..-::...~. . .

.....,_ f'12

·········..· ?!.~L ··..::::::::..·::::: ·

34 ~' ~8 <........... 34

..~~,,:~;:;~~=-p;;;::~~:~~~::::~~:~._---:::.:::: ..:-::'______.."10. J/l ---~~-- .·15

...--"'-

--------=::::; .

28 28

--_...._....~::::,._'~

-20

-25

....- - ...

20

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4

'.Figure 2.1 The Nilsson diagram of the N, Z", 38 region.

- 26 ..

The binding energy of a nucleus is usually expressed in terms of ils "mass excess"

which is defined as the aclual mass of the nucleus minus A atomic mass units, where A is

the mass number defined as the sum of the proton and neutron numbers of the nucleus.

This actually expresses the mass excess over that of a proportional amount of carbon-12

since one atomic mass unit is defined as exactly 1/12th of that of a carbon atom.

Thus the greater the overall binding energy of a nucleus, the less is its mass excess.

The mass excess is therefore a measure of the total effeet of all the intemucleon forces and

the more attractive are these forces the lower is the mass excess. In fact, except for very

Iight and very heavy nuclei the binding energies of the nuclei are such that the mass

excesses are negative (i.e. become a "mass defeet"). This is because carbon-12 is not as

weil bound as nuclei of medium mass. (The most tightly bound nuclei are weil known to

be those of stable iron.)

The mass excesses in the region around ~, Z =38 is shown in Fig. 2.2. It is seen that

they span over 25 MeV. It is clear thatto see rme detail in the nuclear binding en~rgies that

might be due to such effeets as sub-shell closure, the greater part of the systematic variation

of the mass excess with particle number must be removed. This can be done by comparing

the actual mass excesses with a theoretical model that accounts for the greater part of the

systematic variations. Six representative models have been chosen for the rubidium­

strontium region, ranging from those wilh many parameters relying on extrapolation

schemes to extend the surface locally (i.e. highly empirical), to tlJOse with few parameters

but having a very strong physical interpretation. They are:

1. An empirical mass relation of the Garvey-Kelson type by Jl!necke et al. [Ja88]

2. An empirical mass relation of the Garvey-Kelson type by Cornay et al. [C088]

3. A senù-empirical shell model by Liran and Zeldes [Li76]

4. A macroscopic-nùcroscopic model based on a liquid drop model with shell and

pairing corrections by Moller and Nix [Mo88]

5. A macroscopic-nùcroscopic model based on a liquid drop model with shell and

pairing corrections by Tachibana et al. [Ta88]

6. A infinite nuclear matter model of Satpathy and Nayak [Sa88]

- 27-

• -50-r----------------------,

-60

0 Krypton

III rubidium--> • Strontiumal:: a Yttrium~

1Il -701Ilal<.l><W

1Il1Ilca::

-80

55504540-90 +-~........-.-~--r-.-~-.-~.,..-,..~~-.-.__-.-~ ........-,..___l

35

Neutron number

.T

Figure 2.2 Mass excess of the N. Z = 38 region. Values for rubidium and strontium are

from the Penning trap measuremenlS and those for laypton and yttrium are

from the Wapstra mass tables (Wa88).

- 28-

r

The (Jarvey·Kelson model:

This mass model does not depend upon a mass fonnulae but uses a set of difference

equations derived from the mass differences between neighboring nuclei to define a

nuclidic mass relation. The technique as used by Janecke et al. involves solving such

diflèrence equations. In the model of Comay et al. the mass relations belWeen neighbors is

used to calculate average mass values to extrapolate to unknown masses. These relations

then provide a simple means of expressing one mass directly in tenns of others.

The semi-empirical.\·hell rrwdel:

This model deduces the total energy of a ground state nucleus dS the sum of threc

contributions, a pairing (strong pairing approximation), a defonnation and a coulomb

energy tenn. The coefficients of the equations vary with the different shell regions.

Thcrefore different sets are used From each region and dedu~ed From experimental values.

The lIIacroscopic-microscopic rrwdel:

ln this model the potential energy of the nucleus is given as a function of the shape

and calculmed as a sum of the two tenns. The macroscopic part is usually a liquid drop

type model which is commonly used to study a variety of nuclear properties, for cxample

tission b:!rriers. shapes and masses. The model is based upon the assumption of a

c1assically unifonn distribution of nucle)ns and ignores any shell effects. The microscopie

cOl1lribution uses a shell model (single particle model) which assumes from the stand-point

of one nucleon that the forces exerted (1.1 it by all the other nucleons in the nucleus can be

represented in a first order approximation by a potential weIl. Two major contributi.ons to

the energy tenn arise, a shell correction and a pairing correction. The shell corrections are

deduced from Il Strutinsky method(St66) and the pairing correction from a Bardeen­

Cooper-Schrieffer approximation.

The Îlifinire nuc/ear malter model:

This model uses u mucroscopic-microscopic model !lut in the macroscopic part the

coulomb tenn is neglected since the coulomb term is the limiting tenn for the size of a

nucleus. By turning it off, nuclei would be stable to any volume. The atomic number A is

set to infinity giving wuy to infinite matter where me volume tenn in the mucroscopic model

predominutes.

- 29-

2.2 Experimental Methods and ResuUs

The measurements on rubidium and strontium radioisotopes were canied out in

essentially the same fashion as those on the cesium radioisotopes reponed in chapter 1

except that the reference isotope in this work was 85Rb. The only significant difference was

that in sorne of this work the presence of a nuclear isomer and the ground state

simultaneously in the measuring trap had to be taken into account (see below).

The results are summariZl".d in tables 2.1 and 2.2 for rubidium and strontium

respectively. Aiso shown are the previous accepted values obtained from Qp and mass

spectrometry studies where all known measurements were compiled in a least-squares fit

[Au91].

A

75

76

77

78

79

80

81

82m

83

84

86

87

Cyclotron frequency

ratio

1.13308625(3)

1.11821657(1)

1.10374881(2)

1.08961715(3)

1.07586850(1)

1.06242673(3)

1.04934339(2)

1.03654283(3)

1.02408112(1)

1.01188607(1)

0.98836718(4)

0.97701732(4)

Mass excess keV

(this work)

-57218(7)

-60477(8)

-64820(8)

-66932(8)

-70802(8)

-72166(8)

-75447(8)

-76114(8)

·79065(8)

-79746(8)

-82737(8)

-84594(9)

Mass excess keV

(Wapstra)

-57210(100)

-60530(60)

-64917(30)

-66980(30)

-70838(23)

-72176(18)

-75459(23)

-76123(30)

-79049(21)

-79748(3)

-82744(2.7)

-84593.1 (2.9)

•

Table 2.1 Cyclotron frequency ratios (to that for 85Rb) and the resultant mass excesses

for rubidium isotopes. For comparison, previous accepted values from the Wapstra tables

are presented in the last column.

- 30·

{

A Cyclotron frequency Mass excess keV Mass excess keV

ratio (this work) (Wapstra)

78 1.08956068(4) -63170(8) -63459(300)#

79 1.07579052(7) -65472(8) -65340(200)#

80 1.06240011 (2) -70300(8) -70190(30)

81 1.04928874(1) ·71521(8) -71470(40)

82 1.03654144(2) ·76012(8) -75998(21)

83 *0.99997049(4)* -76785(13) -76781(21)

87 0.97702054(2) -84857(9) -84875.5(2.5)

# Mass excesses are estirnated from systematics.

Table 2.2 Cyclotron frequency ratios (to that for 85Rb) and the resultant mass excesses

for strontium isotopes. For comparison, previous accepted values from the Wapstra tables

are presented in the last column. The value of 83Sr was obtained by comparing with the

value for 83Rb. This leads to the comparatively large uncertainty of ils mass.

2.3 Discussion of Results • Comparison Between Theory and Experiment

2.3.1 Mass Excesses

When comparing measured nuc1ear masses with model predictions one should take into

account the purposes of the models. In general, there is a tendency to emphasize the

prediction of nuc1ear masses that have not yet been measured This is particularly the case

for nuc1ei very near the limits of nuclear stability which are of interest in nuclear

astrophysics and for which even a rough guess can he very important. The agreement

hetween the model and new measurements of nuc1ear masses that did not exist when the

model was created therefore becomes a test of the usefullness of the mode!. However, a

more basic purpose of the models is to gain som!' insight into the nuclear force by noticing

the agreement that can he obtained with existing data by incorporating certain parameters

into the models. In general, the degree of development of the present models can he seen

by noting that comparisons of experimental masses with model predictions are shown on

graphs that span severa! MeV on the vertical axis. It seems that, at present, a theoretician

will regard a model prediction as a success if it agrees with a measurement to within about

100 keV.

Figures 2.3 and 2.4 show a comparison of the measured mass excesses for rubidium

and strontium isotopes with the model predictions. The Garvey·Kelson type formulae of

- 31 -

•

Janecke and Masson and Cornay et al. represent extrapc!ations based upon rneasured

values of nearby nuclei to predict unknown values. In general, these type of forrnulae give

a good fit to experirnental values, as shown in the cornparisons with the rneasurernents of

this work. The forrnulae of both Cornay et al. and Janecke et al. predict the new masses of

78.79Sr (N = 40, 41) fairly weil. However, the predictions of the less ernpirical rnodels are

also fairly good, except for that of Liran and Zeldes which is in error by up to 2.5 MeV. As

suggested by Moltz et al. [M082], this may he frorn the Wigner energy terrns on

approaching N = Z, or frorn a possible quasi-sub-shell at N = 39.

o

o

2-..-------,~ ~oll<'fand Nix• Slllpathy and Nayak• Tachibana et al

-1~...CIl::;~ -2<Il

<Il • 38 40 42 44 46 48 50CIl 0.""~~~ 2

,~ .....co .. • 1.'ran and Zeldes::;53

..c ~- Ianeckc and .~Iasson

E- • Cornay el &J•1

555045Neutron number

40-1 -1-.....--.-...................,...--.---.----r--.---,r-..--..--..--.......-,---.-........-.---.----I

35

,,.

Figure 2.3 Differences between the model predictions and the experirnental values

for rnass excesses of the rubidium isotopes.

- 32-

In general, it is seen that the macroscopic-microscopic models of Moller and Nix have a

very poor predictive ability with slrong deviations (~\.5 MeV) in the region N = 43 to 47.

This may be due to the sudden change in nuclear structure where these models usually

assume a smooth behavior of the nuclear surface as a function of A and Z. According to

shell energies (see section 2.3.2), deformations begins at approximately N = 44. The

overbinding can be explained as an over-estimation of the pairing energies.

2~---------------------,

504846

~ Uran and Z.ldes• Janecke and Massona Cornay et al.

..........--lll--ii-_..--...

444240

2

a

~ Moller and Nil<• Satpathy ""d Nayaka Tachibana el al

a

-1~

>..:;~

,t '"'" ."Co'-' ><~'"''""' ...."' ..:;~

oCE-

504840-1 -!--..---,----.--,---.---r---.--,--..-----,,----.--j

38 42 44 46Neutron numller

Fignre 2.4 Differences between the model predictions and the experimental valul:s

for mass excesses of the strontium isotopes.

- 33-

2.3.2 Two-Neutron Separation Energies

Presenting the mass measurements as a plot of two-neutron separation energies (S2n)

versus neutron number provides a method of removing the odd-even neutron pairing

energy effects so that nuclear structure features, such as deformations and energy gaps in

the single-particle levels, stand out more clearly. Figures 2.5 and 2.6 show the S2n

deviations of the models from the experimentally derived values. It is seen that the non­

empirical models are more prone to large deviations (= 1.5 MeV) at N '" 44 in both

rubidium and strontium, signalling a possible on-set of an expected prolate deformation in

this region. Indeed, this can even be seen in the direct comparison of the mass excesses.

2

a

~ Ta.hibana el al• Moller & Ni.a Satpalhy & Nayak

c -1.:?-~<':1>.....<':I~fr~

·2en.Cl. 38 40 42 44 46 48 50 52c ..eW 2-.::l

~ Illnecke & Masson.....Z'" • Liran & Zeldes00"

Comay el al~.c aE-<E-<

a

-1

5250484240-2 -1----..-...,----,,......-r--.---r--.----r-.....---,--....---r-......---j

38 44 46Neutron Number

Figure 2.5 Deviation of the two-neutron separation energies of the modcJs from the

experimental values for rubidium isotopes.

- 34·

2,.....------------------------,~ Moller and Nix

- ...- Salpathy and Nayak• Tachibana et a!

o

o

-,=o~.- >- ..ï:::;"'~ -2e.... .

40 42 44 46 48 50cne..><

=~0 •..->,:1 .."0 3. :z ..

1 .r:~~

f-o2

~ Liran and Zeldes• Jancckc and Masson• Cornayeta!.

504844 46Neutron number

42., +--~--._-....,....-__,.__-~-___r--.,......- ........--.----1

40

{

Figure 2.6 Deviation of the two ·neutron separation energies of the IT'txJels from the

experimental values for strontium isotopes.

- 35-

2.33 Nuclear Defonnarion ar N, Z = 38

For even finer analysis of nuc1ear structure effects on the binding energy using the new

accurate mass values, a useful method is to present those values in terms of experimental

microscopie energy (see Bengtsson et al. [Be84)). This representation is based upon a

macroscopic-microscopic model [Nin] where the macroscopic part is best described as a

Iiquid-drop model, and the microscopie part as a single-partic1e sheli mode!. This approach

is successfulIy demonstrated by Strutinsky [St67,68]. The total energy is assumed to

consist of three parts,

E(Z,N,shape) = Emacro(Z,N,shape)

+ MsheU(Z,N,shape)

+ Mpairing(Z,N,shape) (2.1)

where Emacros is derived from the gross properties of the nuc1ear model, Le. the Iiquid

drop model, and MsheU and Mpairing form the microscopie parts associated with the

single-particle shelI and pairing effects respectively. The energy levels (E sp) in the

microscopie part are calculated, then the average trend (Ë ) is calculated by a smoothing

procedure applied to the discrete levels to yield,

M=Esp-E (2.2)

To observe the separate effects in the experimental data the procedure of Bengtsson et

al. [Be84] is folIowed. To plot the experimental shelI energy the difference between the

experimental mass and the contributions from the macroscopic model for a spherical shape

are calculated. This difference includes both the pairing energy and the effects of nuclear

deformation. However, the macroscopic fùrmula used by Bengtsson is replaced by the

new revised formula of MôlIer and Nix [Mô88] that was used in section (2.3.1). The major

difference of the IWO formulae lies in the pairing energy which has been substiluted by the

average pairing energy formula of Madland and Nix [Ma88].

In figure 2.7, the shell energies are plotted against the neutron numbers for the Rb. Sr,

Kr, and Y isotopes, where the Penning trap experimental results were used for Rb and Sr,

and the other values are taken from the Wapstra tables [Wa88].

- 36-

ConcenlTating only on the Rb and Sr data, a flallening of the microscopie energy is

observed at about N =42. If the nucleus remains in a spherical state, the shell energy

increases to a maximum (somewhere in the middle between the magic numbers N = 28 and

N = 50), and then decreases to a new minimum at N = 28.

4000

~ KIyp.on

• Rubidium

a Strontium

0 Yttrium

2000

~

> 0.....:.:~

!Il...

iCl).....c...

c:;·2000-en

·4000

605040

Neutron Number

·6000 +----.,.-----r----..----,-----..------l30

Figure 2.7 Shell energies plotted against the neutron number for Rb, Sr, Kr, and Y

isotopes.

- 37-

•

Such a f1attening, or general decrease before the maximum is reached, can be

interpreted as the onset of deformation at N= 44. When the deformed state becomes more

stable than the spherical one. the contributions of the microscopic energy to stabilizing the

system need not increase any further. In fact, large deformations are known to exist

between A =70 and 80. FurthemlOre, from nuclear [Li821 and laser spectroscopy [Th81,

Bu901. it is known that Rb and Sr nuclei in this region are deformed with minor to major

axis ratios as large as 2:3 being observed. The accurate mass measurement results of the

present work indicate that this deformation sets in at about N =42.

Below N = 42 the experimental microscopic energy for the rubidium and strontium

isotopes exhibits a pronounced odd-even staggering. Closer examination of this staggering

reveals that the odd neutron isotopes have less microscopic energy than the even ones, a

reverse of what might normally be expected frem pairing forces.

Such a staggering can be explained by an alternation between two almost equally

favoured but very different shapes in the even and odd cases for N, a situation that is

referred to as "shape coexistence". According to Bengtsson et al. [Be841, shape

coexistence in Sr is very probable since the transition frem a spherical to a deformed shape

is, in general, very sudden and appears in Sr at between N = 43 and 44. For N equal to

42 and 44, calculations show one minimum energy at nearly a spherical shape and another

at a strongly deformed shape. For nuclei with N '" 43, the minimum for the deformed

shape is lowest, while for N~ 44 the minimum for the spherical shape is lower.

This is the situation that is expected to give rise to shape coexistence and reversed odd­

even staggering. Such reversed odd-even staggering has been noticed in the root-mean­

square radii of the neutron deficient rubidium [Th81,Bu9l1. in strontium isotopes [Bu901,

in radium [Ah881 and in mercur'l isotopes [Bu901, the latter two being interpreted as shape

coexistence involving an octupole deformation.

The reversed odd-even staggering is not seen in the data for As, Se and Br (not shown)

but Kr and Y data do show a very slight sign of it indicating that the filling of the 1tlfSfl

sub-shell has an influence upon shape coexistence in this region. The odd-even staggeringin the Kr and Y data is of the order of ±50 keV so that measurments to determine its

strength in these nuclei should have accuracies of about one tenth of this or about ±5 keV,

as is obtained in the work of this thesis. Thus further high accuracy investigations of the

masses around N S 42, but which were not accessable in the present work, should prove

useful in judging the significance of the 1tlfSfl sub-shell.

- 38-

(

(

(

2.4 The Direct Observation of Nuclear Isomers

For accurate mass measurements on unstable nuclei il is highly desirable to be able to

resolve isomeric stat~s from ground states. This is because the relative amounts of the

isomer and the ground state in a sarnple delivered from a facility such as ISOLDE cannot be

known to very good accuracy and this can introduce uncertainties in the mass

measurements of either the isomer or the ground state. Furthennore, for highly unstable

nuclei the half-Iives of the isomer and the ground state are often not weil enough separated

to a110w decay of the sample to enhance the content of one over the other.

The high resolution of the Penning trap mass measurement system maje it attractive for

us to try resolving sorne isomers in rubidium from their ground states. This thesis is the

first report on a success in this endeavour. Observation of the 20 minute isomer of 84Rb

concurrently with its ground state (half-Iife of 32.8 days) is shown in figure 2.8.

This ability is unique to the Pe:ming trap mass measuring system. In fact the

observation represented by figure 2.8 is the first time any such direct separation of a

nuclear isomer from its ground state has becn achieved by mass spectrometric methods.

To achieve the measurement of figure 2.8, we perfonned the experiment immediately

after the collection of the ions delivered from ISOLDE. Ions of bath the isomeric state and

the ground stale were û,,;refore in the trap simultaneously. It is seen that the resonances for

the ground and the isomeric states are clearly resolved. The cyclotron frequency for the

ground state is Vc = 1085kHz and from the filted theoretical resonance curve to the

experimental data we obtain a half-width of I:1vc (fwhm) = 1 Hz. Such a resolution is as

expected from the chosen excitation time of Trf = 900ms. In figure 2.gb, the cyclotron

resonance was obtained after severa! half-lives of the isomer, so that only the ground state

was observed.

Typically, these measurements were perfonned with as few as ten ions in the precision

trap so as to reduce Coulomb interactions between the two species. This is because such

interactions couple the cyclotron motions of the two species and can cause a significant

perturbation in the frequency of bath motions. (lt has becn known for sorne time that if

only ions of the same mass are stored in Penning trap, the driving field will act on the

center of mass of the ion cloud and no frequency shift will be observed from the Coulomb

interaction [De69]). In the case of two species of differing masses (ml ~ m2) it was

observed in this work that frequency shifts of the sums of the cyclotron and magnetron

frequencies do occur. To explore this effect a systematic study was performed.

- 39-

350 81 QRb

,1

300 .Liu.lJ-10 -8 -6 -4 -2 0 2 .,

1.1 - 1084863.4 [Hz]

él )450

1 Il

Il 1 1\

40081mRb

.ll,....., o5r J'CS+ O"Q"!\o 0.1615 20.5 mU1 liliL1 l:1 350 81 QRb....... 0.3 ns

r- o - 0 32.9 d

J: 64Rbc.:J 371-< 300..Jr......

r...... b )0 450

W:::E1-<

r-400

.,,:,::-

"

Figure 2.8 The cyclotron resonances for 84Rb and 84mRb. The mass difference is

delermined 10 he 463(10) keV. The measuremenls were performed a) shortly after

the collection of ions and b) with a delay of several half lives of the isomeric state.

- 40-

(

Il was found that the number of stored ions in the trap increased the frequency shifts

and that the sign of the shift depended on the magnitude of the difference in the cyclotron

frequencies compared to the half-width of the resonances. When an unperturbed resonance

cannot be resolved. only one single resonance is observed which is narrower than expected

from a simple superposition. This resonance corresponds to the center of mass of ion cloud

in the trap. However, if the mass differences are large enough for the unperturbed

resonances to be separated by more than their width. the measured resonance will be

shifted to a lower frequency. The size of the shift of ions of mass ml was found to be

proportional te the number of ions with mass m2 and vice versa. This is the flfSt time such

a cyclotron frequency shift has been seen in a Penning trap although a similar collective

effect was previously seen in a Paul trap by Jungman et al. [Ju87]. It is possible Ihat the

shifts in both cases may be quantitatively explained by a two coupled oscillator model and

work is in progress to investigate this possibility.

The measurements shown in figure 2.8a was perforrned with both isomer and ground

state ions in the trap. In order to examine the effects of the Coulomb interaction, the

cyclotron resonances were measured for different delay times Td after the collection. In this

way the ratio of the number in the isomeric state to that in the ground state was varied from

an initial value of Nml Ng = 1 to approximately zero. These measurements were made for

three different numbers of stored ions and the results are shown in figure 2.9. The

cyclotron frequencies were obtained for about 15 detected ions as a function of the delay

time Td. No frequency shifts were observable within the statistical uncertainty. Therefore it

was concluded that the effects of the coulomb interaction can be neglected for such small

loadings and the mean values for the isomer and ground resonances are determined with a

difference of ÔV = 6.4(1) Hz. This yields a mass difference of 463(10) keV for the 84Rb

ground state and its isomer, which is in good agreement with the value known from nuclear

spectroscopy of 463.62(10) keV reported by Müller [Mü89].

However, as can be seen in figures 2.9c and 29d the situation changes drastically as

the number of ions in the trap increases. The frequency shifts for 25 and 70 detected ions

as a function of the delay Td were measured. In the case of 70 ions the cyclotron resonance

of the isomer was shifted out of the scanned frequency range. The size of the shift

increases with the number of total ions confined. The dashed curves show the result of a fit

with the ansatz that the frequency shift for the ground state is proportional to the number of

ions in the isomeric state and vice versa. The shifts are always negative within the statistical

accuracy and decrease for the ground state and increase for the isomeric state with increase

in the delay time.

- 41 -

n .. t '5

al

-1- .••.. i····· ., ~ .1. .•••• ,

1 n - 15

.I.·························r ····l1 1

""Rbb J

,.N

"'"U

;l

U · ,;l

., .,.

-N"

E

u;l

u · ,;l

""1

.. c 1 n - 25- J...I.. Of _.L - _. T" • _., ••••• 1N

n .. 70" · ,1 1

'" -1,1

U .1 .;l "I.S

Il\

u -l.1;l

"'Rb·2 '5

"- d J ""RbN L'"

Eu .. ·k· f;l

··j ..L...L .... !... ,u "'\ n - 25

;l ., .-l, S

" .. .. .. "T d (ml n J

Figure 2.9 Cyclotron frequencies of the ground and isomeric states of 84Rb as a function

of the delay time Td between collection of the ions and the measurement. Series of

measurements were performed with 15, 20 and 70 detected ions. The dashed

horizontallines in a) and b) correspond to the unperturbed cyclotron frequencies of the

ground and isomer mean values. The dashed curve. ir, c) and d) indicate the effect of

the ion-ion interactions.

- 42-

f

A similar extrapolation procedure was used for 78Rb. However, due to the smaller

statistical significance that could be achieved in lhis case ùnly an upper and lower limit (94

keVand 127 keV) for the mass difference can be given. To within the accuracies of our

work this :.s in good <:greement with the excitation energy of the ~'8Rb (t1/2 =5.7 min)

isomer that has recently been determtned using gamma spectroscopy 1" be 111.2 keV by

Mcneill et al. [Mc90].

In the case of the 82Rb isomer (t1/2 =6.5hr), that lives much longer than the ground

state (t1/2 = 1.3 min), the procedure is different. Here the amount of the ground state

nuclides that could be collected was insufficient ior a measurement and it was allowed ta

decay on the collection foil before a measurement was started. The energy difference

between the two states is not known to very good accuracy [Mü89].

The ability to directly res01w nuclear isomers from the ground state is an extremely

important feature of the Penning t:ap mass spectrometer system in its possible application

10 short lived radionuc!ei. This is because for such radionuclei the isomer and the ground

state usually both beta decay to the daughter nucleus leaving no trace of a direct transition

of the isoJTler to the ground state. Without the possibility of a direct mass measurement the

only way to d~lermine the mass difference is by the difference in th>l QfJ of the isomer and

the ground state decay. Becausc uf the higl. QfJ that is involved in such decays, the decay

schemes are very complicated with large fractions of the decays lcading to high energy

states in the daughler nuc1t:us. Furthermore, the selection of daughter states are usually

very different for the isomer and the ground state decays. Accurate determinalions of the QfJof the decays is therefore generally very difficult, if not practically impossible. The

resolved direct mass measurements of both the isomer and the ground state in the Penning

trap mass spectrometer therefore will be s very important feature for the study of these very

interesting radionuclei.

2.5 Limitations of the system

The results presented above show that the Penning trap mass spectrometer is potentially

a very powerful tool for ~ '1taining iu[v.ma,tion about the nuclear forces from the nuclear

binding energies. However, 'tS presently configured it suffers from obvious deficiencies.

These deficiencies severely limit both the number of elements and the numbers of isotopes

of these elements that can be studied.

This is because of the collection system that is used for the 60 keV ISOLDE

radionuclide ions. As pointed out eurlier, this is based on evaporation and surface

- 43·

ionization following implantation into a rhenium foil and limilS the system to the alkali and

alkaline earth elements, a restriction to approximately 12 elements of the over 66 elements

available at ISOLDE [Is86). A specific reason for going beyond the surface ionizable

elements is shown in the data of Rb and Sr. By extending the mass measurements to the

non-surface ionizable elements such as Kr, Br, Y and Zr, where mostly there are only old

unreliable QjJ results from which to deduce the nuclear masses, the region can be explored

in much finer detail.

Contamination problems also arise from heating the foil which releases ions of species

other than those to be measured. Because of the small number of radionuclide ions

deposited in the foil compared to the natural impurity atoms in even highly purified metals,

these have to be c1eaned fron. the trapped ion cloud before measuremenlS can be carried out

to the precisions described in this work. This heating also raises the temperature of the ion

cloud which reduces the transmission efficiency of the ejected ions to the proper phase

space volume in the measuring trap and increases the chance of ionizing impurity molecules

in the residual gas in the collecting trap.

Furthermore, even for the surface ionizable elements the collection efficiency is very

poor. In the present system it has been observed that $ 10-5 of the ions delivered by

ISOLDE are pulsed out of trap#l. With such low efficiency, studies are limited to those

ions which have a high production. Yields of rubidium and strontium at ISOLDE are

shown in figure 2.10. It is seen that even on such a logarithmic plot of the production

yields the curves drop drastically for nuclei far from stability, Le. the nuclei of interest.

Thus highly efficient handling systems are needed to retain enough of these ions to be able

to make interesting measurements.

For example, extending the mass measurements deeper into the Rb and Sr neutron

deficient region would allow the point at which the inverse odd-even staggering ceases to

exist to be probed. In the case of rubidium the restriction to high yield isotopes is

particularly restraining. Extending the measurements to just one more isotope. 74Rb.

would aid in exploring the Wigner terms at N =Z = 37. However. is is to be noted that in

figure 2.10 the production rate drops from 75Rb to 74Rb by a factor of over 1000.

-44 -

'0-.~ 10 7....

• •• ••

•• •

•

• a '"a •a

a

•E!J

a Strontium yields

• Rubidium yields

0

•

• •70 75 80

mass

85 90

Figure 2.10 ISOLDE production yields for rubidium and strontium radionuclides.

- 45-

•

2.6 A Suggested Improvement to the System

Obviously th!: only major deficiency of the present tandem Penning trap mass

measurement system is in the collection system for the ISOLDE radionuclide ions.

Substitution of the foil collection system by a system which would manipulate the original

ISOLDE ions into the measuring trap while maintaining them as ions would be a major

improvement to the system. It would greatly improve the versatility of the system. lower

the life times of the radionuclides that could be observed and, if the efficiency of the

transfer could be improved. allow the observation of radionuclides with low production

yields.

This however is a difficult endeavor. The basic source of the difficulty is the high

energy. typically 60 keV, with which the ISOLDE ions are Most efficiently delivered to the

experimenter. The energy of the ions when they are injected into the proper phase space

volume for precise measurements in the Penning trap is typically tens of millivolts. In

phase space terms, the phase space volume of the DC beam which is to be collected in one

measurement cycle is huge compared to the desired phase space volume of these same ions

within the measurement trap.

Various possible schemes have been investigated for injecting high velocity ions

directly into a Penning trap. These are discussed in Appendix A. However, for the son of

nuclear mass measurements presented in this thesis they suffer from very low transfer

efficiencies or from a very large phase space after injection. What is required is a collection

and manipulation procedure which is accompanied by phase space cooling. Aiso it is clear

that the flfst step is the most difficult; that of efficiently collecting and bunching a 60 keV

DC ion beam into shon pulses that are delivered at approximately 1 second intervals. This

will involve decelerating the ions into sorne son of hold-up device where for up to one

second they will have no net velocity in any direction. AIso, because of the high rate at

which the incoming beam delivers phase space volume to the hold-up device. the ions

already in it must be continuously cooled as they enter.

Such a device does indeed exist and has been widely used by atomic physicists and

analytical chemists for over a decade. It is the radiofrequency quadrupole trap (RFQ)

invented by Paul and Steinwedel in 1956 ( U.S. Patent 2,939,952) and now commonly

referred to as the "Paul trap". A corrunon method of operation such a trap is to deliberately

introduce a Iight molecule background buffer gas such as helium into the trap (at up to a 0.1

Pa) to cool the motion of the contained ions. In this way ions can be efficiently collected

- 46-

:\.

(t

from a variety of sources such as eIectron or laser bombardment of the residual gas in the

trap or even of the electrodes of the trap itself.

However, the Paul traps that have been used to the present are relatively small devices

(never more than 3 cm separation between electrodes) and have been used to contain ions

produced within the trap itself or introduced at very low energies (S 1 eV) from an outside

source. Up to now no one has reported on any attempt to use such a device for lhe direct

capture of high velocity ion bearns such as those of ISOLDE. To use such a device for an

ISOLDE type ion beam would require a much larger version and would require that it be

operated in such a fashion as to accept high velocity ions. This will involve decelerating the

ions before injection into the trap. Deceleration systems have been built for soft

implantation of mass separated ion bearns of tens of keV energy. However, the energy

reduction factor that is normally regarded as feasible in such work i:; about 100. By careful

design and limitation of the aberrations a factor of 1()()(} might be regarded as feasible but

this wOlild stillleave a typical ISOLDE bearn ion with about 50 eV of energy. Clearly, for

a Paul trap collection ~ystem to be useful for an ISOLDE type beam, injection at tens of eV

must be made acceptable.

It was shown by Moore and Gulick [M086] that ions of kinetic energy considerably

greater than 1 eV could be injected into a lypical Paul trap with effidencies ~ 50% if they

were injected at a particular phase of the RF applied te the trap. Furthermore, it was shown

that by using helium buffer gas cooling, ions could be collected at this efficiency for up to

one second or longer (provided the total number of ions collected did not produce

significant space charge effects, a limitation to < 1()6 ions in their case), and then extracted

in a single pulse of less than IIlS duration. This encouraged an attempt to inject the

ISOLDE beam in a Paul trap as the flI'St stage of an efficient beam collection and ion

cooling system for the Penning trap mass measurements. The major thrust of the following

chapter is to explore the feasibility of such a use of a Paul trap.

- 47-

•'.

(This page left blank ir.tentionally.)

·48 -

CHAPTER 3

THE PAUL TRAP AS A COLLECTION DEVICE FOR APENNING TRAP

The idea of a Paul trap as an ion bearn collection device for mass spectrometry using a

Penning trap originated during the sabbaticalleave of Dr. R. B. Moore at Mainz university,

Germany in 1982. The first step in proving the feasibility of the idea was to inject extemal

ions into a Paul trap, and this was performed at the Foster Radiation Laboratory at McGill

in 1985 t>y Gulick. Lunney and Moore [Gu86. Lu86]. Encouraged by this success. pulsed

injection phased to the rf of the trap was developed by Moore and Gulick [M088] and

capture efficiencies of up to 50% were achieved. That result inspired the work described in

this thesis; the successful injection of 60 keV ions into the trap.

The first step in this work was the construction of a test system which was begun in

1988. with the fust injection of 10 keV ions at McGill. The Paul trap collection system was

then moved to ISOLDE at CERN and tested. fust with up to 65 keV ions from an off-line

test source and then on-line to a 60 keV stable xenon Ïr.''l bearn from the ISOLDE 3 facility

in the summer of 1990. il was then transferred to the ISOLDE 2 facility and tested off-line

as an injector for the first Penning trap of the mass measuremenl system in the summer of

1991. The remainderofthis thesis will describe this work and the resuIts achieved.

This chapter will present the basic principles of a Paul trap and its use as a collection

device for a Penning trap. The presentation of its use as a collection device will be made in

terms of the phase volumes of ISOLDE bearns and Paul traps and what is involved in the

manipulation of the phase spl.;e volume of a bearn into a trap. Practical considerations for

such manipulations are then presented.

3.1 The Dynamics of Ions in a Paul Trap

Until recently the Paul trap was known as the radio-frequency quadrupole (RFQ) trap;

the name given to il by its inventors Paul & Steinweder in 1956. The electrode

configuration of the Paul trap is the same as that of the Penning trap; Le. two axiaUy

symmetric end elec:rodes placed cquidistant along the axis from the center of a ring

electrode surrounding the trapping region as shown for the Penning trap in figure 1.1.

- 49·

•However, instead of confining the radial motion by a magnetic field along the axis, the

eleetric potential between the cylinder and the end electtodes is oscillated.

This has the effeet of continually changing the action of the eleetric field on the particle.

At the one instant the field will he repel1ing the particle from the end electrodes and

atttacting it to the ring and at the next it will be atttacting the particle to the end eleetrodes

and repel1ing it from the ring. At fust it would seem that these two actions would cancel

each other, leading to no net pL~sh of the partir.ie toward the trap center. However, Wilh

weak fields oscillating at high frequency there is such a net force.

A simple mechanical analogy which illusttates this effeet is a ball resting on a horiwntal

membrane stretched over a circular rim, the rim being capable of being deformed 50 as to

be high on two opposite sides and low in the regions between these two highs (see figure

3.1).

Figure 3.1 A membrane analogy to the Paul trap.

If the regions of highs and lows are oscillated up and down, then the action of gravity

on the bail will he very similar to that of the electric field in a Paul trap on a charged

particle. If the motion of a bail is observed in such an apparatus it will be secn that the bail

can be made to roll about the center of the membrane as if it were in a round·bouomed dish.

This action is most easily visualized for a bail which is temporarily stationary on a

region of the membrane which is, at that instant, downward sloping away from the

membrane center. As a result of this downward slope, the bail will star! moving away

frorn the center 50 that by the time the membrane has switehed to being sloping downward

- 50-

toward the center, the ball has moved a small distance outward. Since the slope of the

membrane increases with distance from the:: center, the "focusing" force at this greater

distance is greater than the initial "defocusing" force. In a complete cycle there would be an

average force on the ball toward the membrane center.

There are, however, limits to the strength of the focusing-<!efocusing forces for which

'le motion is confined or "stable". This will be when the slopes of the membrane are 50

stc::ep or the reversing of the direction of the slope 50 slow that the outward motion of the

parrlcle due to the defocusing force carmot be reversed by the focusing force.

This limit te the stability of the Paul trap type of containment can be more easily secn in

the opticallens analogy to the Paul trap shown in figure 3.2 of two equal power lenses of

opposite sign; one focusing and one defocusing.

{cl

(b)

(dl

Figure 3.2 Lens analogy to a Paul trap.

If the lenS(':e are of separation less than the focallength of either, then the overall effect

of the twn wH! always be a focusing action. This can be seen for both the case when the

focusing lens is ftrst and the defocusing lens second, (a) in the figure, and for the reverse

case (b). In each case the beam in the focusing lens is wider than the beam ia the

defocusing lens and 50 the focusing effect is stronger than the defocusing effect.

However, ü the focusing action of the lenses is made too sttong «c) in figure 3.2), or ü the

·51 .

•lenses are moved too far apan «d) in figure 3.2), an intermediate focus will he formed

hetween me two lenses and me overall effect will he defocusing.

The full optical analogy to a Paul trap would he a continuous equally spaced sequence

of equal strengm lenses of a1temating sign of focusing. In fact the Paul trap and the

a1temating gradient synchrotron, which uses me principle of a1temating focusing outlined

above, were invented at about the same time and are descrihed by the same basic

mamematical equations.

3.1.1 The Equations o/Motion in a Pure RFQ Paul Trap

As in me Penning trap, me electric quadrupole is a1so me basic field used in the Paul

trap. However, since me electric field is me only field in me trap, me equations of motion

for a quadrupole field are simply

ï = !L. Ez - K zm - mzo2

;: = !L. Er =- -.!lL rm 2mz02

(3.1)

The important difference wim me Penning trap is mat me voltage is no longer constant

and so me solutions are not purely simple harmonic.

Again me simplest form of lime variation for me voltage is simple harmonic. For such a

variation, and assuming mat there can still he a OC component, me voltage V can be

expressed as

(3.2)

where VRF is me amplitude of me voltage variation. Such a lime variation for me field can

he shown to give equations of motion for z and r which are of me Mamieu type. Defining

the following symbols

".-

(rA lt lf/';=2;';0=4"-2

az = - 2ar = 4qVpcmz02aJ.

qz= -2qr = _2qVACmz02aJ.

• 52·

(3.3)

and taking tp to be -1r/2 gives bath equations of motion the canonical fonn of Mathieu's

equation;

d2r- + la, - 2q, cos 2('; -.; 0) l r = 0dÇ2

(3.4)

CA more general fonn of periodic voltage variation will give Hill's equation, of which

Mathieu's equation is a particular fonn.)

3.J.2 SolUlions ofthe Equations ofMotion in a Pure RFQ Paul Trap

The general solution to Mathieu's equation are expressed in Mathieu functions. These,

like the exponential functions, can be stable, as for sinusoidal functions (i.e. exponential

functions with imaginary exponents), or unstable, as for exponential functions with real

exponents. There are many regions of values of a and q that give stable solutions.

However, the most imponant region of stability for trap operation is that for which a and q

are small. This implies either small values for the electric field and charge to mass ratio of

the partic1e or large values for th,:: voltage frequency.

Figure 3.3 shows the form of representative solutions of the Mathieu equation for the z

motion when q is small and a is zero. Staning with an RF voltage (88 Vpeak) and trap

operating parameters RF = 250 kHz Zo = 14mm and a singly charged 133Cs ion, giving a

qz of about 0.28, is seen to give a slow sinusoidal type oscillation under!ying micro­

oscillations due to the RF field (top left-hand graph of figure 3.3), the frequency of the

underlying oscillation being about I/lOth that of the RF. The solution depicted is for the

panicular phase of the RF of 9()0 forward relative to this underlying oscillation and with a

chosen amplitude of the Mathieu iunction such that the staning energy of the motion is

2 eV. As shown in (3.3), the staning phase corresponds to .; 0 = zero. Other phases will

give the same type of picture but with the micromotion shifted in phase relative to the

underlying oscillation.

- 53-

·1.0

1.0

::E~ Ol-+""-\\-+-'r-:J-r=-~r-:JHN

VlItF

- 88: q•• 0.28

VI. 0.11.0

-1.0

::E~ 0 IC------~,._---__,MN

•

o 5liME· RF CYCLES

10 5liME - RF CYCLES

V,.,_ 289: q•• O.SI1v•• 0.51.0

-'.0

1.0

::E~ Of----"~-~'---~--r__i

N

5TIME - RF CYCL~S

5TIME • RF CYCLES

105liME· RF CYCLES

o

·1.0

1.0

::E~ 0 p..--....._"'-'~r-......+-+-I---4N

Figure 3.3 Representative solutions to the Mathieu equation for the axial motion of a

l33es ion in an ideal Paul trap of la = 14 mm operated at an RF of 250 kHz.

The slow underlying oscillation is generally referred to as the "beta" oscillation

following conventions established in altemating gradient synchrotron study. where this sort

of oscillation was fll'st encountered in beam dynamics. The energy associated with the beta

motion shown in figure 3.3 for Vz = 0.1 is about 1.7 eV.

Simply raising the voltage and changing no other parameters. except the initial

conditions of the particle motion so as to give an appropriate vertical scale, gives the

sequence of pictures shown in the remainder of figure 3.3. It is seen that. as the driving

voltage increases, the beta oscillation frequency increases. but so does the rela.; 'le

amplitude of the RF nùcromotion. At qz of about 0.91. the beta oscillation has become half

the frequency of the RF and beyond this the motion is no longer stable.

This is a general fealure of Mathieu functions; stable beta oscillations of frequency

greater than 1/2 of the driving frequency are impossible. This cornes from the nature of the

- 54-

Mathieu functions It is therefore sometimes convenient to define a f3 parameter of the

motion as twice the ratio of the beta oscillation frequency to the driving frequency. This

allows ail values of f3 from zero lO one. Here, instead, the symbol v =f3I2 will be used.

A graph of the beta oscillation frequency versus qz is shown in Fig. 3.4. It is seen that

the axial motion becomes unstable at qz '" 0.91. Included in this graph is the beta

oscillation frequency of the radial motion. From (3.3) the radial beta oscillation frequency

at a particular qz will be the same as the axial beta oscillation frequency for half that value of

qz. Thus the radial motion will become unstable at qz '" 1.82.

END OF STABILITY '--....---------------- ----0.5

u::­a:ëc:a.~

::::..>

oo 0.5

Vz

...••....

••

1.0

Figure 3.4 The beta oscillation frequen"ies (as a ratio of the drive frequency) versus

qz in a Paul trap. (The OC component az is taken to be zero.)

Il is seen that for Vz up to about 0.2, the beta oscillation frequency increases linearly

with qz. This can be shown to be a propeny of the Mathieu solutions for a =0 and the

proportional relationship is

{

1v= -q2..f2

- 55-

(3.5)

The effect of a positive OC component to the voltage applied to the ring will be to

introduce a further degree of stability to the radial motion (for positive charged particles)

while decreasing the stability of the axial motion. Thus a positive OC component will tend

to bring the !Jeta oscillations of the two motions closer to the same frequency. This effect is

seen in the graph of Fig. 3.5 where. from (3.3). a positive applied voltage corresponds to a

negative az. This graph is for qz = 0.54. giving Vz and Vr respectively of about 0.2 and 0.1

for az =O. It is seF;n that at about az =-0.075 Vzand Vr are about equal at 0.135.

0.2

-oc:o~ 0.1

:::;.

o-0.15 -0.10 -0.05 o

az

0.05 0.10

Figure 3.5 The beta oscillation frequencies (as a ratio of the drive frequency) versus

az in a Pual trap. The AC component qz is taken to be 0.54. The dotted lines

represent the approximation of eqn 3.6.

Again this behavior can be approximated for small a and q by a simple relationship

which is an expanded version of (3.5)

1( 2) 1V = 2 a +T 2' (3.6)

As shown in figure 3.5. equation 3.6 is an adequate expression for estimating the beta

frequencies of most Paul traps to sufficient accuracy. except when they are deliberately

operated near instability 50 as provide mass selection in their storage capabilities. For such

operation. il is necessary to have a diagram of the full region of stability (stability in both

radial and axial motion together) as shown in Fig. 3.6. A full discussion of such trap

operation is to be found in [Oa76].

- 56-

~l,

:;z

0.2 ~

0.1

-0.1

-0.2

-0.3

-0.4

-0.5

-0.6

1.00.5-0.7 L---L_.l-----l_--L_L----l._...L-----l_--L_.l---.l_....I-_L--l

o

r

Figure 3.6 111e Mathieu stability diagram showing beta oscillation fr:quencies v, and

l': (as ratios of the drive frequency) versus qz and Qz in a Puai trap. The doued

line represents the slice through the graph shown in figure 3.5.

- 57 -

3.1.3 Energy ofthe beta oscillation

The beta oscillation of a panicle in a Paul trap represents a component of the energy of

the motion. Il was shown be Dehmelt [De69] that this motion can be thought of as an

oscillation in a "pseudopotential" well. Il is therefore sometimes useful to deline a well

depth of the trap as the energy of a lieta oscillation of amplitude equal to the trap

dimensions.

Consider, for example, the well depth of the axial motion of Vz =0.1 pictured in figure

3.3. The amplitude of a beta oscillation equal to the trap dimension Zo would be 1.4 cm.

The pseudopotential well depth for this motion would be the oscillation energy of this

amplitude al 25 kHz for a cesium ion, or 3.33 V. This is only about 1/25th of the drive

potential on the ring electrode. The well depth for the radial motion, which has -./2 times

the axial dimension and approximateiy half the beta oscillation frequency (there is no DC

component to the field in this case), would be about halfthis or 1.6 V.

It can be easily shown that this corresponds to having the gradient of the

pseudopotential well, for equal radial and axial distances from lh~ ~~ap center, being

only 1/2 in the radial direction of what it is in the axial direction. This is, of course, in

keeping with the radial electric field of a quadrupole being only 1/2 that of the axial for

equal radial and axial distances from the trap center.

The gradient of the pseudopotential weil can be thought of as exerting a pressure on a

collection of panicles in a trap. Thus for a Paul trap with only an AC component to the

applied quadrupole field, the pressure on a collection of stored panicles is less in the radial

direction than in the axial. The collection can therefore be expected to he spheroidal,

flattened in the axial direction. However, by adding the appropriate DC component to the

quadrupole field, the radial and axial frequencies can be made the same, The

pseudopotential weil then becomes isotropic and a collection of stored panicles should tend

to form a spherical shape.

The well depths for the motions at higher beta oscillation frequencies scale, of course,

with the square of the frequency. Thus the greatest weil depth possible, at beta frequencies

for both radial and axial motions equalto half the drive frequency, would be about 80 V for

the axial motion and 160 V for the radial motion,. At more reasonable upper limilS for beta

oscillation frequencies , Le. l/3rd of the drive frequency, the weil depths arr; about 30 V

and 60 V respectively for the axial and radial motions.

- 58-

r

It can be seen from the relationship of the dimensionless parameters of the Mathieu

equation to the driving voltage on the ring (equation 3.3) that the pseudopotential weil

depths for the same point on the stability diagram, Le. the same values of Vz and v" the

applied voltage will increase with the square of its frequency. Thus the pseudopotential

weil depth attainable would increase in proportion to the applied voltage. Assuming that

the maximum applied voltage could be raised to about 15 rimes the values used for the

calculation of figure 3.3, i.e. to about 5000 Vpeak, the pseudopotential weil depths at Vz and

v, =0.33 could be raised to about 450 V and 900 V respectively for the axial and radial

motions.

It can aise be seen from (3.3) that the voltage required to maintain the same frequencies

scales as the square of the trap dimensions. For a trap which is 10 times larger than that

used for the calculation in figure 3.3 the applied voltage would have to he 100 times as

great or about 35 kV for Vz and v, = 0.33 at an applied frequency of 250 kHz. The

pseudopotential weil depths would then be about 3000 V and 6000 V respectively for the

axial and radial motions.

For a collection of charged particles in a trap, the pressure of the pseudopotential weil is

resisted by the coulomb repulsion of the particles. This leads to a "space-eharge limit" for

the number of ions that can be contained in a trap. For the type of trap operation depicted

in figure 3.3 for Vz =0.2, this limit has been found experimentally to be about 1 million

ions. However, in the larger, more powerful traps mentioned above, il should be possible

to contain up to 109 ions.

Thus very large traps can, in principle, he used to con.ain very large numbers of

relatively high-energy ions. The Paul trap can therefore be considered as not only a useful

device for small bench-top level experiments but as a possible major component in

collection devices for large scale systems 5': '1 as particle accelerators.

3./.4 Energy oflhe micro,.-.otiofi

Although the beta oscillation in a Paul trap is usually the motion of interest, there can

still be significant micromotion d:.e to the RF field, pa:tïcularly when the particle is far

from the center of its motion. This micromotion, being superimposed on the beta

oscillation, will reduce the amplitude of the beta oscillation !hat can be pennitted within the

trap to less [.'Jan the distance to the electrodes. In figure 3.3 it can be seen that fc,r high

quadrupole field strengths the amplitude of the micromotion can be up to half that of ilie

beta oscillation.

- 59-

•Furthennore, while the amplitude of the RF micromotion is always smaller than that of

the beta motion, the kinetic energy associated with this motion can be much larger. This is

because of the high frequency of the micromotion compared to that of the beta. A

representative diagram is shown in figure 3.7 where the instantaneous kinetic energy of the

particle is plolted for the case when Vz = 0.2 and the energy associated with the beta

oscillation is only 4.4 eV. It is seen that, due to the micromotion. the instantaneous kinetic

energy of the partic1e can reach as high as 16 eV or almost 4 times that of the beta motion.

VRF= 170; qz = 0.53Vz = 0.21.0

::i:Ü 0,N

-1.0

0 5 10TIME • RF CYCLES

~ 20

~wz 10wü

~z52

1 1

- VRF= 170; q. = 0.53v. = 0.2

- i' rJ ·0 '" -- -- r- -- r-' -

\1\1 ~. w 1 \1\1 ..01 1

o 5TIME - RF CYCLES

10

Figure 3.ï The inslantaneous kinetic encrgy for typica! ion nl';tiC'll in a Paul trap.

Th:: upper graph shows the axial displacement versus time. The Jower graph

shows the kinetic energy on the sarr· c rime scale. The dotted line represents the

kinetic energy of the macromotion.

.This RF "micromotion" can have important implications on trap operation. While the

amplitude of the rf micromotion is typically small compared ta that of the f3 oscillation, this

- 60-

(

micromotion, being superimposed on the beta oscillation, will reduce the amplitude of the fJoscillation that can be pennilled within the trap te lt:ss than the distance to the electrodes. A

typical reduction factor will he to 70% of the electrode distance. However, there is another

important feature of the micromotion. While its amplitude is usually much smaller than that

of the f3 motion, it was shown above that the instantaneous kinetic energy associated with it

can actually he much larger than the pseudopotential weIl depth. This is because of the

high frequency of the micromotion compared to that of the f3 motion. A typical value for

the peak instantaneous energy due to the micromotion is about 5 times tha: associated with

the f3 oscillation. Thus typical instanlaneous energies in a modest Paul trap can reach to

almost40 VOliS for a typical trap with a pseudopotential weIl depth of only 15 volts.

This feature of panicle motion in a Paul trap is extremely important when considering

external injection into it. By phasing the time of injection so that it corresponds to an

inslantaneous maximum of the particle ve10city in the direction of injection, the particle can

be injected and t'"qpped even though its energy is large compared to the pseudopotential

weIl depth. Essentially, by injecting atthe proper phase the kinetic energy of the incoming

panicle is removed by a high instantaneous retarding electric field at that time.

Of course, for successful capture the subsequent motion of the particle must not result

in an encounter with an electrode or the entrance or extraction holes. In electric fields that

are oscillating at a constant frequency and amplitude the long-time average of the kinetic

energy of the particles will he constant. In other words, ail the motions are essentially

cyclic. Therefore, even if the particle misses ail of the electrodes for the first few

oscillaitons, there will he an instant at sorne finite time after injection that the particle will

relurn to ilS injection point but with its velocity reversed so that il leaves the trap. For

pennanent capture, energy must therefore be removed from the motion before this

eventuality. The buffer gas idees this by continuously removeing energy so that the ions

only have to he kept from encountering a hole or an electrode for a certain fraction of the

time constant of cooling due to the gas. In a study by Lunney significant reduction in the

phase space volume of stored ion clouds have becn observed after 1 ms in 0.01 Pa of He at

room temperature [Lu92]. Assuming the reduction after 1 ms would he sufficient to

remove the possibility of ions escaping from the trap, a trap operating at a axial fJoSI.:Ilation frequency of ISO kHz would have to contain the ions for about ISO fJoscillations before il became certain that they would not subsequently escape.

The most important period during which the ions must he kept away from the

electrodes or the holes is during the fmt few fJ oscillations. In the technique of Moore and

Gulick for pulsed heams, a properly phased damping voltage at the fJ oscillation frequency

- 61 -

•

.T

was applied to the far electrode to quickly reduce the amplitude of this motion. This is a

vollllge which is phased so that it produces a maximum retarding field atthe instantthnt the

particles are at the center (of the trap and therefore at their maximum velocity. Atthis phase

the integral of the product of retardation force times velocity over a complete cycle, which

is the energy taken out of the oscillation in one cycle, is a maximum.

Of course, this damping voltage reverts into an excitatory voltage aCter the inilial fJoscillation has been damped to zero. The technique used to avoid Ihis was to lune the

damping frequency slightly off resonance to the f3 oscillation so thal this subsequent re­

excitation was hindered long enough for the higher order multipoles of the trapping field ID

push the ions out into the radial regions. This allowed a collection efficiency of about 5~.

However, taking into account that the pulsed beam that was used for this type of injection

had a duty cycle of about 5%, the overall capture efficiency using this process for a DC

beam would be only about 2.5%.

Another approach would be to gradually convert the initial axial f3 oscillation into radial

f3 oscillation (i.e. ttansfer the axial energy into radial). This can be accomplished by higher

order multipoles in the trapping field. Of course such a process would also be cyclic in lhat

after the initial ttansform of axial motion te radial motion is complete, the radial motion will

transform back to axial. Agnin the transform rate must be such that enough energy is

removed in the flfSt f3 oscillation to prevent escape from the axial holes or by impact with

an end electrode. However, the rate must not be so high thal the reconversion back te axial

motion occurs before sufficient energy is removed by the buffer gas.

In general, successful capture involves such manipulation using higher order multipoles

of tl}e field within the trap. It is very difficult to analyze the complicated sequence of

motions in a trap leading to possible successful capture of an incoming particle for a given

trap geometry and operaling condition, panicularly since the actual effect of buffer gas

collisions in the energy range of ions in a Paul trap is not weil known [EI78). However, a

view of the scope of the problem and sorne useful conclusions can be reached by a general

consideratio:l of the phase space dynamics of the capture process.

3.2 Phase Space Considerations of Trap Injection

3.2.1 Phase Space and Liouville's Theorem

Collecting a beam of particles inlo any confmed region of space involves ttansferring an

ensemble of panicles from one region to another of six-dimensional phase space. Ane1emental volume of this space is defined as

·62 -

dS =dx dy dz dpx dpy dpz (3.7)

The significance of this space lies in the density of panicles within il. For manipulation

of any collection of panicles by the son of forces generated by applied electromagnetic

fields this density is governed by Liouville's theorem which states:

Under the action of forces that can be derived from a

Hamiltonian, the motion of a group of particles is such that

the local density of representative points in the appropriate

phase space remains everywhere constant.

ln other words, to such forces the collection of panicles behaves in phase space like an

incompressible f1uid. This implies, of course, that if at sorne instant the collection of

panicles can be specified to be within a cenain volume in phase space then at any later time,

when the panicles are in a different region of phase space, the volume of the occupied

region will be the same.

The volume of an ensemble in phase space is

(3.8)

where the integration is to the spatial and momentum limits of the partic1e collection limits

occupied by the particles, By Liouville's theorem, this integrated six-dimensional volume

is conserved in any transformation involving Hamiltonian derivable force fields, such as

would normally be applied for in-flight capture of an ion beam. Thus the phase space

volume of a trap becomes the fundamentallimit of ilS capacity to hold an ion beam.

3.2.2 Phase Space ofan Ion Bearn

In the manipulation of charged particle beams one generally tries to avoid aberrations.

ln aberration-free, or "linear", systems, the subintegrals of phase space

(3.9)

are individually conserved. In the panicular case of the Iimits of integration being

constanl.~, the overall phase space volume becomes

- 63-

•

(3.10)

In beam optics, where z is usually regarded as the coordinale in the beam direcùon, the

transverse components of the phase space volume are usually expressed in terms of

"emittance". This is defined as the area occupied by the panicles in a diagram in which

their angular divergences from the central beam axis are plotted against their displacemenls

from the beam axis. The connection belWeen the emittances çand the transverse phase

space volume components for a beam of parùcles with central momentum Po is

(3.11 )

The conservation of il phase space component in a beam causes the eminance diagrams

10 shrink if the central momentum increases, even if there is no interdependence introduced

belWeen the three coordinale directions. To have an emittance measure which is preserved

under a simple acceleration, such as is intended for beams from ion sources, the emittance

is often expressed as a "normalized emittance" which is defmed as

(3.12)

where ris the ratio of the relativistic mass m of the particlt~ !<> their reGl mass mo and f3 is

the ratio of their velocity to ~;..: velocity of light. Thus the normalized emiltance in a given

coordinate (say x) is directly related by a multiplication constant to the phase space area in

that coordinate;

(3.13)

where mo is the rest mas" of the beam particle, c is the velocl.y rf Iight and ÇIlX is the

normalized emittance in the x coordinate.

The longitudinal phase space component of a length 1 of beam w!Jich has a momenlum

spread 6p is simply

s. =!:J.p 1 (3.14 )

•

The phase space volume of a length of beam is thus delermined from its normalized

emittances in the two coordinales of its transverse plane and its momentum spread;

(3.1 5)

-64-

3.2.3 Phase Space Volume ofa Particle Trap

To first order, in a particle trap the particle motions in eaeh eoordinate will he simple

harmonie. In the phase space diagram for each coordinate, the particles will therefore move

clockwise in trajectories which are all ellipses of the same shape and aligned with the

momentum-displacement axes (fig. 3.3).

pz

.-b~""'I---- Max value of pz

= mroz max

-I-_'""C!T-;--+t-- Z

Amplitudeofoscillation = Zmax

Figure 3.8 The two-dimensional phase space diagram for a collection of particles

undergoing simple harmonic motion in a trap.

Ali particles will have the same orbital period in this diagram but individual phases and

amplitudes. This will result in the phase space area occupied by the collection being that of

the ellipse for the particle with the maximum amplitude of oscillation. For example, in the

x coordinate this would he

(3.16)

where a>x is the angular frequency of the x oscillation and Xmax is the maximum amplitudeof that oscillation.

Since the motions in the three coordinates of an ideal trap are completely independent,

the phase space volume wiJl he the triple product of the phase space areas. For a Paul trap

which has cylindrical symmetry about a z axis, th:: x ar:d the y motions will have the same

- 65-

•frequency and maximum values, which may be expressed as Cllr and rmax. The phase space

volume of such a trap is then

(3.17)

Comparing (3.15) and (3.17) gives the maximum length of beam that can be stored

following in-flight capture in a Paul trap. A typical RFQ trap, such as is used for mass

spectrometry in chemistry, will alIow oscillation amplitudes of up to about l cm and can be

operated so as to have equal axial and radial oscillation frequencies of up to 150 kHz for

mass 100 ions. The normalized emittance of a beam of such ions from a quality separator

such as ISOLDE is typically 7 x 10-3 lt-mm-rnrad in each transverse coordinate and the

energy spread is less than 6 eV in 60 keV. The velocity of mass 100 ions at 60 kV is

about 3 x 1()5 rn/s. The beam segment that could be :..\ooeoretically collected in such a trap is

about 200 km or 0.5s.

This analysis has not included space charge effects. The numher of ions in the phase

space Iimit of trap could easily exceed the space charge Iimit which, for the trap described

above, has been shown by Dehmelt [De69] to be about 1()6. However, the purpose of the

collection system for the mass measurements at ISOLDE is to be able to deal effectively

with very weak beams of short-Iived radioisetopes. Aise, for highly precise measurements

the precision Penning trap should never have more than about 100 ions delivered to iL The

space charge limit of the collection trap is therefore not a concem in this work.

3.2.4 Adapting the Phase Space ofa Bearn to that ofa Particle Trop

A capacity for 0.5 s of beam wûuld appear te be more than sufficient for collecting ions

in a Paul trap. Essentially, it means that Liouville's theorem imposes no fundamental

restriction on collecting a long section of a DC ion beam in a Paul trap. Unfortunately,

Liouville's theorem gives no prescription for how the phase space volume of the beam is

actually te be manipulated into the shape required te fit the trap and there is a very difficult

prcblem in this manipulation. The relative sizes of the phase space projections into the

three coordinate planes are very different for the two cases. The phase space volume of the

ions within the trap is nearly evenly projected into these planes; about 500 eV-ILs in each

from a phase space volume of 1.25 x HI8 (eV-ILs)3 for the trap mentioned above.

However, in the incoming beam the ions occupy only about 7 eV-ILs in each of the two

transverse components but about 2.5 x 1()6 eV-ILS in the longitudinal component.

·66-

The problem this presents is similar to that of multiple stacking of injected beams in

synchrotron storage rings. For such injection each incoming beam length that fills the

circumference of the ring must be placed in different regions of the phase space volume of

the ring. Such "stacking" can typically be achieved for up to 100 orbits, or a total beam

length of 100 times the storage ring circumference. However, about 5000 axial strings of

beams would have to be threaded into a trap to fill il. Thus, while there is a great deal of

phase space available in the radial direction in a trap, the fine threading of the beam required

to lill it does not seem feasible.

However, the problem is considerably reduced by buffer gas cooling of the ions that

are already in the trap, as outlined in the previous section. Such cooling was originally

studied by Dehmelt [De69) and is now commonly applied. Cooling may be defined as an

exponential reduction of the phase space volume. The reduction in the phase space area of

the axial motion is especially importa..t sinee any such reduction is necessary to prohibit

particles from reaching an end electrode or from leaving the trap through the hole it entered,

both of which are at the extremes of the phase space area.

Cooling of ions by buffer gas in a Paul trap typically has a time constant of about

1 ms. Thus, if ions can be transferred into a trap for about 1 ms without overfil1ing the

phase space capacity, then with buffer gas cooüng it should be possible to transfer ions into

the tr~p continuously. The primary concem then becomes that of manipulating the

incoming beam 50 that the projection of th.:- l'hase space of 1 ms of that beam into the axial

phase space component does not exceed the trap capacity in that dimension.

The axial phase space component of 1 ms of ISOLDE beam still greatly exceeds the

capacity of a typical Paul trap. This means that Ihe incoming beam must be manipulated 50

that its axial phase space coordinate is turned toward the radial direction, thereby reducing

its projection onto the axial phase space volume. This, in turn, will require the coupling of

the axial motion to the radial motion that has aln:ady becn discussed. Traps that have pure

electric quadrupole fields provide no such coupling. Small acceptances and small rf phase

windows are then to be expected, as has been predicted by Scheussler and 0 [ScSI].

Axial injection of ions into the phase space of the trap that is available at larger radii will

require the higher order multipoles in the electric field that provide the necessary coupling

of the axial and radial motions.

Unfortunately, as pointed out earlier, accurate calclJlations of the effects of higher order

multipoles on the behavior of ions in a Paul trap containing buffer gas are difficult. This is

particularly so over the large number of rf cycles before successful capture can be

established. However, it rnight be expected tha.t for a given beam and buffer gas pressure

- 67-

•

r

the capture efficiency should be roughly proportional to the overall phase space volume of

the trap. What must be known in designing a trap for high collection efficiency is. first.

whether the collection efficiency is indeed proponionalto the phase space volume of the

trap and. secondly. ifthis is so what is the proportionality constant.

A typical Paul trap was therefore built to experimentally determine its acceptance of a

typical high velocity beam as a function of its phase space volume. To achieve this it was

necessary to design a system to decelerate an ISOLDE type beam to the severaltens of eV

required for Paul trap injection and to build a trap which could be operated at on a high

voltage platform to achieve this deceleration. It was aise necessary to design the trap for

rapid pulsed ejection of the collected ion cloud so as to measure the overall efficiency with

which the incoming beam is collected into a pulse suitable for Penning trap injection.

3.3 The Deceleration of Ions lnto a Paul Trap

In general. the deceleration of charged parricles to very low energy requires highly

linear or aberration Cree systems. This is required in order that the large axial energy is not

transformed into transverse energy during the deceleration process. resulting in an over­

reduction of the axial energy and a reflection of the parricles back along the axis before they

have reached the desired overall energy. It is the higher order multipoles, or aberrations,

that cause this transformation.

Deceleration systems for ISOLDE type beams have been designed for implantation

studies [Fr76l. but with energy reductions of only about a factor of 50. For Paul trap

injection deceleration to tens of eV is required, a reduction of over 1000. In such a case

much more carefui attention mest be given to the aberrations of the system.

Assessment of the aberrations when there is a large energy deceleration factor over the

short distance required to obtain a sharp focus of the beam onto the entrance hole of the trap

requires very precise calcuiations of the ion trajectories. The precision required is not easily

achieved by numerical integration of the equations of motion using a mapped set of field

values and ordinary interpolation techniques. This is due to the large inherent errer in the

first-order (plane) interpolation of the fields in the tight geometry involved and the

prohibitive computation time required for higher order interpolations.

This problem was circumvented by fitting the caIculated values of the electric fields to a

set ofaxially symmetric multipoles and using this setto calculate the fields used in the

numerical integrations. A 6th order Runge-Kul!a computer routine ( a 4th order Runge-

- 68-

(

Kutta algorithm with adaptive step-wise error c,orrection) was written to carry out the

calculations using a MacIntosh cii. Since the aberrations in the focus is due to the

I1ltiltipoles beyond the quadrupole. multipoIes up to I2th order (leading to 6th order

aœrralion terrns) were inclu':ed.

By tailoring the geometry of the deceleration system the effects of the higher muItipoles

couId he made insignificant for deceleration from 60 keV to about 100 eV. As a general rule

il appcars lhat to reduce the aberrations to the required level atthis deceIeration factor the

irllcrnal diamcler of the deceleration electrodes in the region of maximum decelerating field

had tll bc a leasl len limes that of the beam being decelerated.

Al the point at which the decelerated ion energy is 100 eV, the fields are deliberately

Illadc to contain higher-order multipoles 50 as to introduce the coupling of the radial alid

axial motions that is required upon entry inlO the trap. As pointed out in the previolls

scclion, this is sa that a considerable amount of the axial phase space component can be

projccted into the radial space upon entering the trap. To achieve this a rapid reduction of

the internai diameter of the main decelerating electrode is introduced just before this point in

the deceleralion (sec fig. 3.9). This creates a strong focusing of the beam atthe entrance

hale of the trap. thcreby, blowing the beam out into the radial regions of the trap where the

abcrralions rcqllired for cOllpling are more effective.

DECELERATIONGROUND ELECTRODESIS IIII@

Il \SI SS@

TRAP RING EXTRACTIONELECTRODE ELECTRODE

~~~,,~~~o'\~:''';''-::--- -J . ~ @S\\I\\\\\\S\\S s§l

/ ~\TRAP END ELECTRODES

EELE';TRONMULTIPLIER

(Figure 3.9 The deceleration and injection system.

·69 -

•The largest aperture electrode system that could easily be inserted into the system for

deceleration into the chosen Paul trap was about 2 cm diameter. To avoid the effects of the

calculated aberrations in the deceleration system, the incoming beam therefore had to bc

Iimited to ahout 2 mm diamete. This was done by introducing a fixed 2mm diameter

aperture ,::ollimator into the bearn system just upstream from the decelera~on system.

3.4 Properties of the Extracled Bearn from a Paul Trap

Although t.he major concem in developing a trap collection system is a high capture

efficiency, another important aspect is the nature of the beam bunch that cal! be extractcd

from il. This depends on the phase space density of the assembled ion immediately beforc

extraction which, from Liouville's theorem, is preserved during the extraction. Therefore if

the ion cloud phase space distribution can be determined just before extraction, in principle

an ion optic system can be designed to m~nipulate the cloud for delivery in the forro most

appropriate for a specific experimenl.

As .... ith the collection efficiency, predictions of the phase space density within a Paul

trap after buffer gas cooling are extremely difficult and for the same reasons; the

complicated interactions between the ions with the buffer g,lS and how these are induced by

the multipolar electric l1eld within the trap. Dehmelt [De69J showed that a thermodynamic

equilibrium characterized by temperature should be exp~cted but the actual temperature

reached in this equilibrium is difficult to determine. This is because of complicatcd

sequence by which an io:! c1c'~d receiv;:. he;:! il! " Paul trap with buffer gas cooIing. A

single ion in such a trap will cool tu the temperature of the buffer ga~ itself but a collection

of more than one ion wîJ1 not. This is because the space charge repulsion of the ions will

force them out from the center of the Lap. They then experience the electric quadrupole rf

field, receiving micromotion of relatively high l. netic energy. While this motion, bcing

coherent with the rf, is not itself characterized as a heating, it does introduce random

collisions with the buffer gas which is a heating. Essentially the ions are heated by

"friction" against the buffer gas while in their rf motion. The heating of the ions by the rf

induced collisions with the buffer gas molecules is, of course balanced by the cooling effcet

of the gas. The actual equilibrium temperature reached depends on this balance.

A review of previous studies of the temperature of ions following buffer gas cooling in

a Paul trap is presented by Lunney et aI.[Lu92a) Because of conflicting measurements

reported in the Iiterature, an experimental study of the phase space volumes of such ion

clouds was undertaken as part of a Phd thesis project of Lunney. The method used was

-70 -

1 careful extraction of the ion cloud followed by observation of the phase space volume of

the extracted ions in a transpon system.

The results of the work of LUllney show !hat the temperature of an ion cloud above that

of the buffer gas in a Paul trap is roughly proponional to the two-thirds power of the

number of ions in the trap. For 20,000 ions in a typical trap with buffer gas cooling, an

ion temperature of about 0.3 eV was observed [Lu92]. For about 1000 ions the

temperature of the ions became essentially that of the buffer gas itself (i.e. room

temperature in that work).

This is an extremely encouraging resuIt. Even at the heavier loading of 20 000 ions,

90% of the ion cloud would be contained in a volume of about 30 mm3. ln terms of a

phase space projection in any momentum-displacement plane this would he about 3 eV-us

for !hat pl(j.ne. For the smaller numbers of interest in the mass measuring system, the

volumes will he considerably less and phase space projections ioto the axial motion of less

than 1 eV-ils should be achievable.

Thus a Paul trap collection is capable of preparing extremely weil defined bunches of

ions from weak ISOLDE type heams. The phase space areas that seem achievable as such

that, with a transpon system designed to provide a time focus of 1 us, the energy spread

could he less than 1 eV.

-71 -

•

(This page left blank intentionally.)

- 'il. -

•i

CHAPTER 4

APPARATUS AND RESULTS

A schematic view of the Paul trap test set-up at the ISOLDE 3 facility along the axis of

the beam is shown in figure 4.1. A more detailed side view of the apparalUs is shown in

fig. 4.2. The system is a modified version of the system that had been set up at McGill for

testing at up to 10 keV injection. Its essential features are:

1. A Faraday cage within which the trap and all its services are maintained at

approximately the potential representing the kinetic energy of the beam to be

collected (in the case of an ISOLDE beam up to 60 kV)

2. A test ion gun capable of injecting ions at up to 6S keV for tuning the apparalUs

and which can be removed from the beam line without breaking the vacuum

once an ISOLDE beam is to be collected. A removeable Faraday plate for

measuring the ion beam is also included in the system

3. An extraction system which delivers a pulse of ions extracted from the trap to

an electron multiplier detector.

The components of this system will be described in separate sections. starting with the

Paul trap itself.

4.1 The Paul Trap

A view of the trap in its relationship to :~, 'leighboring components was shown in

figure 3.9. The trap electrodes are conjugate hyperboloids of revolutions about the z axis

and symmetrical about the radial axis with internai surfaces defmed by ,2 - z2 =2 zo2

where Zo is 14 mm. This results in a internai radius of the ring electrode of 20 mm. To

create a nearly quadrupole field. the separation belWeen the end electrodes was set to 2zoor

28 mm. Injection and extraction apertures of 8 mm diameter are drilled on-axis in the I~nd

electrodes. The electrodes are isolated from each other with ceramic spacers capable of

withstanding voltages up to 8 kVp RF. The trap is mounted for axial injection and installed

in a 4-way beam pipe vacuum chamber cross ofinternal diameter 160 mm. and placed with

its axis aligned with the ISOLDE beaniline. Alignment of the apertures to the beam center

was achieved with a surveying theodolite.

-73 -

J

M

,.. 120CM -1FARADAY CAGE

--FIBRE-OPTIC

LINK ~

PAULTRAP PAULTRAPPAULTRAP DRIVERS·CONTROLS

ISOLDE-3:--~ BEAMLiN

6r/vL.-. (J E,..-

250C

~ 1--

ISOLATION--- TRANSFORMER

'V"'~' '"'","'~ ~ ,v,",,,,,'.""""

Figure 4.1 The configuration of the Paul trdp collection system as installed on theISOLDE 3 beamline.

-74·

E"o'"

Z:J(,:l

Zo-

•;

Figure 4.2 A sectional view of the Paul trap collection system as installed at the

ISOLDE 3 facility.

-75 -

•

To bias the trap '.0 60 kV, a high-voltage pedestal is constructed by using two elcctrical

isolation flanges on either side of the ttap. These are machined from 5 cm 'hick plexiglass

with deep grooves cut on the interior and exterior surfaces to avoid high-vonage spark­

over. The whole ttap system is SllITOunded by a Faraday cage for electrical isolation and

safe!y.

The driving RF signal is applied to the ring electrode through a high-voltage

feedthrough on one of the vacuum flanges of the 4-way cross. The RF voltages are chosen

to keep the values of qz ~ 0.4 so as to remain weil within the stable operllting rcgion.

Pseudopotential trapping weil depths of up to 100 volts are easily achicvcd.

Details of the injection side of the trap are given in section 3.3.

4.2 Vacuum System

Since the Paul ttap operates with a helium buffer gas in its ttapping region. an ultra­

high vacuum is not required. However, the vacuum system should be c1ean and wilhout

signific~llt outgasing since these would introduce contaminant molecules into the rcsidual

gas which could be ionized and load the trap. The only vacuum difficulty is that the trap

volume presents a large gas load through the enttance and extraction holes to the rest of the

beam transport system, which generally must èe maintained to about 1 mPa. This was

achieved by pumping the system with a 450 Vs turbomolecular pump irnrncdialcly on cither

side of the trap Faraday cage. To hinder helium from escaping upstteam into the ISOLDE

beam line a small 8mm diaphragm was pIaced in front of the test ion gun.

Due to lack of space on the trap flanges, a vacuum gauge could not be installed for

pressure readings at the trap while it was in operation. However. a calibration was carried

out by temporarily installing a vacuum gauge and comparing its readings with another

gauge located outside the trap Faraday cage. The pumping system could achieve a base

pressure of 6 x 10-5 Pa (6 x 10-7 mbar) before the buffer gas was inttoduced.

To avoid discharges in the gas in the plastic transfer tube leading the buffer helium gas

up to the high potential of the trap. the gas is introduced by a manually controllable leak

valve situated on the ttap chamber 50 tha! the helium in the plastic transfer tube could be

kept above attnospheric pressure. The helium used was 1 part in 107 purity.

-76-

i4.3 Faraday Cages

{

The Faraday cages are containers for the -::leclfonics and the devices which must be

maintained at a high DC potentia!. Each Faraday cage is surrounded by a grounded cage

for electrical shielding and safety, the grounded cages ail having atleast 12 cm separation

from any point on the exterior of their enclosed Faraday cages. Since space is very limited

in the ISOLDE beam hall, the Faraday cages were designed to be as compact as possible.

The final design decided upon was to have three separate cages for the instrumentation, the

trJp and the ion ~')urce sections. Ali Faraday cages were constructed of an aluminum frame

covered by a me';h screen for observation of the int;rior cC"lponents and air-flow to cool.

lhem. To eliminate corona and electrical breakdown aIl sharp edges and corners were

removed from both the outsic'e of the Faraday cages and the inside of the grounded cages.

High-voltage tests were performed to ascenain that ail componerats couId withstand up to

75 kV applied potential.

For safety a minimum 4 cm wide braided cable was used to connect several points on

th~ grounded cages and aIl electronic equipment at ground potentialto weIl established

ground points in the ISOLDE 3 bearn-hall.

Due to combi!ling the isolation transformer and the instruments ioto one cage system,

this is the larger of the three (1.5 m x 1 m x 2 m outside ground cage). The transforrn~ris

placed on the floor of the grounded cage under the instrumentation Faraday cage. '!bis

avoids the use of an aoctitional cage for the isolation transConner.

Connections between the cages are achieved by passing the signal cables through metal

tubes at the high-voltage potential, This eliminates the electric field of the 60 kV potentisl

from the oUlSide of the ground retum shield of the signal cables.

4.4 High.voltage System

The high-voltage source is a Spellman 80 kV supply. A precision of ± 1 volt can be

achievv:l with its external control. Voltage stability is rated at 10-4. Initially it was thought

lhat a voltage comparator might be required between the ISOLDE acceleration voltage and

the trJp potential platform in order to maintain the trap platform potentialto the accuracy

required to maintain the proper injection energy (~30 eV), This was carried out as a test

but it was found that the Spellman supply did indeed maintain its output voltage to the

precision necessary for the trapping tests (several voit~). This was fonunate because the

-77 -

•

extensive cabling and apparatus to be maintained at 60 kV using the comparator system

presented an operational difficulty as weil as a safety hazard.

When the high-voltage is not in service it is grounded (by a grounding hook) to the

outer cage. Aiso a flashing warning light is activated when the high-voltage is on. Upon

completing the final installation, the system had to pass a rigorous safety inspection by the

CERN safety division.

Electrical power is supplied to the instrumentation in the inner Faraday cage by a

100 kV isolation transformer. Since the apparatus within the trap Faraday cage at 60 kV

was developed at McGill using North Amc:ican standard equipment (110 V input), this

isolation transformer had a 2:1 transformer ratio for use with a standard Europe...l 220 volt

supply. However, the isolation transformer seemed to have been wound with its input coil

symmetrically placed at ± 110. When connected to the single phase 220 European power

(with one sià.; neutraI) a capacitively fed-through 50 Hz ripple appeared on the neutral side

of the 110 V output and hence on the rdative ground of the trapping Faraday cage. To

reduce this to acceptable vailles, a 100 kV 3 nanofarad capacïtor was connected between the

Faraday cage and the grounded cage. This cured the problem but at the expense of

significantly raising the stored electrical energy, and hence the hazard of the high-voltage

system.

The design of the 5ystem and ilS Faraday cages succeeded in eliminating problems with

corona and electrical arcing within the system itself. However, an occasional discharge

occurred within tile isolation transformer, observed by a sound from within the transformer

housing, when the system was tumed on after it had not been used for several days. lt is

suggested that this was because of air bubbles that built up in the transformer oil aftel it

was allowed tO cool. An avalanche discharge can then yield a large current looking for

ground. If there is a ground loop in the return current of the discharge, severe problems

can be prcsented to any electrical equipment in ils vicinity. This is because of the

electromagnetic pulse produced by the ground loop current. In fact, one such ~i!>charge

caused a breakdown between neutral and ground near the main power outlet used for the

apparatus, producing an electromagnetic pulse which knocked out a computer system

approximately 10 m away.

Unfonunately, because of the necessity of using three separate grounded cages to

contain ail of the equipment, ground loops were difficult to avoid in the test set-up at

ISOLDE 3. The particular discharge problem presented by the isolation transformer was

avoided by leaving the input voltage on the isolation transformer at alltimes to keep the oil

continually warm.

-78 -

••4.5 Electronic System

The electronic system provides for the generation and control of the various signals that

are required in 1he operation of the Paul trap. The system is divided into two sections; one

al ground potenlial and the other at high-voltage (60 kV) inside a Faraday cage. A fiber

oplic link establishes the communication between the two sections. In order to facilitate

control of the trapping paramelers, ail components requiring adjustment or tuning during

operation (Le. RF voltage, frequency, phase and pulse width) are placed at ground

potentiaI. The signais are converted into analog optical signais and transmitted to the

Faraday cage via optical fibres where they are detected and amplified to the appropriate

level. There is very little anenuation in the optical signal by the approximately one meter of

fibre used.

The signal~ received inside the Faraday cage are then amplified by fixed gain amplifiers

and distribuled 10 the different deviccs within the cage. A schematic of the overall system is

shown in figure (4.3).

4.5./ Ejection Pu/se

To regulate the storage time, a circuit was built to count the number of RF cycles. Up

to 1()6 counts couId be retained, corresponding to storage times of up to about 1 second at

the typical operating RF frequency of 1 MHz. The counter circuit was designed to give a

signal to the extraction pulse circuit and clear itself at a preset number of counts. The

extraction pulse is produced as a trigger pulse at ground in the Paul trap control box and is

transmitted 10 the Faraday cage where it is applied to a fast high-voltage switching

transistor to generate pulses off 300 volts with a fall time of 100 ns. These ejection pulses

are applied to the far end electrode and to the extraction lens. Filter coupling is required to

block any RF from the ring electrode from apJl<:aring on the end electrode sincc this would

dislort the trapping pseudopotential weil.

Tht phase of the ejection pulse relative to the RF frequency can he adjusted over a

complete RF cycle and can he monitored from an oscilloscope by triggering on the RF

signal.

4.5.2 Radio{reqllency Generation

The radio-frequency signal is produced in the portion of the electronic system at

ground. Voltage control is accomplished with an RF control module which regulates the

amplitude of the signal to ± 1 volt, before being transmitted through the fiber optic link.

-79 -

•

aTRAP

f.O.l.INK

HJGH VOLTAGEORO~

4 CIL F.O. UN](---, 1R.F. CON"IROL 1 ENIAMP.r-- CH·' <RFl 1-~ MATCIIINO 11ElECTRONlC OUT XMTR RCVR

IŒIWO~ 1 :IATŒNUATOR r-- CH·2(EXT.) rXMTR RCVR

4= ALCDELTA CH·](RFŒVEL)

DELTA ..... PULSSAMP. 1IDEMOO

RCVR XMTR lMOO. ,:+L- CH"(CLOCK)

..Jcu< 1 RF. DE:ŒCTO" tRCVR XMTRRFU!VEL cu<

EXTRACTIONPULSEATŒN.

H CONTROL 1 ..MODl1Π1-

;-

yS1GNAL .....GENERAlOR

::n1IQa~

'"CI>C'l:r0

~a.C'l0-.g-o!l.

~00 "0

ë,~0c:,...

1• The RF signal is received in the high voltage section and applied to the input of a

broad-band EMI mode! A-300 RF power amplifier. The output of the amplifier is fed to a

toroidal core ferrite transformer system which produces a high voltage that is applied to the

ring -::lectrode and acts as a matching transformer for the 50 ohm output. To generate the

necessary RF voltage, 5 toroidals cores with a tums ratio of 1: 25 were wound in parallel,

crealing up to 6 kV peak. Cores were hand wound with standard Formal insulated magnet

wire. The number of windings on the transformer were chosen to provide a low Q

resonance with the trap ring capacitance at about 1 MHz.

A complication occurred when running at high power levels in that the toroidal cores

became overheated, presumably by core saturation. Two solutions were tried; one to air

cool the cores by a fan attached to the housing and the other to submerge the coils in an oil

bath. The first solution proved the casier of the two to implement and worked sufficiently

weB for our purposes. The second method was tested and could be used when higher RF

voltages are required.

4.6 Ion Sources

4.6.J Off-/ine source

Prior 10 on-Iine operation, trapping was extensively tested off-Iine using an ion source

capable of producing 60 keV beams of Cs or Rb. The source used was a zeolite ion gun

developed at the Foster Radiation Laboratory for the tests carried out Ihere but redesigned

for 60 kV operation. Zeolile is a sodium aluminosilicate which loosely binds alkali atoms

and, by an ion exchange process, the sodium aloms can be replaced by another alkali

clement. Heating of these ion-exchanged zeolites releases the alkali clements primarily ...,

ions with a few neutral atoms. A heated platinum wire can then il:: t'~ed to surface ionizc

these neutrals. Both cesium and rubidium ion sources were devdoped but, for the purpose

of testing the ISOLDE 3 Paul trap set-up, cesium was chosen as it requires less heat for the

ion creation, has only one stable isotope and is closer to the mid-mar.s region of the

clements. Furthermore, the heavier mass ions (cesium-133) require a lower RF frequency

for trapping, somewhat reducing the demands on the electronics. Ion rurrents of the order

of tens of nanoamperes over a lüe tirne of 300 hours ofopelûtion were achieved.

However, severa! problems were encountered before a source that could he operal~d at

60 kV was availablt:. One problem was the cooling of the source. Creating a beam of 10

nanoam"s required a power input of several tens of watts to heat the zeolite. In a vacuum,

- 81 •

•

•

this heat has to be removed or intolerable temperalUres are achieved in the general system.

At McGilIthis heat had been removed by water cooling but at CERN the low resistivity of

the cooling water (no demineralized cooling water system was available), and the high

voltages which the cooling water lines had to withstand, lead to intolerable loading of the

high voltage supply to th~ system. The ion source therefore had to be redesigned with a

large cross-section feedthrough to allow conduction of the h"a ( to ol,tside the vacuum for

air cooling.

Another problem was that the geometry of elltraction electrodes for the source had to

be changed to be appropriate for 60 kV operation. Finally, of course, the design had to

prevent any breakdowns from the 60 kV operating potential inside the v~uum.

These problems were compounded by the nl"ed to have the ion source moveable

transverse to the ISOLDE beam line so that it could be moved out of the way of the beam

line without disturbing the vacuum system. This was necessary because of the elltensive

tuning of the trap system that has to be carried out to get it working to mallim".n

perfonnance for accepting incoming ions. Because of the limited ISOLDE 3 beam time

available for the tests, this lUning was not feasible with the ISOLDE 3 beam itself.

The final design is shown in figure 4.4. The ions are elltracted by an elltraction

electrode located 5 mm in front of the source and forming close to lens of a Pierce

geometry. The beam is then further focussed by an acceleration lcns before the ions leave

the source. For the delivery of ions at the energy appropriate for injection into the trap, the

zeolite ion source is biased a few volts above the pedeslal voltage (60 kV).

4.6.2 On-Une ISOWE Sources

The ISOLDE 3 facility produces ion beams by a variety of techniques from over 60

elements. The beams are provided with high mass resolution ( between 5000 and 300(0)

and at currents that can reach the microampere range. The facility d~livers a 60 keV beam

with an emittance of < 207t-mm-rnrad and an energy spread of a few eV.

The ion chosen for the flfst on-line test was that of stable xenon-132. These ions :Ire

created in a high temperature plasma ion source. Xenon gas is bled into the source by a

water cooled üansfer line, permitting only gaseous elements (at room temperature) to pass

through. Xenon-132 is selected by the mass separator of the ISOLDE 3 facility. This

technique produces the very pure beam required to test trapping efficiencies.

- 82-

TO FIT STANDARDHV .. INCH VACUUM FLANGe

HIGH VOLTAGE SHIELD

HEATSHIELD

ElECTRODE MOU'lTING PlATE +---1-_-+__

YEATERLEADS ::::f:::t=I~~

GUNBODY

EXTRACTION ELECTRODEACCELERATION ELECTRODE

ANODECERAMIC INSULATOR (AL021

~

1 Figure 4.4 The test off-line ion source.

- 83-

•

There were severa! reasons for the choice of xenon-132. lt is ~asily and reliably

available from the ISOLDE 3 facility at the tens of nanoampere level when it is not being

used for delivering radioactive bel.ms. Il has a rnass very close to that of cesium-133 uscd

for the off-line testing and tuning of the electronics. il also has the attraction that it is an ion

which cannot be produced by surface ionization so that successful capture in the Paul trap

would establish that trap as a very powerful addition to the mass measurement system.

To funher demonstrate the versatility of the Paul trap as a collection device, a beam of

negative ions farther from the atomic mass of 133Cs was then selected. The actual selection

was the halogen 79Br, an e1ement which also cannot be surface ionized by the system used

in the cC'lleçtion Penning trap of the rnass measurement system. However, the high electron

affinities of the halogens does allow the use of negative surface ionization. In the

ISOLDE 3 facility the halogens are ionized by impinging on a lanthanum boron (LaB6)

surface, an efficient electron emitter due to its low work function. Stray electr<'ns are then.

removed from the beam by means of a magnetic field and a catcher electrode [Vo~1J.

To produce a halogen beam, a niobium target of 131.6 grams of Nb (thickness 85.2

g/cm2) is bombarded by a 600 MeV proto!\s of 1 microampere current. Halogens are

release(l. from the target and ionized by the above technique before extraction at 60 kV.·

The 79Br test was run parasitically at the end of an ISOLDE experiment when the

cyclotron beam had been turned df. Therefore, the available time for testing was limited

due to the lirnited amount of brornine 1eft in the target. In order to keep the beam intensity at

a few nanoamperes, the heating current of the ion source was raised every half hour; after

approximately four hours, it was finally dep1cted. There was not sufficient time for a

complete analysis, but enough inforrration could he gathered to show that negative ions are

trapped quite effectively.

4.7 The Ion Observation System and calibration

Ion observations were made by measlJring electrical currents throughout the system.

For ail but the ions e"':tracted from the trap, currents were measured by connecting various

electrodes te high gain picoarnmeters. To ensure that the current observed representcd the

true ion current, secondary electron.; that might be liberated by an ion impinging on the

surface were retained by app1.ying a positive DC potential te that surface sufficient to retu.n

any such electrons to the surface.

To measure the amount of current entering the trap, ils electrodes were connected as

Faraday cups to picoammeters. Since these electrodes are at the pedestal voltage, the

- 84-

picoammeters were placed in the instrumentation Faraday cage. In this way the

deceleration system was <hen tested for an ISOLDE xenon·132 beam and it was found that,

with the beam collimator mentioned above in place, vinually 100% DC injection into the

trap could be achieved at decelerations down to about 50 eV.

Extracted ion currents (see figure 4.5 for a view of the extraction system) were

observed by using an open-ellded RCA electron multiplier model 4643-4B with 3 kV

negative biasing of the cathode surface so as to achieve efficient ion detection. The output

was monitored with a oscilloscope across a 100 ohm resistor to give a low time constant.

1l\APEND ELECTRODE

\EXmAcnON ELECTRODE

IOem

EXmAcnON CAVITY

~ECTRON'MUL llPLlER

PULSB-DOWNmODE

Figure 4.5 The extraction system. (This extraction system includes a pulse-down

triode which is to be used to reduce the potential of the ion cloud while it is inside

the extraction cavity. This aIlows the ion cloud extracted from the Paul trap at a

potential of 60 kV to be delivered to a subsequent transpon system at a much

reduced kinetic energy. It was not used during the tests reponed in this thcsis but

will be an important element of the system for delivery of the ion cloud to the

Penrâng trap mass measurement system.)

In order to calibrate the current gain of the electron multiplier, a weak ISOLDE 3 beam

current was aIlowed to faIl directly on the cathode of the electron multiplier with the whole

electron multiplier acting as a Faraday cup connected to ground through a picoammeter. As

The electron multiplier was biased at 9 volt positive to ground by using a banery between it

- 85-

'J..

and the picoamm::ter, as mentioned above, to capture any secondary electrons emitted from

the cathode surface. The CUITent gain was then obtained by switching the electron multiplier

connections to operate it in ilS normal mode and measuring the anode CUITent with lhe sanne

ion beam. This was carried out for a variety of ion beam currents to test for possible

saturation effects. The current gain was deterrnined to he 15,000 with a possible error

estimated to he ±20%.

4.8 Experimental Procedure for Efficiency Measurements

To measure the overall trapping efficiency the electron multiplier was fust calibrated,

as outlined in the previous section, by passing a weak version of the ion hearn that was to

he collected through the trap system while the trap was at ground. (To detect any possible

change in the electron multiplier gain during the run, this calibration was repeated at the end

of the collection testing.) The ion bearn was then increased to an intensity appropriate for

the testing of collection (one nAmp or less), ascertained to he steady, and then measured at

the entrance to the system by the up-stream Faraday plate shown in figure 4.2. The

Faraday plate was then moved out of the way and the trap tuned to opuate in a col1ecting

mode with periodic extraction ( extraction intervals ranging from 10 to 100 n,:;. As

mentioned previously, the extracted ion pulse was accelerated back to groUl\d 50 1;,2t the

energy of the ions when they entered the electron multiplier would he the sarne a~ no~e

used for establishing its gain. The extracted ion pulse was observed by sending the OULi-<1t

of the electron multiplier directly to a calibrated oscilloscope of measured input impedance

(1 Mn). Possible saturation of the output pulse of the electron multiplier was tested by

observing the output pulse under the sarne ,trapping conditions for different input hearn

currents and noting whether the output pulse was proportional to the input CUTTent. No

saturation effects were detected for the range of output pulses that could he obtained from

trap extraction.

The total capacitance loading the output signal of the electron multiplier was measured

by noting the fall-time of the extracted ion signal and dividing this by the input impedance

of the oscilloscope. Typical fall-rimes were about 150 Ils corresponding to capacitances of

about 150 pF. Thus the cable-oscilloscope combination formed an integrating circuit with

an integration time constant of about 150 Ils. Since the duration of the output ion pulse

from the trap was about 1 ils, the height of voltage pulse on the oscilloscope could he

simply multiplied by the capacitance of the circuitto give the the integrated CUITent from the

electron multiplier. Dividing this by the measured electron multiplier gain gives the total

- 86·

..

charge of the extracted pulse. Comparing this with the total charge of the incoming beam,

which is simply the measured incoming current divided by the extraction repetition rate,

gives the overall efficiency of the collection system.

To establish the collection efficiency of the trapping system for a particular ion beam

under given trapping conditions, several factors other than just the current ratios in the

detection equipment must be considered. These are:

1. The injection beam purity

2. The actual phase space properties of the injected beam compared to that

regarded as the limit for successful trap injection.

3. Detennination of the actual trap operating parameters.

4. Purity of the buffer gas and any possible contamination by residual

background gas in the trap.

The selection of xenon as the elemental species for the collection efficiency test ensured

the purity of the incoming ion bearn. However, as mentioned above the raw bearn from the

ISOLDE facility was collimated ta ensure that its emiltance was limited ta that which could

be accepted by the deceleration system of the trap (2lt-mm-mrad in each transverse

coordinate). Tuning of the transport system of the ISOLDE beamline allowed about 20%

of the delivered beam to be iI'aI1smitted through these apertures, indicating thatthe emiltance

of the raw beam was effectively about Slt-mm-rnrad. This is regarded by other workers at

the ISOLDE facility as a representative value for its beam emittance.

The most significant trap operating pararneters are the amplitude and frequency of the

applied RF frequency and the actual pressure of the helium buffer gas. Observation of the

buffer gas pressure has been discussed abave. Measurement of the radiofrequency is

easily accomplished by an electronic counter. Measurement of the applied RF voltage was

obtained by using a high-voltage probe connected to an oscilloscope to calibrate the reading

of the RF r.mplifier oUlput in the instrumentation Faraday cage while the system was at

ground potential.

The quality of the buffer gas and the presence of possible residual contaminants in the

trllpping volume was a concem until 60 keV xenon ions were actually injected into the

system. It was then discovered that the system itself became a very sensitive monitor of the

presence of such impurity ions. These could be observed by the current appearing on the

ground electrode of the deceleration system when a picoarnmeter was connected ta il.

·87 -

Fig. 4.6 shows the CUlTent in the deceleration ground electrode due to the deceleration

of the Xe beam at various trap voltages. Curve (a) is for a 0.8 nA beam when the residual

pressure (in the absence of helium buffer gas) was 2 mPa (2 x 10-5 mbars), shortly after

closing the system. Curve (b) displays a 0.6 nA beam when the vacuum was much belter

(a residual pressure of 0.06 mPa (6 x 10-7 mbars), obtained from pumping ovemight

10

0::-::::«(;

1;:Iol<:t: 5 (al[5 •u

•(al

60020

•

60000

TRAP POTENTIAL ( VOLT)

(a)

10

(b) 0::-::;«~

!Z 5Iol

'"!Su

0

59980

(b)

50

TRAP POTENTIAL ( KVOLTI

o

Figure 4.6 CUlTents detected on the deceleration ground electrode at various trap

pedestal potentials. The two curves represent the quality of the vacuum, for (a) a

vacuum of 2 x 10-5 mbars and (h) 6 x 10-7 mbars. Data is for a xenon beam.

The CUlTent in the retardation ground electrode with the trap at potentials less than

60 kY is no doubt due to electrons produced by ionization of the background gas of the

system by the xenon beam. When this is relatively pure helium, as il is after pumping for

an extended period, the degrec of ionization is considerably less than when there is more

contamination. The secondary ions produced in this ionization process are mostly

accelerated onto the deceleration ground electrode which directly faces the trap and induce a

CUlTent in that electrode. Also the CUlTent associated with the motion of the Iiberated

electrons toward the trap is supplied primarily through this electrode. The CUlTent in this

electrode at reduced trap potentials is therefore a very good indication of the quality of the

vacuum.

rAnother dividend that cornes from measuring the CUlTent in the deceleration ground

electrode is the clear indication of when the trap is at the injection beam energy. It is secn

- 88·

that at that potential the CUITent rises very sharply. This is because of rel1ection of the

incoming ion beam back onto the deceleration ground electrode. Il is noted thal the CUITent

that is ind~ced in the electrode when this occurs is about 12 times the acrual CUITent of the

ion beam. In curve (b) of figure 4.6 for a 0.6 nA input CUITent the CUITent rises from

1.0 nA :0 about 8 nA. This would have three components; the ref1ected ions themselves

·...~.ich contribute 0.6 nA, a doubled residual gas ionization due to the d(;ubling of the ion

path back onto itself which would give 2 nA and secondary electrons released from the

electrode when this occurs and which are pulled from the electrode up 10 trap by the high

ion retardation field contributing the rennainder (about 5.4 nA). Il is seen that the secondary

electron CUITent is about 9 times the incident Xe ion current, a factor that is ell:pected for a

60 keV Xe ions faIIing on an aluminum surface.

The rate of change of the current in the deceleration ground electrode as a function of

trap pedestal voltage at the sharp break at 60 kV also gives an indication of the energy

profile of the iSOLDE beam. From figure 4.6 (b) it is seen that this could not be more thM

about 10 eV.

The observation of the current in the deceleration ground electrode greatly simplified

the setting of the trap potential for the appropriate injection energy. Subsequently, tuning

the trap parameters for lI:enon ions based on the tuning for cesium resulted in their

immediate caprure.

The collection efficiency was then observed for a variety of trap operating conditions

and pedestals. The ell:traction pulse level and ell:traction phase were adjusted to ensure a

100 % extraction of the ion cloud. This was done by adjusting the ell:traction phase to

maximize the output pulse and then increasing the extraction pulse level until the output

pulse height did not increase any further. l The best efficiencies were obtained with an

injection energy of approximately 20 eV. Finally the helium buffer gas was adjusted to

yield the largest numOOr of ions and the oost collection ~fficiency which OCCUITed at about

20 mPa (2 x 10-4 mbars. The trap parameters are summarized in table 4.1.

IThe extraction phase is the phase of the RF on the ring electrode al which the extraction pulse is

applied. This is an imponant parameler for c1ean extraction from the trap since altempted extraction al sorne

phases ean resull in severe relardation of the extraction by the RF field of the trap juSlIl.'l the ions approach

the extraction hole. The cleanest extraction occurs when the ions arrive al the extraction hale al a phase of

the RF such thal the axial eleclrlc field is ncarly a positive maximum. (Sec [Lu92J).

- 89-

Table 4.1 The Paul trap parameters.~

End electrode separation 28 mm Extraction voltage +300 V

Radio frequency 1 MHz Extraction phase o-lt adj.

Radio frequency amplitude 1200 V Pseudopotential weil depth 80 volts

DC voltage 0 Ion mass 1332amu

Buffer gas pressure (helium) 20mPa

Various filling currents and filling times were tested. It was found that the maximum

output pulse that couId be extracted contained about 200 000 ions. This was probably not

the maximum numOOr of ions that could 00 trapped since only a small fraction of an ion

cloud at fullioading would clear the extrac:tion hole. By bypassing the RF counter limit for

the trap cycle time, filling times of g1.ater than 1 second were tested, the filling current

OOing reduced for the longer filling times so as to not saturate the trap. For the same input

ion current the output pulse rose linearly with small filling times but seemed to saturate at

about one second, indicating that this was about the lifetime of the ions in the trap.

Collection times of 100 ms or less were therefore used for testing overall trapping

efficiency of the system.

4.9 Experimental ResuUs

The most imponant parameters in tne collection efficiency are the RF voltage and

frequen-:y. Since the 0péimum frequency is strongly correlated to the amplitude, the RF

amplitude oc~omes the most dominant factor in determining the collection efficiency of the

Paul trap.

The highest collection efficiencies that could 00 obtained at various RF amplitudes is

shown in figure 4.7. This efficiency is the ratio of the numOOr of ions passing through the

apenure cfJllimator in front of the system to that which is collect.:d ami delivered as a pulse

to the electron-multiplier. While the data shown in that figure indicate a measurement

repeatability to within severa! percent of the extraction efficiencv, the systematic errors in

the measurements are believed to 00 as high as perhaps 50%.

Il is seen that an efficiency of slightly over 0.002 is obtained at an RF amplitude of

1150 volts, which was the maximum voltage possible with the transformer system that was

used. Not only does this efficiency exceed the oost of the surface-ionization technique in

the Penning trap collector by a factor of over 200 but il also trapped a species that coula net

- 90-

•he handled by that technique. It is also very encouraging to note that the eflicicncy lises

rapidly with the RF amplitude.

, ,

0.2

~

!li!~

(jZtu0 0.1 -

lEtu

...­,.'

.'..'......'.' .........

.....'..'.'•••••.'

-

.

1200o +---,-,-..,.--,--,--,-,-..,.--;

900 1000 1100

RF AMPLITUDE (VOLTS)

Figure 4.7 Overall collection efficiency as a function of RF amplitude.

Closer examination of the capture efliciency as a function of bias voltage over a ISO

volt scan (fig. 4.8) reveals the efficiency to he a maximum at a 15 eV injection energy with

a FWHM of 30 eV. The br('lad high energy tail may he explained by the known rapid

decrease in the mobility of ions of greater then 10 eV kinetic energy in a background gas

which causes them to he cooled at a much faster rate than the lower energy ions. Higher

energy ions have more collisions which pierce the outer electron shield of the buffer gas

molecules and so undergo higher angle scanering, resulting in a much larger fraction cf the

kinetic energy of the ion heing transferred to the gas molecule.

The tests with negative 79Dr ions were carried out by merely reversing the polarities of

the appropriate voltages. Because of the short time for which a usable heam was available.

the collection efficiency could not he detennined but it appeared to he less than that of the

xenon beam. A possible explanation for this may be the ease with which the negative

bromine ions are neutralized in a remaining residual gas in the trapping volume.

·91 -

59800 59850 59900 59950 60000

TRAP PEDESTAL

60050

•;

Figure 4.8 Collection efficiency as a function of the pedestal voltage.

4.10 Interpretation of Results

The collection efficiency as a function of RF amplitude shown in fig. 4.7 is quite

interesting. The dashed line in this graph represents a cubic power of the RF amplitude and

it is seen that witJùn the range of observations it fits the observed efficiencies. The possible

significance of this is that, for the tunings used in tJùs experimenl, the phase space volume

could he roughly proportionalto the cubic power of the RF amplitude. If this is the case,

then at small phase space volumes the collection efficiency increases in proportion to this

volume.

This would lead 10 the expectation that atlarger phase space volumes there would he an

exponential saturation to sorne maximum attainable efficiency. For incoming ions notto he

thrown back out of a Paul trap by the RF quadrupole field, they have to enter the trap in an

RF phase window. From simulations of the dynamics of incoming ions carried out by

Gullick, this phase window is estimated to he about 10% for our operating conditions. The

- 92-

maximum anainable efficiency for a OC beam in any trap would therefore be about 10%. If

this is correctthen the collection efficiency as a function of trap phase space volume would

be as in fig. 4.9.

10

o 50 100 150

,.

PHASE SPACE VOLUME OF TRAP(ARBITRARY UNITS)

Figure 4.9 Expected coUection efficiency as a function of trap phase space volume.

Adminedly, t1ùs is a large extrapolation from the phase space volume actually achieved

in the test trap. (The phase space volume of that trap would be about unity on the

horizontal axis of fig. 4.9.) However, if the graph is at all repres,mtative of what can

happen, then 9% collection efficiency, or 90% collection cfliciency within the RF window,

can be expected with a trap which has a phase space volume of about 100 times that of the

test trap.

Such an incrcase in trap phase space volume should be quite feasible. By increasing

the trap dimensions by a factor of 3 (ta end electrode separations of about 8 cm) and raising

the RF amplitude by a faetorof9 (to about 10 kVp) the phase space volume will inerease

by a factor of 36 or aboul 600. These operating figures should be possible for a properly

dcsigned trap. Ali that would then be required for 90% collection efficiency for a OC beam

would be a prebuncher operating al the RF of the trap.

- 93-

4.11 Testing of Extracted Pulse Delivery to the Mass Measurement System

To examine possible problems with delivering an extracted ion pulse from a Paul trap 10

the cooling Penning trap of the mass me~surement system atthe low energies required for

acceptance by that system, the collection system was reconfigured and connected to the

mass measurement system located atthe ISOLDE 2 facility ( fig. 4.10). Because of the

very limiled space at the site where the trap could be installed and the limited rime that was

available between the permanent shut-down of the ISOLDE 2 facility and the complete

dismantling of the components of that facility, the version of the Paul trap control system

that was used for this test was a much reduced version of what was used in the ISOLDE 3

collection efficiency test. The most important limitation was that the trap could only be

operated safely at a potentialles~ than 10 kY. This, hov'ever, was regarded as sufficientto

deliver the extracted ions at an enel~ range which could be captured ion a Penning trap.

13.5M

lISOLDE­UR9

lSOLDE­UR10

PAlA.TRAP

TESTIONGUN

.. ... ............. .. .. .. .... .. .. .. .. .. ...• •••••••••••••••••A ••••·..... ......

• A •••••••••·......................·...........

COOlINGPEIl>IINGTRAP

.... .. ..... .. .. .... .. ... .. .. .. ..................... .. ... .. .. .. ....... ... .... .. .... ... .. .. ... .. .... .. .. .. ...... .. .. .. .. .... .. .. ... .. .. .. .... ... .. .. .. .. ..:..: ..: ..: ..:..:-t-'''-ir'"- ........ .. .... .. .. .... .. .. ................ .. ... .. .... .. .. .... ............... .. .. .... ............... ... .. .... ....................................\ ........................................... .. ...... .. ....: ..: ..: ..: ..: L:.".'1r1".:-:-.'".'".oc.oc ":.-;."."."... .. .. .. .. .. .. .... .. .. ... .. .. .. .. .. .. ......................................... .. .

...................... . .

.i

Figure 4. JO The configuration of the transmission test at the ISOLDE 2 facility.

To carry out the transmission tests, ions from the test ion source were used to load the

trap with the trap held at various pedestal potentials. The ion cloud was then extracted and

delivered to the ISOLDE 2 beamline which was at ground potentiaI. The extracted ions

therefore had a kinetic energy equalto this pedestal potential plus, of course, the kinetic

-94-

•

energy they received upon ejection from the trap. Transport detection was carried OUI with

a channel plate detector mounted about 50 cm on the far side of the Penning trap.

Transport was testeà over the energy range that was regarded as feasible for Penning trap

acceptance (i.e. less than 10 keV).

For this test the electron multiplier used to tune the trap performance had to be

remounted to allow it to be mo·,eà off axis when the beam was delivered to the beam

transport system. This is accomp!ished by sliding it in and out along an o-ring seal in the

vacuum-flange. The multiplier entered the vacuum system radially and the ions were

deflecteà 90 degrees into it by a deflection electrode.

The test set-up was far from ideal. Because the section of the ISOLDE 2 beam !ine that

was useà is primarily within a hole through the floor separating UR9 from UR 10, there

was no possibility of installing all the pumping that was necessary to remove the helium

buffer gas escaping into the \ine from the trap. Consequently, the vacuum was very poor

for the transmission of low energy ion beams. A1so, the ISOLDE beam\ine focusing

quadrupoles and their supplies were designeà for 60 keV ion bearns and their operation for

much lower energy bearns was very difficult ta control.

The problems of ion transport can easily be seen in figure 4.11. Because of the

extreme difficulty in adjusting all of the transport system parameters, transmission data

could only be obtaineà for three transport energies in the time available for the lests.

However, they show that the beam which reaches the Penning trap drops significantly

when the transmission is carrieà out at an energy less than 4 kV. (The lowest energy at

which any deteetable ion current could be delivereà through the system was 2 keV.)

This indicates the weakness of low energy beams, by which it is meant that stray

electric and magnetic fields can easily deflect the ions over a long flight path. Strayelectric

fields very often arise in low energy ion beam transport systems under poor vacuum

because of the scanering of ions onto the surfaces of electrical insulators useà to support

the e1ecttodes in such systems. Stray magnetic fields, of course, are almost always present

in an accelerator based facility such as ISOLDE. Furthermore, low energy ions are much

more susceptible to loss by collisions with background gas in the poor vacuum of the

system. These resuIts lead to the suggestion that a transfer system between a Paul trap

collector and a Penning trap cooler such as to be useà in a mass measurement system

should be designeà to handle beams of about 6 keV.

Another aspect of an ion cloud from a Paul trap that must be considered in dealing with

a long flight path is the time spread of the ions arriving at the Penning trap. This could

- 95-

complicale the calching of the ions in that trap. To test this in the ISOLDE 2 set·up, the

pulse shape of the currenl in the ejected ion cloud was observed just after extraction by the

electron multiplier and then at the Penning trap by the channel plate det.'ctor, a distance of

aboul 3.5 melers from the electron multiplier. Figure 4.12 shows a representative resull.

10 ·8

~ ...............................~ ..... J1I

b 10 ·9..,0.0C'ë

/c.,Q.,

1O,Io'oC0.0;:l

f0.s :... !c 10 ·11- 0

~00

:u i•

10,12 ..1 1 1 1

,1

~ 0 2 4 6 8 10 12Bearn Energy - keV

Figure 4.11 Transmission test of the current measured at the Penning trap as a

function of the bias voltage on the ion source located 3.5 meter away. The

current just above the Paul trap was kept constant by adjusting the heater current

of the source so that a current of 2.3 nanoamps \.;;:; measured.

,,

ln comparing the two pulse shapes it should be noted that there was an unavoidable

inlegration hl the current pulse from the electron multiplier due to the electronic system used

for its detection. However, it is still clear that the ions leave the trap in a time interval of

about 1 to 2 ilS. On the other hand, the ion cloud when il arrives at the channel plate

detector has clearly resolved ilself into severa! components. Furtherrnore, the relative

intensity and timing of these components are not sta.Jle, the picture shown in figure 4.12

being for a single pulse.

This son of behaviour is inlolerable in a beam which must be caught in a Penning trap.

il clearly indicates that the extraction method is not sufficient to pull the ion cloud out of the

trap in a single well-defined bunch.

·96·

• 1 ,,

(a)

.. .2 micro seconds

(h)

'.

rigure 4.12 Pulse shapes of the current in an ejected ion cloud from the Paul

trap detected a) just above the trap and b) at the Penning trap, a distance of

approximately 3.5 meters further downstream.

However, it should he noted that the ion c10uds involved in this test were the largest

that could he colIected in the Paul trap. This was necessary in order to get an adequate

signal in the channel plate detector. In the work of Lunney [Lu92] is has been shown that

c1ean extraction of 5uch ion clouds is virtually impossible, particularly through smaII

extraction holes. In his work, the extraction end electrode of the trap was, in fact,

completely formed of a mesh so that, in principle, a cloud of any size that could he

contained in the trap could he extracted. Even then it was found that at fulIloading of the

trap, the t;me taken to extract the fuII cloud was sufficient for the RF quadrupole field

within the trap to break it into two bunches.

However, Lunney also found that the size of ion cloud shrunk dramaticalIy as the

number of ions in the cloud was reduced. For clouds of 1000 ions or less there was

absolutely no problem in getting very clean extraction of the ion cloud in single bursts

which lasted no more than 0.2 Ils.

- 97-

This leads to the conclusion that the instabilities shown in figure 4.12 b) were due to

the very large trap ioading that was extracted. (lt is now fairly weil established that, even

with buffer gas coolir.g, large trap loadings can exhibit chaotic phenomena due to the large

coupling of t:le Coulomb space charge forces with the pseudopotential weil forces of the

trap.) The plObkms indicated by figure 4.12 should therefore disappear with the level of

trap loading for which the Paul trap collection system is to be operated when con:lected to

the mass measurement system.

However, this still presents a problem in a practical system which will have many

parameters which must be highly lUned when making measurements on low production rate

radioisotopes. Il means that only small trap loadings can be used, even when there is more

than adequate beam available for testing and tuning with heavier trap loadings. Thus very

sensitive beam monitoring devices must be provided at ail stages of the collection system

and the simple c1ectrometer measurements, and even the relatively large trap loadings used

for the efficiency measurements of this thesis, cannot be used for tuning the system for

dclivery of the desired ions to the Penning trap ion cooler.

This, however, does not put an impossible limitation of the design of a Paul trap

collection system. It is just tha!, as with many things in this life, il is not as simple as il

first appears. In order for a Paul trap ~ystem to be of use in a tandem Penning trap mass

mcas<lrement system il must be designed wilh a great deal of care in engineering detaiI,

both to the system itself and to the operation of the system in an aclUai nuclear mass

measurement experiment.

- 98-

•

CHAPTER 5

CONCLUSION

The efficient capture and cooling of a 60 keV ISOLDE type ion beam has becndemonstrated using a modest Paul trap. The trapping efficiency of a DC bearn of 0.2% that

was achieved is about a factor of better than 200 improvement over the present foil

implantation technique used in the Penning trap mass measurement by the Mainz-McGill

collaboration at ISOLDE. With this improved trapping efficiency, an intensity limit for

usable beam can be setto 1()4 to lOS ions per second, giving the capability of measuring the

masses of at least one or more of the Iight rubidium isotopes, leading almost out to the

proton drip line, with an accuracy of 1()6. In addition, this technique opens up the ability of

measuring the non-surface ionizable elements, hence a1mostthe whole region of N, Z • 38,

to an unprecedented accuracy, possibly in a few weeks of running time.

The objectives of this thesis has been allained by determining the engineering

arguments to design a collection system approaching nearly 100% efficiency for very low

intensity 60 keV radionuclide ion beams. With such a system a complete survey of the low

mass elements outto the neutron and proton drip-Iines becomes possible, and would define

the ultimate goal of the mass measurement system.

The retirement of CERN's synchrocyclotron in December 1990 has prompted the

ISOLDE community to re-establish itself at the proton-booster ring. During this layoff

period of two years, a re-construction of the mass measurement system is under way. This

shut-down period is being used to put the knowledge gained by the results presented in this

thesis to build an improved Paul trap collection system. In this concluding chapter a layout

of the proposed system atthe time of writing will be given.

The redesigning is being earried out a10ng IWO Iines using the principle of separation of

functions. At McGilI a Paul trap system is being designed for maximum efficiency of

collection of the ISOLDE bearn. Meanwhile a new Penning trap cooler system is being

designed at Mainz to accept the output of the Paul trap system. A schematic of the planned

system is shown in figure 5.1. In the new sct-up the Penning traps will retain their venical

orientation and will be situated on two wooden platforms reaching a height of 6 meters

above the ISOLDE bearn-Iine which is at a height of 1.26 meters from the floor. Dclivered

beams will be bent 90 degrees by an electrostatic deflector.

- 99-

CYCLOTRONRESONANCEPENNING TRAP

I...·----- SM ..~ TIME-OF-FLIGHTlf DETECTOR

1

oCM

PULSEDCAVITY

60 KV BEAM PAUL 1 QUAD.ISOLDE BUNCHER TRAP + LENS

BE~A~_1 ~ - 0-01 f--

FLOOR

COOLINGPENNINGTRAP

DEFLECTOR

<1

Figure S.\ The configuration of the new mass measurement system to be installedon the new ISOLDE facility at the CERN booster accelerator.

Since the Paul trap is primarily intended for very weak beams it will not always beused. However, the enlarged entrance holes of the enlarged Paul trap design will allow the

ISOLDE beam to pass through to other possible collection schemes. One of these is

implantation ontu a foil followed by pulsed laser desorption and resonance ionization,

which could be of use on some particular elements. A major advantage of having such a

source is thatthe pulsed laser needed can produce many different ionized carbon clusters to

be used as absolute calibrations for the mass measurement system. In Ibis way, not onlydirect but aIso absolute mass determinations couId he performed. Furthermore, the creation

of both positive and negative ions are possible. One of the planned uses for such a sourceis the investigation of refractory elements which are only available as daughter products of

radionuclides implanted in a foil.

The planned installation of the new system will take place gradually. First the Penning

traps will he installed as they were before with the 60 keV iOn!, implanted on the foil. This

is to make sure that ail the components had not suffered any damage during the

transportation and setling up. Then the new superconducting Penning trap cooler system

will replace the present one based on the room-temperature eIectromagnet. TItis trap will be

·100 -

•

•.,

cylindrical and based on a superconducting (6 T) magnet. The high magnetic field and the

capability of placing high voltage on the elewodes will deepen the trap potential weIl,

simplifying the injection requirements and aiding in the cooling process. A deceleration

system forthe 6 keV ions will be constructed on the same principles as that of the Paul trllp

system with the exception that it will be for the lower energies. In addition the high

magnetic field will give higher mass selectivity in the cooling process leading to the

possibility of performing isobaric separation before cjection to the measurement trllp.

Wilh this new trap a pulsed laser ion source system will be installed to create ions

extemal to the cooling trap and to inject them into it using a 6 keV ion transpon system.

Meanwhile, the new Paul trap to be built at McGill will be installed on one of the ISOLDE

beam-lines other than the line leading to the mass measurement system. Once it is properly

working it will be connected to the mass measurement system for actual mass

measurements. Finally, the pre-buncher is to be inslalled. il is expected that the system

will be completed in about tl>.ree to four years fiom the time of writing (i.e in 1995·96).

Based on the information that has been presented in this thesis several ideas are being

developed to achieve 100% collection efficiency. The most obvious is to make a larger trap

to achieve a mach larger phase space volume to contain the incoming ions. The higher RF

voltages needed for this trap may cause a problem with a large energy spread in the

extracted ion cloud if the ions were extracted while the full RF field is applied. However,

with a programmable waveform generator il is easily possible to reduce this amplitude just

before extraction.

To more effectively use the available phase space volume of the trap, higher order

aberrant fields can be introduced by increasing the diarneter of the injection and extraction

holes and, possibly, by increasing the separation of the end electrodes relative to that which

is appropriate for a quadrupole field. A further method to fillthe phase space would he to

manipulate the panicles into the azimuthal phase space component by coupling the x and y

motions through a rotating transverse dipole field, which can be created by splitting the end

electrodes into quadrants and applying properly phased excitatory voltages 10 these

quadrants at the radial f3 oscillation frequency.

In the design of the overall system severallessons leamed from the work of this thesis

will he applied. One is that aIl the electronic signaIs must be very slable and ripple free.

One component where this is panicularly imponant is the energy pulse down cavily where

the ions exiting the trap al 60 kV polential are brought to about 6 kV potential while inside a

cavity. This is to be acC'omplished by a switching triode connected 10 the cavity and to a

60 kV supply. To facilitate the tuning of the complex system, there must be adequate

- 101 -

diagnostic equipment, including heam current monitoring devices and a test ion source that

can easily he inserted into the heam-Iine. Also, computer control of ail the devices is

planned. Finally, adequate pumping must be provided to ensure a clean reliable transport

system that can he operated at the high voltages required.

Finally, although this thesis is basically a nuclear physics project, the possibility of

efficient external injection of high energy ions into a trap should have wide ranging

applications in physics were there is an emphasis on accuracy and sensitivity. For

example, highly charged ions or radioactive isotopes could he prepared in one trap and

injected into another trap with a minimum of electr,;de material to occlude observation by

lasers or other electromagnetic radiation. Such a trap could also he designed for full

observation of the decay of a radioisotope, including recoil of the daughter nucleus. On the

other hand, a containment trap could he built with strong enough electromagnetic fields to

contain the recoiling daughter products, allowing their subsequent extraction after cooling

for observation in yet a third trap. Another example would he the design of a Penning trap

to hold a collection of positrons for cooling fully stripped heavy ions. A final example is to

extract from a Paul trap a small, cooled but high velocity ion cloud for collinear laser

observation. The advantages here would he greatly decreased emiuances over that of the

typical original heam hefore collection and a very great reduction in the background noise

by having the cloud pass the detector in a very short time interval allowing the detector to

he open for only that period.

ln short, electromagnetic traps should no longer he considered as merely hench-top

toys but as essential components of sophisticated apparatus which can he engineered to

accomplish a multitude of tasks in physics.

-102 -

•

APPENDIX

THE INJECTING OF HIGH VELOCITY PARTICLES

INTO AN ELECTROMAGNETIC TRAP

What is meant by high velocity here is the ion velocity from a ISOLDE type facility.

The conditions for quaiity OOams tend to 00 oost at an extraction voltage of about 60 kV.

this resulting in the oost intensities and in emittances as low as 21t-mm-mrad. It is tempting

to consider the possibility of direct injection of such beams into a trap at their full energy.

Direct injection into a Paul trap would appear to be very difficult since the full energy

would have to be absorbed by an electric field generated within the trap itself. Thi.. wouid

mean RF voltages of over 100 kV, a possibility with large traps but not a Iikely one if

buffer gas cooling has to be applied to retain the collected ions.

However, a large penning trap would offer sorne interesting possibilities. High energy

particles have already been captured in a Penning trap in the work of Oabrielse et al.

[Oa88] in the trapping of antiprotons at an energy of 200 keV. The particles are decelerated

by a degrader foil to an injection energy of 15 keV. Then by a simple 15 kV pulse applied

to one of the end caps the particles are slowed down and trapped.

Unfortunately, this process works only because the incoming particles are tightly

bunched in time and even then the capture is not very efficient. This is acceptable for the

antiproton experiment since it is desired that very few antiprotons be ion the trap at any one

time. However. for ISOLDE beams a degrader foil is nOl so feasible. 0 et al. [081] have

estimated by such a technique but the efficiency tums out to be too low to he practical.

particularly for a DC bearn.

Yet, the Penning trap does offer an interesting possibility for extemai injection at high

energy, providing the trap is very large. The ions could be made to enter the trap in a

fashion that sorne cyclotron motion is deliberately introduced in a fringing field region of

the magnetic. If the magnetic moment sa introduced could be adiabaticaily preserved as the

ion proceeds aiong the axis of the system, then the large axial energy could be transformed

aimost completely in cyclotron energy. By removing the smail amount of axial energy

remaining, the ions particles could then be trapped, aiOOit at a very large cyclotron energy.

However. this could then 00 removed by buffer gas cooling. Sorne of the aspects of such a

capture will 00 considered in this appendix.

- 103 -

•

.j

A.t Penning Trap Phase Space

The principles of a Penning trap are discussed in chapter 1. The phase space volume of

the Penning trap can not 50 easily he expressed in rectangular coordinates as it is for the

Paultrap. 'Ibis is due to the azimuthal motion in the magnetic field of the Penning trap.

Ion momentum in a Penning trap can œgiven in canonical components following the

formalism of Brown and Gabrielse [BrilS]. In this formalism the transverse velocity of the

ions is expressed as two velocity coordinates defmed as,

vc =r. (J)m x r

Vm =r· (J)cxr

where r is ihe displacement vector from the axis, r is the velocity relative to this axis, and

Wc and rom are axial vectors representing the CYCIOtrOl: and magnetron angular frequencies

respectively. The geomeoical interpretation of these velocities can hest he visualized by

lheir decomposition as shown in figure A.I.

By considering the case of maximum displacement, when the magnetron and cyclotron

radii Iineup, the velocity components are easily obtained,

Vc = (Wc· rom) Pc in the direction of rVm = ((J)c • rom) Pm in the direction of ·r

where Pc and Pm are respectively the radü of the cyclotron a."ld magnetron motions.

The Hamiltonian for an ideal Penning trap with no external forces is given by [Br86]

with the radial component as,

1 1Hr="j m ( )

wc·wm

r

and the associated momentum as

1Pr="j m(Vc . Vm)·

·104 .

•

.. ~ ~ .." ............

.........~

./,.~ /

--........ , .................- ~ ..

.,

Figure A.l Cyclotron and magnetron motion in a Penning trap.

The radius vector can be calculated from the difference (V+ • y.) and is proponionallO

Z x p, and found te> be,

r= 1 zX(Ve -Ym).((JJe - (JJm)

The magnitude of the angular momentum is

- 105·

The radial phase space volume components (cyclotron and magnetron motions) can be

obtained from the canonical coordinates of the angular momenrum. Since these motions can

vary at any panicular instant from 0 to 2lt, the radial areas are simply calculated by

multiplying the components of Lz by 2lt and using relations for the velocities to get,

Sc =lt m (Wc - COrn) p/ maJC

Sm = lt m (Wc - COrn) Pm 2maJC

where Pc max and Pm max are the maximum allowable cyclotron and magnetron radii.

ln the axial direction the phase space area is similar to the Paul trap

and therefore Ylelds a total phase space volume of

S = 0.0077A3 ( f c - f m;2 f z Pc max Pm max Zmme2

expressed in terrns of (eV-lJ.s).

The phase space can he represented in lCrrns of adjustable parameters: the magnetic

field, the radii and the ionic charge number (Z). It was shown in chapter 1 that the three

frequencies (cyclotron, magnetron and axial) are related and can he expressed in terms of

the free cyclotron frequency la = qlm B. Substituting these, along with the relation (,dJ =2z0 2) yields the following practical forrnulae for the maximum phase space volume in unitsof eV-lJ.s,

21m 2Scyc =Smag =0.8 ( 1 - 10 )Bresla 'omm

fz 2Sz = 1.6 (la) Bresla 'omm

S 'a z3 2Im., fz 3 6pennlng =1. ( 1 - la r (la) Btesla 'omm'

- 106-

These equations can he further simplified by the following ratios.

fzfo = 0.144

and the maximum phase space volume will he when

fz ~0.4fo

whereupon the total phase space volume is

fm ~O.lfo

..

This forrnulae reveals the simplicity with which the phase space volume can he

calculated. In the cooling Penning trap having a ring electrode of the inner radius ~ 1cm

and a magnetic field of 10-4 T. the usable phase space volume for singly charged ions babout 3 x 105 (eV-Jls)3. giving rise to 100 eV-Jls in each degree of frt.edom. As in the

Paul trap. the phase space volume is quite large. A Penning trap which is large enough ta

contain ions with 60 keV of cyclotron energy (a practical but perhaps expensive possibility)

shoulà have such an enorrnous phase space volume that its actual value is of little concem.

- 107-

[Be90)

{

[B089)

(B090)

(Br86)

[Bu90)

l

f..

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