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US-Japan Cooperation in the Field of High Energy Physics - Progress report -

Development of picosecond CO2 laser for production of polarized positrons at linear colliders

April 20, 2003 T. Hirose

1. Introduction 2. Experimental results obtained in 2002 at KEK and BNL 3. Research plan in 2003

T. Hirose, S. Kashiwagi, M. Washio: Advanced Research Institute for Science and Engineering, Waseda University T. Kumita, Y. Kamiya: Department of Physics, Tokyo Metropolitan University Y. Kurihara, K. Nakajima, T. Omori, T. Okugi, J. Urakawa, K. Yokoya: High Energy Accelerator Research Organization (KEK) I. Ben-Zvi, M. Babzien, K. Kusche, I. V. Pogorelsky, V. Yakimenko: Accelerator Test Facility, Brookhaven National Laboratory D. P. Siddons:

National Synchrotron Light Source, Brookhaven National Laboratory

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1. Introduction It is considered that a next generation accelerator at a high energy frontier is an electron-positron linear collider (LC) which plays a complementary role to the hadron collider LHC at CERN. Especially, specific features of a LC is to allow us to make precise observation of interesting and exotic phenomena which usually have a small production rate. In particular, being different from circular accelerators, the LC can in principle accelerate polarized electron and positron beams without depolarization. The linear collider GLC* has been designed to start at an initial center-of-mass energy ECM ~ 500 GeV which is considerably higher than the electron (positron) rest mass [1]. In these high energy regimes, the helicity may be interpreted as the chirality which is one of the important quantities in the field theory. It was also pointed out that a specific prescription for enhancing exotic processes was provided if positrons as well as electrons were transversely polarized [2]. Consequently, the controllability of both a positron spin and an electron spin will be able to bring further possibilities for LC's to extract small but significant signals by using spin dependent characteristics of reaction processes. The polarized positron project started in 1995 when we proposed, as illustrated in Fig.1 designed for the GLC positron source, a new method in which highly polarized positrons can be generated via two fundamental processes, namely Compton scattering of circularly polarized laser beams and successive pair creation [3,4]. Since then, proof-of-principle experiments have been pursued at KEK using an electron beam of 1.28 GeV and a second harmonic laser photon with a wave length of 532 nm generated from a Nd:YAG laser. In a first stage experiment, we had developed basic technologies for creating positrons using an unpolarized laser photon and then a first observation of pair created positrons was successfully accomplished [5,6]. In parallel with these experimental studies, we have been carrying out a conceptual design of a polarized positron source for the GLC which requires considerably high-intensity positrons and a complicated multi-bunch structure [7-9]. For this purpose, a ultra-high energy CO2 laser was adopted owing to its long wave length of λ~10 µm which, comparing solid-state lasers (λ~1 µm), permits to create one order larger number of photons at a given laser energy.

* The name of the linear collider JLC has been recently changed to be Global Linear Collider, GLC.

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e- beam5.8 GeV

CO2 laser ( =10.6 m, E=0.117 eV )

e-

e+

-rayEmax = 60MeV

e-e+ pair creation

Thin conversiontarget

Figure 1: Principle of the polarized positron source

In 1998, the project was extended over an international collaboration with the BNL-ATF group using a 60 MeV linac and a GW CO2 laser [10] and a series of laser-Compton experiments [11,12] has been carried out leading to ultra-high brightness x-ray generation as seen in Fig. 2

BNL-ATF Thomson source(2001)

BNL-ATF Thomson source(1999)

LLNL Tomson source (design)

LBL Thomson source (demonstrated)

laser plasma

NRL Thomson source (demonstrated)

NRL Thomson source (design)

X-ray lasers

High order harmonics

Peak

Bri

ghtn

ess

phot

ons/

mm

2 mra

d2se

c (0

.1%

band

wid

th)

Photon Energy (keV)

Figure 2: Peak brightness of existing and projected laser driven x-ray sources

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In 2002, great progress has been accomplished at both KEK and BNL as summarized below. KEK (i) Development of advanced technology for electron and laser beam diagnostics

[13]. (ii) Establishment of γ-ray poralimetry for short-bunch γ-rays [14]. (iii) Conceptual design on a polarized positron source of a linear collider GLC [15]. BNL (i) Construction of a x-ray spectrometer for measuring a non-linear Compton process

[16. 17]. (ii) Laser and electron beam interactions in a plasma channel. [18-20]

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2. Experimental results obtained in 2002 2-1 Advanced technology of electron and laser beam diagnostics [5,9,13,14] A series of experiments has been conducted at the KEK-ATF (Accelerator Test Facility), which incorporates an S-band linac, a damping ring and an extraction line. Table 1 puts together parameters of the electron beam extracted from the damping ring and the laser beam provided from a Q-switch Nd:YAG laser. The laser light is converted into a circularly polarized light while passing through a quarter wave plate. Generated γ-ray beams, which are longitudinally polarized, have a maximum energy of 56 MeV and a time duration of 31 ps, the same as that of electron beams. It is remarked that γ -rays are highly collimated and 97 % of whole γ-rays are included within the scattered angle of 3 mrad: This characteristic is beneficial to the design of the transmission-type polarimeter.

Electron beam Laser beam Energy 1.28 GeV 2.33 eV (532 nm)

Intensity bunche /1065.0 10 −× 400 mJ/pulse Bunch length (rms) 31 ps 3.6 ns

σx 87 µm 154 µm σx 72 µm 151 µm εx mrad91094.1 −× mrad8105.11 −× εy mrad111036.2 −× mrad8109.12 −× βx 0.513 m 0.104 m βy 52.859 m 0.058 m

Rep. Rate 3.12 Hz 1.56 Hz σp/p 4102.8 −×

Table 1: Parameters of the electron and laser beams Fig.3 shows an apparatus called a Compton chamber, in which laser-electron collisions take place, together with a laser beam optics and elements of the γ-ray polarimeter including a photodiode, an aerogel Cherenkov counter, magnetized iron (called a magnet hereafter) and an air Cherenkov counter. In order to achieve precise diagnostics for both the electron and laser beams, we install screen monitors, a wire scanner and a knife edge scanner in each cell of the Compton chamber as shown in Fig. 4. The screen monitors are mounted in the central cell located at the collision point and in the side cells placed at the distance of 265 mm from the collision point, so as to adjust the transverse position and angle of both beams. Furthermore, the wire scanner and the knife edge scanner are set in the central cell; the former allows to measure the electron beam size at the collision point with the accuracy of 3 µm, whereas the latter determines the laser profile to the extent of ~15 µm. The laser beam is transported to the collision point over the distance of about 10 m using six mirrors which are coated with multi-layer dielectric. The downstream three mirrors can be remotely controlled to adjust the laser beam at the collision point.

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bendingmagnet

exit window(quartz)

straight section (4m) lensf = 4330mm

remotelycontrolled mirrors

Al port(2mm)

entrance window(quartz)

power meterbendingmagnet

e- e-

Laser

γ-rays

remotely controlled mirrorCompton chamberSi PIN

photodiode

AerogelCherenkov

counter

Air Cherenkovcounter

magnetizediron

γ-rays

γ-ray polarimeter

Collision point

Figure 3: Experimental setup, including the Compton chamber, the laser optics, and the γ-ray polarimeter.

20 m

m

Min. step: 1µm

Stay position, φ = 20 mm

X wire

Y wire

X edge

Y edge

X screen

Y screen

Figure 4: Screen monitors, a wire scanner and a knife edge scanner set in each cell of the Compton chamber To maximize the luminosity of laser- and electron-beam collisions, we optimized the laser optics as follows. The laser beam is expanded to an r.m.s spot-size of 4.7 mm and transported to the last lens whose focal length is relatively long, i.e. 4330 mm resulting in a collision distance of about 10 cm (see the large values of the laser βx and βy in Table 1). Furthermore, in order to realize the head-on collision, the last mirror of 3 mm thickness is placed on the axis of γ-rays as shown in Fig. 3. Note that the absorption of generated γ-rays is negligible while passing through the mirror. 2-2 Gamma-ray polarimetry for short bunch γγγγ-rays [14] Gamma-ray polarization can be determined through spin-dependent Compton scattering of γ-rays on 3d electrons in a magnetized iron as shown in Fig. 5 where the cross sections of the inverse Compton process are given separately for the cases that the γ-ray spin and the electron spin are parallel and anti-parallel to each other. The electron and positron pair-creation causes considerably large background, which becomes serious obstacle to the polarization measurement. In order to avoid background, we ordinarily have to select only the Compton process by means of a coincidence method. Unfortunately such a short bunch width of the γ-ray beam prevents us from identifying both the electron and γ-ray photon emerging from a single Compton process. We therefore adopted a "transmission method" in which we measured at a downstream position of the magnet only intensity of transmitting γ-rays +N and −N for parallel and anti-parallel cases respectively, in order to determine the asymmetry defined as

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( ) ( )−+−+ +−= NNNNA / . Indeed the transmission method can be applicable to the polarization measurement of γ -rays with any time structure and is influenced little by background arising from the pair creation because transmitting γ-rays are collimated to the narrow forward-cone while Compton-scattered γ-rays, recoiled electrons, and pair created e+e- pairs are emitted over relatively wide angular regions.

0 10 20 30 40 50 60

Cro

ss se

ctio

n [m

b]

Energy of the incident γ-ray [MeV]

pair creation

Compton (para)

Compton (anti)

10

1

102

103

104

Figure 5: Total cross section of pair creation and Compton scattering for the cases in which the spin of a g-ray are parallel and anti-parallel to that of an electron. In the pair creation process, the scattering is considered.

Proper thickness of the magnet is determined to be 15 cm by considering accelerator related background and a time period needed for data taking. For maintaining the magnetization as flat as possible along a longitudinal axis, we made dents at the magnet ends (see Fig. 3). Gamma-rays leaving the magnet were measured with an air Cherenkov counter whose air pressure is maintained to be 1 atm, thus corresponding to the energy threshold of 21.4 MeV. Background produced inside the magnet is dominantly attributed to Compton-scattered γ-rays and recoiled electrons as well as pair-created electrons and positrons. Nevertheless, because of their angular distributions spreading over considerably wide angular-region, we can suppress these backgrounds by making the distance between the magnet and the air Cherenkov counter sufficiently long as 4.4 m. Hence we can suppress background less than 0.1% of the signal. Taking account of the whole elements of the polarimeter shown in Fig. 3 we made various simulations to estimate an expected asymmetry with the help of following simulation codes i.e. CAIN for the Compton scattering of the electron and laser beams whose parameters are given in Table 1, GEANT3 for electromagnetic interactions in material, GRACE particularly for spin dependent processes of electron-γ collisions in the magnet and POISSON for the magnetization of the iron. The simulation program traces γ-rays through the magnet and brings them into the air Cherenkov counter. The number of Cherenkov lights were counted by reversing the magnetization at a certain time interval. On the assumption of the 100% polarization of the laser light and the energy-dependent efficiency, the expected asymmetry was obtained to be 1.3% leading to the predicted magnitude of the polarization of 88 %.

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In experiments, in order to maximize the spatial overlap between the electron and laser beams, the position and angle of the laser beam is precisely adjusted by the remotely controlled mirrors i.e. three mirrors shown in Fig. 3. Because the repetition-rate of 1.56 Hz for the laser beam is half that for the electron-beam, we are able to record alternately signals and backgrounds, eliminating therefore systematic error due to long-term variation of apparatus parameters. The average number of γ-rays thus obtained is ( ) 6102.01.1 ×± γ’s/bunch where 0.2 is a systematic error: This is in good agreement with the values of 6100.1 × which is simulated using the beam parameters in Table 1. A magnitude of the laser-beam polarization were fixed at the collision point as follows. The laser-light transmitting through a quarter wave plate and a Glan laser-prism were detected with a phototube by changing the prism angle. Variation of laser-light intensity gave the Stokes parameters which resulted in a degree of the laser circular-polarization as given in Table 2.

Run number (i) Circular polarization Asymmetry 1 179 ±− % (L) 15.093.0 ±− % 2 176 ±− % (L) 13.073.0 ±− % 3 124 ± % (R) 14.029.0 ± % 4 179 ± % (R) 15.018.1 ± % 5 194 ± % (R) 19.050.1 ± %

Table 2: Result from the γ-ray polarization measurement.

Polarization measurements of γ-rays were carried out at the five different values of the laser polarizations. For a fixed magnitude of the laser polarization and the fixed direction of the magnetic field as well, the transmission measurement was carried out for ten min. and the same was made for the reversed magnetic field; this set of the measurement (20 min.) was repeated four times and accordingly 8000 collisions were recorded for the total time-period of 80 min Figure 6 (a) shows the transmission of γ-rays with the right handed polarization transmitting through the magnet for the cases in which the spins of γ-rays are parallel and anti-parallel to the magnetization. Figure 6 (b) is the same as Fig. 6 (a) except for the left handed γ-ray polarization. Table 2 puts together measured asymmetries with statistical errors for each laser polarizations. The measured asymmetries are plotted as a function of the laser polarization in Fig.7 where the solid line represents the results of linear fitting and the intercept with the laser polarization of %100− is 12.029.1 ± where the error includes the statistical and systematic errors and the reduced 2χ of the fitting is 0.89. The experimental value of the asymmetry is consistent with the simulated value of 1.3 %.

In conclusion, we have established the transmission method in which we demonstrated for the first time the polarization measurement of short-bunch γ-rays. This is highly due to precise diagnostics of electron and laser beams as well as extensive simulations on laser-beam and γ-ray interactions with material. Consequently we can accomplish a reliable description of the whole experimental processes incorporating collisions of laser and electron beams as well as the gamma-ray polarimetry. This study has pushed one step forward in the polarized positron project of the linear collider.

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Indeed, technical information obtained in this study shall allow us to design a positron polarimetry which will soon be put into practical use, leading to the final step of the proof-of-principle demonstration for the proposed scheme of the polarized positron source.

0.2 0.4 0.6 0.8Transmission [a.u.]

100

200

300

0.2 0.4 0.6 0.8

Entry

Transmission [a.u.]

e-γ-ray

(a) (b)

0

Figure 6: Transmission of polarized γ-rays passing through the magnetized iron for the cases that the γ-ray spin is parallel or anti-parallel to the magnetization. The transmission separately measured for the laser polarization ( )%179 ±m are goven in Fig. (a) and Fig. (b).

-2-1.5

-1-0.5

00.5

11.5

2

-100 -50 0 50 100

Asy

mm

etry

[%]

Circular polarization of laser light [%]

datafit

Figure 7: Measured asymmetry as a function of the circular polarization of the laser beam at the collision point. 2-3 Conceptual design on a polarized positron source of a linear collider GLC [9,15]. A future linear collider of the TeV-energy region requires an extraordinary large number of positrons (~1010 e+/bunch) in a multi-bunch time structure. To meet these requirements, we employ a high-current, low-emittance electron beam of 5.8 GeV, ten CO2 lasers, and multiple laser-electron collision-points. The overall scheme of the positron source is shown in Fig.8, mainly consisting of four parts: (i) an electron accelerator, (ii) a set of CO2 lasers, (iii) a multiple-collision system, and (v) a system which captures created positrons and damps them.

10

RF-Gun

3 GeVLinac

3 GeVDR

BC 2. 8 GeVLinac

1. 98 GeVPre-DR

1.98 GeVDR

1.98 GeVLinac

BCCapturesection

electron beam 5. 8GeVhigh current and low emittance

CO2 lasers

Conversiontarget

γγγγ-rays

Collision points(Parabolic mirrors)

Figure 8: Configuration of the polarized positron source for GLC. A first key element for realizing multiple collisions is to introduce a pair of parabolic mirrors which has a hole at its center. The pair of mirrors focuses and extracts the laser beam as shown in Fig. 9. Back scattered γ-rays and electron beams can pass through the hole. A second key for multiple collisions is to provide an electron beam with a pretty small emittance. In order to place many mirrors along an electron beam line, the beam must be tightly focused over a long distance. Hence, we require a normalized emittance to be 61025.1 −× rad-m in both horizontal and vertical directions. The beam energy is 5.8 GeV, a time-structure of the beam is the same as that of GLC, and each bunch of the micro-beam contains 10105× electrons. As shown in Fig. 8, the accelerator system which provides such a high-current, low emittance beam consists of a photo-cathode RF-gun, a 3 GeV damping ring (DR), a bunch compressor (BC), and a 2.8 GeV licnac. A initial normalized emittance of 5x10-6 rad-m generated using the RF-gun can be reduced to 61025.1 −× rad-m after passing the DR. A bunch compressor located after the DR can compress a longitudinal beam size to be 1 mm in r.m.s. Then the beam is again accelerated using the S-band linac up to 5.8 GeV.

Collision point (CP)

Electronbeam

Laserbeam

f = 90 mm

Figure 9: A pair of parabolic-mirrors and an axicon expander.

A focus system with β* = 3.6 m is adopted to focus an electron beam to a small spot size over a relatively long distance. For example, a spot size at the waist is 20 µm and that at 2.1 m away from the waist point is maintained still small i.e. 23 µm. Because of the length of the mirror pair is roughly 200 mm, we can install 20 pairs over a distance of 1.2± m away from the waist point as

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shown in Fig. 10. The collision section (CS) thus designed has a total length of 5.2 m and contains 20 parabolic- mirrors pairs and diagnostic apparatus for both electron and laser beams. A single laser provides laser bunches for those 20 collision points through all 20 parabolic-mirror pairs. If the laser beam has 114 bunches in one train, and if the laser path length between adjacent collision points are properly arranged, it can be realized that all 95 bunches in the electron beam collide 20 times at the 20 collision points. The energy of each laser bunch is assumued to be 0.25 J, so that one laser should provide a total photon energy of 28.5 J in a train. The bunch spacing of the laser beam should be the same as that of the electron beam, i.e. 2.8 sec [15].

focus

CP1CP2CP20

to CP2

from CP1

to CP3

from CP19

to dump

Electron beam waist

4. 2m : 20 collision points (CPs)

5. 2m : A collision section (CS)11

4 bu

nche

s/tra

in0.

25J/

bunc

h

A la

ser

beam

An electron beam

ββββ* = 3.6m

95 bunches/train

(both x and y)

210mm

σσσσ = 23µµµµme σσσσ = 20µµµµme σσσσ = 23µµµµme

σσσσ = 1mmz

N = 5 10 /bunch10e

γγγγεεεε = 1. 25 10 /bunch- 6

Figure 10: Collision section

Because the number of γ-ray generated during 20 collisions is not sufficient to create the required number of positrons, the electron beam is refocused after the first collision section using a triplet, and put to the next collision section which equips another 20 mirror poirs for the next 20 collisions. A space needed for a refocusing triplet is 1 m. In order to obtain the required γ-ray intensity, we have to provide 10 laser systems in total for 10 CS as illustrated in Fig. 11, resulting in 200 collision points. The total length including 10 collision sections and 9 refocusing triplets is 61 m. The long β value of the electron beam as well as the insertion of the refocusing triplet can maintain the electron spot size to be the same as that in the first collision section, i.e. 20 µm. The total number of γ-rays generated during 200 collisions is 11103.8 × photons/bunch.

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f f f f

σσσσ = 20µµµµme σσσσ = 20µµµµme σσσσ = 20µµµµme

to dump

∆∆∆∆E/E = 0 %5. 74 GeV 5.36 GeV1. 2 % 5.9 %

5. 2m 1mCS1

20 CPs

5. 2m 1m 5.2m1m

to dump to dump

1 2 10

Laser 10. 25J/bunch

Laser 20. 25J/bunch

Laser 100. 25J/bunch

CS2 CS1020 CPs 20 CPs

61m : A collision region10 collision sections200 collision points

Bende beam-

e beam-to

dump

γγγγ-rays

target

E = 5. 80 GeVe

N = 5 10 /bunch10e

N = 8. 3 10 /bunch

11γγγγ

Figure 11: There are 10 collision sections in total.

Generated γ-rays passing through collimators with a hole of a 4 mm diameter laced between mirrors are guided to a W target of 1.75 mm thickness to generate electron-positron pairs as shown in Fig. 12. A γ-ray spectrum measured just before the W target is shown in Fig. 13 which indicates a large population of left-handed γ-rays in the high-energy side of the spectrum. Using a modified version of the EGS code in which spin polarization of pair-produced positrons are taken into account, we obtain the number of emitted positrons, 10109.6 × positrons/bunch. The positron energy distribution is given in Fig.14 as a function of a longitudinal momentum of positrons. As demonstrated in the figure, a high degree of polarization is expected for positrons in a high energy region.

f f fe beam-

targettungsten t = 1 . 75 mm

γγγγ-rays

61 m : A collision region 20 m

Be nd

e beam-

e -e +

σσσσ = 3 . 0 mmγγγγ σσσσ = 4 . 0 mme /e+ - Figure 12: Collimators put in the beam line for mirror protection and the W target for electron-positron pair creation.

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0

0.5

1.0

1.5

2.0

2.5

0 20 40 60 80 100Eγ [MeV]

Num

ber

ofγ-

rays

[MeV

-1]

1010

Rc

Lc

SUM

SUMc

Figure 13: The spectrum of the γ-rays which reach the target as well as all generated γ-rays (SUM). The γ-rays which reach the target are indicated separately for the left-handed ones (Lc), the right-handed ones (Rc), and the total (SUMc).

0

1.0

2.0

3.0

4.0

5.0

6.0

0 10 20 30 40 50 60

x10-3

SUM

R L

Pz at target exit [MeV/c]

Ne+

/Nγ

Figure 14: Number of positrons at the target normalized by the total number of g-rays on the target. The solid line shows all positrons, and dotted (broken) line corresponds to those which have left-handed (right-handed) helicity. Figure 15 shows a schematic design of a positron capturing system. Just after the conversion target, an L-band (1.428 Ghz) accelerating structure is placed to collect positrons with high energy. Both the accelerating structure and the conversion target are located inside a super conducting solenoid magnet with a magnetic field of 6 Tesla. The length of the accelerating structure is 1.5 m and its accelerating gradient is 30 MeV/m. After the capture system, positrons are accelerated up to 1.98 GeV using a linear

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accelerator, and cooled down in a pre-dumping ring. Spin precession of positrons passing through the capture system are studied using a Monte Carlo simulation code. Positron acceptance conditions of the linac and the pre-dumping ring are applied for estimating a capture rate of positrons into the capture system. Then we obtain, as shown in Fig.16, a positron momentum distribution (a) immediately after the W target, and (b) at the exit of the capture system. The solid line in Fig 16(b) represents all positrons coming out of the capture system, corresponding to 95% of positrons emitted from the W target while the dotted line indicates accepted positrons of 10102.1 × /bunch, which meets the GLC requirements. The magnitude of polarization for positron beams provided to the GLC main linac is 54%.

γγγγ-rays

Capture section

1. 98 GeV linac

1. 98 GeVpre-damping

ring

L-band acceleratingstructure

6 Tesla solenoid coilTarget

to DR

Figure 15: Schematic design of the positron capturing system.

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 20 40 60 80 100Pz [MeV/c]

Ne+

/Nγ

x10-3

(b)

0

1.0

2.0

3.0

4.0

5.0

6.0

0 10 20 30 40 50 60Pz at target exit [MeV/c]

Ne+

/Nγ

x10-3

(a)

Figure 16: Positron distribution (a) immediately after the target and (b) at the exit of the capture section. Breakdown of the power consumption is estimated as follows. The total power efficiency of the 3 GeV and 2.8 GeV linacs from the wall-plug to the beam is assumed to be 8% and thus the required wall-plug power for the electron linacs is 8. 3 MW. The 3 GeV damping ring consumes 2 MW. The 10 CO2 lasers requires a power of 1.1 MW, if the power efficiency is assumed to be 4%. The accelerators after the L-band accelerator structure consume powers as follows: 2.7 MW for the 1.98 GeV linac assuming the power efficiency of 2%, 3.7 W for the pre-damping ring and 4.1 MW for the positron damping ring. Consequently the tatal power consumption of the polarized positron source is approximately 22 MW.

We have also considered various options as follows: Do not use the 3 GeV damping ring.

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Use non-coated copper parabolic-mirrors which are more resistive against radiation damage. Use lenses to focus the laser beams instead of parabolic-mirrors.

Detailed comparison of these variations with the original view is referred to ref.15. 2-4 Construction of an x-ray spectrometer for measuring a nonlinear Compton process [11, 18]

A 10 atm 0.15 litter preamplifier was installed in the BNL-ATF CO2 laser system as shown in Fig. 17. It enables the laser system to shorten the pulse duration from 180psec to 3 psec and the peak power is expected to reach 1 TW after the shakedown period. In this stage, Compton scattering occurs in the nonlinear regime. Namely, an electron absorbs multiple laser photons before emitting a single photon of higher energy.

Figure 17: New CO2 laser system at BNL-ATF

Magnitude of the nonlinear Compton scattering is characterized by the normalized

vector potential, µ

µ AAmc

ea −= 2

where e is the charge of the electron, Aµ four-vector potential of the laser, and mc2 the electron’s rest energy. It can be written in a more convenient form as a function of wavelength λ and power density I of the laser as follows;

]/[][1060.0 22/19 cmWIma µλ⋅×= − . Compton scattering occurs in the linear regime for a<<1, while the nonlinear process is comparable to the linear process for a=1.

The normalized vector potential of the CO2 laser is expected to be a=0.77 when the new preamplifier is being operated. To study the nonlinear Compton scattering in this stage, the energy spectrum and angular distribution of x-rays have been simulated by an MC simulation code, CAIN [22].

Figure 18 shows the result of the simulation. The solid line of Fig. 18(a) shows the calculated energy spectrum of generated x-rays for the upgraded laser (a=0.77), while

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the dashed line shows that corresponding to conditions in the 2001 run (a=0.04). In comparison with the dashed line, the solid line has a smooth shoulder due to an electron mass shift in the laser field and higher energy photons are seen due to the higher order interactions. Fig. 18(b) is a scattered plot of x-ray energy and emission angle for a=0.77. One can clearly separate higher order harmonics from the 1st harmonic in the two dimensional plot.

0 02 24 46 68 810 1012 1214 1416 1618 1820 20

104

105

106

0

2

4

6

8

10

12

14

107

108

=~ta

nθ

θ[m

rad]

Scat

tere

d A

ngle

(b)

Xray Energy [keV]

[Pho

tons

/0.1

keVb

in]

# of

Gen

erat

ed P

hoto

ns

Xray Energy [keV]

(a) Figure 18: (a) Energy spectrum of Compton x-rays for a=0.77 (solid line) and a=0.04 (dashed line). (b) A scattered plot of x-ray energy and emission angle for a=0.77.

To observe the higher order harmonics experimentally, we have designed an x-ray

spectrometer utilizing a multilayer crystal and a two-dimensional position sensitive detector. Figure 19 shows a schematic view of the spectrometer. The multilayer crystal consists of 45 silicon/molybdenum layer pairs curved cylindrically with the radius of 4.8m. The curvature causes the incident angle to vary from 25 mrad to 10 mrad along the crystal circumference. For the multilayer crystal described above, this corresponds to Bragg-reflected energies of 6 keV to 15 keV. The angular divergence in the vertical plane causes a negligible change in the Bragg angle, but allows us to record the source angular profile at each energy. Thus, energy and angular distributions of x-rays can be observed using the 2-D detector for each collision of the laser and electron pulses. The 2-D detector used is a CCD based x-ray detector (MarCCD x-ray detector, Mar USA Inc.). It consists of a 162 mm diameter scintillation screen coupled to a fiber optic taper which guides scintillation light and reduces the size of the image, and a cooled CCD detector.

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Figure 19: Schematic view of the spectrometer

The spectrometer was assembled and tested using a copper-anode x-ray tube

operating at 15 keV which provides 8 keV Kα x-rays. The tube was arranged to present a line source of mmmm 101.0 × cross-section at 1.3 m from the spectrometer. The two-dimensional image produced in this experiment is uniform in the Y-axis direction, since the source is isotropic.

Fig. 20 shows an X-axis slice of the two-dimensional detector image which indicates the energy distribution. The peak at cmX 9.5−= is consistent with the calculated position of the 8 keV line of the x-ray source. The systematic uncertainties in this preliminary measurement lead to a band of positions indicated as a shaded region in the figure.

11 10 9 8 7 6 5X Position [cm]

0

200

400

600

800

1000

1200

1400

Xray

inte

nsity

[a.u

.]

Figure 20: An X-axis slice of the two dimensional image on the detector taken with the 8keV x-ray generator.

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2-5 Laser and electron beam interactions in a plasma channel Intensity of the x-rays (or γ-rays) produced by the laser Compton scatterings can be

increased by increasing power of the laser beam. However, high-power high-repetition CO2 laser is technically difficult. Furthermore, high power density introduces the nonlinear process. If the nonlinear process is dominant, polarization of Compton γ-rays becomes smaller and thus it is not suitable for the polarized positron source for linear colliders.

An alternative way we have been investigating to obtain high intense x-rays (γ-rays) is to utilize the plasma channeling of laser light. If Compton scattering of laser and electron beams occurs in free space, the interaction distance is limited by the Rayleigh length, which is about a millimeter when a CO2 laser beam is tightly focused and thus pulse duration of the laser must be picoseconds for efficient use of its energy.

The plasma channel extends the interaction distance over several centimeters. This approach allows the use of nanosecond laser pulse instead of picosecond pulse to obtain the same x-ray intensity. Furthermore, lower power density suppresses the nonlinear Compton process and polarization of produced γ-rays stays higher. Therefore, use of the plasma channel benefits both of the high intense x-ray source and polarized positron source.

We utilize a capillary discharge plasma channel to guide the CO2 laser beam. The schematic design of the plasma channel device is shown in Fig. 21. A 3-mm long capillary (trigger capillary) and a 17-mm long capillary (main capillary) are placed between three electrodes connected to a high voltage pulse generator and a capacitor, to which a DC high voltage is applied. Both capillaries are made of polypropylene and have a 1 mm inner diameter.

The plasma channel is formed in the following way. A high voltage pulse is applied to the trigger capillary and then the initial plasma is formed by ablation of the wall material due to the electrical discharge, then the plasma leads the discharge along the main capillary and the secondary plasma is formed in it. Lower density of plasma in the center of the capillary leads to a higher index of refraction and thus laser beams are guided as in optical fibers.

MainCapillary

Trig

ger

Cap

illar

y

Spark Gap

HV Pulse

Figure 21: Schematic design of the capillary discharge plasma channel.

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An experiment of plasma channeling was performed using the CO2 laser at

BNL-ATF. The 180-ps, 5-J CO2 laser is focused with a parabolic mirror (focal length = 25cm) at the entrance of the capillary and a portion of the laser transmitted through the capillary is imaged onto a pyroelectric IR camera with 7 times magnification.

Figure 22 shows the images taken on the IR camera. Fig. 22(a) is the image at the focal point, while Figs. 22(b) and 22(c) are the images at 17 mm downstream from the focal point corresponding to the capillary exit. Fig. 22(b) is obtained in free space (capillary retracted) and Fig. 22(c) is obtained with the capillary discharge. Note that Figs. 22(b) and 22(c) are taken with the same scale and optical attenuation. Thus, transportation of the CO2 laser beam with a small size comparable to the focal spot is verified for the first time.

(a) (b) (c) Figure 22: The CO2 laser images at (a) the focal point, (b) 17mm downstream without the capillary (c) 17 mm downstream with the plasma discharge. The plasma capillary was set to a beam line of the BNL-ATF linac and transportation of the electron beam through the capillary was tested. The experimental setup is shown in Fig. 23. Two phosphor screens were placed downstream the capillary. One placed straight ahead (straight ahead screen) was used for direct measurement of the electron beam size, while the other one placed after the dipole magnet (spectrometer screen) was used to measure energy of the electron beam passing through the plasma channel.

CapillaryDischarge

ParabolicMirror

DipoleMagnet

electronbeam

Spectrometer Screen

Straight Ahead Screen Figure 23: Experimental setup to test the e-beam transportation through the plasma capillary.

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Figure 24 shows electron beam images on the screens with and without plasma discharge. One can find a portion of the electrons is focused while the rest is defocused by the plasma channel from the images on the straight ahead screen. On the other hand, acceleration and deceleration of the electron beam are seen in the images on the spectrometer screen. These effects can be understood as the plasma wakefield acceleration. Namely, the leading edge of the electron bunch generates plasma wakefield, and the bunch tail is accelerated and focused by the wakefield. Maximum amount of the acceleration is estimated to be 0.6 MeV, which corresponds to an average acceleration gradient of 35 MeV/m. This quite interesting phenomenon is also subject to study for future accelerators [20].

Spectrometer Screen

with plasma

Energy

no plasma

Straight Ahead Screen

x

x y

Figure 24: Images of the electron beam taken on the straight ahead screen and the spectrometer screen with and without plasma discharge. 3. Research Plan in 2003 In 2003, as a natural extension of results which have been obtained in 2002 at both KEK and BNL, we will make various proof-of-principle demonstrations as follows. It may be considered that a final step of substantiating the proposed scheme of the polarized positron source can be accomplished by completing a positron polarimetry. On the basis of the transmission method, we have designed a positron polarimeter whose schematic diagram is depicted in Fig. 25. Polarized γ-rays of 107/bunch are incident on a W plate of 1 mm thickness resulting in creation of +× e4103 /bunch. As shown in Fig. 25, a separation magnet consisting of a pair of the dipole magnet is installed after the W plate to extract efficiently high energy positrons, which should have a high degree of polarization. Figure 26(a) shows simulated results of polarized-positron energy distributions before the separation magnet separately for left-handed and right-handed polarized positrons. When these positrons are passing

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through the separation magnet, the energy distribution is drastically modified as given in Fig. 26(b). Obviously we can obtain high energy positrons around 37 MeV, whose passing rate is 4.1 %. It is remarked that we can achieve a high degree of the polarization of 77 %. Thus separated positrons are injected on a Pb converter and circularly polarized γ-rays are generated via bremsstrahlung process. On the assumption that left-handed positrons injected on the Pb converter have an energy of 40 MeV, we obtain, as shown in Fig. 27, simulated results of energy distributions (a) for left-handed(L) and right-handed(R) γ-rays and (b) for a magnitude of the γ-ray polarization. The polarization of thus generated γ-rays can be measured in the similar manner to the γ-ray polarimetry except using a CO2 Cherenkov counter with a pressure of 5 atm so as to accept γ-rays whose energy is higher than 10 MeV (see Fig. 25). It is planned that the polarization measurement will be carried out in the 2003 summer. Technical details of the positron polarimetry is referred to Ref. 21.

Pair production

γ-ray

γ-rayCO

Cherenkovcounter

(5 atm, threshold: 7.6 MeV)

PbW- target

e+

e+

e-Separation

magnet

e-

e+

Pb

Positron beam polarimeter

polarized

10 /bunch7

γ-ray

Magnetizediron

Magnetic field

BremsstrahlungCompton

2

Pair production

Figure 25: Schematic design for the positron beam polarimeter.

Pol. 77%

0 200 400 600 800

0 10 20 30 40 50 60

Entry

Energy of positrons [MeV]

0 2000 4000 6000 8000

0 10 20 30 40 50 60

Entry

Energy of positrons [MeV]

(a) Before the separatin magnet (b) After the separation magnetC. E. 4.1%L

RSum

LR

Sum

Figure 26: The energy distributions of positrons before (a) and after (b) the separation magnet. The capture efficiency (C.E.) is 4.1% and then the polarization is 77%.

22

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40Energy [MeV]

Pola

rizat

ion

[%]

dσ/d

E [

mb/

MeV

]γ

Energy [MeV]

L

R

0 5 10 15 20 25 30 35 40

4

3

2

10

10

10

(a) (b)

Figure 27: The energy distribution and polarization of γ-rays by bremsstrahlung process in lead calculated by the GRACE. Here, it is assumed the incident positron is left-handed and the energy is 40MeV. At BNL, the long-waiting TW CO2 laser will be soon in operation. We are now on standby for conducting precision measurements of nonlinear Compton process using the x-ray spectrometer [16, 17]. If we can measure separately each harmonic component, we will be able to perform a detailed study to elucidate reaction mechanisms of the non-linear QED. Although we were able to transport efficiently the CO2 laser through a plasma capillary, much more theoretical study is needed to understand the Compton scattering in a plasma channel. Since an electron beam is modulated in a plasma as we observed, the energy and shape of electron beams are modified and as a result, the interaction of electron beams with laser beams seem to be far complicated. Hence we may not expect enhancement of produced x-rays by simple extension of the collision distance which we realize in the plasma channel. The careful measurement of x-ray signals using the spectrometer as well as a realistic theoretical study will give essential information on electron-laser-plasma interactions. Actually we have started a cooperative study on this with those at Korea Electrotechnology Research Institute (KERI) using a simulation code PIC. Figure 28 displays one example of the PIC calculations on the assumption of a uniform plasma distribution with a density of 1016 /cm3 and the parameters of the electron and laser beams at the BNL-ATF: (a) a longitudinal electric field and (b) a longitudinal momentum of electron beams. At present, there is no PIC codes which can deal with radiations of electrons. It is highly desired to incorporate the CAIN simulating Compton scattering into the PIC code.

(a) (b) Figure 28: PIC simulation on the assumption that the plasma distribution is uniform and the plasma density is 1016 /cm3. (a) longitudinal electric fields along the longitudinal axis due to the plasma wake field. (b) electron longitudinal momentum as a function of the longitudinal distance.

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D.P. Siddons, T. Hirose, S. Kashiwagi, M. Washio, D. Cline, F. Zhou, D. Kaganovich, and A. Zigler: Proceedings of ICFA Workshop of Quantum Aspects of Beam Dynamics, January 7-11, 2003 Hiroshima University, Hiroshima, Japan [19] T. Hirose , I.V. Pogorelsky , I. Ben-Zvi , V. Yakimenko , K. Kusche , P. Siddons, T. Kumita , Y. Kamiya , A. Zigler , B. Greenberg, D. Kaganovich, I.V. Pavlishin, A. Diublov, N. Bobrova and P. Sasorov:To be published in the Proceedings of 17th International Conference on the Application of Accelerator in Reseach and Industry, Nov. 12-16, 2, Univ. of North Texas [20] V. Yakimenko , I.V. Pogorelsky , I.V. Pavlishin , I. Ben-Zvi , K. Kusche , Yu. Eidelman , T. Hirose , T. Kumita , Y. Kamiya , J. Urakawa , A. Zigler , B. Greenberg: Submitted to Phys. Rev. Lett. [21] M. Fukuda, T. Hirose, Y. Kurihara, T. Okugi, A. Ohashi, T. Omori, J.Urakawa, M. Washio and I. Yamazaki: Proceedings of ICFA Workshop of Quantum Aspects of Beam Dynamics, January 7-11, 2003 Hiroshima University, Hiroshima, Japan [22] P. Chen, G. Horton-Smith, T. Ohgaki, A. W. Weidemann and K. Yokoya, Nucl. Instrum. Meth. A355, 107 (1995)