PST05, November 14-17, 2005 at Tokyo 1 Design of a polarized 6 Li 3+ ion source and its feasibility...

1

PST05, November 14-17, 2005 at Tokyo

Design of a polarized 6Li3+ ion source and its feasibility test

A. TamiiResearch Center for Nuclear Physics,

Osaka University, Japan

2


Contents

1. Motivation2. Outline of the ion source3. Simulations (depolarization)4. Recent Status (pictures)5. Summary

3


Collaboration of the Polarized 6Li3+ Ion Source Project

RCNP, Osaka University, JapanK. Hatanaka, A. Tamii, Y. Sakemi, Y. Shimizu, K. Fujita,

Y. Tameshige, and H. Matsubara

CNS, University of Tokyo, JapanT. Uesaka and T. Wakui

CYRIC, Tohoku University, JapanH. Okamura

Kyushu University, JapanT. Wakasa

RIKEN, JapanT. Nakagawa

4


Motivation

5


Study of nuclear structures by using polarized 6Li beam at 100MeV/U.– Study of spin dipole excitations (2-,1-, and 0-), especially 0-, via (6Li,6He)

reaction. Tensor analyzing power at 0º is sensitive to J of SD excitations.

– Study of isovector spin-flip excitations via (6Li,6Li) reaction.

Study of reaction mechanism of composite particles– elastic scattering, inelastic scattering, (6Li, 6He) Reaction

– diff. cross section and analyzing power

6

6


For these purposes, development of a polarized 6Li3+ ion source is required.

Requirements (or goal):Injection energy to AVF cyclotron: 57 keV (19 kV)Beam intensity: ≿ 10nA on targetBeam polarization (ratio to maximum): ≿ 0.7

Reduction of depolarization of 6Li nuclei in the ionization process is one of the key points of the development.

Feasibility test has been planned.

7


Outline of the ion source

8


Outline of the polarized 6Li ion source(6Li0+ injection to ECR)

6Li0+: 50 pA Pol. >90% at Heidelberg and Florida State Univ.

Mean free path of single ionization in ECR plasma is 10-30cm.6Li0+→6Li1+

9


Simulations

10


Assumption of the Plasma Condition

The following plasma condition is assumed according to an empirical study of the laser ablated Al ion intensities from a 14.5 GHz ECR ionizer (SHIVA).

(M. Imanaka, PhD thesis, Univ. of Tsukuba)

Buffer Gas: Oxygen

RF Power: 250 W

Neutral Gas Density (ngas): 1.4×1010 cm-3

Electron Density (ne): 2.2×1011 cm-3

Electron Temperature (Te) : 580 eV

Ion Temperature (Ti) : 5 eV0 0.01 0.02 0.03

0

0.5

1

1.5

beam

inte

nsity

[a.u

.]

ne=2.23(± 0.06)e11[cm-3]Te=582(± 46)[eV]τ c=9.1(± 0.5)[ms]T i=5[eV]ngas=1.44e10[cm-3]

6+7+

8+

9+

3+

4+

tim

11


Confinement Time of Ions in the ECR plasma

Form the same study using 14.5GHz SHIVA, confinement time of 27Al3+ was obtaine

d by fitting the data as (M. Imanaka, PhD thesis, Univ. of Tsukuba)

c(27Al3+) = 2.3msec

By applying the following relation (Shirkov, CERN/PS 94-13)

i: charge state, Ai: mass

confinement time of 6Li ions are

1+ = 0.3 msec, 2+ = 0.7 msec, 3+ = 1 msec

From our laser ablation experiment by using 18GHz SC-ECR at RIKEN, we obtained

c(7Li2+) = 0.4 msec

It is more or less consistent with the above values.

ii Ai

12


Study of the Confinement Time of Li ions by the Laser Ablation method

18GHz SC-ECRIS

Lens, Mirror and LiF rod

YAG 523nm 5nsMax 100mJ/pulse

Laser ablation testin atmosphere

= 0.4 ms

13


Assumption of the Plasma Size

Plasma size is not well known.

We conservatively assume that the plasma size is the same as the volume inside of the ECR region.

Two times larger size will be used as an optimistic assumption.

14


Critical Magnetic Field

Calc. by H. Okamura

The critical magnetic field for decoupling the hyper-fine interaction between an electron and a nucleus in 6Li2+ is Bc=3kG.

Our SC-ECR has a minimum magnetic field of B~ 5kG.

Thus

dep. on the assumption

of the plasma size.

7.1cB

Bx

5.21.2 x

15


Depolarization

Major sources of the depolarization in the ECR ioninzer

1. Depolarization due to electron cyclotron resonance (ESR) caused by RF field.

electron polarization→nuclear polarization

2. Depolarization due to inhomegeneous magnetic field.

3. Depolarization due to ionization/recombination/excitations processes in the ECR plasma.

16


Depolarization caused by the electron spin resonance (ESR) effecton 6Li2+ (following the procedure of M. Tanaka et al., NIMA524,46)

If a 250W microwave is fed in a non-resonating cylinder with a diameter of 78mm.

The thickness of the ESR region is

The effective thickness averaged over isotropic ion motion and averaged length between the ESR regions are

Spin rotation angle of an electron caused by ESR is, by random-walk approx.

Nuclear depolarization is further caused by the hyper-fine coupling between electronand nucleus. Hence depolarization caused by ESR effect is negligibly small.

Gauss15.0 J/cm3,107.1 0110

2 uB

cr

Wu

direction) radial(in cm9.1at9.0

direction) axial(in cm0.5at0.4

RmR

RmR

cmmR

RL 9.2

3

29.10.5R,22

2ln2

3

29.00.4

5.3rad100.6180rad105.4 23N

Plasma size may be larger than the ESR region. We conservative assume this worst case.

17


Nuclear depolarization caused by inhomogeneous magnetic field(6Li1+ and 6Li3+)

The T1 relaxation time is expressed by, Schearer et al., Phys. Rev. 139 (1965) A1398

For 6Li1+ and 6Li3+, by putting the following numbers

It is larger than the assumed confinement time

1+ = 0.3 msec, 2+ = 0.7 msec, 3+ = 1 msec

but it still reduces the polarization.

2

42

2

1 3

21

y

H

H

v

Ty

zcI

sec103.1

sec102.1

//rad1094.3

6

6

7

v

Ts

c

I

Quantum axis is taken along the direction of the local magnetic field.

cm/rad25.01

T 70.0

y

H

H

H

y

z

z

T1 = 9.2 msec

2-2-2

2

4Tcmrad18.0

1

y

H

Hy

z

10cm

3.8cm

20cm

18


Reaction Rates and Depolarization in (de-)ionization/(de-)excitation processes in the ECR plasma

rates in Hz

944.0056.0000.0

056.0910.0033.0

000.0033.0967.0

depD

following the procedure of M. Tanaka et al., NPA524, 46.

when x=2.1

19


Ionization Rate by Electron Impact

Voronov’s empirical fit

]scm[1 13

2/1

1

UKeii eU

UX

PUAv

e

i

T

IU

G.S. Voronov, Atom. Data and Nucl. Data Tables 65 (1997)1.

Ii: Ionization Energy10-6

10-7

10-8

10-9

10-10

1 10 100 1000 10000

Te [eV]

i+1,i [

cm3 s

-1]

6Li0+→ 6Li1+

6Li1+→ 6Li2+

6Li2+→ 6Li3+

A, P, X, K: Fitting Parameters

Te: Electron Temperature

eiiii n11

ne: 2.23×1011 cm-3

6Li i 6Li i+1i+1,

6Li0+→ 6Li1+: 4.52×10-8 cm3s-1

6Li1+→ 6Li2+: 3.26×10-9 cm3s-1

6Li2+→ 6Li3+: 7.53×10-10 cm3s-1

20


Charge Exchange Reaction Rate with the Neutral Gas

Muller and Saltzborn Empirical Fit

]scm[1015.3 1376.217.161

i

igasiii A

TIiv

A. Muller and E. Saltzborn, Phys. Lett. A62 (1977) 391.

Igas: Ionization Energy of the Neutral Gas (Oxygen: 13.6 eV)

Ai: Ion Mass in AMU

Ti: Ion Temperature (5 eV)

]cm[1043.1 276.217.112 gasIi

6Li1+→ 6Li0+: 2.14×10-9 cm3s-1

6Li2+→ 6Li1+: 4.81×10-9 cm3s-1

6Li3+→ 6Li2+: 7.72×10-9 cm3s-1

gasiiii n11

ngas: 1.44×1010 cm-3

6Li i-1 6Li ii-1,

21


Atomic Excitation Rate by Electron Impact (1/2)

6Li0+→ 6Li0+* 2s→2p

D. Leep and A. Gallagher, Phys. Rev. A 10 (1974) 1082.

a factor of ~10 larger than the ionization rate coefficient

6Li1+→ 6Li1+* 1s→2p

assume that a factor of ~5 larger than the ionization rate coefficient

eenv *00

6Li i

6Li i*

i*

eV600~at]cm[101.35.3~ 21620 eTa

(including cascade)

]scm[105.4 137 ev

]scm[106.1 138 ev eenv *11

22



6Li2+→ 6Li2+* 1s→2p

Fisher et al., Phys. Rev. A 55 (1997) 329.Empirical fit of 1s→2p excitation cross sections of hydrogen-like atoms

Summing up transitions 1s→2,…,6 and taking the Boltzmann distribution


]scm[106.1 139 eveV550~at]cm[101.10.1~ 21842

0 ei TZa

6Li i

6Li i*

i*

eenv *22

]scm[1082.1 139 ev

23


Reaction Rates and Depolarization in (de-)ionization/(de-)excitation processes in the ECR plasma

rates in Hz

944.0056.0000.0

056.0910.0033.0

000.0033.0967.0

depD

following the procedure of M. Tanaka et al., NPA524, 46.

when x=2.1

24


Results of the simulation(confinement time dependence)

The total depolarization (pol~0.75) is expected to be at acceptable level, while the efficiency (beam intensity) is not high.

The intensity can be improved by increasing the electron density in the ECR plasma and/or improving the Li oven and Laser system.

25


Results of the simulation(confinement time dependence)

optimistic case

The results much depends on the plasma assumption. If an optimistic assumption is applied, i.e. 2.3 times larger electron density (5×1011 cm-3) and 2 times larger plasma size, the estimated beam intensity much increases.

Feasibility test experiment is required.

26


Present Status (Pictures)

27


CR

150 750 1000 1000 750 180 1370

’ “d “± ƒ~ ƒ‰[ ƒR ƒC ƒ‹ ’† S

ƒo ƒb ƒt ƒ‹ ”Â

ƒA ƒC ƒ“ ƒc ƒF ƒ‹ ƒŒƒ“ ƒY ’† S

ECRƒv ƒ‰ƒY ƒ} o Œû ŒŠ Šù Ý ƒX ƒŠ ƒb ƒg

Šù Ý •ª Í “d Ž¥ Î ‹ó ƒt ƒ‰ƒ“ ƒW–Ê

Ã “d •â ³ ”Â i …•½j

“ñ ‹É “d Ž¥ Î ŽO A Žl d ‹É ƒŒƒ“ ƒYŽO A Žl d ‹É ƒŒƒ“ ƒY ƒE ƒB [ ƒ“ ƒt ƒB ƒ‹ ƒ [

1495 525 1375 1375 555

5325

1650

1100

1500

250

850

570

570

850

140

1000

140

‚± ‚¿ ‚ç ‚É Ú “®o —‚È ‚¢ ‚©H

‚± ‚¿ ‚ç ‚É Ú “®o —‚È ‚¢ ‚©H

755

ƒ‰ƒb ƒN

Ã “d •â ³ ”Â

…•½ƒX ƒŠ ƒb ƒg ’† S

ƒt ƒ@ƒ‰ƒf [ ƒJ ƒb ƒv ’† S

‚ ’¼ƒX ƒŠ ƒb ƒg ’† S

TrNoemaf i os PS

…—â ”z ŠÇ( 10K- 65Aƒt ƒ‰ƒ“ ƒW)

Neomaf i os“d Ž¥ Î

‚ ³ ƒ{ ƒb ƒN ƒX

‚ ³ “d Œ¹

Vacuum Vacuum

‚ ³ “d Œ¹

‚ Žü ”g “d Œ¹

ƒ ƒ“ ƒe ƒi ƒ“ ƒX Žž

Ž¥ ‹C ƒV [ ƒ‹ ƒh ’† S

Ú“®

‹——£

1000

ƒ{ ƒ‹ ƒg ‘} “ü ‰Â ”\ H

700

400 ’Ý ƒs ƒb ƒg ŒŠ

800

18GHz

SC-ECR

6Li Atomic Beam Source Wien Filter

for controlling the polarization axis

Top View

injection to AVF(downward)

28


29


Summary

• Simulations have been done about the depolarization and ionization efficiency of a 6Li3+ ion source by using an ECR ionizer.

• Under an assumption of the plasma condition, the calculated polarization (0.75) is acceptable. The beam intensity is somewhat low (~100 nA) and improvements may be needed. This method looks hopeful.

• Feasibility test experiment is required for conforming the simulation, and optimizing plasma parameters by tuning magnetic field, RF power, gas density, and extraction geometry.

• Final design and construction is in progress.

30


Outline of the polarized 6Li3+ ion source (I)(6Li1+ injection to ECR)

6Li1+: 20-30 pA Pol. 80-90% at Florida State Univ.

F=1/2F=3/2

F=3/2

-3/2 -1/2 1/2 3/2

2S1/2

2p1/2

Level Diagram of a6Li atom

31


From calculations and simulations• Emittance of the 6Li1+ beam from the surface ionizer

vertical dir.: 300 mmmrhorizontal dir.:200 mmmr

• ~70% of the beam is reflected at the deceleration electric field (19 kV→10 eV) placed at the entrance of ECR.

• Dense plasma with a thickness of ≿50 cm is required to efficiently decrease the energy of 10 eV 6Li1+ ions and trap them in the plasma.

Efficient injection of the 6Li1+ beam into ECR plasma is not expected in the assumed setup.

32


Simulation of the Optical Pumping

Li Oven

70 mm

Laser-1

Lase

r-2

Polarizing CubeBeamsplitter

/4 plates

Polarizing CubeBeamsplitter

/4 plate

70

0 m

m

CylindricalLens

Retro-reflector

10mW

F=1/2F=3/2

F=3/2

-3/2 -1/2 1/2 3/2

2S1/2

2p1/2

Level Diagram of a6Li atom

MF

158

61

151

31

52

21

52

53

61

158

151

31

52

21

52

53

F=1/2

1%

33



18GHz SC-ECRIS

Lens, Mirror and LiF rod

YAG 523nm 5nsMax 100mJ/pulse

Laser ablation testin atmosphere

= 0.4 ms

34



= 0.3, 0.4, 0.5 ms

Note: the ECRIS operation has not tuned to 6Li3+

35


Magnetic-Substate Transition Matrix (1/2)(according to the calc. of 3He by M. Tanaka and Y. Plis)

The wave functions i(t) of the electron-nucleus system in a magnetic field system are written as a linear conbination of |IJ> states as

The time revolution of the |↓+1> state is

The probability to find |↓+1> and its time average (after sufficient time) is

10

01

01

10

sincos)0(

sincos)0(

1)0(

cossin)0(

cossin)0(

1)0(

VI

V

IV

III

II

I

fieldmagneticcritical:

32

1

31

)1(2

1cos)1(

2

1sin

2

cc

BB

Bx

xx

x

)exp(sincossin

)exp(cossincos

)exp()0(sin)exp()0(cos

)(sin)(cos1

IV

II

IVIVIIII

IVII

10

10

tiE

tiE

tiEtiE

ttt

)1(2

1sincos

cossincos2sincos

)exp(sin)exp(cos)(

244

IVII2244

2

IV2

II2

P

tEE

tiEtiEtP

36


Magnetic-Substate Transition Matrix (2/2)

By similar calculations we obtain

We are not interested in the electron spin. In the case that the orientation of the electron spin is random at t=0, by taking the average for the initial state and sum for the final state concerning the electron spin, we obtain

When x=5/3, the matrix is

1

1

1

1

12

11

2

1

12

11

2

11

12

11

2

1

12

11

2

11

'1

'

'1

'1

'

'1

0

0

0

0

22

22

22

22

1

0

1

34

11

4

10

14

12

4

11

4

1

014

13

4

1

'1

'0

'1

22

2222

22

917.0083.00

083.0871.0045.0

0045.0955.0

depD

37


Ionization Rate by Electron Impact

Voronov’s empirical fit

]scm[1 13

2/1

1

UKeii eU

UX

PUAv

e

i

T

IU

G.S. Voronov, Atom. Data and Nucl. Data Tables 65 (1997)1.

Ii: Ionization Energy10-6

10-7

10-8

10-9

10-10

1 10 100 1000 10000

Te [eV]

i+1,i [

cm3 s

-1]

6Li0+→ 6Li1+

6Li1+→ 6Li2+

6Li2+→ 6Li3+

A, P, X, K: Fitting Parameters

Te: Electron Temperature

eiiii n11

ne: 2.23×1011 cm-3

6Li i 6Li i+1i+1,

6Li0+→ 6Li1+: 4.52×10-8 cm3s-1

6Li1+→ 6Li2+: 3.26×10-9 cm3s-1

6Li2+→ 6Li3+: 7.53×10-10 cm3s-1

38


Charge Exchange Reaction Rate with the Neutral Gas

Muller and Saltzborn Empirical Fit

]scm[1015.3 1376.217.161

i

igasiii A

TIiv

A. Muller and E. Saltzborn, Phys. Lett. A62 (1977) 391.

Igas: Ionization Energy of the Neutral Gas (Oxygen: 13.6 eV)

Ai: Ion Mass in AMU

Ti: Ion Temperature (5 eV)

]cm[1043.1 276.217.112 gasIi

6Li1+→ 6Li0+: 2.14×10-9 cm3s-1

6Li2+→ 6Li1+: 4.81×10-9 cm3s-1

6Li3+→ 6Li2+: 7.72×10-9 cm3s-1

gasiiii n11

ngas: 1.44×1010 cm-3

6Li i-1 6Li ii-1,

39



6Li0+→ 6Li0+* 2s→2p

D. Leep and A. Gallagher, Phys. Rev. A 10 (1974) 1082.


6Li1+→ 6Li1+* 1s→2p

assume that a factor of ~5 larger than the ionization rate coefficient

eenv *00

6Li i

6Li i*

i*

eV600~at]cm[101.35.3~ 21620 eTa

(including cascade)

]scm[105.4 137 ev

]scm[106.1 138 ev eenv *11

40



6Li2+→ 6Li2+* 1s→2p

Fisher et al., Phys. Rev. A 55 (1997) 329.Empirical fit of 1s→2p excitation cross sections of hydrogen-like atoms

Summing up transitions 1s→2,…,6 and taking the Boltzmann distribution


]scm[106.1 139 eveV550~at]cm[101.10.1~ 21842

0 ei TZa

6Li i

6Li i*

i*

eenv *22

]scm[1082.1 139 ev

41


Confinement Time of The Ions

It is very difficult to estimate the confinement time of ions in anECR plasma.If we assume (M.Imanaka, PhD Thesis; Shirkov, CERN/PS 94-13 )

and scale the value of 3+=2.3msec, which was fitted tothe Al data,

ii Ai

[ms]99.0

[ms]66.0

[ms]33.0

3

2

1

1 ii

6Li i

i

42


Nuclear depolarization caused by inhomogeneous magnetic field(6Li1+ and 6Li3+)

The T1 relaxation time is expressed by, Schearer et al., Phys. Rev. 139 (1965) A1398

For 6Li1+ and 6Li3+, by putting the following numbers

If the plasma size is larger by a factor of 2 (in length)

2

42

2

1 3

21

y

H

H

v

Ty

zcI

sec103.1

sec102.1

//rad1094.3

6

6

7

v

Ts

c

I

Quantum axis is taken along the direction of the local magnetic field.

cm/rad25.01

T 70.0

y

H

H

H

y

z

z

T1 = 9.2 msec

2-2-2

2

4Tcmrad18.0

1

y

H

Hy

z

2-2-2

2

4Tcmrad11.0

1

y

H

Hy

zcm/rad28.01

T 1.1

y

H

H

H

y

z

z

T1 = 15 msec

10cm

3.8cm

20cm

7.0cm

43


Summary of the Processes in the ECR Ionizer

6Li0+ 6Li1+ 6Li2+ 6Li3+

6Li0+* 6Li1+* 6Li2+*

1

1

Ddep 1

1 Ddep

1

1

1

1

Dd

ep

Escape

1

Escape Escape Escape

1

1

1

Feeded

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PST05, November 14-17, 2005 at Tokyo 1 Design of a polarized 6 Li 3+ ion source and its feasibility...

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