Proceedings of the Mini-Workshop on

Channeling Radiation Phenomena and Positron Production
17 January, 2003, KEK, Tsukuba
Editors
Tsuyoshi Suwada and Masanori Satoh
KEK, High Energy Accelerator Research Organization,
Oho 1-1, Tsukuba, Ibaraki, 305-0801 Japan
Physical processes for channeling radiationand coherent bremsstrahlung
CrystalNucleus

Beam

ChannelChanneling Radiation

Coherent BremsstrahlungA mini-workshop on “Channeling Radiation Phenomena and Positron Production”
has been held at KEK on 17 January 2003. Six talks (theory 2, design 2, experiment 2)
were presented.
The channeling radiation in crystal material is well known from old days. The
application to positron-production source of high-energy electron accelerators was
proposed in 1989 by R. Chehab, et al. in Orsay. In Japan, Yoshida, et al. at INS ofTokyo University (at that time) started to carry out a proof-of-principle experiment on
the positron production through the channeling radiation phenomena in a crystal target.
Since then, these two groups have been continuing the experimental research in order toinvestigate the application to the high-intensity positron source for the next generation
linear colliders and B factories.
On the other hand, the theoretical unified formulation is now under way on thepositron production scheme through electromagnetic-shower development bychanneling radiation along with classical bremsstrahlung and coherent bremsstrahlung
processes. Thus, it is a very interesting theme to understand theoretically andexperimentally the channeling radiation phenomena as an elemental physical process.
From the applicative point of view, the channeling radiation phenomena are investigated(or utilized) for cooling of charged particles, bending of a proton beam, andpolarization/polarimetry of charged particles, etc. and its application extends widely toanother area.
This workshop was held to discuss, exchange and summarize present theoretical andexperimental ideas on the channeling radiation phenomena and positron production by
the experts. We expect that the channeling phenomena in crystal will further be studied
and extend its area widely.
These proceedings were compiled by Tsuyoshi Suwada and Masanori Satoh of KEK.

Tsuyoshi Suwada
Accelerator Laboratory, KEK
20 February, 2003

Mini-workshop on Channeling Radiation Phenomena andPositron Production(January 17, 2003 at KEK)

Program(1) V. N. Baier (BINP)
Comparison of theory with experiment for positron production from high energy electrons
moving along crystal axes.

(2) T. Suwada (KEK)
Positron-production experiment using Diamond and Si crystals in the KEKB 8-GeV linac.

(3) R. Hamatsu (Tokyo Metropolitan Univ.)
Review of the positron production experiment using axial channeling at the KEK.

(4) T.Kamitani (KEK)
Positron source design in Japan linear collider.

(5) A. Potylitsyn (Tomsk Univ.)
Comparison of undulator-based and crystal-based positron sources.

(6) H. Nitta (Tokyo Gakugei Univ.)
Semiclassical Theory of Crystal-Assisted Pair Production:
Beyond the Constant Field Approximation.

Presentation paperPositron-production experiment using
Diamond and Si crystals in the KEKB
8-GeV injector linac

T.Suwada (tsuyoshi.suwada@kek.jp)
Accelerator Laboratory, KEKCollaboration
S.Anami, A.Enomoto, K.Furukawa, K.Kakihara,
T.Kamitani,Y.Ogawa, S.Ohsawa, T.Oogoe, M.Satoh,T.Sugimura, T.Suwada and K.Yoshida
Accelerator Laboratory, KEK
H.Okuno,Institute of Particle and Nuclear Studies, KEK
K.Umemori,Institute of Materials Structure Science, KEK
R.Hamatsu, J.Hara
Physics Department, Tokyo Metropolitan University
V.Ababiy, A.P.Potylitsin, I.E.Vnukov,
NPI, Tomsk Polytechnic University
R.Chehab,
LAL, IN2P3-CNRS, Universite de Paris-Sud
KEK Linac/
Tsuyoshi Suwada

e+ Production Mini-Workshop@KEK,
17/Jan,2003

Motivationz High-intensity positron sources are required
for future linear colliders and B-factories.
z Conventional methods using amorphousheavy metals limit to increase the intensity ofprimary electron beams due to the heat loadon the target.
z New method using the processes of coherent
bremsstrahlung (CB) and channelingradiation (CR) is one of the bright schemes
for high-intensity e+ production.
KEK Linac/
Tsuyoshi Suwada

e+ Production Mini-Workshop@KEK,
17/Jan,2003

Introductionz New method utilizing a crystal target was
proposed by Chehab, et al. In 1989.
(R. Chehab, et al., PAC’89, Chicago, IL, USA,
Mar. 1989, p.283)
z Yoshida, et al., demonstrated a clear
enhancement of the e+ yield in a tungsten
crystal target using a 1.2-GeV electron beam.
(K. Yoshida, et al., Phys. Rev. Lett. 80, 1437,
1998)
KEK Linac/
Tsuyoshi Suwada

e+ Production Mini-Workshop@KEK,
17/Jan,2003

Introduction (cont’d)z A series of e+ production experiments basedon the new scheme has been continued,⇒by Yoshida(Hiroshima/KEK), et al.,using 1.2-GeV e- beam of the ES at KEK-Tana branch,
3-GeV e- beam at e+ station, and e- beam(<8GeV) atthe end station of the KEKB injector linac.

⇒by Chehab(LAL), et al.,using 5-40 GeV secondary e- beam at CERN-SPS.

KEK Linac/
Tsuyoshi Suwada

e+ Production Mini-Workshop@KEK,
17/Jan,2003

Introduction (cont’d)z Theoretically unified treatment taking into
account both processes of CR and CB has not
yet been established on the simulation.
z More experimental data are expected toclearly understand the elementary physicalprocesses of the CR and CB, and they arealso required to develop the design of a realtype positron source.

KEK Linac/
Tsuyoshi Suwada

e+ Production Mini-Workshop@KEK,
17/Jan,2003

Historical View of the KEK Experiments
Month/Year
May/1997

KEK Tanashi, ES

1.2

Crystal W (Wc) [1.2]Apr, Jun/1998

KEK Tsukuba,3

Wc [1.7]

Electron Linac
Nov/1998

KEK Tanashi, ES+ Amor. W (Wa) [7]
Wc [0.4, 1.2, 2.2],

0.6, 0.8, 1

GaAs [0.36], Diamond[1.1]
Sep, Oct/2000

KEK Tsukuba,8

Wc [2.2]+Wa [5, 10, 15]Electron Linac
Apr/2001

KEK Tsukuba,

Wc [2.2],

8

Wc [2.2], Wc [9]Electron Linac
Sep/2001

KEK Tsukuba,

Wc [9]+Wa [2, 4]
8Combined targets(Wc +Wa)

Electron Linac
Jan/2002

KEK Tsukuba,

4

KEK Tsukuba,

Wc [2.2], Wc [5.3], Wc [9]Combined targets(Wc +Wa)

Electron Linac
Aug-Sep/2002

Wc [2.2], Wc [5.3], Wc [9]8Electron Linac

Si <110> 2.6, 30, 48
Diamond <110> 4.57
Combined (Si/Dia.+Wa)

Dec/2002

KEK Tsukuba,
Electron Linac

8

Si <110> 10, 30, 48
Diamond <110> 4.57
Combined (Si/Dia.+Wa)

KEK Linac/
Tsuyoshi Suwada

e+ Production Mini-Workshop@KEK,
17/Jan,2003

Channeling Radiation & Coherent
Bremsstrahlung Processes
Physical processes for the channeling radiation andcoherent bremsstrahlung
CrystalNucleus

ChannelBeam
Critical Angle of
Channeling Radiation

Channeling Radiation

F c=(2U0/Eb)1/2~0.43mrad@Eb=8GeV
U0:Potential Energy of a Channel
Eb:Beam Energy

Coherent Bremsstrahlung
KEK Linac/
Tsuyoshi Suwada

e+ Production Mini-Workshop@KEK,
17/Jan,2003

New Positron Production Schemes

KEK Linac/
Tsuyoshi Suwada

e+ Production Mini-Workshop@KEK,
17/Jan,2003

Experimental Setup
Goniometer

Positron Detectors
Lead-Glass Cherenkov Calorimeter
Lucite Cherenkov Detector{V
e- Beam

TargetLead Shield

+

H

+

X
-

+

A

e+

+

Targete- Beam

Wall-Current Monitor

KEK Linac/
Tsuyoshi Suwada

Screen Monitore+eVacuum Chamber
Analyzer Magnet

e+ Production Mini-Workshop@KEK,
17/Jan,2003

Linac Beam Line at the 3rd switch yard

KEK Linac/
Tsuyoshi Suwada

e+ Production Mini-Workshop@KEK,
17/Jan,2003

Experimental Setup (cont’d):Photo pictureof a crystal target on a goniometer

KEK Linac/
Tsuyoshi Suwada

e+ Production Mini-Workshop@KEK,
17/Jan,2003

Experimental Setup (cont’d):Photo pictureof crystal & amorphous targets

KEK Linac/
Tsuyoshi Suwada

e+ Production Mini-Workshop@KEK,
17/Jan,2003

Experimental Setup (cont’d):Positron
spectrometer

KEK Linac/
Tsuyoshi Suwada

e+ Production Mini-Workshop@KEK,
17/Jan,2003

Acceptance of the Positron SpectrometerPe+

Acceptance (∆P∆Ω)(MeV/c)(10-4 x (MeV/c)•sr)

51.08 ± 0.03

10

2.47 ± 0.07

15

3.80 ± 0.1

204.81 ± 0.12

KEK Linac/
Tsuyoshi Suwadaz The acceptance (∆P∆Ω) was obtained byusing the simulation
code (GEANT3).
z Typical acceptance
Momentum:∆P/P=2.4% (FWHM)&
Geometrical:∆Ω=1msr
at Pe+=20MeV/c.

e+ Production Mini-Workshop@KEK,
17/Jan,2003

Experimental Condition
Electron Beam:• Beam Energy = 8 GeV• Angular Spread ~22 µrad (H), ~44 µrad (V)• Transverse Beam Size ~0.8mm (FWHM) in diameter• Beam Charge = 0.1 nC/bunch• Bunch Length (Single Bunch) ~9 ps (FWHM)• Beam Repetition = 25Hz
Angular Spread of the Electron Beam at the Positron Target• Φ ~ 55 µrad < Φc (due to multiple scattering by a beam-extraction
vacuum window(30µm-thick SUS))
Critical Angle for the Channeling Condition at the Positron Target
Linhard Crytical Angles• Φc ~ 170µrad @8 GeV for Silicon Crystal• Φc ~ 130µrad @8 GeV for Diamond Crystal

KEK Linac/
Tsuyoshi Suwada

e+ Production Mini-Workshop@KEK,
17/Jan,2003

Experimental Condition (cont.)
Positron-Production Targets:• Crystal Silicon Target : 2.55, 9.9, 29.9 and 48.15mm thickness• Crystal Diamond Target : 4.57mm thickness• Amorphous Tungsten Target: 3-18mm (3mm step) thickness (forthe purpose of hybrid targets and for the e+ production yieldcalibration)
Detected Momentum Range:• 10 MeV/c ≤ Pe+ ≤ 30 MeV/c
Positron Detectors•Lead-Glass Calorimeter:Measurement of total energy of e+•Acrylic Cherenkov Counter:Measurement of number of e+
Beam Monitors•Wall-current monitor for the electron beam-charge measurement•Screen monitor for the beam-profile measurement

KEK Linac/
Tsuyoshi Suwada

e+ Production Mini-Workshop@KEK,
17/Jan,2003

Experimental Results:
2-Dimensional Axis Scan for 5mm-thick Diamond
Crystal at Ee-=8 GeV (Pe+=20MeV/c)

KEK Linac/
Tsuyoshi Suwada

e+ Production Mini-Workshop@KEK,
17/Jan,2003

Experimental Results:
2-Dimensional Axis Scan for 30-mm thick Si
Crystal at Ee-=8 GeV (Pe+=20MeV/c)

KEK Linac/
Tsuyoshi Suwada

e+ Production Mini-Workshop@KEK,
17/Jan,2003

Experimental Results:
Rocking Curves (Axis <110>) for 5mm-thick
Diamond and 30mm-thick Si Crystals at Ee-=8
GeV (Pe+=20MeV/c)

KEK Linac/
Tsuyoshi Suwada

e+ Production Mini-Workshop@KEK,
17/Jan,2003

Experimental Results:
Variations in the width of the rocking-curve peakfor Ee-=8 GeV (Pe+=20MeV/c)σ)[mrad]Rocking-Curve Peak Width (1σ2Preliminary

Si Crystal
Diamond Crystal+

Pe =20MeV/c
1.5

1

0.5

0
0

0.1

0.2

0.3

X
KEK Linac/
Tsuyoshi Suwada

0.4

0.5

0

e+ Production Mini-Workshop@KEK,
17/Jan,2003

0.6

Experimental Results:
Variations in the enhancement (Ne+@peak/ Ne+@base)of the e+ yield at Ee-=8 GeV (Pe+=20MeV/c)
Crystal Thickness vs. Enhancement
20

Preliminary

SiliconDiamond16+

Enhancemnet

Pe =20MeV/c
12

8

4

0

0.1

0.2

0.3

X
KEK Linac/
Tsuyoshi Suwada

0.4

0.5

0

e+ Production Mini-Workshop@KEK,
17/Jan,2003

0.6

Experimental Results:
Positron momentum dependence for the e+ yieldenhancement at Ee-=8 GeV
Positron Momentum Dependence
25

Preliminary+
Pe =20MeV/c

1 0mm Si
3 0mm Si
50mm Si
5mm Diamond

Enhancement

20

15

10

5

0
5

10

15

20

25

30

+

Pe [MeV/c]
KEK Linac/
Tsuyoshi Suwada

e+ Production Mini-Workshop@KEK,
17/Jan,2003

35

Experimental Results:
Variations of the e+ production yield for theamorphous tungstens and off-axis crystal targets
at Ee-=8 GeV (Pe+=20MeV/c)++

Normalized e Yield from Off-Axis Combined Target

Normalized e Yield from W Target

400

400

Preliminary+350

Pe =20MeV/c

Positron Yield [Arbitrary Unit]

Positron Yield [Arbitrary Unit]

Preliminary
300
250
200

Normalization

150

10mmSi
30mmSi
50mmSi
5mmDiamond

100
50

350

+

Pe =20MeV/c

300
250
200
150

10mmSi
30mmSi
50mmSi
5mmDiamond

100
50
0

0
0

5

10

15

20

0

1

W Thickness [mm]
KEK Linac/
Tsuyoshi Suwada

e+ Production Mini-Workshop@KEK,
17/Jan,2003

2

3

X

4

0

5

6

Experimental Results:
variations of the e+ production yield for the onaxis crystal targets at Ee-=8 GeV (Pe+=20MeV/c)+

Normalized e Yield from On-Axis Combined Target
400

Positron Yield [Arbitrary Unit]

Preliminary350+

Pe =20MeV/c

300
250
200
150

10mmSi
30mmSi
50mmSi
5mmDiamond
W Base e+ Yield

100
50
0
0

1

2

3

X

KEK Linac/
Tsuyoshi Suwada

40
e+ Production Mini-Workshop@KEK,
17/Jan,2003

5

6

Experimental Results:
Variations of the e+ production enhancement forthe crystal targets at Ee-=8 GeV (Pe+=20MeV/c)
Thickness (in Total) vs.Enhancement
20

Preliminary+

Pe =20MeV/c

Enhancement15

2 .2mmWCrystal
5.3mmWCrystal
9mmWCrystal
Reference

10

5

0
0

1

2

3

X

KEK Linac/
Tsuyoshi Suwada

40
e+ Production Mini-Workshop@KEK,
17/Jan,2003

5

6

Experimental Results:
Crystal effects for the Diamond and Si crystal
targets at Ee-=8 GeV (Pe+=20MeV/c)
Crystal Effect6

iliconiamond+Pe =20MeV/c

5.5

at Shower Maximum0

Thickness[X ] of a Combined Target

Preliminary

5

Thickness at Shower Maximum (W base)

4.5

4Palabora Fitting

3.5

3
0

0.1

0.2

0.3

X
KEK Linac/
Tsuyoshi Suwada

00.4

e+ Production Mini-Workshop@KEK,
17/Jan,2003

0.5

0.6

Experimental Results:
Multiple Scattering Effect of the Vacuum
Windows Using the Diamond crystal at Ee-=8
GeV (Pe+=20MeV/c)
Multiple Scattering Effect
5mm Diamond Crystal

120
Width[mm]Enhancement

Enhancement

15
0.8

0.7
10

0.6

Preliminary+
Pe =20MeV/c
5
0

0.1

0.2

0.3

0.4

0.5

0.5
0.6

Thickness of Vacuum Window (SUS304) [mm]
KEK Linac/
Tsuyoshi Suwada

e+ Production Mini-Workshop@KEK,
17/Jan,2003

Rocking-Curve Peak Width [mm]0.9Conclusions♠Positron production experiment using Diamond andSilicon crystal targets has been successfully performedat the KEKB 8-GeV electron linac.
♠Rocking curves⇒ The obtained widths of the rocking-curve peak islarger than the critical angle,⇒ and broaden with the thickness of the crystal target.
⇒ These broad width of the rocking curves indicate that
coherent bremsstrahlung is the predominant process
over the channeling radiation process in this energy
region.
⇒ The increase of the peak width depending on thetarget thickness may come from the multiple
scattering of the incident electrons in the target.
KEK Linac/
Tsuyoshi Suwada

e+ Production Mini-Workshop@KEK,
17/Jan,2003

Conclusions (cont’d)♠Enhancement (En) and momentum dependence of the e+ yieldfor the crystal target alone from 8-GeV channeling electrons at a e+
momentum of 20MeV/c⇒ En= 9.3 ±0.5 (9.9-mmSi), 9.9 ±0.5 (29.9-mmSi),⇒ En= 6.4 ±0.3 (48.15-mmSi), 16 ±0.8 (4.57-mmDiamond)• The enhancement is much reduced with an increase of the total target
thickness.
• No crystal effect enhances the e+ yield at the target thickness larger than
~4.2 X0 in total.
•The e+ yields with Pe+=20MeV/c at Ee-=8GeV were almost the same level
as the maximum e+ yield obtained for the amorphous tungsten target.

♠New scheme using the combined crystal target indicates that heatload in the amorphous tungsten part of the target could beconsiderably reduced due to a small amount of the energy loss intotal.
⇒ It is of great benefit to apply such a crystal target to a high-intensity e+source required for high-luminosity e+e- colliders and B-fatories.
KEK Linac/
Tsuyoshi Suwada

e+ Production Mini-Workshop@KEK,
17/Jan,2003LC e+ sources
By Takuya Kamitani
At Channeling e+ source Workshop
2003.Jan.17 at KEKComparison of the LC e+ sources1.4

Number of Beam-Pulses exposed [106]Target Destruction Issue
Energy density limit= 2.0 GeV*10 12 /mm 2

1.2

A1

1
0.8

G

E

A2

Survived targets
Cracked targets

B1

0.6
0.4

D1
F2

D2
0.2
0

B2

F1

0

1

2

3

Beam Energy density per area [GeV*10412/mm 2 ]

W75Re25 targets were irradiated by 20GeV, 16-nC e- beam at SLAC. Bychanging the beam spot size, theenergy density threshold for thedestruction was studied.
(S. Ecklund, SLAC-CN-128, 1981)Local volume Energy Density
SLAC Limit condition

CLIC Design

Local volume density is more essential
for the destruction.

Redection of energy density
by enlarging the beam spot size
[ 10^10 GeV / mm^3 ]Peak deposit-Energy density per volume

10**19eV/mm3/pulse
SLAC-limit(EGS4 simulation)

1.6

Energy density Limit
expected fromSLAC Experiment

1.2

e = 76 J/g
0.8

Recent Limit
expected from
SLC failed targete = 35 J/g
0.4

CLIC design
0

0

0.5

1

1.5

2

Incident Beam radius [mm]2.53Multiple Target system
From http://www-project.slac.stanford.edu/lc/wkshp/snowmass2001/

A bunch train is separated into 3 sparse trains by the RF separator
 Each trains hit one of the three target - capture section system They are merged by another RF deflectorTESLA e+ source

Beam intensity in a pulse is too large
to irradiate directly the target material.
Instead, very high energy e- beam andundulator are used to generate
20 MeV photons.
Target material is very thin (0.4 X0) to
reduce the energy deposition, however,
sufficient for the low energy photons.

JLC Positron Source
DC Solenoid

Flux concentrator
Rotating
Converter
TargetPositrons
Primary
ElectronsE(e-) = 10 GeV
N(e-) = 192x10^10150 Hz Rep. Rate

L-band Accelerating
structure•W75Re25 target•Thickness 6.0 X0(=21mm)•Adibatic matching system
Bi = 7.0 T, Bf = 0.5 T•L-band capture section
up to 180 MeV•S-band Linac
up to 1.98 GeV•Pre-damping ring andMain damping ringat 1.98 GeV

Target Thickness Optimization
Target Thickness vs Positron Yield

0.2

Positron Yield (Ne+/Ne-/Ee-) [1/GeV]

Ne+/Ne-/Ee-[1/GeV]
E(e-) = 10.0 GeV
N(e-) = 192. x 10 10 /pulse

0.15

0.1

0.05

0

0

1

2

3

4

5

6

7

Target Thickness [x80]Total Energy Deposition
Target Thickness vs Energy Deposition Fraction
Total Energy Deposition / Beam Power

Total Energy Deposition / Beam Power

0.5

0.4

E(e-) = 10.0 GeV
N(e-) = 192. x 10 10 /pulse

0.3

0.2

0.1

0
0

1

2

3

4

5

6

7

Target Thickness [x80]30% of Beam Power is deposited on the target

Local volume Energy density
100

E(e-) = 10.0 GeV
N(e-) = 192. x 10 10 /pulse

Energy deposit density [Joule/gram]

90

Target Thickness
80= 6.0 x 0

70
60
50
40
30
1 target2 targets
3 targets
4 targets
SLC Limit

20
10
0
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Incident e- beam size ( σ =σY) [mm]X

To makethe peak energy denisty
below the destruction limit,
very large spot size or multiple
target system is necessary.

Positron Yield vs Beam spot size

Positron Yield at PDR (Ne+/Ne-)

1.5

E(e-) = 10.0 GeV
N(e-) = 192. x 10 10 /pulse

1.25

Target Thickness= 6.0 x 0

3

4.5

1

0.75

0.5

0.25

0
0

1 target (sig-x=4.8)
2 targets (sig-x=3.2)
3 targets (sig-x=2.5)
4 targets (sig-x=2.1)
Design Yield
0.5

1

1.5

2

2.5

3.5

4

5

Incident e- beam size ( σ =σY) [mm]X

With large spot size, thepositron yield is lower.
Single or 2 target system
is not acceptable. At least,
3 target system isnecesarry.

Positron Yield Estimation
2020(Tracking simulation)
targetFC aperture
positrons

2000

After SBECS(PDR acceptance)Longitudinal acceptance = 24 mm
Energy acceptance = +/- 1.0 %20Particle Energy [MeV]Particle position in Radius [mm]2515Flux Concentrator
10

Target

1980

1960

1940

1920

5
1900

0

-8

0

8

16

24

32

Distance from target exit [mm]

40

48

1880
-50

-40

-30

-20

-10

0

10

Particle position in a bunch [mm]

 Positron Generation at target (EGS4)
 Positron Tracking in the capture section (SOLEIL)
 Positron Tracking in the e+ 1.98-GeV linac (SAD) Elimination with Pre-damping Ring acceptance(both in transverse and longitudinal phase space )Proposals to Channeling Experts
Design Goal of Channeling target for JLC
to replace W75Re25 to crystal
Comparable positron yield with
1/3 of Peak energy density

Search for the target material (crystal or hybrid)
which generates sufficient positrons andcomfirm it experimentally
 Establish the channeling simulation code whichis consistent with the experimentsTo generate sample particles for realstic yield estimation
To estimate the energy density distribution in the targetSummary paperFig. 1

Fig. 2

Fig. 3Fig. 4

Fig. 5(a)(b)
Fig. 6(a)(b)
Fig. 7(a)(b)
Fig. 8(a)(b)
Fig. 9(a)(b)
Fig. 10(a)(b)
Fig. 11

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

121001-1

 2002 The American Physical Society

1098-4402=02=5(12)=121001(7)$20.00

121001-1

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
121001-2

121001 (2002)
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
121001-2

PRST-AB 5

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

121001 (2002)

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).

121001-3

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PRST-AB 5

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.

121001-4

121001-4

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.

121001-5

121001-5

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.

[1] V. N. Baier, V. M. Katkov, and V. M. Strakhovenko, Phys.
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).

121001-6

PRST-AB 5

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.

121001-7

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.

121001-7

POSITRON-PRODUCTION EXPERIMENT USING SILICON AND
DIAMOND CRYSTALS IN THE KEKB 8-GEV INJECTOR LINAC
Tsuyoshi Suwada†, KEK, Tsukuba, Ibaraki, 305-0801 Japan.

Abstract
Intense positron sources are widely investigated forthe next-generation of linear colliders and B-factories. A
new method utilizing an axially-oriented crystal as apositron-production target is one of the bright schemes
since it provides a powerful photon source throughchanneling and coherent bremsstrahlung processes whenhigh-energy electrons penetrate the target. A series of
positron-production experiments with heavy and light
crystals hit by 4 and 8-GeV single-bunch electron beams
have been carried out at the KEKB 8-GeV injector linac.
This report gives the brief summary on the positronproduction experiment using silicon and diamond
crystals carried out in December 2002 at KEK. Later thereport based on the more precise analysis will be
published elsewhere.

1 INTRODUCTION+

For future e e - linear colliders and high-luminosity Bfactories, it is critically important to develop a highintensity positron source. In a conventional method using
an amorphous heavy-metal target, the target thickness is
optimized by taking into account the electromagnetic
shower process and the positron capture efficiency in the
succeeding acceleration section. The optimum thickness
is 4-5 X0 (radiation length) for a 4-8 GeV electron beam.
In this case, the only possibility to increase the positron
intensity is to increase the incident electron intensity.
However, the electron intensity is limited due to a heatload on the target. One promising method utilizing acrystal target was proposed by Chehab et al. in 1994[1].
The benefit of this method is on its high positronproduction efficiency due to channeling radiation(CR)[2] and coherent bremsstrahlung (CB), since CR
and CB increase low-energy photons in the radiation
process. This results in a thinner target compared withthe conventional method. It is also expected that the thintarget relaxes its heat load, and that the spatial spread of
positrons due to multiple scattering in the target is
reduced. Yoshida et al. demonstrated a clear
enhancement of the positron yield in a tungsten crystal
target using a 1.2-GeV electron beam[3]. This new
scheme has been tested at the positron-production stationand the end station of the KEKB injector linac[4].
Chehab et al. also studied the positron yield from acrystal target for 5-40 GeV electrons at CERN-SPS[5].
Although a positron enhancement is observed, there______________________________________________†

E-mail address: tsuyoshi.suwada@kek.jp.

have so far been only a few experimental results over awide energy range of a primary electron beam.
On the theoretical side, various simulation studies havebeen carried out by various authors. Among them, Baier,
Katkov and Strakhovenko have developed the simulation
code of the electromagnetic shower formation at axialalignment of a crystal by using the semiphenomenological radiation spectrum[6]. This scheme
allows one to consider a positron-yield enhancement at
the relatively low energy range (a few GeV) of the initial
electrons, which is suitable for the B-factory injector.
The substantial enhancement of the positron yield fromcrystal targets is expected due to the increase in thenumber of relatively soft photons in comparison withthat from an amorphous target. Thus, more systematicand precise experimental data could help us tounderstand the complicated mechanism of theseelementary radiation processes and to design a highintensity positron source. A series of experiments[7,8] toinvestigate the positron yields using various crystal
targets are underway for an incident electron energy
lower than 8 GeV. The following table shows a historicalview of the positron-production experiments carried out
at KEK-Tsukuba and KEK-Tanashi branch.
Table 1: Historical view of the positron-production
experiments at KEK.
Month/Year Accelerator
E
Positron Target
[GeV]
[mm]
May/1997
Tanashi/ES
1.2
Crystal W (Wc)[1.2]Apr, Jun
KEK/Linac3
Wc[1.7] + Amor. W/1998(Wa)[7]
Nov/1998
Tanashi/ES0.6,
Wc[0.4, 1.2, 2.2],
0.8, 1
GaAs[0.36],
Diamond[1.1]
Sep, Oct
KEK/Linac
8
Wc[2.2],/2000
Wc[2.2]+Wa[5,10,15]
Apr/2001
KEK/Linac
8
Wc[2.2], Wc[9]Wc[9]+Wa[2, 4]
Sep/2001
KEK/Linac
8
Wc[2.2], Wc[5.3],
Wc[9]Combined targets
Jan/2002
KEK/Linac4Wc[2.2], Wc[5.3],
Wc[9]Combined targets
Aug-Sep
KEK/Linac
8
Si [2.6, 30, 48]/2002
Diamond[4.57]
Combined targets
Dec/2002
KEK/Linac
8
Si [10, 30, 48]
Diamond[4.57]
Combined targets

2 EXPERIMENTAL SETUP

detectors are installed in a vacuum chamber kept at a
vacuum pressure of 10-1 Pa.

2.1 Beam Line
Our experiment was performed in the beam switchyardof the KEKB 8-GeV injector linac (see Fig.1).

Figure 2: Schematic drawing of the experimental setup.

Figure 1: Photograph of the beam line and theexperimental setup viewed from the electron beam.
An electron beam with a pulse width of 10 ps (S-band
single bunch) and with an energy of 8 GeV impinged ona tungsten target at a repetition rate of 25 Hz. The beam
charge (~0.1 nC/bunch) was measured by a wall-current
monitor for each pulse. The transverse profile of theelectron beam at the target was monitored by a screen
monitor during the experiment. The transverse beam size
was 0.8 mm (FWHM) in diameter. The angular spreadsof the electron beam were expected to be about 22 and44 mrad in the horizontal (H) and vertical (V) directions
for the 8-GeV electrons, respectively. However, since theelectron beam impinged on the target after passing
through a vacuum window made of 30mm-thick stainlesssteel (SUS304), the angular spreads (H and V) of theelectron beam at the target were estimated to be 59 and70 mrad in total by taking into account the multiple
scattering at 8 GeV, respectively. The multiple scattering
effect of the vacuum window was investigated by using
SUS foils with several thicknesses. These angularspreads were less than the critical angles (170 mrad for Si
crystal and 130 mrad for Diamond crystal) of thechanneling condition at 8 GeV.

2.2 Experimental Setup
Figure 2 shows a schematic drawing of theexperimental setup. This comprises a positronproduction target mounted on a precise goniometer, amagnetic spectrometer, collimators, and two kinds ofpositron detectors (a lead-glass calorimeter and anacrylic Cherenkov counter). All of the collimators andIn this experiment, silicon and diamond crystals of<110> axis with different thicknesses were tested either
alone or in combination with an amorphous tungsten
plate (Wa). These Was’ with different thicknesses from 3
to 18 mm by 3mm steps are installed on a horizontal
movable stage 82.5 mm after the crystal target. Thesetungsten plates were also used to calibrate the positronyield without the crystal targets. The specification of thecrystal targets is summarized in Table 2.
Table 2: Tested crystal specification.
Elem. Denom. Thickness
X0[mm]
DiamondC
5mmDia4.57
0.0372
SiliconSi
2.5mmSi
2.55
0.0272
SiliconSi
10mmSi9.9
0.1058
SiliconSi
30mmSi
29.9
0.319
SiliconSi
50mmSi
48.15
0.514*1X0=123mm (Diamond), 1X0=93.6mm (Silicon). It
should be noted that the radiation length of anamorphous carbon (2.3 g/cm3) is different from that of adiamond crystal (3.5 g/cm3). This was pointed out by A.
Potylitsyn.
CrystalThe positrons emitted from the target in the forward
direction were momentum-analyzed in a momentum
range lower than 30 MeV/c by the magnetic field, where
the deflection angle was 60o from the beam axis. The
positron trajectory was determined by five collimators
installed before and behind the magnetic spectrometer.
The geometrical acceptance and momentum acceptanceis summarized in Table 3, which were calculated byusing the simulation code GEANT3.
The momentum-analyzed positrons were detected witha 3mm-thick acrylic Cherenkov counter and a lead-glass
calorimeter shielded by lead blocks. The lead blocks
suppressed any background caused by electromagnetic
showers generated upstream of the beam line due to theoff-momentum electrons, and caused by electromagnetic
showers generated at the collimators. Since the emitted
positrons were also shortly bunched, the number of
positrons per bunch was measured as a pulse charge fromeach detector. Signals from the positron detectors and thesignal of the electron beam charge were sent to a dataacquisition system using a PC-based CAMAC/ADC
system, where all signal charges were simultaneously
digitized. The goniometer could rotate the crystal target
around two axes (H and V axes) by a pulse motor. The
angular resolutions of the goniometer were 10.5 and 34.9
mrad/pulse in the H and V axes, respectively. The crystal
axis, <110>, was determined by changing the relativerotational angles around the two axes with a step of 2 (or1) mrad. The positron yields were measured for eachtarget as a function of the rotational angle of thegoniometer and as a function of the positron momentum.
Table 3: Acceptance of the positron spectrometer.
Pe+
Acceptance(MeV/c)(10-4 x (MeV/c∑sr))
5
1.08 ± 0.03
10
2.47 ± 0.07
15
3.80 ± 0.10
20
4.81 ± 0.12

3 EXPERIMENTAL RESULTS
3.1 Two-Dimensional Crystal Axis Scan
We developed a computer software which quickly
scans a crystal axis in two dimensional plane. The
scanning time (10~20 min depending on the step sizes)
was much reduced compared with that of the previous
one-dimensional scanning. Figures 3(a) and 3(b) show
the typical results of the crystal axis scanning measured
for the diamond and 30mm-thick silicon crystal,respectively, at the positron momentum of 20 MeV/c.
You can clearly see main sharp peaks for both the
crystals generated from the <110> axis orientation
together with many weak peaks. The main sharp peak
was formed as the intersecting point of the several lines(see the density distribution in the projected plane in
Fig.3). These weak peaks or lines may come from planechanneling in the crystal. It is interesting that the numberof the weak peaks for the diamond crystal is larger thanthat of the silicon crystal.

3.2 Rocking Curves
Figures 4(a) (for diamond) and 4(b) (for 30mm-thicksilicon) show the measured rocking curves at thepositron momentum of 20 MeV/c. You can see very
narrow peak widths for both the crystals. The peakwidths were obtained to be 0.7 (for diamond) and 1 mrad(for 30mm-thick silicon) in one sigma by the leastsquares fitting procedures with two gaussian functions.
Figure 5 shows the variation of the peak width as afunction of the crystal thickness in unit of X0. The peakwidth increases gradually with the increase of the crystal
thickness and its value is about 1 mrad level dependingon the crystal thickness.

3.3 Positron-Yield Enhancement
Figure 6 shows the result of the positron-yieldenhancement measurement for the crystal alone as afunction of the crystal thickness in unit of X0 at thepositron momentum of 20 MeV/c. The enhancement of
the silicon crystal changes by a factor of 8-14 dependingon the crystal thickness, and for the diamond it is about
17 which is clearly larger than that of the silicon crystals.
It means that the crystal effect of the diamond is larger
than that of the silicon.
Figure 7 shows the result of the momentum
dependence of the positron-production enhancement.
The enhancement is slightly dependent on the positron
momentum in the measured region.
Figure 8 shows the summarized result of theenhancement measurement together with the tungsten
crystal data, which were obtained from the previous
experiment. The result shows that although in the regionof the thin thickness the enhancement obtained for thelight crystals is a little bit high, in the region of the large
thickness the enhancement obtained for the tungsten
crystals is clearly higher. It is presumed that thechanneling photons generated from the light crystal aresoft, and thus, the positrons generated in the later
amorphous tungsten are absorbed and multiply scatteredin the target because they are also soft.

3.4 Positron Yields and Crystal Effect
The detected positron yields were calibrated by using
the data from the amorphous tungsten plates withdifferent thicknesses. Figure 9 (a) shows the variations of
the positron yield depending on the thickness of theamorphous tungsten plates alone, and they were obtained
as the positron-yield calibration data in each crystal
measurement. For all the amorphous tungsten data, thepositron yield was normalized by using the data of the
9mm-thick amorphous tungsten obtained in the 30mmthick silicon crystal measurement. Figure 9 (b) shows thevariations of the positron yield depending on the total
thickness in unit of X0, where the crystal axis was set in
the direction of off axis. These results show that thepositron-yield normalization was performed quite wellwithin the experimental accuracy.
Figure 10 shows the summarized result of thenormalized positron yield obtained for all the crystal
measurements. It is clearly found several following
things:∑∑The maximum positron yield is almost the samelevel compared with that of the amorphoustungsten except for the data of the 10mm-thicksilicon crystal.
The shower maximum thickness of each crystal isreduced compared with that of the amorphous∑

tungsten, which means that the radiation thickness
is effectively reduced.
The reduction of the shower maximum thicknessof the diamond crystal is relatively large
compared with other crystals although the
thickness of the diamond is thin.

Figure 11 shows the result of the crystal effect. If weplot the shower maximum peak thickness as a function of
the crystal thickness, we can estimate how large thecrystal effect is. For the silicon crystal, the effect issaturated around the thickness of 30 mm, and for the
diamond crystal, although we have only one data point,
the effect is larger than the silicon crystal. This resultshows that the maximum positron yield from the 5mmthick diamond crystal is almost the same level as that of
the 30mm-thick silicon crystal, which gives larger crystal
effect than that of the diamond even with a 5mmthcikness. We can expect higher positron-production
yield if we use a thicker diamond crystal.

3.5 Effect of the Vacuum Window
Figure 12 shows the result of the positronenhancement measurement depending on the thicknessof the vacuum window, where the diamond crystal alone
was used in this test. From the result, the enhancement isalmost constant up to the window thickness of 200 mm,
and the rocking-curve peak width slightly increases with
the increase of the window thickness. This may comefrom the increase of background generated at thewindow. It is noted that the window thickness of 100 mm
has been used in the previous channeling experiment.

4 SUMMARY
The positron-production experiment using diamondand silicon crystal targets has been successfully carriedout at the KEKB 8-GeV injector linac. The obtainedrocking peak widths are very narrow less than 1 mrad in
one sigma for both the crystals. For the crystal target
alone, the enhancements of the positron yield are 9.3±0.5(10mmSi), 9.9±0.5 (30mmSi), 6.4±0.3 (50mmSi), and
16±0.8 (5mmDiamond) at the positron momentum of 20
MeV/c. The enhancement is much reduced with theincrease of the total target thickness. The maximum
positron yields are the same level as the maximum yieldobtained for amorphous tungsten targets.

5 REFERENCES[1] R.Chehab, Orsay Report No. LAL/RT94-09, 1994.
[2] A.H.Sorensen and E.Uggerhoj, Scientific American
June (1989) 70.
[3] K.Yoshida, et al., Phys. Rev. Lett. 80, 1437 (1998).
[4] I. Abe, et al.,”The KEKB Injector Linac”; KEKPreprint-2001-157 (2001); To be published in NIM A.
[5] R. Chehab, et al., RREPS01, Lake Aya, Russia,
September 2001, published in NIM B103 (2003) 243.
[6] V.N. Baier, V.N. Katkov and V.M. Strakhovenko,
NIM B103 (1995) 147.
[7] H. Okuno, et al., RREPS01, Lake Aya, Russia,
September 2001, published in NIM B103 (2003) 259.
[8] T.Suwada, et al., Phys. Rev. E67, 016502 (2003).

(a)

(b)

(b)

Figure 4: Rocking curves measured for (a) the 5mmthick diamond and (b) 30mm-thick silicon crystal at thepositron momentum of 20 MeV/c.

Figure 3: Results of the two-dimensional axis scan for (a)the diamond and (b) silicon crystal. The software of theaxis scan was developed by Tokyo Metropolitan Univ.

(a)s)[mrad]Rocking-Curve Peak Width (1s2Preliminary

Si Crystal
Diamond Crystal+

Pe =20MeV/c
1.5

1

0.5

0
0

0.1

0.2

0.3

X

0.4

0.5

0.6

0

Figure 5: Variations of the rocking-curve peak width
measured for (a) the diamond and (b) silicon crystal as afunction of the crystal thickness at the positron
momentum of 20 MeV/c.

Thickness (in Total) vs.Enhancement

Crystal Thickness vs. Enhancement
20

20

Preliminary

Preliminary

SiliconDiamond16+

Pe =20MeV/c+

15

Enhancement

Enhancemnet

Pe =20MeV/c
12

8

2 .2mmWCrystal
5.3mmWCrystal
9mmWCrystal
Reference

10

5

4

0

0

0.1

0.2

0.3

X

0.4

0.5

0

0.6

1

2

3

X
0

Figure 6: Variations of the positron yield enhancement
depending on the crystal alone thickness in unit of X0 at
the positron momentum of 20 MeV/c.

Positron Momentum Dependence

4

5

6

0

Figure 8: Variations of the positron-yield enhancement
depending on the target thickness in total in unit of X0 at
the positron momentum of 20 MeV/c. The crystal
tungsten data with three different thicknesses are also
added.
(a)25

Preliminary+
Pe =20MeV/c

1 0mm Si
3 0mm Si
50mm Si
5mm Diamond

20+

Normalized e Yield from W Target
Preliminary

15

10

5

0
5

10

15

20

25

30

35

+

Pe [MeV/c]

Figure 7: Variations of the enhancement depending on
the positron momentum.

Positron Yield [Arbitrary Unit]

Enhancement

400

+

350

Pe =20MeV/c

300
250
200

Normalization

150

10mmSi
30mmSi
50mmSi
5mmDiamond

100
50
0
0

5

10

15

W Thickness [mm]

20

(b)
Crystal Effect+Normalized e Yield from Off-Axis Combined Target

6400

Preliminary+

Pe =20MeV/c

300
250

0

200
150

10mmSi
30mmSi
50mmSi
5mmDiamond

100
50
0
0

1

2

3

X

4

5

iliconiamond+Pe =20MeV/c

5.5

at Shower Maximum

350

Thickness[X ] of a Combined Target

Positron Yield [Arbitrary Unit]

Preliminary

5

Thickness at Shower Maximum (W base)

4.5

4Palabora Fitting

3.5

3

6

0

0.1

0.2

0.3

X

0

Figure 9: Variations of the shower development curve(positron yield) for (a) the amorphous tungsten plate
alone and (b) off-axis combined target depending on the
thickness of the combined target at the positron
momentum of 20 MeV/c.

0.4

0.5

0.6

0

Figure 11: Variations of the crystal effect for the diamondand silicon crystal depending on the crystal thickness.

Multiple Scattering Effect
5mm Diamond Crystal
120
Width[mm]Enhancement

Enhancement

400

Positron Yield [Arbitrary Unit]

Preliminary350+

Pe =20MeV/c

300
250

15
0.8

0.7
10

0.6

200

Preliminary+
Pe =20MeV/c

150

10mmSi
30mmSi
50mmSi
5mmDiamond
W Base e+ Yield

100
50

5
0

1

2

3

X

4

5

0.2

0.3

0.4

0.5

0.5
0.6

Thickness of Vacuum Window (SUS304) [mm]

0
0

0.1

Rocking-Curve Peak Width [mm]0.9+Normalized e Yield from On-Axis Combined Target

60

Figure 10: Shower development curves (positron yields)
measured for the diamond and silicon crystal as afunction of the combined target thickness in total at thepositron momentum of 20 MeV/c.

Figure 12: Vacuum-window thickness effect. The effectwas estimated by using two parameters “Enhancement”
and “Peak width” of the diamond crystal data as afunction of the thickness of the vacuum window.

COMPARISON OF UNDULATOR-BASED AND CRYSTAL-BASEDPOSITRON SOURCES.
A. Potylitsyn
Tomsk Polytechnic University,
Lenin ave., 2A, 634050, Tomsk, Russia

1. A positron source for linear collider has to provide the positron beam intensity
close to the electron beam one. Currently there are two approaches to construct a
positron source with the required parameters. First one is the conventional source
based on an electromagnetic cascade-shower process whereby a heavy-metal target
irradiated by high energy electrons from the linear accelerator [1,2]. Among thepositrons, only those which have transverse momentum and energy within a certain
range are accepted for the consequent acceleration. The target thickness is determined
to maximize the number of accelerated positrons, which depends on the incident
electron energy. The positron yield is naturally proportional to the incident electron
intensity, but when the intensity exceeds a certain limit, the target may be destroyed
due to the excessive heat load.
Second one is the rather new and based on the long undulator (∼100 m) where
electron beam with energy E 0 >100 GeV is generated the undulator radiation beamwith mean photon energy ω ~ 20 MeV. The photon flux is enough to create a few
positrons per each initial electron in the thin amorphous target (~0.4X 0 , X 0 isradiation length) [3,4]. In this case the heat power deposited in the target and,
consequently, temperature stress remain at the acceptable level.
An oriented crystal may be considered as some kind of a solid-state undulator withextremely low period. In principle, the appropriate crystal may be used as a “photon
emitter” instead undulator with huge length.
Experiments with electron energy E 0 ~ 1 GeV [5-7] demonstrated the possibility toobtain so-called channeling radiation in oriented crystal targets with thickness
t~ 0.1÷0.2 X 0 >> Ld (Ld stands dechanneling length [8]) to produce photon beam with
spectrum enriched by “soft” photons.
2. Let’s compare the main characteristics of radiation spectra for ordinary
bremsstrahlung (BS), coherent bremsstrahlung (CBS), and channeling radiation (CR).
Radiation losses for BS may be estimated as∆ EBS ≈

t
E ,
X0 0

t ≤ X0 .

(1)
1

The mean photon energy in the BS spectrum is:< ωbs > ≈∆E BS,
< N BS >(2)

where < N BS > is the mean number of photons emitted by electron [9]:t 0 dω
t
mc 2
t
=
ln
~ 10
< N BS > ≈∫X 0 γωp ω X 0
ωp
X0
E

(3)

Here γ is the Lorentz-factor, ωp is the plasmon energy of target material( ω p ≈ 30 eV for Al and Si). From (1), (2), (3) one may obtain< ω BS> ≈ 0.1 E0.

(4)

The mean energy for CR may be estimated as following (see [8]):V0 λ e< ωCR >
mc2 a s,≈u=
1 V0
E 0 − < ωCR >1+ γ 22 mc
2 γ1 / 2(5)where V0 is a potential of axis (or plane), a s is a screening radius, mc2 = 0.511 MeV,
λe = 3.86⋅10-13 m. For <111> axis of Si target and E 0 ~ 1 GeV < ωCR > ~ 15 MeV << ω BS >.
For a coherent bremsstrahlungu=< ω CBS >πγθ
~,E0 − < ω CBS >a(6)

θ stands orientation angle, a stands interplanar distance. As was shown in [5] thefirst Born approximation for a CBS theory may be used if θ >> θc =V0
. For anγmc2

axial orientation of a thick monocrystalline target the rough estimation of an angle θ
may be obtained as:
θ ~ < θms >=21 1 t
,E0 2 X0E 0 in MeV.

For instance, for Si, t=10mm and E 0 ~ 1 GeV < ωCBS > ~ 0.05 E0 ~ 50 MeV,
< ωCR > < < ω CBS> < < ω BS>.

(7)

For axial orientation radiation losses may be considered as consisting of two parts∆E = ∆E BS + ∆E cr ,where first term is connected with a radiation from amorphous target with the same
thickness, but second one is determined by coherent radiation processes (channelingradiation plus coherent bremsstrahlung). Ratio between these parts was measured forelectron energy E 0 = 900 MeV [10]:2∆E cr=∆E BS

diamond <100>t=10 mm

Silicon <111>
t= 10 mmtungsten <110>
t=1.2 mm

~ 2.5

~ 1.8

~ 1.5

Having in mind the relation (7) one may obtain:<Ncr> ≈
because of3.

∆E cr > ∆E BS , < ω cr >∆E cr>> <Ncr>< ωcr >

(8)

< < ω BS >.

Authors of experiment [11] that was carried out with electron energy E 0 = 10
GeV had measured the energy
losses
for
<111>
axial
orientation of Si crystals withthickness t = 0.8 and 3.0 mm(see Fig. 1). From Monte-Carlosimulation they obtained themean photon number (photon
multiplicity)< N >=< N BS > + < N cr >for each case:<N (0.8 mm)> = 1.8 ph/e-,<N (0.3 mm)> = 5.4 ph/e-.
Themeasurements
andsimulations were carried out for
the threshold photon energyωt = 20 MeV. The contributiontothemultiplicity
frombremsstrahlung is negligible(see eq. (4)):-3
Fig. 1. Radiation losses spectra for channeled electrons with
< N BS (0.8) >≈ 0.9⋅10 ph/e
E 0 = 10 GeV in Si crystal with thickness 0.8 mm (a) and 3.0-3< N BS (3.0) >≈ 3.2⋅10 ph/e ,mm (b). Solid lines are the simulation results [11].
In the paper [12] there wasproposed an approach to estimate the photon multiplicity from the measured
distribution of an energy losses(energy straggling). Disregarding by abremsstrahlung losses the photon multiplicity and the mean photon energy may be
estimated in the following manner [12]:< Q >2< N cr > ≈
σ2

(9)

3

<ω> ~∆E cr,< N cr >where < Q > is the mean value of the radiation losses calculated from energy losses
distribution, σ is the distribution variance, ∆E cr is the total energy losses for axial
orientation. Fitting the experimental results [11] by a smooth curve one may obtainfor t=3 mm (see Fig. 1).
<Q> ≈ 2.3 GeV, σ ≈ 1.1 GeV and, consequently:<Ncr> ≈ 4 ph/e- and <ωcr> = 0.2 GeV < <ωBS> = 1 GeV.
The multiplicity estimated from this model agrees with Monte-Carlo simulation
reasonably. The model of photon multiplicity developed in [7] gives for theconsidered case (E0= 10 GeV, t = 3 mm, Si <111>) (see Fig. 17.3 there):< N tot > ≈ 24 ph/e
It means there is a large contribution of the soft photons ( ω ≤ 1 MeV ).
Using the same approach let’s estimate thephoton multiplicity in the experiment [13].
This experiment was performed at theelectron beam with energy E0 = 4.5 GeV
for axial <111> orientation of the natural
diamond target with thickness t=10 mm(see Fig. 2a). Fig. 2b shows the fit by agaussian ( < Q > = 1660 MeV, σ = 536
MeV, ∆E cr = 1300 MeV), which gives thefollowing result:< N cr > ≈ 10 ph/e ,(10)< ωcr > ≈ 130 MeV.
It allows to think that photon multiplicity
may achieve the value < N cr > ~ 20 if one
shall use the electron beam with energy
E 0 ≈ 10 GeV and diamond target withthickness t ≈ 20 mm.
Data from Dubna’s experiment [14] showthat the radiation losses of 10 GeVelectron moving along <111> axis in the
10-mm silicon (~ 0.11 rad. length) reachFig. 2: a) Radiation losses spectra for channeled30%. According to [8] losses from adiamond crystal
electrons with E0 = 4.5 GeV inwith thickness 10 mm [13], b) Fit by a gaussian
diamond of the same radiation thickness
with <Q> = 1660 MeV, σ =536 MeV, ∆ E=1300
MeV.

(~ 13 mm) increases ina Si= 1.5 times.
a di4

The usage of diamond with thickness t ~ 20 mm leads to radiation increasing also. As
a result one may expect that each electron will emit about 50% of the initial energy( ∆E ≈ 5 GeV).
The well known dependence of multiple scattering angle on an energy and target
thickness makes possible to estimate the mean photon energy for the considered caseusing formula (6):< ω cr ( E 2 , t 2 ) > ~E 2 < θ ms ( E 2 , t 2 ) >< ω cr ( E1 , t1 ) > ≈E1 < θ ms ( E1 , t1 ) >t2< ω cr ( E1 , t1 ) >
t1

(11)

For E 2 = 10 GeV, t 2 = 20 mm, E1 = 4.5 GeV, t1 = 10 mm, < ωcr (E1 , t1 ) > ≈130 MeV one
may obtain < ωcr (E 2 , t 2 ) > ≈ 180 MeV and < N cr > ~ 14 ph/e-.
This photon flux may be used to produce positrons in a thin amorphous target in acomplete analogy with an undulator radiation beam. Moreover there may be some
addition to positron yield from an
initial electron with remaining part ofenergy.
4. The positron yield for an initial
electron with energy E 0 interactingwith a rather thin amorphous target( t ≤ 1 rad. length) may be calculatedusing a simple analytical model [15].
In this model an electron passing thelayer with thickness t /3 emits
bremsstrahlung photon which createse + e − pair at the next layer with
Fig. 3. Comparison of positron spectra from Monte
Carlo simulation (histogram) and analytical thickness t /3 and, at last, createdexpression (13). Initial electron energy E0=1 GeV, positron moves through remaining
converter thickness t= 0.5 rad. length.
layer ( t /3) changing outgoing angle
due to multiple scattering. The
positron spectrum (neglecting ionization and radiation losses) can be written as  ε+  E0 
 ln 2  − 0.19 ln 2  − 0.19 mc   mc 
,
− 


ε+
E0





(12)

positron energy. This formula is valid for the case E 0 <

2
mc2
λ

 t 
dN +

= 0.07dε + X0 

where ε + is the2z1 / 3stands screening parameter). For higher energies of the initial electrons
111
2mc2
2mc2
( E0 >, ε+ >) we have
λ
λ

(λ=

5

2

 t   1
dN +
 1
1
 ln  − 0.5  − ,
= 0.07dε +  ε+ E0 
 X0    λ 

 1 

.
 MeV (13)

Accuracy of the expressions (12), (13) may be estimated upon comparison with theMonte Carlo simulations [15] (see Fig.3).
As follows from the figure, for the target
thickness t ≤ X 0 one may observe a
reasonable agreement, which makes theabove approximation applicable toestimations of positron yield.
The similar model may be developed for
initial photons. For a simplicity let’s
consider a “flat” photon spectrum with aphotonmultiplicity
N ph(“triangle”
intensity spectrum closed to UR and CBSones):
 N ph,=  ωmaxω0,ω ≤ ωmaxdN phFig. 4. Positron spectra initiated by anelectron with E0 = 10 GeV in a combined
target (20 mm thickness diamond target and
1 rad. length amorphous converter). Upper
curve is the spectrum of positrons producedby photon flux from photon emitter, lower
curve is the spectrum of positrons produced
by an electron passed through photon
emitter.

(14)
ω > ωmaxRadiation losses may be calculated easily
from (14):
∆E =

ω max

∫ω
0

dN ph
dω

dω = N phωmax= N ph < ω >,2

ωmax = 2 < ω > .

The positron spectrum produced byphotons with the energy ω in the converter with thickness t may be approximated by
the expression [15]:dN + (ω)
=
dε +


 ω 
ln 2  − 1.19
t
 mc 
0.14
,
Lrad
ω


1

ln − 0.5t
λ0.14 L
ω
rad


ω<

ω>

2 2
mc
λ

.

2 2
mc
λ

After convolution of this spectrum with photon one (14) it is possible to obtain theanalytical expression for output positron spectrum:dN +t N ph  ωmax   1  E + ωmax   ln 2 4  − 1.2= 0.14lndε +X 0 ωmax  ε +   2  m c 


(15)

6

Flottmann’s calculations [3] for UR with ω max = 21 MeV, N ph = 2ph / e − give the resultdN += 0.020 for ε + = 10 MeV and t = 1 rad. length. Using (15) one obtain the value
dε +

dN +
=0.021 for the same parameters.
dε +Fig. 4 shows spectra of positrons generated in the 1 rad. length amorphous converter
by a photon flux with Nph = 14 created by an initial electron with energy E0 = 10 GeV
in a thick diamond target (upper curve) and by the same electron with decreased
energy E f = E 0 − ∆E = 5 GeV (lower curve). The total positron yield for an energy
interval 5 MeV ≤ ε + ≤ 25 MeV achieves ∆N + ≈ 2 per each initial electron. From thisamount 85% are generated by photons and only 15% by electrons.
5. The proposed scheme of positron source based on using of a combined target(photon emitter from a thick diamond target ( t d = 20 mm) and amorphous converterwith thickness t am = 1 X 0 ) and electron beam with energy E 0 = 10 GeV looks more
preferable in comparison with a homogeneous crystalline target because of theconverter thickness in the former case is much less than in latter one and problem ofheat loading will be much weaker also.
Such advantages of a diamond as a high thermal conductivity (660 W/m/K against
170 W/m/K for tungsten), high Debye temperature (1860 0 K against 379 0 K for
0

tungsten) and the shortest lattice constant ( a =3.56 A ) allow to consider a thickdiamond crystal as the best candidate for a photon emitter.
The problem of growth of an artificial diamond with thickness ~ 20 mm may beresolved in the nearest future (S.A. Terent’ev, private communication).
The measurements of the straggling of an electrons passed through an oriented thickcrystal (radiation losses distribution) become very important to verify the proposedmodel. The detailed 6-D simulation of a crystal-based positron source is also needfulto choose the source configuration and to design the new positron source for a linear
collider.
In summary it may be noted the considered scheme may provide an efficiency of
positron source (the number of accepted and accelerated positrons per initial electron)as high as 1 e+/e- at least. The efficiency of an undulator-based positron source [3,4]may achieve the same value also but proposed scheme is much cheaper.
REFERENCES
1. The NLC Collaboration, 2001 Report on the NLC. Preprint SLAC-R-571, 2001.
2. L. Rinolfi, T. Kamitani. The positron production at CLIC. CLIC Note 465,
7

CERN, 2002.
3. K. Flottmann. Investigations toward the development ofpolarized andunpolarized high intensity positron sources for linear colliders. Preprint DESY 93161, 1993.
4. K. Flottmann. Positron source for TESLA and SBLC in Proceedings of theWorkshop on new kinds of positron sources for linear colliders. SLAC-R-502,
1997.
5. R.D. Babadjanov, A.N. Didenko, B.N. Kalinin et al. Rad. Effects, v. 91, No 3-4(1986) 233.
6. G.L. Bochek, V.I. Kulibaba, N.I. Maslov et al. Nucl. Instrum. and Methods B 145(1998) 146.
7. S. Anami, M.Yu. Andreyashkin, A. Enomoto et al. Nucl. Instrum. and Methods B
183 (2001) 459.
8. V.N. Baier, V.M. Katkov, V.M. Strakhovenko. Electromagnetic Processes at
High Energies in Oriented Single Crystals. World Scientific, 1998.
9. I.E. Vnukov, B.N. Kalinin, G.A. Naumenko et al. Sov.Phys. Journal, v.34 (1991)
540.
10. K.Yu. Amosov, I.E. Vnukov, B.N. Kalinin et al. Sov. Phys. Journal, v.34 (1991)
472.
11. M.D. Bavizhev, Yu. Nilsen. B.A. Yur'ev. Sov. Phys. JETP, v.68 (1998) 803.
12. A. Kolchuzhkin, A. Potylitsyn., Nucl. Instrum and Methods B 173 (2001) 126.
13. R. Avakian, A.E. Avetisyan, R.A. Asatryan et al., Sov. Tech. Phys. Lett., v.14
(1988) 395.
14. E.I. Tsyganov. Fizika elementarnyx chastits i atomnogo yadra, v. 20 (1989) 5(in Russian).
15. A.P. Potylitsyn. Nucl. Instrum. and Methods A 398 (1997) 395.

8

Semiclassical Theory of Crystal-Assisted Pair Production:
Beyond the Uniform Field Approximation
H.Nitta, Y.Nagata, and S.Onuki
Department of Physics, Tokyo Gakugei University
M.Kh.Khokonov
Department of Physics, Kabardino-Balkarian State University
Within the semiclassical theory of QED, a simple expression of pair production
in strong field is obtained that approaches to the constant field approximation
at the strong field limit while it gradually behaves like the Bethe-Heitler typewhen the field becomes weaker. By using the impact approximation for the
calculation of trajectory, a simple expression is obtained. Though simple, it
agrees well with the experimental result of crystal-assisted pair production.

1

Introduction

It is widely known that electron-positron pair production is well described by the BetheHeitler formula as far as the process can be regarded as the incident photon collides
with an isolated atom. However, when photons enter a strong electromagnetic field, theperturbative approach such as the Bethe-Heitlers becomes inappropriate for describing
the pair production process. For such strong field QED effect, Baier and Katokov[1]proposed a semiclassical expression for radiationdN
αc=(Jc + Js ),
dη
πλ0 γ

Jc
Js


Z ∞
dτ
γ2
π
2
=
1 + (δβ⊥ ) sin∆
− ,
2
τ
2
Z ∞ 2
0
0
γ
dτ
γ−γ
(δβ⊥ )2 sin∆
,
=
0
2γγ
2
τ
0

(1)

(2)
(3)

where ω ∗ = (γ/γ 0 )ω, η = ~ω/E, δβ⊥ = β⊥ (t+ ) − β⊥ (t− ), t± = t0 ± τ /2, E 0 = E − ~ω,γ(γ 0 ) = E/(m0 c2 )(E 0 /(m0 c2 )), E being the initial energy of the particle and m0 its rest
mass. The phase determined by the trajectory of a radiating particle is given byZωτωω t+ 2 0 0
2∆(τ ) =−(δρ) +β (τ )dτ ,(4)2γ 2 2c2 τ
2 t− ⊥
where δρ = ρ(t+ ) − ρ(t− ), ρ(t) being the transverse coordinate. Though there are somediscussion on the derivation of the Baier-Katokov formula [2, 3], this formula explains
very well the radiation as well as pair production in strong fields.

1

2“Th-trajectory” and pair production

The pair production probability is obtained by using the crossing symmetry for Eq.(5)
[3].

ǫ
G

G

G

ǫ

Figure 1: Crossing symmetry. The left-hand figure represents the channeling radiation
while the right-hand one represents the pair production.
By changing the variables as→ −E+ (produced positron) E (initial energy)
0
E (final energy)→ E−(produced electron)ω (emitted photon) → −ω
(absorbed photon)and multiplying the ratio of the density of final states,
E+2 dE+,(~ω)2 d(~ω)

we obtain the pair production probability for the th-trajectory approximation as well as
the synchrotron approximation, though one may feel that the idea of particle trajectoryis rather “spooky”[3]. We obtain,



αc
m0 c2
dN+
=
J,
(5)
dη+
πλ0
~ω
where dN+ /dη+ represents the number of produced positrons, η+ = E+ /~ω, E+ being
the energy of the produced positrons, α the fine-structure constant, and λ0 the Compton
wavelength.
The factor J for the CFA is given by



Z ∞
1
1
∗
Jcf = √
1 − η+ +K 2 (ξ ) −K 1 (λ)dλ ,(6)3
3
1 − η+
3ξ∗
where ξ ∗ = 2/[3η+ (1 − η+ )χ] and χ = ~ωλ0 F (t0 )/(m0 c2 )2 and F (t0 ) is the force by thefield acting on the positron at time t0 . Eq.(6) is obtained by assuming that the trajectoryof produced positrons are circular.
The CFA is applied to evaluate the pair production process when high-energy photons
enters a crystal along the major crystal axis. It is reported that when photons are2directed exactly parallel to the crystal axis, CFA agrees very well with the experimental
result [5]. However, naturally, CFA does not explain the angular dependence of thepair production rate. For the purpose to calculate the angular dependence, the authorsof Ref.[5] calculated the Baier-Katkov formula with some “numerical experiments” [6]and a good agreement of their numerical approach with the experimental result has
been demonstrated. However, the process of the “numerical experiments” has not been
described in their paper. Therefore, nobody can reproduce the calculations.
Recently, two of the present authors obtained a radiation probability [4] by using amodel trajectory called the “th-trajectory” tβ ⊥ (t) = b0 + b tanh
,
(7)
T
where
b0 =

β − β ⊥1
β ⊥1 + β ⊥2
, b = ⊥2,2
( 2
β ⊥1 ≡ β ⊥ (t → −∞)β ⊥2 ≡ β ⊥ (t → +∞).

The th-trajectory approaches to the free motion (i.e. straight paths) at t → ±∞ while
the trajectory is substantially bent at |t| . T depending on the strength of the field.
Since Eq.(7) is integrated analytically, we obtain an analytic expression for J:
 


Z ∞
h
i
dz 2 1 − η+η+2
˜ − µ tanh z) + π ,
Jth =
ν
+
tanh z − 1 sin ξ(z(8)
zη+
1 − η+
20
where ν = γ+ b and ξ˜ = ν(1 + ν 2 )/[η+ (1 − η+ )χ].

3

Numerical results

A typical ν dependence of Eq.(8) is shown in Fig. 2. When ν becomes larger, the resultof Jth approaches to Jcf . From Fig. 2 it is clear that the spectra become CFA-like as theangle decreases while Bethe-Heitler-like as the angle increases.
Based on Eq.(8), we have calculated the crystal-assisted pair production (CAPP)
probability as a function of the photon incident angle in comparison with the experimental data by Belckacem et al.[5]. For simplicity, first we calculate the scattering angle
by the impact approximation where the momentum change during the collision is proportional to the force multiplied by the “interaction time”. The interaction time has
been estimated by aρ/v⊥ , where ρ is the impact parameter of the radiation point (for
CAPP, we should have called it the “pair production point” ) and a is the parameter(a ∼ 1). In Fig. 3 we have shown the results of the impact approximation. Taking
account of the simplicity of the impact approximation, the agreement is satisfactory. Jthwith the impact approximation will be useful for planning experiments.
In Fig. 4, a more involved calculation has been made by using thermally-averaged
one-string Molière potential [7] at T = 100K. Though in this case we have no free parameter, the agreement is well. The peaks at higher photon energies look like somewhat
3

PAIR CREATION RATE J

0.16

0.14

← 0.5

0.12

← 0.7

← 0.4

← 0.3

←1

0.1

← 0.2
0.08
←5
0.06

← 0.1

0.04

0.02

0

0

0.1

0.2

0.3

0.4
0.5
0.6
POSITRON ENERGY

0.7

0.8

0.9

1

Figure 2: The ν-dependence of pair production probability calculated by using Eq.(8) asa function of the energy of produced positrons E+ /~ω. The dotted line represents theconstant field approximation (CFA) of Eq.(6). (χ = 1)

Figure 3: Comparison of the impact approximation results with the experimental databy Belkacem et al. [5]. The symbols mean the experimental results corresponding theenergy of photons in the range of: ◦: 150-120GeV, :120-90GeV, 5:90-60GeV, 4:5040GeV,√ ♦:40-20GeV. The dotted lines, solid lines, and broken lines correspond to a = 2,
a = 2 2, and a = 4, respectively.

4

Figure 4: Comparison with experimental data by the rigorous scattering calculation withthe use of the Molière one-string potential. No fitting parameter is included.
steeper than the experimental data, which may be due to neglecting of the many-string
effect.
More detailed discussion will be published elsewhere.

References[1] V. N. Baier, and V. M. Katkov, Sov. Phys. JETP,26,854 (1968).
[2] J. Lindhard, Phys. Rev. A43, 6032 (1991).
[3] J. C. Kimball and N. Cue, Radiat. Eff. Defect in Solids 122-123, 481 (1991).
[4] M. Kh. Khokonov and H. Nitta, Phys. Rev. Lett. 89, 094801 (2002).
[5] A. Belkacem et al., Phys. Rev. Lett. 58, 1196 (1987).
[6] A. Belkacem, N. Cue, and J. C. Kimball, Phys.Lett. 111A, 86 (1985).
[7] Y.H.Ohtsuki, Charged Beam Interaction with Solids (Taylor and Frances, London,1983).

5