IEEE Transactions on Nuclear Science, Vol. NS-28, No. 2, April 1981

CHARACTERISTICS AND APPLICATIONS OF CHANNELING RADIATION FROM RELATIVISTIC ELECTRONS AND POSITRONS

R.H. Pantell and R.L. SwentDepartment of Electrical Engineering

Stanford University, CA 94305

S. DatzOak Ridge National Laboratory

Oak Ridge, TN 37830

M.J. AlguardMeasurex, Inc.

Cupertino, CA 95129

B.L. Berman and S.D. BloomLawrence Livermore Laboratory

Livermore, CA 94550

Summary

Relativistic electrons and positrons channeled incrystals radiate electromagnetic waves in relativelynarrow spectral bands. The radiation is forward-directed, linearly polarized, and occurs in picosecondbursts. Photons in the 20 to 130 keV range are emit-ted by 50 MeV particles, and the emission spectrumvaries with the incident particle energy. Severalapplications of channeling radiation are considered:to study the properties of crystals in which channel-ing occurs, to investigate aspects of the channelingphenomienon, and as a source of x-rays.

Introducti on

The periodic motion of relativistic, charged par-ticles channeled in crystals results in the radiationof electromagnetic waves that are forward-directed,have a narrow linewidth, have an intensity that is upto an order of magnitude larger than the bremsstrah-lung background, and have spectral emission peaks that

can be varied by changing the particle energy.1'2'3These properties have been confirmed experimentally insilicon for electrons and positrons in the 28 to 56

MeV energy interval channeled between planes,4'5 andin the 1.5 to 4.0 MeV energy range for axial channeled

electrons.6Additional properties of the radiation predicted

from the electric dipole model are that the waves arelinearly polarized for planar-channeled particles, andthat the time structure of the emission follows thetime structure of the particle beam. This latter prop-erty means that the x-rays occur in bursts -- 10 pslong, since this is the duration of the particle beampulse produced by a typical linear accelerator.

From a quantum mechanical standpoint, the par-ticles are trapped in the potential well establishedby the crystal planes or axes, and radiation resultsfrom spontaneous transitions between eigenstatesderived from this potential. For positrons, the planarpotential is approximately harmonic, 1 which means thatthe eigenvalues are nearly equally separated and allspontaneous transitions give about the same photonenergy. Therefore, there is a single spectral peakemitted by planar-channeled positrons. Electrons, onthe other hand, are in a planar potential that variesapproximately exponentially with distance from the

plane7 so that the eigenvalues are not equally spaced,giving a multiplicity of spectral peaks.

Figure 1 shows the raw data for y = 107 positrons,obtained from the Lawrence Livermore Laboratoryelectron-positron linear accelerator, channeled between(110) planes in silicon. The crystal thickness is 9 ,umand the full-width, half-maximum (FWHM) angulardivergence of the beam is 1.7 + 0.3 milliradians. Alithium drifted germanium detector is used for photon

detection, and a bending magnet prevents the positronsfrom striking the detector. Further details of theexperimental arrangement are given in References 4 and8. Channeling radiation produces the large peak near40 keV photon energy; the two smaller peaks near 80 keVare Ka and K fluorescence from lead bricks used to

shield the detector; and the 511 keV emission is frompositron annihilation.

800

600

D 40000

200

() I

10 50 100

PHOTON ENERGY (KeV)500

Figure 1. Radiation from y = 107 positrons channeled by(110) planes in Si. The crystal thickness is9 jim. Channeling produces the large peaknear 40 keV photon energy; the two peaks near

80 keV are fluorescence from Pb bricks near

the detector; and the 511 keV peak is frompositron annihilation.

The FWHM linewidth of the channeling emission peakin Fig. is 26%. Factors contributing to this line-

width and the corresponding percentage broadenings are:

solid angle intercepted by the detector which intro-

duces a Doppler shift (23%); potential anharmonicity(8%); finite crystal length (8%); and multiple scatter-

ing parallel to the (110) planes (7%). Quadrature add-

ition of these linewidth contributions gives 27%, which

is close to the measured value. If the solid angle of

the detector were vanishingly small the linewidth would

be approximately half the value shown in Fig. 1. Other

factors that contribute to linewidth but are less sig-nificant are: length in the crystal for which the par-ticles radiate coherently; energy spread of the par-ticles; and Bloch wave broadening.

Radiation has also been observed in germaniumcrystals. Positrons with y = 107, channeled by (110)planes, emitted a spectral peak at 47 keV with 42% FWHM

0018-9499/81/0400-1152$00.75 1981 IEEE

* _

. . . _

10'1 %I,

I , , III

M I I t I I j 1-1 I I 1 7

1152

linewidth. The limited distance over which the parti-cles radiated coherently is believed to be the primaryline broadening mechanism for Ge.

Figure 2 shows the radiation data from y = 107electrons channeled between (110) planes in Si. Thesignificant difference between the positron emissionin Fig. 1 and the electron emission in Fig. 2 is thatthe latter gives many peaks. Peaks marked (1) through(5) correspond to spontaneous transitions between ad-jacent eigenstates (i.e. An = 1). The sum of the pho-ton energies for (1), (2), and (3) is 152 keV, and itis seen that there is a peak in the photon spectrum atthis energy corresponding to a An = 3 transition. AllAn-odd transitions are allowed as single photon elec-tric dipole interactions. Similarly, the sum of theenergies for peaks (2), (3) and (4) is 199 keV and forpeaks (3), (4) and (5) is 273 keV. The latter twoAn = 3 transitions are also evident in Fig. 2. Rela-tive intensities of the An = 3 to An = 1 transitionshave been determined from the electric dipole radiationformula, and preliminary calculations indicate thatthese values agree, within experimental error, with themeasured intensities.

A1(A + 1 + 2r r2

V(r) =

Br2 + B2 0

r > u

(1)

r < u

was chosen, where r is the distance from the axis andu, A. and B. are undetermined. With the requirementthat the potential be continuous at r = u, there arefour adjustable coefficients in Eq. (1). Using data

presented by Anderson and Laegsgaard, 6 these fourcoefficients were varied to reproduce the measured pho-ton energies obtained from electrons channeled alongthe <111> axis in Si. The result is illustrated by thesolid lines in Figure 3, along with the data points.It is seen that almost all the 15 data points can bematched, within the experimental error bars, by anappropriate choice for the coefficients in Eq. (1).Also shown in Fig. 3, with dashed lines, are the pre-dicted photon energies using the Moliere potential 9approximation to the Thomas-Fermi model of the atom.

!250 F

1000K-

Ic, 750 Ez_

00 500-

A,

250_

O-1

iIi

,T-T-

(D)g.) (E.) (Dr"

.. ...t.

.-

.: ..

*.

*.

I I, ,II1f

152

273*s, i1

I

-2

8

7

> 6

0

r-

Lj4zLXiZ 300'rIa.

I2

50 100PHOTON ENERGY (KeV)

500

Figure 2. Radiation from y = 107 electrons channeled by(110) planes in Si. The crystal thickness is20 pm. Peaks labelled (1) - (5) result fromAn = 1 transitions and the peaks at 152, 199and 273 keV are An = 3 transitions.

Applications of Channeling Radiation

Three applications can be considered: to determinepotentials in crystals; to study the channeling phenom-enon; and as a source of x-rays. The use of electronplanar channeling radiation to determine interplanarpotentials has been reported for silicon.7 To accom-plish this a potential function is assumed with undeter-mined coefficients, and the coefficients are adjustedto produce the measured An = 1 photon energies. Thisprocedure was used for the five spectral peaks obtainedfrom 56 MeV electrons channeled by (110) planes in Si,and the derived potential function could be used topredict, with two figure accuracy, the photon energiesmeasured at 285 and 4 MeV.6

A similar procedure can be used to determine thestring potential. This is a more complicated problemthan the planar case because the eigenfunctions are nowtwo dimensional and the effect of the nearest-neighborstrings is more difficult to incorporate. A potentialfunction of the form

2 3ELECTRON ENERGY (MeV)

4

Figure 3. Measured photon energies emitted by electronschanneled along the <111> axis in Si for dif-ferent electron energies. Solid curves arethe photon energies calculated from anassumed potential function with adjustablecoefficients and dashed curves are potentialscalculated from the Moliere model.

The solid line in Figure 4 illustrates the derivedstring potential function, and the dashed line is theMoliere potential. The latter gives a 2p Eigenvaluethat is too low, resulting in errors in the photonenergies for transitions involving this state.

Of course, there is not a great deal of interestin determining potentials in silicon, since high accur-acy can be obtained from modeling the crystal. However,this procedure can be used when the configuration issufficiently complex that calculations would be diffi-cult. For example, it would be interesting to measurethe changes in interplanar potentials for a crystalapproaching a phase transition.

A second application of channeling radiation is tostudy channeling. Consider the dipole radiationformul a

1153

CHANNELING RADIATION< I I > Si

BEST FITMOLIERE FIT

3 p-Is

2p - Is

3d - 2p

2s - 2p

I0C

..

.1 fI

P~~~tN - 2i2xjjj.2dQ Pip(zz)dz (2)

where N is the number of photons collected per electronfor the i -+ j transition, ac 1/137 is the fine struc-ture constant, xij is the matrix element for positionfor the relevant transition, dQ is the solid angleaperture of the detector, t is the crystal thickness,and P (z) is the probability state i is occupied. Allthe parameters in Eq. (2) can be measured or calculatedwith the exception of Pi(z), so that channeling radia-tion offers a method for determining I - Pi(z)dzfor the individual eigenstates.

0

aaco

z

-J

zLii

0~

Figure 4. Potential energy curves for the <111> axisin Si. The solid line is obtained by match-ing an assumed potential energy to themeasured photon energies, and the dashedline is the Moliere potential.

Designating the lowest eigenstate as i = 0, Figure5 is a plot of I (z) as a function of z for i = I

through 5 for y = 107 electrons channeled by (110)planes in Si. These data at four different thicknesseswere measured using two crystals of different thick-ness giving two data points, and two additional datapoints were obtained by rotating each crystal to in-crease the sample thickness. The orientation of thechanneling planes relative to the direction of the in-cident particle beam was kept constant for the rotation.Each curve passes through the origin, and the slopes atthe origin were calculated from the overlap integralsbetween the eigenstates of the particle in the crystaland the state of the particle in the incident beam.Within the accuracy of the measurements, I1 and I2 are

indistinguishable and I 3 and I4 are indistinguishable.The curves in Fig. 5 can be differentiated to ob-

tain the occupation probabilities Pi(z) as a functionof z. The e1 distances for occupation for the differ-ent states are then found to be 16 vm for the i 1and 2 states, 11 vim for the i 3 and 4 states, and

5 pm for the n = 5 state. States with lower energy,i.e. deeper in the potential well, retain their popula-tions for longer distances than the states with higherenergy. These distances are much longer than the coher-ence lengths for radiation, which were found to be

1 vim. The reason for this is that the electron

1154

oscillates between states i and j such that its meanlifetime in these states can be much longer than themean coherence time in each state. This situation isanalogous to the T1 and T2 lifetimes for electronic

transitions in atoms where T1 is the lifetime of a

state (equivalent to the distance a state remainsoccupied) and T2 is the coherence time for fluores-cence (equivalent to coherence length).

2 IN Fm

Figure 5. The spatial integral of the occupation prob-abilities for the n = 1 through 5 states asa function of crystal thickness. These datawere obtained for y = 107 electrons channel-ed by (110) planes in Si.

A third application of channeling radiation is toprovide a source of x-rays. The radiation is linearlypolarized, forward-directed, relatively narrow band-width (10 - 25%), the peak photon energy is adjustable,and the pulses are of picosecond duration.

To determine the intensity of such a source it isnecessary to consider the maximum tolerable electroncurrent density that could be used to generate thex-rays. Three factors are important: the current limi-tations of an accelerator, heating of the crystal, andrate of defect formation in the crystal. Based uponthese considerations, a reasonable average current is100 viA in a 5 mm diameter beam. This beam can be pro-duced by a linac, the temperature rise in an 18 umthick Si crystal with radiation cooling only is

600 °C, and there is -1 chance in 103 of a defectforming per hour at an atomic site. This latter condi-tion means that the crystal would have to be rotated toa new position on a time scale of a second, but Si isself-annealing at this elevated temperature so thatdefect formation may not be a limitation.

Assuming an average current of l00,vA, Table Ilists the time-averaged photon emission rate. Thisrate was calculated from the measured photons per elec-tron per electron-volt at the low currents

(10-10 - 101 A) used to obtain the data shown inFig. 2. The values given in Table I are for the singleline marked (5) in Fig. 2, which corresponds to then = 1 to n = 0 transition for (110) electron planarchanneling in silicon.

These rates were calculated by determining the

Table I

Emission Intensity for Electron Planar ChannelingRadiation is from the n = 1 to n = 0 transition for the (110) planes in 18 pm thick silicon

FWHM Beamy Divergence55.5 2.0 mrad

111 2.0107 1.0

PhotonEnergy40 keV

128

122.5

Channeling Radiation(l)2.3xlO9 photons/sec

in 10%bandwidth

3.8xlO99.2xlO9

SSRL Radiation(2)400xlQ9 photons/

sec in 10%bandwidth

1.4xlO91.6xlO9

Energy Radiatedper Electron= .15 keV

.781.8

(1) For 100 pA of average current.

(2) SSRL operating at 3 GeV energy, 20 mA current, 5 mrad acceptance angle, and 40% monochromator efficiency.

ratio of channeling radiation to higher energy (400keV) bremsstrahlung, and using the bremsstrahlung for-mula for randomly directed particles. This assumesthat even under optimum channeling conditions most ofthe particles are not channeled (this is true), andthat most of the bremsstrahlung comes from electronspassing through the silicon crystal.

The bottom row in Table I was obtained with abetter collimated beam, and the channeling radiationincreases by a factor of 2.4. Part of this increase

results from the fact that a higher percentage of par-ticles are channeled, but this would only account for

30% improvement. Probably the rest of the increaseis attributable to the fact that with better collima-tion less background bremsstrahlung is generated inother parts of the beam transport system.

Included in Table I is the synchrotron radiationfrom the Stanford Synchrotron Radiation Laboratory(SSRL). To obtain these numbers the storage ring wastaken to operate at 3.0 GeV energy, 20 mA current, 5mrad acceptance angle of the 2ir synchrotron emission,and 40% monochromator efficiency. At the lower photonenergy SSRL has a higher emission rate and at thehigher energy the converse is true. Adding a wiggleror undulator to the storage ring can increase synchro-tron emission, but at sufficiently high photon energieschanneling radiation will still be brighter.

Table I also shows the measured energy radiatedper electron and the loss per electron in passingthrough 18 im of silicon. With efficiency defined asthe ratio of the energy radiated to the energy lost,

efficiency is < 10-4. However, as electron and photonenergy increase efficiency also increases, which sug-gests that higher efficiencies can be obtained forharder x-rays and y-rays.

This work was supported by the Division of Advan-ced Energy Projects, Office of Basic Energy Sciences ofthe United States Department of Energy under contractnumber DE-AM03-76SF00326.

References

1. R. H. Pantell and M. J. Alguard, J. Appl. Phys. 50,598 (1979).

2. R. W. Terhune and R. H. Pantell, Appl. Phys. Lett.30, 265 (1977).

3. M. A. Kumakhov, Phys. Lett. 57A, 17 (1976) and Phys.Stat. Sol.(b) 84, 581 (1977).

4. M. J. Alguard, R. L. Swent, R. H. Pantell, B. L.Berman, S. D. Bloom, and S. Datz, Phys. Rev. Lett.42, 1148 (1979).

5. R. L. Swent, R. H. Pantell, M. J. Alguard, B. L.Berman, S. D. Bloom, and S. Datz, Phys. Rev. Lett.43, 1723 (1979).

6. J. U. Andersen and E. Laegsgaard, Phys. Rev. Lett.44, 1079 (1980).

7. R. H. Pantell and R. L. Swent, Appl. Phys. Lett.35, 910 (1979).

8. M. J. Alguard, R. L. Swent, R. H. Pantell, B. L.Berman, S. D. Bloom, and S. Datz, 1EEE Trans. Nuc.Sci. 26, 3865 (1979).

9. B. R. Appleton, C. Erginsoy, and W. M. Gibson,Phys. Rev. 161, 330 (1967).

1155

Loss perElectron

12 keV

16

16