PHYSICAL REVIEW SPECIAL TOPICS - ACCELERATORS AND BEAMS, VOLUME 3, 011301 (2000)

Observation of plasma wakefield acceleration in the underdense regime

N. Barov and J. B. Rosenzweig

Department of Physics and Astronomy, UCLA, 405 Hilgard Avenue, Los Angeles, California 90095-1547

M. E. Conde, W. Gai, and J. G. Power

High Energy Physics Division, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, Illinois 60439
(Received 22 July 1999; published 13 January 2000)
Initial experiments which have explored the physics of the underdense (blowout) regime of the
plasma wakefield accelerator (PWFA) at the Argonne Wakefield Accelerator facility are reported. In
this regime, the relativistic electron beam is denser than the plasma, causing the beam channel to
completely rarefy, and leaving a high quality accelerating region which also contains a uniform ion
column. This ion column in turn allows the drive and accelerating beams to be well guided over
many initial beam beta-function lengths. The results of these experiments, which have taken place over
several years, are reviewed. Notable achievements in the course of these studies include the creation
and measurement of drive and witness beam generated in an rf photoinjector, as well as previously
published studies on drive beam guiding in the underdense regime. In addition, these experiments
allowed measurement of both beam energy loss and gain, at a maximum average rate of 25 MeV兾m in
this regime of the PWFA, which is consistent with a peak acceleration gradient of 62 MeV兾m in the
excited waves. Difficulties associated with this type of experiment are discussed, as are prospects for
mitigating these difficulties and achieving high gradient acceleration in planned future experiments.

PACS numbers: 52.40.Mj, 52.75.Di, 29.17. + w, 29.27. – a

I. INTRODUCTION not on transverse offset; and (iii) multi-GeV gradient

operation at mm wavelengths. The physical reasons for
Much progress has been made in recent years in the
these attributes are displayed in part by Fig. 1, and are
experimental demonstration of acceleration in plasmas.
discussed further here.
The basic mechanisms for excitation of electron plasma
The beam, which has peak density nb well in excess
waves which support accelerating fields has been verified,
of the ambient plasma electron density n0 , ejects all
and accelerating gradients in excess of 30 GeV兾m have
of the plasma electrons from its propagation channel
been observed [1,2]. Despite this progress, however,
before the bulk of the beam has passed. Behind this
many problems concerning preservation of the beam
point inside of the plasma electron-rarefied region, the
quality during acceleration in high gradient plasma waves
fields are a superposition of an electrostatic component
remain experimentally unaddressed; plasma wave fields
due to the nearly stationary ions and a relativistic phase
tend to be nonuniform in their accelerating fields, and
velocity traveling electromagnetic wave. The ion-induced
nonlinear in transverse focusing fields. It is critical, from
fields provide electron beam particle focusing which is
the point of view of application of plasma acceleration to
high energy physics, that these concerns be mitigated.
Operation of the plasma wakefield accelerator (PWFA)
0.2
[3] in the extremely nonlinear (“blowout,” where the beam
is denser than the plasma) regime was originally proposed
by Rosenzweig, Breizman, Katsouleas, and Su in 1991 0.15
[4]. While this system is nonlinear from the point of view
of the plasma response—all of the plasma electrons are
r (cm)

driven out of the beam channel by the intense fields of 0.1

the driving beam—the attributes of the accelerating and
focusing fields are what accelerator physicists commonly
refer to as linear. Development of this regime represents 0.05

a serious attempt at formulating a version of a plasma

Drive beam region
accelerator which has the attributes of a standard rf linear
0
accelerator [5]. These attributes include: (i) focusing 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3
which, for electrons, is linear in offset from the symmetry z (cm)
axis, and independent of longitudinal position within FIG. 1. (Color) Particle-in-cell code (Barov [6]) simulation of
the wave; (ii) acceleration which is dependent only on blowout regime, with beam density much larger than plasma
longitudinal position within the accelerating wave, and density.

1098-4402兾00兾3(1)兾011301(10)$15.00 © 2000 The American Physical Society 011301-1

PRST-AB 3 N. BAROV et al. 011301 (2000)

dependent only on the plasma ion charge density 1en0 , already begun designed to run at densities in excess of
1 n0 艐 1014 cm23 , this implies possible accelerating gradi-
Fr 苷 2eEr 苷 22pe2 n0 r ⬅ 2 2 me nb2 kp2 r , (1)
ents around 1 GeV兾m for presently used plasmas. The
where 苷 kp2 vp2 兾nb2 .
This force thus allows simple, relatively long wavelength is an advantage for beam dy-
uniform, and linear focusing of the portion of the drive namics, as the injected beam parameters are relaxed [15],
beam inside of the rarefied region, as well as the beam and the smaller plasma density mitigates transverse emit-
which accelerates near the back of the rarefied region. tance growth due to multiple scattering of the beam off of
The focusing fields arise purely from the ions; the net plasma ions [4,16].
transverse force due to axisymmetric electromagnetic While the strength of the acceleration in the underdense
(TM) Er and Hf fields cancel in the ultrarelativistic limit. (blowout) regime, with nb . n0 , can exceed the nonrela-
Acceleration inside of the rarefied channel displays a tivistic wave-breaking limit, it is necessary to excite
nonsinusoidal dependence on longitudinal position 共j 苷 the plasma wave with a short pulse driving electron
z 2 nb t兲 within the accelerating wave, typically a saw- beam, in order that the plasma electrons not move to
toothlike electric field profile [3] which rises steeply as the shield the beam charge during beam passage. This
very high plasma electron density region (z ⬵ 2.44 cm in requirement can be stated as kp sz # 2, where sz is
Fig. 1) is approached. This density spike is formed when the rms length of the driving electron bunch. The
many of the plasma electrons which are blown out return mean electric field experienced by the driving beam
to the axis and cross it in a nonlaminar manner. Note that can be estimated by viewing the wakefield generation
even though laminarity is violated (the wave is broken), as a generalized coherent Čerenkov interaction [4,17],
a new rarefied region exists behind the density spike, and to give eEz,dec ⬵ e2 Nb kp2 兾2. The accelerating wakefield
the nonlinear wave pattern can continue beyond the first amplitude behind the driving beam is typically Ez,acc ⬵
half-oscillation of the plasma electrons. 2Ez,dec , so we may write
As the axisymmetric, TM electromagnetic wave which eEz,acc e2 Nb kp2
travels with plasma disturbance has an ultrarelativistic ⬵ 苷 re Nb kp , (2)
phase velocity, not only does its net transverse force eEWB me c2 kp
cancel [to order gb22 苷 1 2 共nb 兾c兲2 ], the acceleration with Nb equal to the bunch population. This ratio
is nearly independent of radial offset in the rarefaction is not necessarily greater than unity for all conditions
region, as shown in the fluid simulation [7] results of blowout— it is, in fact, approximately 0.1 in the
displayed in Fig. 2. experiments described in this paper.
It is interesting to note that in the simulations shown This situation, in which the beam is denser than the
in Figs. 1 and 2, the fields approach or exceed the non- plasma, but does not drive longitudinal wakes near to the
relativistic plasma
p wave-breaking limit [8–12], eEWB 苷 wave-breaking amplitude, is encountered when the beam
me c2 kp ⬵ n0 共cm23 兲 共eV兾cm兲. This allows for high radius or length is too small, so that even though the
gradient operation at longer wavelengths, due to lower beam is dense enough to achieve blowout, it does not
(relative to the linear regime) plasma densities and rela- have enough charge to drive large wake fields. This is
tivistic lengthening of the plasma oscillation period. The quantified as follows: for a bi-Gaussian beam distribution
experiments described here operate in the range n0 艐 with dimensions sz 苷 az 兾kp and sr 苷 ar 兾kp , with
1013 cm23 , with experiments [4,13,14] either planned or the requirements ar , 1 (the plasma electron motion is
strongly radial), az # 2 (the excitation is near to the
1.5
maximum attained with an instantaneous impulse), the
ratio of beam to plasma density is
Fr
1 nb Nb kp3 2re Nb kp
Fz
⬵ 苷 . (3)
n0 共2p兲 ar az n0
3兾2 2 共2p兲1兾2 ar2 az
0.5
Thus we have, combining Eqs. (2) and (3),
F/m e cω p

0
r
eEz,acc p 2 nb
⬵ a az , (4)
-0.5
eEWB 2 r n0
and, even for ratios of the beam兾plasma density larger
-1 than unity, the accelerating fields may fall well short of
wave breaking if the beam is narrow 共ar ø 1兲 or short
-1.5
0 0.5 1 1.5 2 2.5
共az ø 1兲. As the maximum wake fields will be obtained
kp r
when the plasma is chosen as dense as possible while still
FIG. 2. (Color) Wakefield forces in acceleration phase of allowing impulsive excitation of the wave, we inevitably
rarefied plasma wave, as a function of radius, from fluid code choose kp ⬵ 2兾sz 共az ⬵ 2兲, and thus the optimized (i.e.,
NOVO (Breizman et al. [7]). the wakes at the most favorable plasma density) wake

011301-2 011301-2
PRST-AB 3 OBSERVATION OF PLASMA WAKEFIELD … 011301 (2000)

amplitude is a strong function of the bunch length, the inequality given in Eq. (6) indicates that the Argonne
Wakefield Accelerator (AWA), which was not originally
2e2 Nb designed for low emittance operation, can drive a plasma
eEz,acc ⬵ . (5)
sz2 wake field in the blowout regime, but with a very small
margin of error.
With this constraint on the optimum choice of kp , the
value of ar is not chosen independently, but for a matched
beam is a function of beam emittance and energy, as we II. PRELIMINARY EXPERIMENTAL WORK
now discuss. AT ANL
All of the wake field characteristics examined so far A number of experimental measurements of the PWFA
concern the attributes of the fields in the rarefaction in the overdense 共n0 ¿ nb 兲 regime were carried out
region, where the accelerating beam must be located in at ANL using the Advanced Accelerator Test Facility
order to be propagated without transverse phase space (AATF) setup [23]. These include first observation of
dilution. The transverse wake fields for the drive beam, plasma wakefield acceleration and focusing [24], self-
however, are not so uniform, because the plasma must focused beam propagation [25], and excitation of non-
take a finite time to respond to the beam. Because of linear plasma wake fields [26]. After the advantages of
this, the leading edge of the beam expands as if it were operation in the underdense, blowout regime were real-
(ignoring small Coulomb scattering effects) in free space. ized, an experiment designed to observe GV兾m accelerat-
On the other hand, the main body of the drive beam ing wakes in this regime at the AWA photoinjector [3,27]
can be stably matched to the uniform focusing of the facility was begun. The experimental goals were based on
electron-rarefied ion channel. If the beam density is high assumption of an electron beam with charge of 100 nC,
enough, and the emittance is low, then the erosion of the sz 苷 0.75, and a normalized rms emittance ´n less than a
beam head is not an important effect in our experimental few hundred mm mrad. The bunch length achieved at the
parameter regime [18,19]. AWA has to this point never approached this value, how-
The question of whether the beam can self-consistently ever, and has been observed to be proportional to charge
propagate in the plasma without excessive transverse ex- above approximately 10–15 nC [5,19,28], below which
pansion has been explored in great detail analytically, it approaches the value sz 苷 2.5 mm. The scaling of
computationally [14], and, as discussed in the next sec- Eq. (5) indicates, therefore, that the optimum wake fields
tion, experimentally [5]. The work of Ref. [18] presents would be observed at the lowest charge where this pulse
an analytical model of how rarefaction must proceed, as- lengthening effect asserts itself. In this case, according to
suming the entire beam is in fact matched (in the be- Eq. (5), operation at 15 nC derates the expected wakefield
tatron sense, with no envelope oscillations) to the ion amplitude from the original design value (1.9 GV兾m), by
channel focusing. We review the relevant results from a factor of 0.03, or 60 MV兾m. As we shall see below,
Ref. [19] here. Given the constraint az # 2, the condi- this simple prediction is consistent with what has been
tion that the plasma electrons be rarefied by radial expul- observed.
sion due to beam space-charge fields before the arrival The initial attempts at measuring wake fields in the
of the tail end of the drive beam yields p the constraint blowout regime occurred in 1995, and were conducted
on the beam parameters, Nb $ 9´n 兾 4pg re , which is, with the experimental setup, shown in Fig. 3, at the AWA.
interestingly, equivalent to nb ⬵ n0 , with az ⬵ 2. This The electron beam in this set of measurements had a
condition can be satisfied by a high quality rf photoinjec- mean energy of 14.5 MeV, with charge of 13–17 nC,
tor [20–22]. It is, however, a bit of an optimistic model; and no rigorous estimate of the emittance available at the
beam-head erosion due to the fact that the beam head time. This beam was focused into the plasma at near the
feels less focusing during the blowout process than the matched beta function
tail is not self-consistently taken into account. Compu- p
tational studies of the effects of beam-head erosion, per- beq 苷 g兾2pre n0 (7)
formed with (i) Maxwell-Vlasov beam兾plasma electron
fluid computational mode, (ii) superparticle beam兾plasma c
electron fluid computational model, and (iii) a fully self- a
f
consistent particle-in-cell code, all indicate that one needs
approximately a factor of 2.5 larger charge to achieve
rarefaction behind the drive beam [15],
d e
6´n ´n 共mm mrad兲 b
Nb $ p ⬵ p ? 1.5 3 109 . (6)
g re E 共MeV兲
FIG. 3. Experimental setup including (a) focusing solenoid,
The results of the study in Ref. [18] are quite relevant (b) cathode assembly, (c) plasma confinement solenoid,
to the experiments we describe below. In particular, (d) anode assembly, (e) bend magnet, and (f) phosphor screen.

011301-3 011301-3
PRST-AB 3 N. BAROV et al. 011301 (2000)

by use of the upstream solenoid. In the measurements of delay time is dependent on the amount of compression the
this run, the plasma density was n0 苷 2.2 3 1013 cm23 , photoelectrons undergo during rf acceleration, the streak
obtained by use of the magnetically confined, hollow camera measurement was necessary to calibrate this delay
cathode arc source, featuring gas feed in the annular time for a specific set of conditions (e.g., beam charge and
off-axis region formed by dual tantalum cathode tubes size, acceleration field, and injection phase).
[5,21,22]. The plasma length is set in this device by the After we had developed the technique of witness
interelectrode distance, which in these experiments was beam generation, systematic measurements were made
12 cm. The plasma density in this device is mapped out with the experimental setup shown in Fig. 3. In these
with electrostatic probes, which have been calibrated by experiments, the drive and witness beams combined had
use of a 140 GHz microwave interferometer [29]. Q 苷 13 17, and could be focused to a sr 苷 450 mm
While the AWA facility now has a 5 MeV witness spot at the plasma entrance. To investigate the possibility
beam derived from a separate photoinjector, this low- of particles accelerated by the plasma wave, we recorded
energy witness beam was not yet commissioned in 1995, images of the high-energy end of the spectrometer’s
and so could not be considered for use. In addition, phosphor screen. Figure 5 shows the intensity profiles
the dramatic focusing provided by the matching solenoid for all possible combinations of switching on and off of
would cause the beam dynamics for a lower energy beam witness beam and plasma. Each point on this plot is the
to be very difficult to simultaneously match to the plasma result of several images from the camera, averaging the
focusing. Because of this, we employed a scheme in set of energies corresponding to a fixed intensity.
which a witness beam was generated in the main AWA With no plasma present, the beam energy distributions
photoinjector along with the drive pulse. This was accom- are identical. This suggests that prior to entering the
plished by removing a central disk region of a cathode- plasma, the witness beam’s high-energy tail is at or below
drive laser transport mirror, and providing a sliding delay that of the drive beam and does not appear in the plots.
(⬃20% of the full laser pulse) of the photons in this disk Without a method to diagnose the witness beam alone, we
by changing the longitudinal position of a small mirror could only conclude that the lower limit on the witness
behind the mirror with the missing disk. This allowed beam’s gain in energy as a result of the beam-plasma
production of a witness beam, which had a similar energy interaction is 0.5 MeV. Note that at lowest intensity,
and density, and thus beam-plasma frequency, as the drive the gain in energy of the tail is approximately twice as
beam. This is a necessary condition for stable propa- large again. Therefore the average acceleration field was
gation of both beams in the strong focusing of a space- at least as large as 4.1 MeV兾m in this run.
charge dominated beam transport system [30,31]. This When trying to compare these data with simulation
two-beam system could produce drive-witness delays as results, we found that a sr 苷 450 mm beam’s core
long as 70 psec, corresponding to laser path differences of focuses to 180 mm rms radial size inside of the plasma,
about 3 cm. Figure 4 shows a streak camera trace result- and then oscillates while staying below 330 mm. This
ing from light emitted inside of a 1 mm thick fused silica implies that in places along the propagation the beam
Čerenkov radiator placed in the path of the beam (inclined is 4 times denser than the plasma, locally satisfying
11± to the normal), with the light directed to a Hama-
matsu C1587 temporal disperser. Since the drive-witness
160

140 wit. and pl.

1 pl., no wit.
120 wit., no pl.
Video camera intensity

0.8 no wit., no pl.

100
Current (arb. units)

0.6 80

60
0.4
40
0.2
20

0
0
0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

t (psec) ∆E (MeV)

FIG. 4. Streak camera trace of beam-derived Čerenkov radia- FIG. 5. Observation of the high-energy tail at spectrometer.
tion, showing 14.5 MeV drive and witness beam profiles gen- In the legend, “wit.” indicates witness beam and “pl.” indicates
erated simultaneously in the AWA photoinjector. plasma present.

011301-4 011301-4
PRST-AB 3 OBSERVATION OF PLASMA WAKEFIELD … 011301 (2000)

the underdense criterion. The witness beam in this

experiment was positioned so far back that it overlapped
with the second peak in the acceleration field. The
simulation corresponding to this case resulted in the
formation of wake fields at 20 MeV兾m averaged over
the propagation, assuming a 13 nC drive beam, a number
not in disagreement with measurements. Major possible
sources of disagreement between the experiment and the
simulations are observed nonaxisymmetries in the beam
distribution due to cathode nonuniformity, space charge,
and transverse wakefield effects. These effects were
observed in the next round of acceleration experiments.
Although these experiments yielded some advances in
our experimental technique, notably the novel method of
witness beam generation, there were several unsatisfac-
tory aspects of the measurements. The first is that the
beam, from these measurements, was known to be roughly
as dense as the plasma at the beginning of the plasma col- FIG. 6. Diagnostics beamline and plasma cell (shown without
the plasma radial confinement solenoid). The anode diagnostics
umn, and suspected to be much denser inside of the col- include (a) tungsten collimator with (b) 1 mm wide slit,
umn. However, no actual experimental information was (c) 500 mm thick quartz Čerenkov plate, and (d) mirror and
known about its propagation within the plasma. Also, the outgoing light.
spread of the witness beam in time (see Fig. 4) was not
much smaller than the wavelength, and so the time reso-
lution of the measurement was not appropriately small. In entrance are established by use of the insertable Faraday
addition, the resolution of the energy spectrometer given cup FC1 and the optical transition radiation (OTR) mirror
such a large transverse emittance beam was not very good. inside of the plasma chamber, respectively. The down-
Because of these shortcomings, we undertook a number of stream diagnostics assembly, located at the plasma exit,
actions to improve the experiment: we upgraded the up- begins with a tungsten collimator having a 1 mm wide
stream beam diagnostics, in order to establish our initial slit aperture in it, followed by a 500 mm thick quartz
conditions better; we performed a detailed measurement Čerenkov plate, and a mirror to relay the Čerenkov light to
of the matched beam propagation in the plasma, estab- either a CCD camera or a streak camera. The Čerenkov
lishing unequivocally that the beam was denser than the light allowed for both time-integrated and time-resolved
plasma; and we upgraded the energy measurement system imaging of the beam profile at the plasma exit. The slit
with a new spectrometer, as well as a slit-collimation in- assembly allowed for an independent check on the fo-
troduced in the propagation experiments. cusing, by giving a fractional charge passed signal ob-
The results of the matched beam propagation experi- tained from comparison of the upstream nondestructive
ments are described in great detail in Ref. [6], but the integrating current transformer (ICT) measurement, and
methods and results of these experiments are of high im- the charge collected in the beam dump Faraday cup (FC2).
portance for understanding of the acceleration results we The combination of the two diagnostics gave a powerful
present in the next section, and so we review them here. veto on shots that were off-slit center, or too asymmetric.
The purpose of the acceleration experiments was to re- The analysis of the data obtained in this experiment
liably measure beam charge, bunch length, and the trans- agreed well with the comparison to simulations, and veri-
verse beam profiles at both the entrance and the exit of the fied the general conclusions of the computational and
plasma column, in order to create and diagnose the self- theoretical analysis of the beam propagation character-
guided conditions necessary for long range acceleration in istics found in Refs. [18] and [19]. In summary, it
the blowout regime. These experiments were the first to was found that the 14.5 MeV, Q 苷 14 nC, ´n ⬵ g´ ⬵
test underdense plasma lens action [32] in the short-pulse 150 mm mrad beam could be focused to an initial spot
(wakefield acceleration) regime [18,19]. at the plasma entrance OTR screen of initial spot of
The experimental setup for these measurements is sr ⬵ 280 mm, corresponding to an initial beam func-
shown in Fig. 6. The upstream region of the beamline be- tion of the waist of bi ⬵ 1.5 cm. In the absence of ion-
tween the AWA photoinjector and the plasma was instru- derived plasma focusing, this beam expands by a factor
mented for charge, energy, emittance, and beam profile of 3 by the time it encounters the slit, and very little
measurements, in order to establish the initial conditions charge is passed to the diagnostics. When the plasma
on the beam state, even in the presence of relatively large 共n0 苷 1.15 3 1013 cm23 兲 is turned on, the body of the
shot-to-shot fluctuations in the beam charge. The beam beam propagates in its self-formed ion channel, with equi-
charge and profile characteristics directly at the plasma librium beta function beq ⬵ 1.25 cm, which is very close

011301-5 011301-5
PRST-AB 3 N. BAROV et al. 011301 (2000)

to a matched case, considering the effects of the initial The collimating slit assembly serves the same primary
ramping up of the plasma density [15]. Most of the charge purpose in this experiment as in the propagation experi-
passes through the slit collimation system at the plasma ment, that of ensuring that one has tuned for the best trans-
exit, with the time-integrated and time-resolved transverse verse focusing match to the plasma, as measured by the
profiles giving a detailed picture of the beam distribution fractional transmission through the slits. It also serves as
at the plasma exit. The beam, with measured temporal a filter to the particles accepted into the spectrometer, as
width FWHM of 25 psec 共kp sz 苷 1.9兲, was determined only particles with small horizontal offset, and therefore
to propagate with peak density of at least nb 兾n0 ⬵ 2.5. within or near the plasma-electron rarefied beam channel
The agreement of the time-resolved beam profile mea- will pass the slits. As the slits provide a horizontally nar-
surements with simulation was very good, as the beam row “source,” the initial conditions for the quadrupole/
showed the characteristic “trumpet” shape of an expanded spectrometer beam optics are well defined, the tuning of
beam head, with the beam body well matched to the fo- the spectrometer optics is made more straightforward, and
cusing, essentially not expanding over a distance greater the ultimate spectral resolution of the device improved.
than 8 times the initial beta function. The success of this The slits also allow the dimension along the slit (vertical)
experiment, at both creating and diagnosing the condition to be used for observation of transverse information, such
of blowout in the beam-plasma interaction, allowed us to as evidence for the electron hose instability [33], while
proceed to the next round of acceleration experiments. the direction normal to the slit is used for energy dis-
persion. This is analogous to setup for the propagation
III. ACCELERATION AND DECELERATION IN experiments, in which the dimension parallel to the slits
THE BLOWOUT REGIME was used for spatial profile information, with the direction
normal to the slits reserved for temporal dispersion.
The latest set of experiments was performed with the The additional experience in operation of the AWA,
upstream beam diagnostics, matching optics and diagnos- and to matching of the beam to the induced plasma focus-
tics, and plasma source in essentially the same configu- ing, over the previous runs was evident in the achieved ex-
ration as used in the blowout propagation experiments perimental parameters, which are summarized in Table I.
described above. After the downstream end of the plasma, The beam charge, as measured in the plasma chamber
the tungsten collimator slit assembly remained , while the at FC1, was raised in this experiment to a mean value
beam diagnostics were converted from transverse to en- of 18 nC (again with large rms fluctuations of 65 nC),
ergy measurements, and the beam charge measurement while the pulse length was shortened a small amount to a
was changed to a nondestructive ICT. The energy spec- mean FWHM value of 20–24 psec. This beam, optimized
trum was measured in this case by use of a high-resolution for energy exchange with the plasma rather than propaga-
(as compared with the device shown in Fig. 5) magnetic tion as in Ref. [6], had larger normalized emittance ´n ⬵
dipole spectrometer constructed expressly for this experi- 180 6 30 mm mrad than before and was again slightly
ment. A vertically focusing quadrupole magnet upstream mismatched to the plasma focusing. The shorter bunch
of the spectrometer allowed all of the beam charge to be length allowed a slightly larger plasma density of n0 ⬵
transported through the dipole magnet gap, and to give an 1.3 3 1013 cm23 共kp sz 苷 1.75 2兲 to be used in this
optimized image of highest resolution, at the focal plane round of experiments. The mean ratio of the beam-to-
of the spectrometer. plasma density for the average case is thus approximately
nb 兾n0 ⬵ 3 at the beginning of the plasma, giving very
underdense conditions. The fractional beam transmission
past the plasma exit slits was not as high (less than 0.4)
in this round of experiments as in the propagation ex-
periments (less than 0.7). This result is consistent with
the simulations of the experiment, which are described
below. It is due to the effects of running with a larger
beam emittance and smaller kp sz in this experiment,

TABLE I. Experimental parameters for blowout regime

plasma wakefield acceleration experiment at the AWA.
Beam energy 15.6 MeV
Beam charge 共Q兲 18 6 5 nC
Pulse length (FWHM) 20 – 24 psec
Initial rms transverse size 共sr 兲 250 mm
FIG. 7. Downstream beam diagnostics, with slit collimation Mean peak beam density 共nb 兲 4.0 3 1013 cm23
in plasma arc anode, quadrupole lens, and high-resolution Plasma electron density 共n0 兲 1.3 3 1013 cm23
magnetic spectrometer with example trajectories.

011301-6 011301-6
PRST-AB 3 OBSERVATION OF PLASMA WAKEFIELD … 011301 (2000)

both of which enhance beam-head erosion, but were a Injection timing jitter of the photocathode drive laser with
necessary result of our experimental maximization of ob- respect to the rf wave, which is estimated at 7 psec rms
served beam acceleration. The use of a larger peak cur- (3.1±) caused the beam to have a momentum centroid jitter
rent beam allowed higher energy gain to be observed, but of 0.9%. A shot with maximal injection centroid error, of
with its higher emittance had the unfortunate attribute of course, has enhanced energy spread. This is illustrated in
enhanced beam-head erosion, as is discussed below. Fig. 8(b), where the momentum spectrum is larger because
Because the witness beam which could be produced in of the correlated energy spread due to injection timing
the main AWA photoinjector was not notably shorter than error. This correlation allows a structure to be observed
the drive beam, as seen in Fig. 4, and furthermore was in the nondispersive dimension. This type of structure
quite difficult to align to the drive beam (to the degree is due to strongly fluctuating intensity nonuniformities
that both could be successfully propagated through the within the laser pulse envelope. These intensity non-
slits), these experiments were performed with only the uniformities, which differ from shot to shot [34], produce
drive beam tail used to measure acceleration. It should be large effects in the energy measurements in some shots.
noted that this method is also to be employed in the plasma These effects are displayed in Fig. 9, which shows
wakefield acceleration experiment E-157 at the SLAC (i) a well-behaved shot, with little structure in the nondis-
Final Focus Test Beam Facility [13]. The full spectrum persive plane and large deceleration/acceleration observed,
of the drive beam was then observed in the focal plane of and (ii) a shot with considerable filamentary structure and
the spectrometer, producing momentum spectra along the less acceleration. It was clear that the more poorly behaved
dispersive direction, as seen in Figs. 8 and 9 for cases with shots had structure in the dimension along the slit, which
and without plasma present. The momentum spectrometer would lead the driving of a less symmetric, poorer qual-
video data, as well as the ICT signals for each shot were ity wave, deflection of the beam tail, and a smaller region
recorded, and a large number of shots at a given set of beam that can optimally accelerate electrons. These effects lead
and plasma conditions were taken for this experiment. to less observed total acceleration in the filamentary cases.
Without plasma present, the beam’s minimum rms As the drive beam itself provides the accelerating particles,
momentum spread of 1% [Fig. 8(a)] was smaller than the observed accelerated spectrum is also a function of the
measured with the previous spectrometer (with no slits), filamentary nature of this beam. Note also the existence of
indicating that the resolution of the momentum (or,
alternatively, energy) measurement system was improved
with a better defined source provided by slit collimation.

FIG. 8. Video image made by beam, with no plasma present,

striking phosphor of focal plane in momentum analyzing FIG. 9. Video image made by beam, with plasma present, in
spectrometer, for (a) typical narrow spectrum case and momentum analyzing spectrometer, for (a) a good acceleration
( b) larger momentum spectrum due to injection phase fluctua- case 共Q 苷 19 nC兲 and ( b) a case where the tail is deflected,
tion. Note the transverse (vertical dimension) structure of the and less acceleration is observed. Note hot spots centered at
image in this case. distinct energies.

011301-7 011301-7
PRST-AB 3 N. BAROV et al. 011301 (2000)

hot spots, centered at distinct energies, in the spectrome- dence on charge. The maximum observed deceleration,
ter focal distribution in both Figs. 9(a) and 9(b), which is which arises from the beam core, had smaller fluctuations
further evidence that the beam distribution is not smooth, at a given charge than the fluctuations in maximum accel-
but filamentary. This filamentation of the beam in energy eration, and a strong negative linear charge dependence.
may indicate that the initial longitudinal distribution is not On the other hand, the linear charge dependence of the
smooth, but has notable structure. This type of structure maximum observed acceleration was positive, but weaker
is not readily observable in picosecond-resolution streak than the charge dependence of the maximum observed de-
camera images, however, due to the inherent noisiness of celeration, with the large fluctuations due to the facts that
this type of measurement. smaller numbers of electrons are available in the tail to be
It would be interesting to be able to attribute the accelerated and these electrons can be easily steered away
transverse filamentation of the beam in the spectrometer from the maximum acceleration region.
to electron hose instability [19,33]. This cannot be done The spectrum for the well-behaved shot of Fig. 9(a)
with confidence from these data, however, as while the is displayed in Fig. 11, along with a simulated spectrum
observed maximum transverse offset in the spectrometer obtained from running the hybrid beam superparticle/
is large for filamentary shots, it is not enough larger than plasma fluid code [15,18] based on NOVO [7]. The
the maximum offset for well-behaved shots, as illustrated simulated particles were loaded initially at the entrance
by Figs. 9(a) and 9(b), to justify the claim of instability of a uniform plasma (the plasma density is uniform to
onset. In fact, it may be possible that the dramatic better than 10% over the interelectrode distance [29])
structures observed in shots like Fig. 9(b) are due in large with a thermal, uncorrelated distribution in all phase
part to the simple expansion of the momentum spectrum planes. Explicitly, this means that Gaussian distributions
in combination with the plasma focusing transporting with rms spreads corresponding to measured values in
more electrons through the slit. These effects certainly all Cartesian coordinate and momentum dimensions were
allow the filamentary nature of the beam in configuration launched at the plasma entrance, with no correlation at
and phase space to be more clearly observed. this point between any of the phase space dimensions.
The energy spectra for the shots observed at the opti- This same type of distribution, although clearly not in
mum beam and plasma conditions given in Table I have detailed agreement with the actual highly correlated beam
been further analyzed. Three quantities have been ex- obtained from the AWA photoinjector, was used in the
tracted from analysis of these spectra: (i) the peak in computational analysis of the propagation experiments
the spectrum, which should be due to the electrons in [6]. In these previous experiments, good agreement
the region near the beam head that are well guided but between the data and simulation was obtained, with a
not strongly decelerated, (ii) the lowest resolvable energy, notable exception being that the erosion of the beam
and (iii) the highest resolvable energy. These quantities head is actually overestimated in the computations. This
have been plotted in Fig. 10 as a function of shot charge exception was due to the fact that the emittance at a given
reported by the upstream ICT. While there was a large longitudinal slice of the beam is smaller than the total
spread in maximum observed deceleration and accelera- projected emittance [20,31].
tion at a given charge due to the intensity nonuniformities, The comparison between simulation and experiment
the momentum of the spectrum peak had small fluctua- in the present case is shown in Fig. 11, which displays
tions and, further, had a very small negative linear depen- the experimental energy spectra for the case of Fig. 9(a)

50
18

40
17
Intensity (arb. units)

30
Energy (MeV)

16
Experiment

20
15 Simulation

14 10

High
Peak
13 0
Low
12 14 16 18 20 22
12 16 20 24 28 Energy (MeV)
Q (nC)
FIG. 11. Measured energy spectrum from the case of
FIG. 10. Minimum, maximum, and peak intensity of mea- Fig. 9(a), compared to simulated (with hybrid superparticle/
sured energy spectra, as a function of charge Q. plasma fluid code) spectrum.

011301-8 011301-8
PRST-AB 3 OBSERVATION OF PLASMA WAKEFIELD … 011301 (2000)

and a computer simulation, which included the final 0.2

slit collimation. As the computational model assumes a
perfectly symmetric, thermalized bi-Gaussian beam, we

e Ez /mcωp , nb (on-axis, norm.)

adjusted the simulation parameters within experimental
uncertainty to give us the best spectral fit. In the case
shown, we used the following parameters: Q 苷 17 nC,
´n 苷 200 mm mrad, FWHM pulse length of 24 psec, 0
an initial energy of 15.6 MeV, and plasma density of
n0 苷 1.25 3 1013 cm23 . The simulation is in fairly good
agreement with the experiment, with the experimental
and simulated spectra displaying the same qualitative E z (z=1 cm)
E (z=12 cm)
signatures in the deceleration and acceleration regions, z
initial beam profile
as well as good quantitative agreement on the actual
placement of the decelerated and accelerated distribution -0.2
0 2 4 6 8 10
end points. The observed peak intensity of the spectrum k p (z-ct)
near the initial energy is not well pronounced in the
case of the simulation. This is due to the fact, known FIG. 12. The initial on-axis beam profile, as well as longitu-
from the propagation experiments, that the beam-head dinal wake field at the beginning of the plasma 共z 苷 1 cm兲
and end of the plasma 共z 苷 12 cm兲, from simulation. The
region, which is weakly decelerated, guides better in wakefield amplitude and phase changes are due to beam-head
experiment than in simulation, due to the slice emittance erosion.
effect discussed above, as well as in Ref. [6]. Even
with the lack of detailed agreement in the measured and
IV. CONCLUSIONS
simulated spectral peaks, the acceleration and deceleration
end points are found to agree well. This round of experiments at the AWA facility gave
The simulations give some further insight into the the first measurements of plasma wakefield acceleration in
mechanisms responsible for the production of the spec- the blowout regime. These measurements were made pos-
tral shapes given in Fig. 11. In particular, it is observed sible by first establishing methods of achieving a verifiable
that beam-head erosion plays a large role in this type underdense plasma condition in a previous round of experi-
of experiment, which employs a relatively large emit- ments [6]. The observed maximum acceleration gradient
tance beam. Erosion of the beam head produces two ef- was 25 MeV兾m, corresponding to a peak field in the
fects: The first is that the beam-head expansion lowers the simulations presented of over 60 MeV兾m. While these
coupling of the beam to the plasma, producing a smaller measurements were consistent with the predictions of
amplitude wake. The second is that the wake, being pro- theory and simulation, they were difficult and fell short of
duced effectively by regions which progress backwards in design. The difficulties in these experiments were mainly
the beam frame, suffers a phase shift. Both of these ef- derived from the beam quality—the emittance was high,
fects give rise to a measured maximum average accelera- the beam was filamentary, with large variations in charge
tion, which in the case of Figs. 9(a) and 11 is 25 MeV兾m, and profile, and, most importantly, it was longer than
which is smaller than the peak maximum acceleration originally expected. At present, the AWA rf gun is under
gradient in the wave. These effects are illustrated in redesign and will be replaced [35]. The next gun should
Fig. 12, which shows the simulated longitudinal wake produce much shorter, high charge bunches more suitable
field near the plasma entrance 共z 苷 1 cm兲 and again near for driving large amplitude wake fields in the blowout
the plasma exit 共z 苷 12 cm兲. The peak accelerating field regime.
is degraded from jeEz j 苷 0.18me cvp 苷 62 MeV兾m to The next round of measurements we currently plan is to
49 MeV兾m. Note though, that an electron initially accel- take place at the Fermilab Test Facility [14,34] rf photoin-
erating on-axis at the wave peak for z 苷 1 cm suffers a jector. This facility has several advantageous attributes,
degradation of acceleration rate from 62 to 35 MeV兾m including a high quantum efficiency cesium telluride cath-
at z 苷 12 cm. This effect partially explains the discrep- ode, which can produce more uniform emission than the
ancy between the peak accelerating field created in the metallic cathodes used in this experiment, emittance com-
plasma and the maximum average acceleration, a dis- pensated optics, and, most critically, a bunch compres-
crepancy which is nearly the same as in the simulation. sor. With this source, we expect to be able to produce
The additional uncertainty associated with determining the 19 MeV, 14 nC bunches, with normalized emittance of
population and initial energy of the longitudinal tail of ´n ⬵ 80 mm mrad, and rms pulse length sz ⬵ 0.4 mm.
the non-Gaussian AWA beam, as well as the difficulty With a plasma source of density n0 ⬵ 1014 cm23 , this
in measuring the end point of the energy distribution in beam is predicted [14] to produce peak accelerating fields
a noisy accelerator enclosure, may provide other mecha- in excess of 1 GeV兾m in the blowout regime. With a
nisms for explaining the observed maximum acceleration. relatively low emittance and high current, the beam-head

011301-9 011301-9
PRST-AB 3 N. BAROV et al. 011301 (2000)

erosion problem is much smaller in this planned experi- [8] A. I. Akhiezer and R. V. Polovin, Sov. Phys. JETP 3, 696
ment than in the one reported here. (1956).
Erosion and driving beam distortion are signatures of [9] J. M. Dawson, Phys. Rev. 113, 383 (1959).
low-energy beam experiments, as they are driven by both [10] J. B. Rosenzweig, Phys. Rev. Lett. 58, 555 (1987).
the larger geometrical emittances and nontrivial energy [11] T. Katsouleas and W. Mori, Phys. Rev. Lett. 61, 90
(1988).
loss incurred in this type of experiment. This should not be
[12] J. B. Rosenzweig, Phys. Rev. A 38, 3634 (1988).
a problem in the upcoming E-157 experiment at Stanford [13] R. Assman et al., Nucl. Instrum. Methods Phys. Res.,
[13], which runs with a beam energy of 30 GeV. It would, Sect. A 410, 396 (1998).
however, enter into the design considerations for a multi- [14] J. Rosenzweig, N. Barov, E. Colby, L. Serafini,
GeV plasma acceleration module for a possible future N. Bigelow, A. Fry, M. Fitch, P. Colestock, and R. Noble,
linear collider design [5]. In this case, the phase shifts Fermilab Report No. P890, 1996.
associated with long range erosion could be compensated [15] J. B. Rosenzweig, Nucl. Instrum. Methods Phys. Res.,
by slow longitudinal variation of the plasma density. Sect. A 410, 335 (1998).
As a final thought we note that, while we achieved [16] B. Montague and W. Schnell, in Laser Acceleration of
the simultaneous creation of both a witness and a drive Particles, edited by C. Joshi and T. Katsouleas (AIP, New
beam in a single rf photoinjector, the witness beam was York, 1985), p. 303.
[17] J. D. Jackson, Classical Electrodynamics (Wiley, New
of limited experimental use. While this was partly true
York, 1975), 2nd ed., pp. 641 –643.
because the AWA gun was not optimized for this task, it [18] N. Barov and J. B. Rosenzweig, Phys. Rev. E 49, 4407
also points to the challenge of creating beams which will (1994).
allow not only cleaner measurements in experiments, but [19] J. Krall and G. Joyce, Phys. Plasmas 2, 1326 (1995).
give good emittances and energy spreads at the exit of a [20] X. Qiu et al., Phys. Rev. Lett. 76, 3723 (1996).
plasma accelerator. The plasma accelerators we have dis- [21] J. B. Rosenzweig, S. Anderson, K. Bishofberger,
cussed here are envisioned to have wavelengths of 1 mm X. Ding, A. Murokh, C. Pellegrini, H. Suk, A. Tremaine,
or so, and thus the accelerating beams must be consid- C. Clayton, C. Joshi, K. Marsh, and P. Muggli, Nucl.
erably shorter than 1 mm (pulses in the sub-100 fsec Instrum. Methods Phys. Res., Sect. A 410, 437 (1998).
regime), and also phase locked to these high frequency [22] M. E. Conde, W. Gai, R. Konecny, X. Li, J. Power,
waves. While there are a number of conventional sugges- P. Schoessow, and N. Barov, Phys. Rev. ST Accel. Beams
1, 041302 (1998).
tions for creating these types of beams with rf photoinjec-
[23] H. Figueroa, W. Gai, R. Konecny, J. Norem, P. Schoes-
tors and compressors [5], another promising path appears sow, and J. Simpson, Phys. Rev. Lett. 60, 2144 (1988).
to be the use of plasma waves themselves as the source of [24] J. B. Rosenzweig, D. B. Cline, B. Cole, H. Figueroa,
the injected particles [36]. As the next generation plasma W. Gai, R. Konecny, J. Norem, P. Schoessow, and
wakefield experiments will need both improved driving J. Simpson, Phys. Rev. Lett. 61, 98 (1988).
and witness beams, this should be an area of active re- [25] J. B. Rosenzweig, P. Schoessow, C. Ho, W. Gai,
search in the coming years. R. Konecny, S. Mtingwa, J. Norem, M. Rosing, and
J. Simpson, Phys. Fluids B 2, 1376 (1990).
ACKNOWLEDGMENTS [26] J. B. Rosenzweig et al., Phys. Rev. A 39, 1586 (1989).
[27] P. V. Schoessow, in Proceedings of the 1997 Particle
The authors would like to thank R. Konecny, Accelerator Conference, Vancouver, Canada, edited by
A. Murokh, and P. Schoessow for experimental aid and M. Craddock (IEEE, Piscataway, NJ, 1998), p. 639.
support. This work was supported by U.S. Department [28] N. Barov et al., in Proceedings of the 1995 Particle
of Energy Grants No. DE-FG03-92ER40693 and No. W- Accelerator Conference, Dallas, Texas (IEEE, Piscataway,
31-109-ENG-38. NJ, 1996), p. 631.
[29] N. Barov, Ph.D. thesis, UCLA, 1998.
[30] J. B. Rosenzweig and E. Colby, Advanced Accelerator
[1] C. E. Clayton et al., Phys. Rev. Lett. 70, 37 (1993). Concepts, edited by P. Schoessow (AIP, New York,
[2] K. Nakajima et al., Phys. Rev. Lett. 74, 4428 (1995). 1995), p. 724.
[3] P. Chen, J. M. Dawson, R. W. Huff, and T. Katsouleas, [31] Luca Serafini and J. B. Rosenzweig, Phys. Rev. E 55, 7565
Phys. Rev. Lett. 54, 693 (1985). (1997).
[4] J. B. Rosenzweig, B. Breizman, T. Katsouleas, and J. J. [32] J. J. Su, T. Katsouleas, J. Dawson, and R. Fedele, Phys.
Su, Phys. Rev. A 44, R6189 (1991). Rev. A 41, 3321 (1990).
[5] J. B. Rosenzweig, N. Barov, A. Murokh, E. Colby, and [33] D. Whittum, W. Sharp, S. S. Yu, M. Lampe, and G. Joyce,
P. Colestock, Nucl. Instrum. Methods Phys. Res., Sect. A Phys. Rev. Lett. 67, 991 (1991).
410, 532 (1998). [34] Eric Colby, Ph.D. thesis, UCLA, 1998.
[6] N. Barov, M. E. Conde, W. Gai, and J. B. Rosenzweig, [35] W. Gai, X. Li, M. Conde, J. Power, and P. Schoessow,
Phys. Rev. Lett. 80, 81 (1998). Nucl. Instrum. Methods Phys. Res., Sect. A 410, 431
[7] B. N. Breizmann, T. Tajima, D. L. Fisher, and P. Z. (1998).
Chebotaev (unpublished). [36] D. Umstadter et al., Phys. Rev. Lett. 76, 2073 (1996).

011301-10 011301-10