Bunched Beam Injection in a Plasma
Accelerator
S. Ya. Tochitsky1, P. Musumeci2, C. E. Clayton1, C. Pellegrini2, J.B.
Rosenzweig2 and C. Joshi1
Department of Electrical Engineering, 2Department of Physics, University of California at Los
Angeles, 405 Hilgard avenue, Los Angeles, CA 90025
Abstract An experiment on phase-locked injection of ~ 100 fs electron bunches in a plasma
beat wave accelerator is presented. We consider using an IFEL microbunching technique to
produce ultrashort electron bunches prebunched at the exact wavelength of the plasma wave
340 Jim (~lTHz). It is proposed to generate 100 MW of 1 THz radiation by difference
frequency generation in a nonlinear crystal, mixing the same two CC>2 lines as used to drive the
plasma accelerator.
INTRODUCTION
Laser -Plasma acceleration of particles is utilizing a relativistic plasma wave driven
by a high-power laser beam. Plasma wave allows to couple energy of a transverse
electromagnetic wave of laser field into a longitudinal electric field of the wave, thus
making acceleration possible. The acceleration gradient has reached in experiments
values from 3 to 100 GeV/m for the plasma density (no) 1016 cm"3 and 1019 cm"3,
respectively [1]. So far all schemes of high gradient acceleration have shown 100 %
energy spread. This is physically due to the experimental difficulties related to the
generation and the injection of an electron beam in the high gradient accelerating
field wave with a typical period of 10-300 jim. It is obvious that if the injected
electron beam samples all the phases of the accelerating field, the energy spectrum at
the output will be continuous. The goal of second generation experiments is to reduce
the energy spread to make an electron beam produced by a plasma accelerator usable
for different applications.
There are two principle approaches to tackle this problem: optical injection of
electrons in the plasma wave and injection of prebunched electrons in a plasma
accelerator. For a 1019 cm"3 plasma density, which corresponds to a plasma
wavelength 10 jim, perhaps the only way for a phased injection is production and
injection of ultrashort electron bunches using different all-optical injection schemes:
CP647, Advanced Accelerator Concepts: Tenth Workshop, edited by C. E. Clayton and P. Muggli
© 2002 American Institute of Physics 0-7354-0102-0/02/$19.00
786
LILAC, LIP A, colliding beams (see these proceedings for more information).
However, forlower plasma densities and, therefore, longer plasma wavelength it
becomes possible to produce a high quality electron bunch (bunches) with a duration
short compared to the plasma wavelength. Injection of prebunched electrons that are
synchronized to the high gradient electric field wave is commonly called phase
locking. Several methods have been considered for injection of a phase-locked ebeam in a plasma accelerating structure [2]. However this has not yet been
experimentally demonstrated.
In this paper we describe an experiment on phase-locked injection of ~ 100
fs
electron bunches in a plasma beat wave accelerator proposed at Neptune Laboratory
(UCLA). It is suggested to use an IFEL technique to produce ultrashort electron
bunches prebunched at the exact wavelength of the plasma wave. For Neptune plasma
accelerator the plasma wavelength is 340 jim (~lTHz). We propose to generate 100
MW of 1 THz radiation by difference frequency generation (DFG) in a nonlinear
crystal, mixing two CO2 lines. Co-propagating the radiation with the electron beam
inside a short undulator achieves the bunching at the required wavelength. Moreover,
because the electromagnetic radiation is generated from the same laser that excites the
relativistic plasma wave, phase-locking could be achieved. In the first part of the
paper we describe the scheme and report preliminary experimental results on
generation of THz radiation using noncollinear DFG in GaAs. Then we present
results of modelling IFEL microbunching and address a beam loading problem.
EXPERIMENT ON INJECTION OF PREBUNCHED
ELECTRONS
The Neptune Laboratory at UCLA is being used to explore advanced accelerator
concepts including Plasma Beat Wave Acceleration (PBWA) of electrons. Here a
plasma beatwave with acceleration gradient 1-3 GeV/m is driven by a 100 ps twowavelength TW CO2 laser pulse at 10.6 and lO.Sjim [3]. For PBWA, electrons from a
photoinjector are injected in a plasma accelerating structure. The injected electron
beam comes from an RF gun followed by a linac which can produce up to 0.5 nC in
several ps at 12 MeV [4]. At present the PBWA experiment is operating and a long
(>340 jim) electron bunch is injected in the plasma structure and accelerated with 100
% energy spread. Production of the monoenergetic beam require a bunch length of
about 40 jim.
In Fig.l we show a proposed scheme for phase-locked injection of electrons in the
plasma beat wave accelerator. As shown in the picture, a high-power CO2 laser beam
is focused by a F/5-F/18 optic at the interaction point (IP) and drives the relativistic
plasma beatwave. A small fraction (~ 4%) of two-wavelength CO2 laser radiation is
splitted by a NaCl beamsplitter, and then sent onto a nonlinear crystal. Here, by
difference frequency generation, as discussed in the next section of this paper, we
should generate up to 100 MW of 1 THz radiation. This 340 jim wave originates from
the mixing of the same two wavelengths that drive the plasma beat wave, so that it
787
Electron
Spectrometer
has a well-defined phase relationship with the accelerating structure. The THz beam
is made collinear with the electron beam and is sent through a planar undulator using
a mirror with a hole. This off-axis
off-axis parabolic mirror has also the function
function of focusing
THz radiation to a spot size of 7 mm located at the end of a 0.5 m long undulator. As
IP
NaCl BS
µm + 10.3 |im
µm
800 GW, 10.6 |im
Final
OAP f’=100 cm DFG
OAP
Focus
f’=30cm
=30cm Triplet THz
THz IFEL
buncher
100 fs e-bunches
1 THz, 340 µm
Plasma wave
From
Neptune
Laser
100 MW,
340 µm
LINAC
RF
Gun
5 ps e-bunch, 12
12
MeV
1 THz, 340 µm
urn
Electromagnetic wave
FIGURE 1. Experimental layout for THz Inverse Free Electron Laser microbunching.
aresult of the IFEL interaction the electron beam propogating through the undulator
magnetic field is microbunched on the scale of 340 µm;
jim; then it is focused with the
final focus triplet at the IP and finally it is accelerated by the relativistc plasma
final
beatwave. Absolute phase between electrons and the plasma wave can be adjusted
simply by using a delay line. The distance between the end of the undulator and the
possibility that debunching
debunching effects,
effects, taking place
place in the
the
IP is up to 2 m. There is a possibility
transport between the THz prebuncher and the plasma, will cause bunch lengthening.
This issue is ought to be studied experimentally. Note that in the successful
successful STELLA
µm),
experiment where tolerances are tighter because of the shorter wavelength (10 jim),
the IFEL accelerator was located 2.3 m downstream of the IFEL prebuncher [5].
HIGH-POWER SOURCE OF THz RADIATION
powerful source of optical
The key element of a laser-driven IFEL prebuncher is a powerful
difference frequency
frequency mixing process in a nonlinear
radiation. We propose to use difference
crystal to produce high-power driving THz radiation (>100 MW) for the IFEL
buncher. It is known that low DFG efficiency
efficiency is a serious problem for the FIR
788
spectral range. The highest FIR power generated by now using this method is a few
kW [6]. At the same time 100 ps, two-wavelength €62 laser pulses from the Neptune
Lab system are naturally very well suited for producing high-power FIR radiation.
Nonlinear frequency conversion efficiency increases significantly for short pulses:
first owing to the power increase and second, this power can be coupled into a crystal
because of the higher surface damage threshold for shorter pulses. According to the
Manley-Rowe relations, the maximum power conversion efficiency can reach 3% for
TW 10 (impulses.
Three methods to generate high-power 340 jim radiation by CO 2 laser difference
frequency mixing in a nonlinear crystal have been considered. They are: standard
birefringent phase matching, quasi-phase matching with periodic structures, and
noncollinear phase matching in isotropic materials. A comparative analysis shown
that the later has the highest potential for FIR DFG [7]. Noncollinear mixing of two
laser beams is possible in any crystal which possesses anomalous dispersion between
the incident CO2 laser radiation and FIR difference frequency radiation. Zernike [8]
and Aggarwal et al. [9] have demonstrated noncollinear mixing of two €62 laser
beams in liquid helium cooled InSb and GaAs samples. Several reasons make GaAs
a good candidate for generation of high-power 340 jim radiation. It has a relatively
high value for the electro-optic nonlinear coefficient d=43 pm/V. GaAs with high
resistivity (> 108 Qcm) is transparent in the FIR beyond 200 jim at room temperature
as well as in the 10 jim region of the €62 laser [10]. High-quality, single crystals with
a diameter of 15 cm and length up to 10 cm are commercially available. The expected
surface damage threshold could reach 10 GW/cm2 for 100 ps €62 laser pulses.
For noncollinear phase-matched mixing of two laser lines of frequencies GOi and 0)2
(coi>co2) to generate the difference-frequency radiation at 0)3, the conditions of photon
energy and momentum conservation require that
co3 =co1 -69 2 ;k 3 = k i - k 2
(i)
where ki, k2 and ks are the respective vectors for radiation of frequencies GDI (10.3
jim), 0)2 (10.6 jim), 005 (340 jim). Fig 2a. shows the direction of propagation of the
incident beams and that of the difference frequency radiation inside the crystal.
Refractive indices for insulating GaAs are ni~n2=3.28 at 10 jim region, and n3=3.61
at 340 jim [10]. According to Aggarwal et al. [9], for these values of refractive index
we obtain 0=0.72° and 9=21.64°. The corresponding external phase-matching angle
is 2.38 degrees. The angle at which FIR radiation propagates inside the crystal is
greater than the critical angle for total internal reflection. Therefore, as it shown in
Fig.2b, the output face of the GaAs crystal has to be cut at 21 degrees to release the
newborn radiation.
Preliminary measurements of the DFG efficiency were done with a 3 cm long sample
of (111) oriented GaAs. The measurements were performed with a two-wavelength
output of a CO2 master oscillator which provided 50 mJ in a 200 ns pulse. Fig. 2b
789
presents a schematic diagram of the experiment. The laser beam was compressed to a
spot size of 1 mm in order to increase the conversion efficiency.
efficiency. By adjusting
adjusting the
distance between a ZnSe beamsplitter and a mirror we set the angle necessary for
ω1
ϕ
Θ
ω2
ω3
a
10.3 +10.6 µm
Filter
llay
Go
l
Cel
GaAs
b
FIGURE 2. Schematic wave vector diagram for noncollinear
noncollinear DFG
DFG (a)
(a) and optical scheme of an
FIGURE
FIR DFG
DFG in GaAs(b).
experimental set up for FIR
produced was detected by a Gollay cell. The interaction length is limited by the
length over which two crossed beams are overlapped and, according to calculations,
was approximately 12 mm. We have observed FIR pulses with peak output power
P340≈100 mW
mW at peak input power Pio.3~20
P10.3≈20 kW and Pio.6~80
P10.6≈80 kW. It corresponds to a
P340-100
-6
6
10
efficiency value. In order to compare the experimentally observed
10~ conversion efficiency
from theory we used the following formula:
FIR power output with that expected from
0.5
PFIR
2
 µ 0   4d eff 2 ω FIR 2  P10.3 P10.6 Leff T1 T2 T3 − αL
e
= 0.5  

S
 ε 0   n1n 2 n 3c2 
(2)
the area of the input beams, TI,
T1, T2
T2 and TS
T3 are the single surface
where S denotes the
transmission coefficients
coefficients at the
the frequencies
frequencies GDI,
ω1, 002,
ω2, and 003
ω3 and aα is the absorption
=50
coefficient of FIR radiation in GaAs. Theory predicts P
coefficient
Ps4o
ff=50
340 =212 mW using deeff
the only available in literature absorption coefficient
coefficient for THz radiation
radiation at
pm/V and the
room temperature of 0.2 cm"
cm-11 . This is in a reasonable agreement with the observed
value (uknown absorption may be a possible reason for this discrepancy), and allows
us to estimate possible FIR power for amplified
amplified pulses. Calculations have shown (see
the pump intensity of 2-4 GW/cm22 and LLeeff
=2.5 cm one can expect
Fig. 3) that with the
ff=2.5
the conversion efficiency
efficiency up to 4xlO~
4x10-33 . It means that for 100 ps
ps pump
pump
growth of the
790
pulses the 100
100 MW level of power could be achieved for a beam diameter of 5 cm (82
10
MW/cm
of the THz power density).
10
5
110"
0
4
11004
Projected
wi h 100
Proje cted power with
100 ps
ps pulses
puls es
L=2.5
L=2.5 cm
11 0 0 0
2
jfi
FIR Power, kW/cm
M
o
+ ^/
S
j^~————
1100
00
10
0)
I
1
0.
0.1
/
0.01
r
with 200
200 ns
n i pulses
perimental power
pov er with
pulses
./* Experimental
Ex
L=1.2
L: ;1.2 cm
0 .001
1
11 0
11 0 0
11000
000
4
1100 4
22
Pump
Pump Power,
Power, MW/cm
MW/cm
FIGURE 3. Measured and calculated power at 340
340 µm
Jim as
as aa function
function of
of pump
pump intensity.
intensity.
Due to high nonlinearity of GaAs interaction of a 10
10 µm
jim beam
beam of
of GW
GW power
power with
with
the nonlinear material may result in spectral broadening, amplitude modulation, etc.
[11] which could limit the allowed pump power besides the damage threshold.
Moreover frequency mixing of different spectral components of a broadened pump
pulse can cause generation of 3-5 mm radiation in aa collinear
collinear geometry.
geometry. A
A detailed
detailed
experimental study of these issues is required.
It is interesting that FIR power level could be scalable beyond 100
100 MW by
increasing the beam diameter. A typical beam diameter of the Neptune TW two2
wavelength CO
2 laser system is 12 cm with an intensity †10
CO2
|10 GW/cm . This beam, in
combination with available large-aperture GaAs crystals, opens possibility to create aa
unique high-power ≥1
>1 GW source of coherent radiation in the range of 100
100 µm
jim —10
mm (0.03 -3 THz) on the base of noncollinear frequency mixing of
CO
laser
lines.
of €622 laser lines.
791
MODELLING
OF IFEL
IFEL BUNCHING
BUNCHING
MODELLING OF
ItIt isis known
longitudinal lens
lens and
and microbunches
microbunches the
theelectrons
electrons
known that
that an
an IFEL
IFEL acts
acts as
as aa longitudinal
on
the
scale
of
the
electromagnetic
wavelength
[12].
At
the
Neptune
Laboratory,
in
on the scale of the electromagnetic wavelength [12]. At the Neptune Laboratory, in
order
to
achieve
efficient
microbunching
in
the
small
experimental
area
available,
we
order to achieve efficient microbunching in the small experimental area available, we
need
Optimization was
was done
done using
using standard
standard
need to
to optimize
optimize the
the IFEL
IFEL parameters.
parameters. Optimization
equations
of
the
motion
for
a
single
electron
moving
in
a
plane
linearly
polarized
equations of the motion for a single electron moving in a plane linearly polarized
electromagnetic
field [13].
[13]. For
For 100
100 MW
MWof
ofTHz
THzradiation
radiation
electromagnetic wave
wave in
in aa planar
planar undulator
undulator field
and
a
magnetic
field
of
0.25
T,
we
achieve
maximum
bunching
through
the
Inverse
and a magnetic field of 0.25 T, we achieve maximum bunching through the Inverse
Free
Electron
Laser
interaction
after
0.5m.
It
is
important
that
having
more
Free Electron Laser interaction after 0.5m. It is important that having more
electromagnetic
power
or
a
longer
undulator
doesn't
increase
the
performance
of
the
electromagnetic power or a longer undulator doesn’t increase the performance of the
system,
the
efficiency
of
the
IFEL
buncher
reaches
a
limit
due
to
the
effects
of
the
system, the efficiency of the IFEL buncher reaches a limit due to the effects of the
non-linearities
emittance diluition.
diluition. Detailed
Detailed results
results of
of
non-linearities and
and the
the longitudinal
longitudinal emittance
optimization
[7]. Parameters
Parameters of
of aa permanent
permanent magnet
magnet
optimization are
are presented
presented elsewhere
elsewhere [7].
undulator
undulator are
are listed
listed in
in Table
Table 1.
1.
Table
Table 1.
1. Undulator
Undulator parameters___________
parameters
Magnetic field
Undulator wavelength
Magnet gap
K parameter
Undulator length
0.6 T
10 cm
2 cm
2.2
0.5 m
Simulations
are shown
shown in
in fig.
fig. 4.
4. The
The
Simulations confirm
confirm well our estimates. The results are
simulations
[14], a 3d
3d Lienerd-Wiechert
Lienerd-Wiechert based,
based, 44ththorder
order
simulations are
are performed
performed using TREDI [14],
Runge
electrons through
through the
the undulator
undulator
Runge Kutta,
Kutta, Lorentz
Lorentz solver code to track the electrons
magnetic
electron beam
beam has
has the
the parameters
parameters
magnetic field
field and
and the laser field. The input electron
typically
mm-mrad, 300
300pC.
pC.The
Theradiation
radiation
typically running
running at Neptune laboratory, 4 ps long, 66 mm-mrad,
isis assumed
in vacuum
vacuum to
to aa 77 mm
mm focal
focal spot.
spot. In
In
assumed to
to be
be a 100 MW THz wave, focused in
Fig.4a
phase space
space at
at the
the end
end of
of the
the
Fig.4a there
there is
is aa snapshot of the electron longitudinal phase
Bunching
Bunching in
in IFEL
Histogram of
of phase
phase distribution
distribution
Histogram
0.1
p
/
p
a
t 0.05
l
e
d
0
0.05
0.2
0.2
% 0.1
0.002
00
z (m)
z(m)
0
0.002
nnnn^nnnlLnl
0
1.57
1.57
lllllhlninljniii
3.14
3.144.71
4.716.28
6.28
phase
phase
bb
a
FIGURE 4. Simulation results for THz IFEL microbunching.
FIGURE
microbunching.
792
undulator.
undulator.The
The longitudinal
longitudinal microbunches
microbunches on
on the
the scale
scale of
of the
the plasma
plasma wavelength
wavelength are
are
evident
evidentwithin
within the
the 44 ps
ps (rms)
(rms) long
long beam
beam envelope.
envelope. Fig.4b
Fig.4b shows
shows the
the phase
phase histogram
histogram
over
over the
the 340
340 µm
jim wavelength.
wavelength. The
The microbunches
microbunches have
have aa width
width of
of ~~ 30
30 µm
jim that
that is
is
small
small (1/10)
(1/10) compared
compared to
to the
the plasma
plasma beat-wavelength.
beat-wavelength. Since
Since THz
THz radiation
radiation driving
driving
the
the IFEL
IFEL isis locked
locked in
in phase
phase with
with the
the plasma
plasma beatwave,
beatwave, all
all these
these microbunches
microbunches are
are
phase-locked
phase-locked with
with the
the accelerating
accelerating structure.
structure. ItIt is
is clear
clear that
that for
for PBWA
PBWA getting
getting more
more
electrons
electronswith
withaasmaller
smaller phase
phase spread
spread will
will result
result in
in less
less energy
energy spread
spread after
after the
the plasma
plasma
acceleration.
acceleration. At
At the
the same
same time
time the
the longitudinal
longitudinal emmittance
emmittance dilution caused by the
nonlinearities
nonlinearitiesisisaaprincipal
principallimitation
limitation of
of the
the IFEL
IFEL microbuncher.
microbuncher.
Further
Furtherimprovement
improvement in
inthis
this respect
respect could
could be
be achieved
achieved by
by driving
driving the
the same
same
rd
undulator
undulatorwith
withboth
both 340
340µm
jimradiation
radiation and
and it’s
it's 33rd harmonic
harmonic as
as suggested
suggested recently
recently by
X.J.
XJ. Wang
Wang for
for aa 11 µm
jim IFEL
IFEL buncher
buncher [15].
[15]. As
As oppose
oppose to
to the 11 µm
jim beam, it is not
rd
durable
durableto
togenerate
generate the
the 33rd harmonic
harmonic of
of THz
THz radiation. However one can generate 114
µm
jimradiation
radiationby
by noncollinear
noncollinear DFG
DFG in
in GaAs
GaAs using
using CO
CO22 laser
laser lines.
lines. In
In fact,
fact, ifif we
we take
take
the
same
asas
forfor
thethebeatwave,
the10.6
10.6µm
jimline
line-the
-the
same
beatwave,then
thenthe
the9.7
9.7µm
jimline
line(the
(the9P(36)
9P(36)line)
line)
rd
will
willprovide
provide the
the difference
difference frequency
frequency equal
equal to
to the
the 33rd harmonic
harmonic of
of beatwave
beatwave with
with aa
negligible
negligiblefrequency
frequency off-set
off-set of
of ~1
~1GHz.
GHz. In
In experiment
experiment another
another laser
laser beam
beam from
from aa MW
MW
power,
power,200
200ns
nsCO
CO22laser
laser could
could be
be used
used as
as aa seed
seed at
at 9.7
9.7 µm
jim in
in combination
combination with
with aa TW
TW
100
100ps
pspulse
pulseatat10.6
10.6µm.
jim.3D
3Dmodelling
modelling have
have indicated
indicated that
that indeed
indeed by
by choosing
choosing an
an
optimal
optimalratio
ratiobetween
between114
114and
and 340
340 µm
jim radiation
radiation (1.5/1)
(1.5/1) one
one can
can significantly
significantly increase
number
numberof
ofelectrons
electronstrapped
trapped in
in slightly
slightly shorter
shorter bunches
bunches (~20
(~20 µm).
jim). Preliminary
Preliminary results
are
areshown
shownin
inFig.5.
Fig.5.
Histogram
Histogramofofphase
phasedistribution
distribution
0.75
Bunching factor
0.3
0.2
0.2
%
0.1
0.1
0.65
0)
0.60
o
c
0.55
D
0.50
CO
0
3rd Harmonic IFEL
0.70
0.45
0
1.57
1.57
3.14
3.14
phase
phase
4.71
4.71
6.28
6.28
00.0
.0
b
00.5
.5
11.0
.0
11.5
.5
22.0
.0
22.5
.5
Line
Line ratio
ratio (3ω/ω)
(3co/co)
FIGURE5.5.Simulation
Simulationresults
resultsfor
forthe
the 33rdrd harmonic
harmonic THz IFEL microbunching.
FIGURE
BEAM LOADING
LOADING IN
INAA PLASMA
PLASMA ACCELERATOR
ACCELERATOR
BEAM
Aswas
wasshown
shown in
in the
the previous
previous section
section THz
THz IFEL
IFEL microbunching
microbunching can produce ~ 100
100
As
fs
electron
bunches,
which
is
ten
times
shorter
than
the
plasma
wavelength.
Here
we
fs electron bunches, which is ten times shorter than the plasma wavelength.
793
examine analytically how many particles could be loaded in a plasma heatwave
accelerator both longitudinally and transverse in order to obtain the small energy
spread AE/E~0.1. It is known that when the electron beam and the plasma wave are
much larger than c/cop, the beam-loading problem is approximately one-dimensional
[16]. This condition is true for c/cop~50 jim for the case when the CO2 laser beam
diameter is 400 jim (F/18 focusing).
Longitudinal beam loading is limited by a wakefield production and the maximum
number of beam electrons is given by
(3)
where 8 is the normalized plasma wave amplitude and S is the cross-sectional area of
the plasma wave. In our conditions, for 10% wave, N0 equals to 6xl09 electrons.
Therefore for AE/E~0.1 one can load up to 6xl08 electrons or 10 pC charge without
significant dumping the plasma wave. In experiment we do not expect to exceed this
charge per bunch.
It is obvious that transverse variation of the longitudinal electric fields will result in
a difference in energy gained by electrons or large energy spread. Typical size of the
plasma wave seen in the 2D-PIC simulations is 170 pm (FWHM) for the laser field
intensity 2xl014 W/cm2 [17]. Such an accelerating structure requires an e-beam size
a^^SO jim. This is approximately 3 times larger what the Neptune photoinjector can
provide at the moment and further work is needed to improve quality of the e-beam.
SUMMARY
THz driven IFEL microbunching is a promising scheme for a phase-locked
injection of bunched electrons in a plasma accelerator. It is shown that for the
Neptune PBWA experiment ~100 MW of 340 jim radiation is required to drive a THz
buncher. Results of preliminary experiments on generation of THz radiation using
noncollinear frequency mixing of €62 laser lines in GaAs are presented.
ACKNOWLEDGEMENT
This work was supported by the U.S. Department of Energy, grant DE-FG0392ER40727.
REFERENCES
1. C. Joshi, and P.B. Corkum, Physics Today, 49, 36-42 (1996).
2. C.E. Clayton,and L. Serafmi, IEEE Trans. Plasma Science, 24, 400-408 (1996).
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