PLASMA FOCUSING OF HIGH ENERGY DENSITY ELECTRON AND
POSITRON BEAMS 
J.S.T. Ng, P. Chen, W. Craddock, F.J. Decker, R.C. Field, R. Iverson, F. King,
R.E. Kirby, P. Raimondi, D. Walz, SLAC, Stanford, CA. 94309, USA
H.A. Baldisy , P. Bolton, LLNL, Livermore, CA. 94551, USA
D. Cline, Y. Fukui, V. Kumar, UCLA, Los Angeles, CA. 90024, USA
C. Crawford, R. Noble, FNAL, Batavia, IL. 60510, USA
K. Nakajima, KEK, Tsukuba, Ibaraki 305-0801, Japan
A. Ogata, Hiroshima University, Kagamiyama, Higashi-Hiroshima, 739-8526 Japan
A.W. Weidemann, University of Tennessee, Knoxville, Tennessee 37996, USA
Abstract
We present results from the SLAC E-150 experiment on
plasma focusing of high energy density electron and, forthe first time, positron beams. We also discuss measurements on plasma lens-induced synchrotron radiation andlaser- and beam-plasma interactions.

1

INTRODUCTION

The plasma lens was proposed as a final focusing mechanism to achieve high luminosity for future high energy
linear colliders [1]. Previous experiments to test this concept were carried out with low energy density electron
beams [2]. The goals of the SLAC E-150 experiment are to
study plasma focusing for high energy, high density particle beams in the regime relevant to linear colliders, toobtain better understanding of beam-plasma interactions,and to bench-mark computer codes for plasma lens designs.
Such studies will help to develop compact and economical
plasma lens designs suitable for collider experiments. In
this paper, we present results obtained by the E-150 collaboration on plasma focusing of high energy density electron
and positron beams.

of the plasma lens, adjustable along the beam axis in arange of 8 to 30 mm from the center of the lens. The
Bremsstrahlung photons were detected 35 m downstream
by an air-Cherenkov detector. The synchrotron radiation
monitor, consisting of a stack of ionization chambers interleaved with polyethylene blocks, was installed 33 m downstream, in front of the Cherenkov detector. This detector
was used to monitor the synchrotron radiation emitted asa result of the strong bending of the beam particles by theplasma lens. It provided an independent measure of the
focusing strength. A toroid located just in front of the electron/positron beam dump was used to monitor the bunchcharge.
To create the plasma lens, a short burst (800 s duration) of neutral nitrogen or hydrogen gas, injected into
the plasma chamber by a fast-pulsing nozzle, was ionizedby an infrared laser and/or the high energy beam. The
neutral density was determined by interferometry to be
4  1018 cm;3 for N2 at a plenum pressure of 1000 psi.
The injected gas was evacuated by a differential pumping
system which made operation of the gas jet possible while
maintaining ultra-high vacuum in the beam lines on eitherside of the chamber.

2 EXPERIMENTAL SETUP
The experiment was carried out at the SLAC Final Focus
Test Beam facility (FFTB)[3]. The experiment operated
parasitically with the PEP-II B-factory; the high energy
electron and positron beams were delivered to the FFTB
at 1 - 10 Hz from the SLAC linac. The beam parameters
are summarized in Table 1.
A layout of the beam line is shown in Figure 1. The
beam size was measured using a wire scanner system. A
carbon fiber 7 m in diameter was placed downstream Work supported in part by the Department of Energy under contracts
DE-AC02-76CH03000, DE-AC03-76SF00515, DE-FG03-92ER40695,
and DE-FG05-91ER40627, and the Univ. of California Lawrence Livermore National Laboratory, through the Institute for Laser Science andApplications, under contract No. W-7405-Eng-48; and by the US-Japan
Program for Cooperation in High Energy Physics.
y Also at UC Davis, Dept. of Applied Science.

Table 1: FFTB electron and positron beam parameters forthis experiment.
Parameter
Value
Bunch intensity
1:5  1010 particles per pulse
Beam size
5 to 8 m (X),
3 to 5 m (Y)Bunch length
0.7 mmBeam energy
29 GeV
Normalized emittance 3 to 5 10;5 m-rad (X),
0.3 to 0.6 10;5 m-rad (Y)Beam density 7  1016 cm;3

Synch. Radiation Monitor/
Wire scanner Detector

Dipole+e- / eCherenkov
target

11111
00000
00000
11111
00000 Photon beam line
11111

111
000
000
111
000
111
p
000
111
000dum111

Final Quads

1
0
0
1
0
1
0
1
0
1

0
Plasma Lens 101

e- / e+Steering dipole

to streak cameraeam

B

Figure 1: Layout of the plasma lens measurement setup.

Plasma focusing

600

Beam size σx (µm)

700
Gas jet OFF
σ = 7.3 µm

500
400
300
200

8
6
4
2

100
0
900

Beam size σy (µm)

Wire scanner detector signal (ADC)

For a bunched relativistic beam traveling in vacuum, theLorentz force induced by the collective electric and magnetic fields is nearly cancelled, making it possible to propagate over kilometers without significant increase in its
angular divergence. In response to the intruding beam
charge and current, the plasma electron distribution is reconfigured to neutralize the space charge of the beam andthereby cancel its radial electric field. For a positron beam,
the plasma electrons are attracted into the beam volume
thus neutralizing it; for an electron beam, the plasma electrons are expelled from the beam volume, leaving behindthe less mobile positive ions which neutralize the beam.
When the beam radius is much smaller than the plasma
wavelength, the neutralization of the intruding beam current by the plasma return current is ineffective because of

Gas jet ON800

σ = 4.2 µm

700
600
500
400

-20

0

Beam position (µm)

2040Figure 2: Wire scanner data of transverse beam profile
showing focusing of a 29 GeV electron beam by a selfionization plasma.

Gas-jet OFF
Gas-jet ON

05

BPIC calculations

4
3
2
1

300
-40

Plasma Lens

3.1

the small skin depth. This leaves the azimuthal magnetic
field unbalanced which then “pinches” the beam. In thisexperiment, typical plasma densities were of the order of1018 cm;3 , corresponding to a plasma wavelength of approximately 30 m which was indeed much larger than theincoming beam radius.
For data taken with beam self-ionization, the plasma wascreated when a small fraction of the neutral gas molecules
was ionized due to collisions with the high energy beam
particles, and the secondary electrons from this impact ionization process were accelerated by the intense collective
field in the beam, transverse to the direction of propagation, to further ionize the gas [4]. That is, the head of thebunch was able to ionize the gas while the core and the tailof the bunch were focused.
The results on beam size reduction due to focusing ofelectron beams by a self-ionization plasma are shown in
Figure 2. The transverse beam profile was obtained bymeasuring the Bremsstrahlung signal as the beam was

0

Plasma Lens

3 RESULTS

-10

-5

0

5

10

15

20

25

Z (mm)

Figure 3: Beam-induced plasma focusing of electron
beams. Statistical error only. Results are compared with
3D particles-in-cell simulations.

The beam envelope was obtained by measuring the transverse beam size as a function of the downstream distance(Z) of the wire scanner from the plasma lens. The results
are shown in Figure 3; a reduction by a factor two in thetransverse beam spot area was observed.
Data on focusing by a laser ionized plasma were also collected. The turn-key infrared ( = 1064 nm) laser systemdelivered 1.5 Joules of energy per pulse of 10 ns FWHM at
10 Hz. The laser light was brought to a line focus at the gasjet; the plasma thus produced was approximately 0.5 mm
thick as seen by the e+ =e; beams. With the relatively long
infrared laser pulse, the pulse front was able to ionize asmall fraction of the gas by multiple-photon absorption; theresulting secondary electrons were accelerated, transverseto the laser’s incident direction, to further ionize the gas.
This process led to an avalanche growth in plasma density,
similar to the beam self-ionization case.
The transverse beam profiles showing focusing of a 29
GeV positron beam by a laser ionized plasma are given in
Figure 4. There are several systematic effects in the beam
size measurement process. First of all, the carbon-fiber size
contributed 1.7 m to the RMS beam size; this was subtracted in quadrature. Since it took many beam pulses tomake a profile measurement, the shot-to-shot jitter in beam
centroid position also had an effect. The amount of jitterwas estimated to be 25% of the beam size, by measuring
the RMS fluctuation at given beam-scan position. Whensubtracted in quadrature, beam jitter accounted for 6% of
the beam size. The positron beam spot was also observed
to have a roll angle of 13 with respect to the beam scan direction. The measured transverse beam size was therefore
a projection of the true spot size. The effect was negligible
except where the aspect ratio of the beam spot was large inwhich case it was found to be up to 30%.
Because of the strong plasma focusing and the resulting increase in beam divergence, narrow apertures downstream could lead to systematic distortions of the measured
beam profile. This effect showed up as an asymmetry in the
beam profile, when a portion of the Bremsstrahlung photons were occluded by downstream collimators. The total
photon flux, as given by the area under the profile curve,
could be reduced by up to 40%. The bunch charge monitored by the toroid just in front of the beam dump showed
no loss in beam particles in the plasma lens. The observed
asymmetry was also partly the result of beam particles inthe tail of the bunch being deflected by wakefields in the
linac. The beam profiles were fitted to two half-Gaussians;
the larger of the two  ’s was taken as the beam size. The
accuracy of this procedure was determined using Monte
Carlo ray-tracing simulations. The collective fields created

Wire scanner detector signal (ADC)

scanned across the carbon fiber. The wire scanner data
were taken with the gas nozzle turned on and off at eachbeam position, so as to minimize the systematics due tochanges in beam conditions when comparing beam sizes
measured with and without plasma focusing.

700

No plasma600

σ = 10.1 ± 0.3 µm

500
400
300
200
100

700

Laser ionized plasma600

σ = 5.3 ± 0.1 µm

500
400
300
200
100
-80

-60

-40

Beam position (µm)-200Figure 4: Wire scanner data of transverse beam profile
showing focusing of a 29 GeV positron beam by a laser
ionized plasma.

by the bunch is [5]:Ey + iEx=;reN(z; t)2 hw; px + iy 
40x 1 ; r2 x 2(1 ; r2 );y 2  ; xr + iy=r ix2
exp ; 2 ; 2 w p
2x 2y x 2(1 ; r2 )where r = y =x is the aspect ratio, (z; t) the longitudinal bunch distribution, and w is the complex error function.
This was used to simulate the the spatial dependence of particle deflection inside a plasma lens. Linear optics was used
to simulate the situation without plasma lens. The simulations showed that the beam size measured by fitting two
half-Gaussians to an asymmetric profile due to occlusion iswithin 10% of the true values.
The beam envelope measurements for laser (and beam)ionization plasma focusing of positron beams are shown in
Figure 5. In the X-dimension, the beam envelope is shown
converging without plasma focusing (square points); whilewith laser (and beam) induced plasma focusing (filled circles), the beam envelope is shown converging towards a
reduced waist and then diverging because of the strong focusing. In the Y-dimension, the waist is at a location close
to the the plasma lens beyond the reach of the wire scanner; the beam envelope is seen diverging more rapidly due
to the strong plasma focusing.
As shown in previous studies [6], a plasma lens can enhance the luminosity of SLC/NLC type colliders by a factorof five. However, careful design optimization is required.
The aberration power describing the phase space dilution

Beam size in X (µm)

penetration profile from the carbon wire alone, then scaling this profile to the signal measured in the last depth section of the monitor with the beam-associated backgroundremoved. After these background contributions were subtracted, an excess in the photon signal beyond a depth of
3 radiation lengths was observed in the electron beam selfionization plasma focusing data, for nitrogen gas at 550
psi plenum pressure. This excess was not observed whenplasma focusing was weak (as determined from beam spot
size measurements) for the case of lowered plenum pressure (to below 100 psi, for example), or for the case of hydrogen gas for which beam self-ionization was much lesseffective.
The penetration profile of the observed signal is consistent with synchrotron radiation with a critical energy of afew MeV according to Monte Carlo simulation. This value
corresponds to a focusing gradient of the order of 10 6 T/m,as expected for the plasma lens parameters in this experiment.

12

6
4

Plasma Lens

8

No plasma
Laser ionized plasma

2
0
7
6
5
4
3

Plasma Lens

Beam size in Y (µm)

10

2
1
0
0

5

10

15

20

25

30

35

40

Z (mm)

Figure 5: Plasma focusing for positron beams in the X (top)and Y (bottom) dimensions. Errors shown are statistical
combined in quadrature with a 10% systematic uncertainty.
by a plasma lens is given for a thin lens by [7]:"P=

1 + 0:15 



0
f1

2 #1=2(1)

where f1 is the plasma lens focal length. Since the luminosity enhancement would be compromised by a factor P ,the function and the strength of the plasma lens need tobe matched to minimize the aberration.

3.2

Synchrotron radiation induced by plasma
focusing

The synchrotron radiation induced by the strong deflection of beam particles inside the plasma lens provides an
independent measure of the plasma focusing strength. It
also provides a pulse by pulse diagnostic of the transient
plasma lens effect. The critical energy of the emitted synchrotron radiation scales with the strength of the focusing;
the synchrotron radiation monitor was designed to measure
the penetration profile, which depends on the energy spectrum of the photon flux.
The photon flux detected in the synchrotron radiation monitor contained various background contributions.
There was Bremsstrahlung radiation accompanying thebeam due to off-axis beam particles interacting with thevacuum chamber wall or upstream collimators, and alsosynchrotron radiation (with a critical energy 250 keV)emitted when the spent beam was deflected towards thedump. This was measured with the gas jet turned off andthe wire scanner removed from the beam. The contribution
from beam-gas Bremsstrahlung, with the gas nozzle turned
on, was determined by first measuring the Bremsstrahlung

3.3

Laser- and beam-plasma interactions

Because the laser avalanche ionization process has a finite build-up and decay time, by varying the laser preionization timing before beam arrival at the plasma, different plasma densities can be probed by the high energy
beam. The signal in the synchrotron radiation monitor wasmeasured as a function of this advanced timing. Since thissignal was predominantly synchrotron radiation induced byplasma lens focusing, the interaction between the high energy beam and the plasma at various stages of formationand decay was monitored. This also means that focusing
was observed well into the “after-glow” regime of the laserinduced plasma [9].
The result for positron beams and nitrogen gas at 1050
psi is shown in Figure 6. Time zero corresponded tocoincidence between the beam arrival time and the peakof the recombination signal detected in a photomultiplier.
The ionization efficiency was measured at time zero also.
The synchrotron radiation monitor signal from beam selfionization plasma focusing was measured at 300 counts(with the laser turned off); the beam-only background signal level was 80 counts (with the gas nozzle turned off).
A quantitative understanding of this delay curve requires
detailed modeling of the laser- and beam-plasma interaction process, as well as gas dynamics. A qualitative explanation of this curve is given here. The initial rapid increase in synchrotron radiation monitor signal most likely
was due to an increase in plasma focusing strength, peaking
at 500 ns. The data shown in Figure 5 were collected withthis time delay, when the plasma density had decayed to an
optimal level with respect to the beam density. The rapid
rise was followed by a sharp decrease to the backgroundsignal level of 80 counts. This was predominantly due toan almost complete expulsion of the neutral and ionizedgas volume driven by a laser-induced shock wave. Eachgas jet pulse, lasting more than 100 s, supplied a continu-

5

REFERENCES[1] P. Chen, Part. Accel., 20, 171(1987).
600

400

[2] J.B. Rosenzweig et al., Phys. Fluids B 2, 1376(1990);
H. Nakanishi et al., Phys. Rev. Lett, 66, 1870(1991);
G. Hairapetian et al., Phys. Rev. Lett. 72, 2403(1994);
R. Govil et al., Phys. Rev. Lett. 83, 3202(1999).

300[3] V. Balakin et al., Phys. Rev. Lett. 74, 2479(1995).

200[4] R.J. Briggs and S. Yu, LLNL Report UCID-19399, May 1982
(unpublished).

100[5] M. Bassetti et al., IEEE Trans. NS-30, No.4, 2182(1983).

SRM signal (counts)

500

0
0

5000

1 10

4

1.5 104

Advance Timing of Laser Pulse (nsec)[6] P. Chen et al., Phys. Rev. E 48, No. 4, 3022(1993).
[7] J.B. Rosenzweig and P. Chen, Phys. Rev. D, 39, No.7, 2039
(1989).
[8] B. Chang et al., Phys. Rev. A 47, No. 5, 4193(1993).

Figure 6: Synchrotron radiation monitor signal (withoutbackground subtraction) as a function of the advanced laser
ionization timing with respect to beam arrival.

ous stream of neutral gas molecules into the vacuum chamber at sonic speed. Therefore, this abrupt reduction was
also assisted by the motion of the plasma, and by its decay.
The remainder of the curve starting at 1.5 s shows a diffusion driven gas recovery phase. Initially, the gas rushed
back to fill the void, giving rise to an increased gas density locally above ambient level at 8 s. During this time,a corresponding rise in beam-ionization plasma focusing
signal was observed, on a slow time scale determined bygas dynamics. This was followed by a decay back to local
equilibrium level of 300 counts within the time interval 8
to 12 s. A detailed simulation study should provide further insight into this delay-correlated modulation of plasma
focusing.

4 SUMMARY AND OUTLOOKResults on plasma focusing of 29 GeV electron and, forthe first time, positron beams have been presented. Beamself-ionization turned out to be an economical method for
producing a plasma lens. The infrared laser with a 10 nslong pulse also proved to be efficient in plasma production,
resulting in the strong focusing of electron and positron
beams. Data on other aspects of plasma focusing were alsocollected; detailed discussion is presented elsewhere [10].
Design studies for linear collider applications are juststarting. One of the issues being addressed is the effectof beam jitter on the achievable luminosity of plasma focused beams. Optimization of plasma lens parameters requires bench-marking of computer codes as well as better
understanding of the various plasma production processes.
The experience gained in this experiment will serve as abasis for further engineering design studies for an eventual
plasma lens application.

[9] P. Bolton et al., Proceedings of the 27th IEEE Int. Conf. on
Plasma Science, June 2000, New Orleans.
[10] J.S.T. Ng et al., Proceedings of the 9th Advanced Accelerator Concepts Workshop, June 2000, Santa Fe, NM.