Macroscopic-Size Accelerator Structures for
CO2 Laser-Driven Linear Acceleration in a
Vacuum
Y. Y. Lin, A. C. Chiang, and Y. C. Huang
Department of electrical Engineering National Tsinghua University, Hsinchu 300, Taiwan
Abstract. We report the simulation and fabrication of a single-stage and a multistage CO2 laserdriven particle accelerator with macroscopic dimensions suitable for conducting proof-ofprinciple laser-driven acceleration experiments in a vacuum. The single-stage copper accelerator
structure, having a 300-|im electron transit aperture, is 10 cm long and provides 210 keV
electron energy gain. The multistage structure consists of 16 ZnSe lenses with 1.5 cm separation
between adjacent lenses. The energy gain over the 24-cm distance is 250 keV for a 200-|im
electron transit aperture. This resonant structure is suitable for studying beam loading, mode
excitation, and phase synchronization among accelerator stages.
I. INTRODUCTION
Laser-driven particle acceleration, if realized, has the advantage of producing
high acceleration gradients and ultra-short electron bunches. Those unique features
would benefit to the applications in radiation and high energy physics. For schemes
adopting linear acceleration, numerous experimental evidences have been generated
from plasma-based laser-driven accelerators. To date, there is still no evidence of
particle acceleration in solid-structure-based laser-driven linear acceleration in a
vacuum. One major difficulty is that the accelerator dimension is too small to operate
at the laser wavelength [1]. To conduct a proof-of-principle experiment at the
Accelerator Test Facility (ATF), Brookhaven National Laboratory, we discuss in this
paper the design and fabrication of large-size single-stage and multistage CC>2 laserdriven linear accelerators. The major design consideration is to have a large energy
again, a macroscopic size, a structure that is flexible enough for investigating
accelerator physics. Although a high acceleration gradient is not considered at this
moment, it can be further improved as soon as the experimental evidence for vacuum
linear acceleration is obtained.
II. SINGLE-STAGE ACCELERATOR STRUCTURE
Figure 1 depicts the design for the single-stage accelerator structure [2]. The
structure consists of a corner reflector for synthesizing the acceleration field and a
45° reflector for bringing in and removing the laser field. The edge of the corner
reflector forms an angle 9 with respect to the x direction. Both the corner reflector and
CP647, Advanced Accelerator Concepts: Tenth Workshop, edited by C. E. Clayton and P. Muggli
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300
the 45° reflector have an aperture for transmitting electrons. This simple design does
not employ any laser mode for particle acceleration, but obtains the particle
acceleration field by combining two properly phased TM plane waves from the corner
reflector. These two plane waves can be split from an enlarged TEM0o laser beam with
the laser coupling configuration shown in Fig. 1. The corner reflector divides a single
wavefront coming from the 45° coupling mirror into two halves and recombines the
two waves inside the accelerator structure. The relative phase of the two plane waves
can be adjusted, for example, by varying the longitudinal position of each arm of the
corner reflector. When the optical paths between the two plane waves are different by
a half wavelength, the transverse fields of the two plane waves cancel and the
longitudinal fields add to provide the acceleration field.
FIGURE 1. The configuration of the single-stage accelerator structure. The particle acceleration field
is derived from two properly phased plane waves from the corner reflector, and is removed by the 45°
reflector.
Assume that a n phase shift is pre-arranged for the two equal-amplitude plane
waves. In the plane-wave approximation, the laser field in the z direction can be
written as
Ez =2EQcos(cot-kcos0'Z + </))'COs(ksm0'x)xsm0,
(1)
where EQ is the electrical field associated with each plane wave, ty is an arbitrary
initial phase, and a> is the angular frequency and k is the wave number of the laser
field. In the electron rest frame, the acceleration field seen by an on-axis electron is
given by
E
= 2EQ cos[(co/ve - £ cos 0) • z + 0] x sin 0,
(2)
where ve = c II - — is the electron velocity. For a small crossing angle 0 « I and a
large electron energy 7 »1, the acceleration field in (2) is reduced to
301
(3)
2 Y
In general, the laser field propagates at a phase velocity faster than the electron. The
electron slips in phase by 180° after a coherence length given by
(4)
Y
From (3) and (4), one sees immediately that a small crossing angle gives a longer
coherence length and thus a larger accelerator size, but reduces the acceleration field.
A longer acceleration wavelength also helps to have a longer accelerator size, as
expected. One may maximize the electron energy gain, U = \EZ edz , to optimize the
laser crossing angle 9. To maximize U, one takes —— = 0 and obtains the crossing
oO
angle for the maximum-energy condition 9 = — . The maximum electron energy gain
7
2
over the coherent length Ay / 2 with the optimized crossing angle 0 = l / y is
therefore
^max=—— A E 0 = —— ^<N/2V>
n
n
(5)
where 7JQ is the vacuum wave impedance, A is the laser wavelength, and / is the laser
intensity. For a given material, a laser wavelength, and a laser pulse width, the
maximum damage intensity / to the structure is fixed. The maximum electron energy
gain is predominantly dependent on the electron energy y and the laser wavelength X.
A large y and a longer X help to reduce the phase slippage and permit the use of a
larger structure size. We conducted a laser damage experiment on optically polished
copper with the 200 ps CC>2 laser at the ATF and found a damage field around
0.25GV/m. With the ATF beam energy of y = 140, the optimized coherence length or
the accelerator stage length is /c = 10.4 cm and the maximum energy gain is about 240
keV.
For structure-based laser driven linear acceleration, one has to open electron
transit holes comparable or larger than the driving wavelength in the accelerator
structure [3]. The leakage field through the hole in the corner reflector reduces the
acceleration field, whereas the leakage field through the hole in the 45° reflector
removes the electron energy gained in the accelerator structure. To estimate the energy
gain reduction, we employ synthesized plane waves to model the electric fields at the
electron transit hole [4]. With A = W.6jum , 9 = \ly =7 mrad, and a 300 jim electron
transit aperture, the acceleration field versus distance seen by an on-axis electron is
shown in Fig. 2. The spiky oscillation near the holes at z = 0 and z = 10 cm results
from Fresnel diffraction.
302
0.15
0:2
z:(m)
FIGURE 2. Simulation of the acceleration field seen by the electron with the leakage fields through the
electron transit hole. The corner reflector is located at z = 0 and the 45° reflector is located at z = 0.1 m.
Figure 3 shows the electron energy gain, integrated over distance from Fig. 2. As
can be seen from Fig. 3, the electron energy reduction is only about 10%, although the
electron transit hole has a width about 30 times the driving wavelength. Therefore,
with the design parameters, one may expect a maximum energy gain of 210 keV from
such a simple, single-stage accelerator structure. This amount of energy gain should be
able to be measured conclusively by using the energy spectrometer with a resolution
of0.1%attheATF.
FIGURE 3. Simulation of the energy gain with the effect of the leakage fields through the electron
transit holes. The gain reduction is only about 10%, although the hole width is about 30 times the
driving wavelength.
III. MULTISTAGE ACCELERATOR STRUCTURE
The single-stage design is suitable for investigating the electron energy gain in a
laser-driven linear accelerator (linac) structure in a vacuum. However, to further
understand beam loading, phase synchronization, and mode coupling, a resonant
structure consisting of multiple accelerator stages is required. Figure 4 shows the
design for such a structure. The multistage laser-driven linac is a 16-stage lens-array
structure. M. O. Scully has proposed a similar structure with on-axis drift tubes for
phase control [5]. In our structure, the phase control is achieved by varying the
refractive index of each lens as a function of temperature. On each ZnSe laser lens,
there is a 100-um radius electron transit hole. The TEM0i laser mode is supported by
this resonant structure and is the desired particle acceleration field. The planar-convex
lens has a focal length of/= 3.8 cm, a thickness of 1 mm, and a diameter of 1.52 cm.
/=5z*/3 = 3.81cm
1.52cm
,
24 cm = 1.5 cm x 16
,
k—————————————————N
FIGURE 4. The configuration of the multistage laser-driven linac.
Laser-driven particle acceleration by using the TEMio laser field has been
analyzed by EJ. Bochove et al. [6]. With a known transverse field for the TEM0i laser
mode, the laser field along the z direction can be calculated from the charge-free and
material-free Gauss law \/-E = 0. In the paraxial limit, the z-component electric field
phasor is approximately
^
k
(
dx
)
dy
,
( 6 )
where ET is the phasor of the transverse laser field.
The focal length of the lens, /, is determined by examining the relationship
q2 = ——-—— between the complex radii of curvature ql before and q2 after the
C - ql + D
lens, where the definition ofABCD is given in the matrix form
304
AB
\ }=
1
0'
(7)
[C D\
~
To satisfy the resonance condition, the real part and imaginary part of the complex
radii of curvature have to satisfy Re{^1} = -Re{^2} =— and lm{q1} = lm{q2} = zR,
where / is the length of each accelerator stage, ZR =7uwl/h is the optical Rayleigh
range, and w0 is the laser waist radius.
We again apply the synthesized-plane-wave method to numerically calculate the
acceleration field and the electron energy gain in this multistage accelerator structure.
In the computer simulation, the amplitude transmittance of the lens is given by
t = exp[-./A:W, -^-)(n-\)-jkd«]
2K
for H > -J,
2
(8)
and
^exp(-7H)for|x|<|
(9)
where dQ= I mm is the thickness of the lens at x = 0, n is the refractive index of the
lens, R = /(«-!)is the radius of curvature on the convex lens surface, and h is the
electron transit hole radius. Because we would like to have a large electron transit hole
for ease of transmitting electrons, we arbitrary choose 100 jLtrn as the transit hole
radius. To reduce the energy loss due to the leakage field from the electron transit
holes, we design a laser waist radius about three times the electron transit hole radius.
As a result, we started with / = —- for our simulation, which gives / = —- from the
resonance condition. In the simulation, we assume that the lens can provide an
arbitrary phase shift to the laser field so that the laser phase in each stage is optimized
for maximum acceleration. This can be done by varying the temperature T of the
dielectric lens by using a thermal electric temperature controller. For ZnSe, the
temperature dependence of the refractive index is dnl dT = 5.7x10~5 /° C. In a 1-mm
thick ZnSe, the CO2 laser phase may vary 180° for a 93°C temperature change.
We also conducted a laser damage experiment for optically polished ZnSe with
the 200 ps CO2 laser at the ATF and measured a damage intensity of 2.25 GW/cm2.
Figures 5-6 show the electric field calculations in the first two accelerator stages at the
material damage field. The plots in the left column show the transverse electric fields
versus the transverse coordinate x at the beginning, at the center, and at the end of the
accelerator stage. The first plot in the right column shows the particle acceleration
field seen by a 70 MeV electron. The second plot in the right column, integrated from
the first one, is the electron energy gain in that particular accelerator stage. The third
plot in the right column shows the angular spectrum of the laser field in our simulation.
The transverse field shows the evolution of a laser mode, and the angular spectrum
shows the field components of different phase velocities.
305
**
FIGURE 5. The left three plots illustrate the transverse laser fields at the beginning, at the center, and
at the end of the first accelerator stage. The right three plots show the accelerating fields, the electron
energy gain, and the angular spectrum of the laser field.
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FIGURE 6. The simulation results for the second accelerator stage with the same arrangement as in Fig.
5. It is seen that the electron transit hole widens the angular spectrum, distorts the laser fields, and
decreases the electron energy gain.
306
By comparing Fig. 5 and Fig. 6, one sees the influence of the 100 jLtm-radius
electron transit hole. Due to aperture diffraction, the angular spectrum of the laser field
becomes wider, high-order laser modes are excited, and the acceleration field and the
electron energy gain are gradually reduced. In the subsequent stages, the laser
eigenmode is gradually established, and the energy gain per stage is stabilized around
15 keV per stage.
Figure 7 is the accumulated electron energy gain over the 16 accelerator stages.
The upper line is the energy gain versus distance without considering the electron
velocity slippage, and the lower line is that with the velocity slippage for a 70 MeV
electron. At a finite injection energy, the electron energy gain is influenced by the
leakage field through the electron transit hole, because the widened laser angular
spectrum contains many high-phase-velocity field components that slip ahead the
electron and decelerate electrons. With our design parameters, the total energy gain for
this multistage accelerator is about 250 keV. Table 1 summarizes the design
parameters and predicted performance for this multistage laser-driven linac.
•••••••••" Energy gain without phase slippage
—— Electron Energy gain over 16 stages (velocity slip included)
O
2>200
0.25
z(m)
FIGURE 7. The electron energy gain versus distance over the 16-stage accelerator structure with and
without electron velocity slippage. For a 70 MeV electron injection energy, the total electron energy
gain is about 250 keV.
TABLE 1. The Design Parameters for the Multistage Accelerator
Single-stage length
1.5 cm
24cm
Total linac length
Number of accelerator stages
16
Electron transit hole radius
100 |im
Laser beam waist in each stage
280 |im
2.25 GW/cm2
Laser damage threshold (ZnSe)
Laser wavelength
10.6 |im
Laser Mode
TEMoi
Phase tuning by temperature
7i over 93 °C
Total energy gain
250 keV
307
IV. CONCLUSION
CONCLUSION
IV.
Although the acceleration gradient of
of aa structure-based
structure-based laser-driven
laser-driven linear
linear
potentially provides
provides stable
stable and
and continuous
continuous
accelerator is limited to laser damage, itit potentially
distance compared
compared to
to other
other types
types of
of
acceleration to the electrons over a much longer distance
designed aa 10-cm
10-cm long,
long, CO
CC^2 laser-driven,
laser-driven,
laser-driven particle accelerator. We have designed
single-stage linear accelerator for demonstrating the feasibility of laser-driven
laser-driven
acceleration in a vacuum. We predict an
an energy
energy gain
gain of
of 210
210 keV
keV with
with aa 70
70 MeV
MeV
electron injection energy. The full width of
of the
the electron
electron transit
transit hole
hole isis as
as large
large as
as 300
300
|LLm.
The
corner
reflector
design
is
easy
to
fabricate,
simple
to
implement,
and
flexible
µm.
is easy to fabricate, simple to implement, and flexible
in phase control under a plane-wave laser coupling.
coupling.
As shown in Fig.
Fig. 8, we have fabricated aa 24-cm
24-cm long
long multistage
multistage CO
CO2
laser-driven
2 laser-driven
linac for studying beam loading, multistage phase control, mode coupling,
coupling, and
and so
so on
on
for vacuum linear acceleration. The accelerator structure
structure consists
consists of
of aa ZnSe
ZnSe lens
lens array
array
for
with 1.5
1.5 cm
cm separation
separation between
between adjacent
adjacent lenses.
lenses. By
By varying
varying the
the temperature
temperature of
of the
the
ZnSe lens, we are able to reverse the acceleration phase by 180°
180°over
over aa temperature
temperature
range of 93°. The maximum energy gain
gain of
of this
this accelerator
accelerator isis estimated
estimated to
to be
be 250
250 keV
keV
with an electron transit aperture of 200 µm.
jLtm. To
To increase
increase the
the energy
energy gain,
gain, we
we are
are
planning to replace the ZnSe lenses with diamond lenses.
lenses. We
We have
have conducted
conducted aa laser
laser
using the
the 200
200 ps
ps CO
CO2
laser at
at the
the
damage experiment with CVD-grown diamond by using
2 laser
ATF and found that the damage threshold intensity in diamond is
is about
about 66 GW/cm
GW/cm22 or
or
2.6 times that in ZnSe [7].
[7]. Since this multi-stage structure
structure has
has many
many similar
similar features
features to
to
acceleration mode
mode and
and phase
phase
an RF accelerator, including the excitation of acceleration
stages, the experimental
experimental results
results from
from this
this structure
structure
synchronization among accelerator stages,
physics linked
linked to
to aa conventional
conventional RF
RF
can be directly compared to the accelerator physics
accelerator.
FIGURE 8. The
The picture
picture of
of the
the multistage
multistage CO
CO22 laser-driven
laser-driven linac.
linac.
308
ACKNOWLEDGMENTS
The authors appreciate administrative and technical supports from the ATF staffs
led by Ilan Ben-Zvi at the Brookhaven National Laboratory.
REFERENCES
[1] Y.C. Huang, D. Zheng, W.M. Tulloch, and R.L. Byer, "Proposed Structure for a Crossed-laser
Beam, GeV per meter gradient, Vacuum Electron Linear Accelerator," Appl. Phys. Lett. 68 (6), 5
(1996)753.
[2] Y.C. Huang, "Particle Acceleration Field derived from a Wavefront-divided Gaussian Beam," Opt
Comm. 157 (1998) 145-149.
[3] Y. C. Huang and R. L. Byer, "Acceleration-field Calculation for a Structure-based Laser-driven
Linear Accelerator", Rev. Sci. Instrum., Vol. 69, No. 7 (1998).
[4] J.A. Edighoffer and R.H. Pantell, "Energy Exchange between Free Electrons and Light in Vacuum,"
J. Appl. Phys. 50 (10), Oct. 1979, p. 6120.
[5] M. O. Scully, "A Simple Laser Unac? Appl. Phys. B 51, 238-241 (1990).
[6] EJ. Bochove, G.T. Moore, and M.O. Scully, "Acceleration of Particles by an Asymmetric HermiteGaussian Laser Beam," Physical Review A,vol. 46, No. 10, 6640 (1992).
[7] A.C. Chiang, Y.Y. Lin, and Y.C. Huang, "Laser-induced Damage Thresholds at CVD-grown
Diamond surfaces for 200-psec CO2 Laser Pulses," Optics Letters 27 (2002) 164-166.Brown, M. P.,
and Austin, K., The New Physique, Publisher City: Publisher Name, 1997, pp. 25-30.
309