PHYSICAL REVIEW SPECIAL TOPICS - ACCELERATORS AND BEAMS, VOLUME 5, 121001 (2002)

Comparison of theory with experiment for positron production
from high-energy electrons moving along crystal axes
V. N. Baier and V. M. Strakhovenko
Budker Institute of Nuclear Physics, 630090 Novosibirsk, Russia(Received 25 September 2002; published 5 December 2002)
Using the approach developed earlier for the description of the electron-photon showers in axiallyaligned single crystals, some characteristics of the positron yield measured in recent experiments arecalculated. Theoretical estimations display a rather good agreement with experimental results obtainedusing 3 to 10 GeV electrons aligned to the h111i axis of the tungsten crystals. Such comparison verified
that the accuracy of our approach is quite sufficient to make a reliable choice for optimal parameters of
the positron source using axially aligned crystals for future linear colliders.
DOI: 10.1103/PhysRevSTAB.5.121001

I. INTRODUCTION

PACS numbers: 12.20.Ds, 03.65.Sq

An efficient positron source is one of the importantcomponents of future electron-positron colliders.
Positrons are generated from electrons in the course of
the e e  shower developing in a medium. In a highenergy region, the basic processes involved in the shower
development are typically considerably enhanced in oriented crystals as compared with corresponding amorphous media. The most pronounced effects take place ataxial alignment when initial electrons are moving along
the main axes of a crystal. This alignment alone will beconsidered below. According to [1], the radiation intensity
in a crystal exceeds that of the conventional bremsstrahlung starting with electron energies "  1 GeV. Simple
estimations of the width of the power spectrum indicateda soft character of this spectrum. So the use of highenergy electrons impinging on the axially oriented crystals ‘‘. . . as a source of hard and directed radiation
concentrated within a comparatively narrow frequency
range . . .’’ was proposed in [1]. Based on mentioned
properties of the photon emission process, the use ofthis phenomenon in the positron source for future accelerators was proposed [2,3]. The pair production rate
which is due to the coherent (crystal) effects exceedsthat of the standard (Bethe-Heitler) mechanism startingwith photon energies ! ’ !th . The value of !th is about
22 GeV for the h111i axis of tungsten being several times
larger for other crystals. (See the review [4] and the recent
book [5] for further details concerning QED processes incrystals.) For energies well above !th , the crystal effects
become really strong and may be used to create effective
and compact electromagnetic calorimeters [6]. For very
high energies ("  !th ) of initial and created particles,
kinetic equations describing the shower development
were solved analytically [7]. Though the initial electronenergies were high enough in the first experimental
investigation [8] of shower formation in crystals, energies
of detected particles were too low to allow us the
direct comparison with [7]. To explain the results of [8],Monte Carlo simulations were performed in [9]. The

probabilities of basic processes used in [9] were obtained
within so-called constant field approximation. A good
agreement was demonstrated in [9] with the results of[8] for Ge crystals.
When the initial electron energy is below !th , photons
are mainly emitted with energies !  !th and so, up tominor modifications (see [10,11]), the pair production
process proceeds in a crystal as in an amorphous medium.
The enhancement of radiation from initial electrons isthereby the main crystal effect in this energy region. The
substantial advance in the description of shower formation at axial alignment was caused by the invention of thesemiphenomenological radiation spectrum [12]. This allows one to consider the relatively low (of a few GeV)
energy range of the initial electrons which is presumed
for the efficient positron source. The radiation intensity
increases with the initial electron energy. As a result, atsome energy the effective radiation length Lef in the
crystal becomes smaller than the conventional radiation
length Lrad and continues its decrease at further increaseof the energy. All numerical examples will be given
below for the electron beam aligned with the h111i axisof the tungsten crystals. Then we have for the quantity Lef
defined as in Sec. 3 of [12]: Lef 1 Gev ’ 0:166 cm,
Lef 4 Gev ’ 0:084 cm, and Lef 8 Gev ’ 0:061 cm. In
the hybrid target which consists of the crystal part followed by the amorphous one, the thickness of the crystal
constituent of several Lef is obviously quite enough.
Indeed, at the depth L0
3–4 Lef most of the particles,
including the initial electrons, are sufficiently soft to
reduce the coherent contribution to the radiation to thelevel of the incoherent one. Thereby, the further development of the shower proceeds more or less in the same way
for the crystal or amorphous type of the remaining partof the target. We emphasize that the crystal part L L0of the target serves as the radiator, and secondary charged
particles are still not so numerous at this stage ofthe shower development. Therefore only a small portionof the total energy loss is deposited in the crystal part of
the target which considerably reduces a danger of its

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overheating. The softness of the photon spectra is anotherimportant feature of the crystal radiator giving additional
advantages for the positron production in comparison
with the entirely amorphous target. To get a more definite
idea concerning the shape of the power spectrum one canuse its explicit form given by Eq. (2) in [12]. To present thescale, let us list some values !max where this spectrum
is maximum: !max 1 GeV ’ 31 MeV, !max 4 GeV ’
170 MeV, and !max 8 GeV ’ 490 MeV. Note that thewidth of the spectrum is typically several times larger
than !max . The increase in the number of relatively soft
photons turns out to be much more pronounced than thatin the total radiation intensity. In the end, just this fact
leads to the substantial enhancement of the positron yieldfrom crystal targets.
Recently the positron production in axially aligned
single crystals was studied in two series of experiments
performed at CERN [13,14] and KEK [15,16]. The initialenergy of electrons was 3 GeV [15], 6 and 10 GeV [14],8 GeV [16], and 10 GeV [13]. In all cases the initial
electron beam was aligned with the h111i axis of thetungsten crystal that sometimes served as the crystal
part of the hybrid target which contained an additional
amorphous tungsten target. A noticeable enhancement of
the low-energy positron yield was observed in all experiments cited above when the yield from the crystal target
was compared with that from the amorphous target of thesame thickness. The experimental results and our theoretical estimations presented in the next section display arather good agreement with each other.
II. COMPARISON OF THEORY WITH
EXPERIMENT
Theoretical results for the conditions of the experiments cited above were obtained using the approachdeveloped in [11,12] where various positron and photon
distributions as well as deposited energies in different
crystals were calculated for the energy range of initial
electrons from 2 to 300 GeV. In these papers, all theformulas used in Monte Carlo simulations of the specifice e -shower characteristics are given in the explicit
form. Remember that our simplified description of theshower development takes into account coherent inducedby the regular motion of particles in the field of crystalaxes) and incoherent like that in an amorphous medium)mechanisms of photon emission and pair production processes. The multiple scattering and the ionization energy
loss of electrons and positrons are taken into accountneglecting crystal effects. The coherent radiation fromchanneling and moving not very high above the axis
potential barrier particles is described using the semiphenomenological spectrum suggested in [12]. The corresponding computer code was developed. This allows
one to calculate energy, angular, and coordinate distributions of positrons emergent from the crystal or hybrid
target and to find an amount of the energy deposition. We
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Positrons per electron

COMPARISON OF THEORY WITH EXPERIMENT FOR . . .
Positrons per electron

PRST-AB 5

0.04

0.02

0.1
0.075
0.05
0.025

10

20

30
40
Energy (MeV)

0

10

20
Angle (degree)

FIG. 1. Spectral (top) and angular (bottom) distributions ofpositrons from 10 GeV electrons traversing a 8-mm-thick crystal tungsten target along the h111i axis. Open circles: simulation; filled circles: experiment.

think that the investigation of such distributions should be
the main object of the experiments having the creation of
the crystal assisted positron source as their ultimate aim.
A. Experiment (CERN) at "0  10 GeV
Among experiments cited above, spectral-angular distributions of created positrons were measured only in theWA103 experiment at CERN (see [13,14]), where ourcode was used in simulations as the event generator.
This simulation allowed for the acceptance conditions
and the efficiency of the detectors used. Shown in Fig. 1
taken from [14] is one example of the measured andsimulated distributions of positrons from 10 GeV electrons aligned with the h111i axis of the 8 mm-thickcrystal tungsten.
The angular acceptance conditions in the WA103 experiment were approximately j#Vout j 1:5 for the vertical and 0 #Hout 25 for the horizontal angle of theoutgoing positron with respect to the initial electron
beam direction. We shall see below that the shape of thepositron spectrum depends on the degree of collimation.
The one-dimensional (over #Hout ) angular distribution ispresented for positrons having energies in the 5– 45 MeV
range. We emphasize that the relative difference between
measured and simulated results typically does not exceed
20% in both spectral and angular distributions as seenin Fig. 1. We are aware that preliminary results forother settings used in the same experiment do notcontradict with the estimated scale of the difference
between the data and theoretical predictions. We hopethat this interrelation will not become worse after performing the complete analysis of the data which now isunderway. This analysis will also give more detailed
information concerning spectral-angular distributions ofpositrons depending on initial electron energies and target thicknesses.
B. Experiment (KEK) at "0  3 GeV
The main goal of the experiment [15] was an attempt toapply the crystal target to the working electron/positron
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V. N. BAIER AND V. M. STRAKHOVENKO

linac, the injector for the electron-positron collider BFactory at KEK. Thus, the acceptance conditions forcreated positrons were determined by the momentum
acceptance of the positron linac with the matching section which is 8:2 < p < 11:6 MeV=c and p? <2:4 MeV=c. The hybrid target used consists of 1.7-mmthick tungsten crystal followed by 7-mm-thick amorphous tungsten. The observed positron yield wasenhanced by the factor 1.40 when the h111i crystal axis
was aligned with 3 GeV incident electron beam as compared to the case of the disoriented crystal. Our number
for this enhancement is 1.47 being only 5% larger thanthe experimental one. Note that in the experiment [15] thecrystal and amorphous parts of the hybrid target wereseparated by the distance of 70 mm. This circumstance,
which, in principle, may slightly change the enhancement
value, was not taken into account in our calculation.
Recollect that the amount of the energy deposited in
the crystal part ("crdep ) of the hybrid target may be muchsmaller than that ("amdep ) in the amorphous one. Suchinterrelation of "cr
and
"am
dep
dep should take place in thecase of [15], where the crystal thickness is about 1.8 Lef(see the discussion in the Introduction). This is confirmedamby our calculations which give "cr
dep ’ 11 MeV and "dep ’
277 MeV per one incident electron.
C. Qualitative features of positron distributions andexperiment (KEK) at "0  8 GeV
In [16] the positron production efficiency from 2.2, 5.3,
and 9.0-mm-thick tungsten crystals was measured using
an 8-GeV electron beam. Positrons produced in the forward direction with momenta 10, 15, and 20 MeV=c weredetected by the magnetic spectrometer. Thus, several
points in the energy distribution were determined under
hard collimation conditions. To give an idea of spectralangular distributions on the whole, let us remind theirimportant qualitative features using 8 GeV electrons andthe h111i axis of the tungsten crystals as an example. For

the sake of comparison, the corresponding distributions
for amorphous tungsten will be presented as well. Below
all the quantities characterizing the positron yield arenormalized per one incident electron.
The use of matching systems implies some collimation(typically #out 25 ) of outgoing positrons. Shown in
Fig. 2 is the energy dependence (energy step is equal to
10 MeV) of the positron yield from crystal (a) and amorphous (b) targets of the same thickness L  2:2 mm. In
the case of the hard collimation, when #out 1 (opencircles), the yield is multiplied by 10 to make it visible.
The larger the positron energy, the smaller the typicalvalue of #out since both production and multiple scattering processes are characterized by smaller angles forhigher energies. This is seen in Fig. 2(a) where the spectral curves for #out < 180 and that for #out 24 areoverlapping within precision better than 1% starting from"cr1 ’ 55 MeV. In turn, from "cr2 ’ 110 MeV the same
happens with curves corresponding to #out 24 and#out 12 . Such behavior is also seen in Fig. 2(b) for1
2
the amorphous target where "am’ 50 MeV and "am’
105 MeV.
In other words, positrons with energies " > " 1 arepractically concentrated within the cone #out 24 andthose with " > " 2 have #out 12 . In accordance withthis picture, the spectral maximum is shifted to the rightwhile the width of the distribution increases when thecollimation angle decreases. The enhancement , being a
bin-by-bin ratio of the positron yield from the crystal
target to that from the amorphous one at the same collimation, is almost constant for " < 45 MeV and monotonically decreases with growing positron energy. Thismeans that positron spectra from the crystal target aresofter. Somewhat lower values of " 1 ; " 2 in the amorphous case point at the same feature. For given collimation, the variation of the enhancement is about 20% over
the whole energy interval presented in Fig. 2. The maximum values of the enhancement at different collimationare max #out 180 ’ 6:09, max #out 24 ’ 5:92,

(b)

(a)

0.6

0.10
0.08
Positron yield

Positron yield

0.5
0.4
0.3
0.2

0.06
0.04
0.02

0.1
0.0

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0

50

100

150

200

Positron energy ( MeV )

250

0.00
0

50

100

150

200

250

Positron energy (MeV)

FIG. 2. Positron yield depending on energy from 2.2-mm-thick crystal (a) and amorphous(b) targets at different collimation. Filled triangles: no collimation (#out 180 );open triangles: #out 24 ; filled circles: #out 12 ; and open circles: #out 1 (multipliedby 10).

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COMPARISON OF THEORY WITH EXPERIMENT FOR . . .
5121001 (2002)
(b)

(a)
2.0

Positron yield

Positron yield

4
3
2

1.0

0.5

1
0

1.5

0.0
0

50

100

150

200

250

0

50

100

150

200

250

Positron energy (MeV)

Positron energy ( MeV )FIG. 3. Positron yield depending on energy from 9.0-mm-thick crystal (a) and amorphous(b) targets at different collimation. Filled triangles: no collimation (#out 180 );open triangles: #out 24 ; filled circles: #out 12 ; and open circles: #out 1 (multipliedby 30).

max #out 12 ’ 5:67, and max #out 1 ’ 5:29.
Apparently, they diminish as the collimation angle
does so.
Figure 3 is the same as Fig. 2 but for the target thickness L  9:0 mm. The yield at #out 1 (open circles) is
multiplied now by 30. The qualitative behavior of spectra
depending on the collimation angle at L  9:0 mm is thesame as at L  2:2 mm. However, all the spectra become
softer for the larger target thickness. This is indicatedalready by the increase in " 1 , " 2 values which are1now "cr1 ’ 85 MeV, "cr2 ’ 185 MeV, "am’ 75 MeV,
2and "am ’ 165 MeV. It is clear that the magnitude of
the yield from the thicker target is essentially larger but
this increase is different in the crystal and amorphouscases. For example, in the energy range " < 45 MeV, theyield is increased by 6 –7 times for a crystal and by 17–
20 times for amorphous samples. As a result, the enhancement at L  9:0 mm is almost 3 times less than at
L  2:2 mm in this energy range. At L  9:0 mm theenhancement is peaked in the first bin [" 2
5–15 MeV] for every collimation. Its maximum values
are max #out 180 ’ 2:25, max #out 24 ’ 2:15,
max #out 12 ’ 2:08, and max #out 1 ’ 2:06.
The enhancement monotonically decreases with growing

positron energy and approximately halves at "250 MeV. Thus, positron spectra from the crystal target
are softer at L  9:0 mm as well, and this property ismuch more pronounced in comparison with L  2:2 mm.
Matching systems can be characterized also by the
maximum transverse momentum pmax
? of accepted positrons. In this connection, spectra of positrons havingp? < pmax? are of undoubted interest. Such spectra at L 
2:2 mm (a) and at L  9:0 mm (b) from crystal andamorphous targets are shown in Fig. 4.
In contrast to the case of the pure angular selection (cf.
Figs. 2 and 3), the position of spectral maxima at limitedp? values is always in the first bin [" 2 7:5–12:5 MeV].
Corresponding maximum values are max 5 MeV=c ’
5:82, max 2:5 MeV=c ’ 5:62 at L  2:2 mm, andmax 5 MeV=c ’ 2:17, max 2:5 MeV=c ’ 2:11 at L 
9:0 mm. The enhancement monotonically decreases withgrowing positron energy. Its variation over the wholeenergy interval presented in Fig. 4 is about 15% at L 
2:2 mm and 40% at L  9:0 mm. So, for this selectiontoo, positron spectra from crystal targets are softer thanthose from amorphous targets of the same thickness. Theinteresting feature of spectral curves in Fig. 4 is thesimilarity of those obtained for two different values of
1

(a)

(b)

4

0.01

3

Positron yield

Positron yield

0.1

0.1

4

0.01

2

2
3

0.001

1

0

20

40

60

80

100

Positron energy (MeV)

120

1

140

0

20

40

60

80

100

120

140

Positron energy (MeV)

FIG. 4. Positron yield depending on energy at L  2:2 mm (a) and L  9:0 mm (b) formaxpmax?  2:5 MeV=c (curves 1 and 3) and for p?  5 MeV=c (curves 2 and 4). Solid curves
represent the yield from crystal and dotted curves from amorphous targets.

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Angular distribution of positrons

V. N. BAIER AND V. M. STRAKHOVENKO
Angular distribution of positrons

PRST-AB 5

(a)

1.4
1.2
1.0

4

0.8
0.6
0.4

3

0.2

121001 (2002)
(b)

4

4

3

2

2

3

1

1

2
1

0

0.0
0

5

10

15

20

0

25

5

Outgoing positron angle (degrees)

10

15

20

25

Outgoing positron angle (degrees)

FIG. 5. Angular distribution dN  =d depending on outgoing positron angle at L 
2:2 mm (a) and at L  9:0 mm (b) for p 2 8:5–11:5 Mev=c (curves 1 and 3) and for p 2
17–23 Mev=c (curves 2 and 4). Solid curves represent the yield from crystal and dottedcurves from amorphous targets.

(a)

0.05
0.04
0.03
0.02
0.01
0.00

0

1

are about 6.5% at p 10 Mev=c and 14% at p
20 Mev=c. At L  2:2 mm the distribution from the crystal target is wider by 15.5% at p 20 Mev=c whereas
this is narrower by 10% at p 10 Mev=c.
Going on to the comparison of our results with thoseobtained in [16], let us remember that to perform an
accurate comparison of such kind, exact information isneeded concerning the acceptance conditions and registration efficiency of detectors in the experiment. As notedin [16], at p  20 Mev=c, the momentum acceptance(p=p) was 3% (FWHM) and the polar angle acceptance
was less than 20 mrad (FWHM). Since the shape of theacceptance curves was unavailable to us, we have tried tosimulate experimental conditions using the same angularmax and the same value of p=p forcollimation #out #out
all momenta and targets. So, at the calculation of themagnitudes of positron production efficiency (PPE), we
max
simply put #out
to 20 mrad. The value of p=p waschosen to reproduce at applied collimation the experimental magnitude of PPE for the 9.0-mm-thick amorphous target. Acting in this way, we have p=p  3:2%.
We realize that our regard for the acceptance conditions israther rough. An additional inaccuracy was introduced

Positron production efficiency (%)

Positron production efficiency (%)

pmax? from the same target. The scaling factors  are cr ’
2:6, am ’ 2:5 at L  2:2 mm and cr ’ 3:1, am ’ 3:0 at
L  9:0 mm. These factors turn out to be practically(within an accuracy of a few percent) independent of
the total positron momentum p. This fact can be easily
understood if we assume that the width of the angular
distribution of positrons is completely due to multiple
scattering being, thereby, proportional to p1 . Such anassumption is confirmed by results of the calculation
shown in Fig. 5 for two groups of positrons. Oneof them contains positrons having momentum in theinterval p 2 8:5–11:5 Mev=c, for another group p 2
17–23 Mev=c.
For the given target, the width of the angular distribution of positrons with p 10 Mev=c is approximately
twice as much that for p 20 Mev=c as expected. The
width of every distribution evidently increases when wego on to the thicker target of the same kind. Comparing
angular distributions from crystal and amorphous targetsof the same thickness, we find that at L  9:0 mm the
distributions are somewhat (about 1:5 ) wider in the
crystal case for both groups. In units of FWHM ofthe distribution from the crystal target these differences

2

3

4

5

6

7

Target thickness ( mm )

8

9

(b)

0.03

0.02

0.01

0.00

0

1

2

3

4

5

6

7

8

9

Target thickness ( mm )FIG. 6. Positron production efficiency from crystal (a) and amorphous (b) targets dependingon thickness. Open symbols: our calculation; filled symbols: results from Fig. 5 of [16]; open
triangles are for p  20 Mev=c, open circles are for p  15 Mev=c, and open squares are forp  10 Mev=c.

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PRST-AB 5

COMPARISON OF THEORY WITH EXPERIMENT FOR . . .
TABLE I.
Momentum(MeV=c)101520Enhancement of the positron yield from crystal targets.

Enhancement(2.2 mm thick)
TheoryExperiment

Enhancement(5.3 mm thick)
TheoryExperiment

Enhancement(9.0 mm thick)
TheoryExperiment

6:0  0:5
5:5  0:3
5:4  0:2

3:2  0:3
3:2  0:2
2:9  0:1

2:1  0:2
2:0  0:1
1:8  0:1

6:5  0:6
6:2  0:8
5:1  0:5

when we determined the PPE numbers from Fig. 5 of [16].
Note that the experimental numbers obtained in such away, which are presented by filled symbols in Fig. 6, do
not reproduce exactly the whole set of mean experimental
values for the enhancement given in Table I of [16].
Moreover, in Fig. 5 of [16] there are no experimental
points for 2.2 and 5.3-mm-thick amorphous targets. For
these two cases, we present in Fig. 6 the values of PPE
given by smooth-curve fits corresponding to simulation
fitting in Fig. 5 of [16]. Bearing all this in mind, we,nevertheless, can assert that a rather good agreement isseen in Fig. 6 of the experimental results and our estimations. A relative difference of them is better than 13%
everywhere except the values of PPE at p  10 and
15 Mev=c from both thinnest (L  2:2 mm) targets,where the experimental yield is underestimated by 19%
to 42%. Note that just for this thickness the largest
inaccuracy was introduced while determining the PPE
numbers from Fig. 5 of [16] at p  10 and 15 Mev=c, as
the magnitude of the yield is especially small in this case.
In contrast to the magnitude of the positron yield, theenhancement is not very sensitive to the acceptance conditions. The calculated values of the enhancement(theory) are presented in Table I along with those takenfrom Table I of [16] (experiment). Purely statistical errors
are figured in Table I as theoretical ones. The relative error
1=2
in PPE was estimated as Nef, where Nef is the mean
number of events in the phase space corresponding to theacceptance conditions used in calculations. The total
statistics was chosen so that approximately to equalize
values of Nef for amorphous and crystal targets of thesame thickness. At given total statistics, the quantity Nef
increases with growing positron momentum in accord
with a shape of the positron spectra at hard collimation
shown in Figs. 2 and 3. This fact leads to a better statistical accuracy for larger momentum. We emphasize thatthe differences of the estimated and experimental enhancement values are smaller than corresponding experimental errors for all momenta and samples figured inTable I.
III. CONCLUSION
Using the simple computer code suggested in [11,12],
we have compared the theoretical predictions for somecharacteristics of the electromagnetic shower developingin axially aligned crystals with experimental results re121001-6

121001 (2002)

3:4  0:7
3:2  0:5
3:0  0:5

2:3  0:4
2:0  0:2
1:8  0:2

ported in [13,14,15,16]. On the whole, theory and experiment are consistent within the experimental accuracy.
From this comparison we also conclude that the accuracy
provided by the existing simplified code is at least better
than 20%. This accuracy may be slightly improved if we
include into consideration some processes like annihilation of positrons or Compton scattering of photons whichwere ignored as corresponding cross sections are small inthe energy region of interest. However, the approximatecharacter of the radiation spectra at axial alignment usedin our calculations still provides the main theoreticaluncertainty. Nevertheless, we believe that the level ofthe accuracy already achieved in the theoretical description is quite sufficient to make a reliable choice for
optimal parameters of the positron source using axiallyaligned single crystals.
ACKNOWLEDGMENTS
We are grateful to Professor H. Okuno for providing uswith details of the experiment [16] and to the authors of[14] for numerous fruitful discussions. Support of thiswork by the Russian Fund of Basic Research under Grants
No. 00-02-18007, No. 01-02-16926, and No. 01-02-22003
is also gratefully acknowledged.

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Status Solidi (b) 133, 583 (1986).
[2] R. Chehab et al., in Proceedings of the IEEE Particle
Accelerator Conference, Chicago, 1989 (IEEE,
Piscataway, NJ, 1989), pp. 283–285.
[3] V. N. Baier and R. Chehab, Positron Source based on
Channeling Radiation, Proposal for an Experiment at
Orsay, LAL, Orsay, France, 1990 (unpublished).
[4] V. N. Baier, V. M. Katkov, and V. M. Strakhovenko, Sov.
Phys. Usp. 32, 972 (1989).
[5] V. N. Baier, V. M. Katkov, and V. M. Strakhovenko,
Electromagnetic Processes at High Energies inOriented Single Crystals (World Scientific, Singapore,1998).
[6] V. N. Baier, V. M. Katkov, and V. M. Strakhovenko, Nucl.
Instrum. Methods Phys. Res., Sect. A 250, 514 (1986).
[7] V. N. Baier, V. M. Katkov, and V. M. Strakhovenko, Nucl.
Instrum. Methods Phys. Res., Sect. B 27, 360 (1987).
[8] R. Medenwaldt et al., Phys. Lett. B 227, 483 (1989).
[9] V. N. Baier, V. M. Katkov, and V. M. Strakhovenko, Nucl.
Instrum. Methods Phys. Res., Sect. B 119, 131 (1996).

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V. N. BAIER AND V. M. STRAKHOVENKO[10] V. N. Baier, V. M. Katkov, and V. M. Strakhovenko, Phys.
Status Solidi (b) 149, 403 (1988).
[11] V. N. Baier and V. M. Strakhovenko, Nucl. Instrum.
Methods Phys. Res., Sect. B 155, 403 (1999).
[12] V. N. Baier, V. M. Katkov, and V. M. Strakhovenko, Nucl.
Instrum. Methods Phys. Res., Sect. B 103, 147 (1995).
[13] R. Chehab et al., in Proceedings of the LINAC2000,
Monterey, CA, 2000 (Stanford Linear Accelerator
Center, Stanford, CA, 2000), p. 143.

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121001 (2002)[14] R.Chehab et al., in Proceedings of the RREPS-01
Conference, Lake Aya, Russia, 2001 [Nucl. Instrum.
Methods Phys. Res., Sect. B (to be published)].
[15] M. Inoue et al., Nucl. Instrum. Methods Phys. Res., Sect.
B 173, 104 (2001).
[16] H.Okuno et al., in Proceedings of the RREPS-01
Conference, Lake Aya, Russia, 2001 (Ref. [14]); KEK
Report No. 2001-146, 2001.

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