A Resonant, THz Slab-Symmetric DielectricBased Accelerator
R. B. Yoder and J. B. Rosenzweig
Dept. of Physics and Astronomy, UCLA, Los Angeles, CA 90095-1547
Abstract. Slab-symmetric dielectric-loaded structures, consisting of a vacuum gap between
dielectric-lined conducting walls, have become a subject of interest for short-wavelength
acceleration due to their simplicity, relatively low power density, and advantageous beam
dynamics. Such a structure can be resonantly excited by an external power source and is known
to strongly suppress transverse wakefields. Motivated by the prospect of a high-power FIR
radiation source, currently under construction at UCLA, we investigate a high-gradient slabsymmetric accelerator powered by up to 100 MW of laser power at 340 um, with a predicted
gradient near 100 MeV/m. Three-dimensional simulation studies of the structure fields and
wakes are presented and compared with theory, and a future experiment is discussed.
BACKGROUND
Mechanisms for obtaining charged-particle acceleration using the high power
density of lasers can generally be divided into two classes: those in which the
accelerating fields are dominated by structures or boundaries with characteristic
dimensions on the order of the laser wavelength, termed near-field devices, and those
in which fields are derived from the diffraction-dominated propagation of one or more
laser beams, or far-field devices. The latter class, which includes "vacuum
accelerators" such as crossed-laser beam devices [1,2] as well as inverse Cerenkov
accelerators [3], has the obvious advantage that the field strength is minimized near
any structures, such as mirrors, that are used to create the field profile; fields are
therefore not limited by breakdown. Furthermore, since there is no structure
surrounding the particle beam, that beam will not be perturbed or destroyed by its own
wakefields. On the other hand, the fields in this class of devices are dominated by
large transverse components, in general much greater than those in the longitudinal or
accelerating direction. Not only are such accelerators clearly inefficient, since the
strongest fields are unused, but they also tend to suffer from a high degree of
transverse instability, since small asymmetries in the fields or misalignment of the
particle beam can result in severe transverse deflections or in acceleration that depends
on transverse position.
In comparison, the strengths and weaknesses of near-field devices are
complementary. The overriding consideration in the design of a near-field structure
must be to avoid field breakdown due to the high power density which will necessarily
be located at the field-shaping boundary. Metallic cavities, standard at microwave
frequencies, are no longer advantageous at near-optical scales, where the most
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
331
promising materials are dielectrics that can withstand fields of a few GV/m for pulses
of a few picoseconds [4]. Notwithstanding this practical limit, near-field structures
have the advantage that they can be resonantly excited, giving fields in the structure
larger than those of the driving laser, and field symmetry and synchronicity can be
enforced in a straightforward way.
The other principal difficulty with near-field structures arises from the presence of
boundaries very near the particle beam. In a conventional linac with a cylindricallysymmetric structure, transverse wakefields quickly become unacceptably large as the
resonant wavelength decreases below a few millimeters. However, if slab symmetry
is employed—i.e. if the structure is rectangular, with one transverse dimension much
greater than the gap spacing—this effect can be mitigated by accelerating a beam
which is spread out in the wide transverse direction until its transverse size is much
larger than the structure gap. Not only can a large amount of charge be accelerated in
this way without beam loading, but it has been shown [5] that such a beam couples
very weakly to the antisymmetric dipole modes of the structure and therefore
generates almost no transverse wakefield, independent of its transverse position within
the gap.
Given these considerations, a slab-symmetric resonant structure consisting of a
vacuum gap between two conducting mirrors, lined on the inside by dielectric, was
first proposed in 1995 [5]. This device was based on a Fabry-Perot mirror pair and
was intended to be driven by a laser incident on the side of the structure and partially
transmitted through the mirror boundary. Clearly, in the absence of any intrinsic
structural periodicity in the longitudinal (acceleration) direction, the fields produced
would be mainly invariant in z, corresponding to the standard Fabry-Perot mode for
the structure; such fields cannot produce net acceleration. Periodic modulation of the
dielectric constant in the z direction was proposed to enforce the correct field
periodicity as well as the desired coupling of the laser power into the accelerating
mode. Simulations showed that the efficiency of this coupling was poor, and in later
versions of this design [6], the functions of coupling laser power into the structure and
enforcing the correct field periodicity were split, with mirror transmissivity being
itself modulated in the longitudinal direction while the dielectric constant remained
fixed. This design performed well in simulations when excited with a laser
wavelength of 10.6 um, with a resonant gap spacing equal to the laser wavelength.
However, producing an electron beam with such a small transverse dimension proved
unfeasible, and no experiment using this structure was attempted.
This paper presents a design for a similar structure, but operated now in the far
infrared frequency range, at a wavelength of 340 um. This wavelength choice reflects
the potential availability of a high-power THz radiation source in the UCLA Neptune
laboratory, to be discussed briefly below. The correspondingly greater gap dimension
in the accelerator leads to a much weaker requirement on the beam emittance, and an
experimental investigation is planned for the near future.
It should be noted that similar slab-symmetric dielectric-loaded structures have
recently been proposed for wakefield acceleration [7,8]; in such a device, longitudinal
wakefields excited by a drive bunch or bunches are used to accelerate a second or
witness bunch following a precise distance after the driver. A theoretical analysis of
wakefield acceleration shows that a very large number of structure modes are
332
produced by the initial driving bunch, some of which combine to produce useful
accelerating fields behind the bunch. By comparison, the scheme outlined here would
use resonant coupling from an external source to drive the structure with a single
dominant mode.
conductor
laser light
i
y
4
ebeam
(a)
(b)
FIGURE 1. (a) Schematic drawing of the structure geometry. Two layers of dielectric-lined conductor
surround a vacuum gap; a very wide electron beam is injected into the gap and travels in the +z
direction, while radiation (polarized in z) is coupled in from above through transverse slots in the
conductor, (b) A cross-section in x, showing the parameters used in the mathematical analysis. (The
dielectric is denoted by cross-hatching.)
DESCRIPTION OF THE STRUCTURE
The structure geometry under discussion here is shown schematically in Figure 1.
It consists of two mirror surfaces, assumed to be infinite in jc and z, displaced from
each other in the y direction so as to create a narrow gap. The gap is partially filled by
two layers of dielectric material having relative permittivity e. For the analysis below,
we take the distance between the conducting boundaries to be 2ft, with the central
vacuum gap having dimension 2a, so that the dielectric thickness on each wall is
(b - a). The particle beam is traveling in the positive z direction. Laser light (also
polarized in the +z direction) impinges on the upper surface as shown, and a series of
narrow transverse coupling slots in the conductor allows transmission of light into the
structure. The slot spacing must equal the free-space laser wavelength; this enforces a
field in the structure which is periodic in z and can therefore accelerate particles
synchronously. Coupling slots in the lower surface symmetrize the field and allow the
detection of transmitted light as a diagnostic.
A mode analysis of the dielectric-loaded slab-symmetric structure has been
presented by Tremaine et al. [9], in the usual approximation of perfectly conducting
boundaries and in the infinite-width limit; that paper also considers the effect of a slow
field variation in jc, corresponding to a large but non-infinite jc-dimension. Recent
calculations of the modes present in a slab structure with conducting boundaries at x =
±L (i.e. an asymmetric rectangular waveguide which is lined by dielectric on two
sides) have been presented by Park and Hirshfield [10] as well as Jing [11], and a
planar structure without sidewalls, though with somewhat different geometry, has
been investigated experimentally by Hill et al. [12] at a frequency of 91 GHz. For the
purposes of this discussion, we quote the results of [9] for the accelerating modes,
with the understanding that some amount of higher harmonic content and/or nonaccelerating modes will be present in any physical and non-infinite structure.
The fundamental accelerating mode must have a sinusoidal dependence on axial
position; thus we solve for an axial electric field of the form E(y)cos(kz)cos(ct)t), there
being no jc-dependence since the structure is translationally invariant in jc. (Of course,
this defines a standing wave, with the forward-going traveling-wave component being
the one of interest.) Within the vacuum gap ([y|<a), we further require for
synchronism that the longitudinal phase velocity is equal to the speed of light, i.e.
a)/kz = c. In that case, the dispersion relation can only be satisfied if ky = 0, which
implies that the axial field is constant my:
Ez = EQ cos(&zz)cos(o#)
(1)
where EQ is the field amplitude and (okz = c. The periodicity of the laser coupling slots,
which enforces periodic rather than constant axial fields, thus provides the field
synchronicity required for particle acceleration. The transverse field Ey must be linear
in y to keep E divergenceless in the gap; we therefore have
Ey = EQkzy sin(*zz)cos(Gif).
(2)
Within the dielectric (a<\y\< b), there must be variation in y in order to allow Ez to
decrease to zero at the conducting boundary. Solution of the Maxwell equations gives
- y)]cos(kzz)cos(a)t)
(3)
and
> - ;y)]sin(&zz)cos(fttf)-
(4)
Continuity of Ez and Dy at the dielectric boundary gives the transcendental equation
k7a ——— = cot[k 7 ^8-\(b- a)]
(5)
8
for the allowed eigenvalues kz and determines the relative amplitude A of the fields in
the dielectric,
__
Since kz is fixed by the laser, the structure dimensions a and b can then be determined
for a given dielectric material.
Equation (5) shows that, for a given geometry, there is a series of eigenvalues kz
which will increase roughly linearly with mode number; plots of the fields in the first
three eigenmodes are shown in Figure 2. It is clear that field strengths within the
dielectric increase proportionately for higher mode numbers, as implied by Eqns. (2)
and (6). To avoid breakdown limitations as far as possible, one must obviously work
in the fundamental mode to reduce the field strength on the boundaries. This
corresponds physically to taking the lowest possible resonant value for the gap
spacing.
334
10
10
15
(a)
(a)
(b)
10
5
00
z
LLI
E /E
y
0
E /E
0
5
0
-5
-10
-10
-5
0
50
50
y (µm)
100
100
150
-10
0
50
y (µm)
100
150
150
FIGURE
FIGURE 2.2. Examples
Examples of
of calculated
calculated ideal
ideal field
field profiles
profiles for
for yy >> 00 within
within aa structure,
structure, showing
showing (a)
(a)
longitudinal
longitudinal and
and (b)
(b) transverse
transverse components,
components, with
with aa == 115
115 µm,
um, bb == 145
145 µm,
um, εe == 3.
3. The
The first
first three
three
eigenmodes
eigenmodesare
areshown:
shown: nn==11(solid),
(solid),22(dashed),
(dashed), and
and33(dot-dashed).
(dot-dashed).
EXPERIMENTAL
EXPERIMENTAL PARAMETERS
PARAMETERS
The
The geometry
geometry of
of the
the experiment
experiment which
which isis planned
planned for
for the
the UCLA
UCLA Neptune
Neptune facility
facility is
is
dictated
dictated by
by available
available radiation
radiation wavelengths.
wavelengths. As
As indicated
indicated above,
above, itit is
is intended
intended to
to use
use aa
novel
novel high-power
high-power radiation
radiation source
source in
in the
the terahertz
terahertz range
range to
to drive
drive the
the accelerator;
accelerator; with
with
aa radiation
radiation wavelength
wavelength of
of 340
340 µm,
urn, the
the slab
slab structure
structure will
will resonate
resonate in
in the
the fundamental
fundamental
accelerating mode
mode when
when aa ==115
115 µm,
urn, bb ==145
145 µm,
urn, for
for εe == 3.
3. A
A vacuum
vacuum gap
gap of more
accelerating
than
than 0.2
0.2 mm
mm makes
makes itit feasible
feasible to
to inject
inject the
the 11
11 MeV
MeV beam
beam from
from the
the Neptune
Neptune
photoinjector,
photoinjector, with
with normalized
normalized transverse
transverse emittance
emittance in
in the
the range
range of
of 6–10
6-10 ›n mm
mm mrad,
mrad,
intothe
the structure
structure successfully.
successfully.
into
We expect
expect to
to obtain
obtain multimegawatt
multimegawatt laser
laser radiation
radiation at
at 340
340 µm
|um using
using aa difference
difference
We
frequency generation
generation scheme:
scheme: two
two frequencies
frequencies from
from the
the Neptune
Neptune terawatt
terawatt CO
CO2
laser
frequency
2 laser
will be
be mixed
mixed atat high
high power
power in
in aa gallium
gallium arsenide
arsenide crystal,
crystal, with
with conversion
conversion efficiency
efficiency
will
into the
the difference
difference frequency
frequency near
near 1%
1% [13].
[13]. The
The two
two input
input frequencies,
frequencies, as
as well
well as
as the
the
into
output radiation,
radiation, are
are non-collinear
non-collinear in
in order
order to
to maintain
maintain synchronism
synchronism over
over aa relatively
relatively
output
large (several
(several centimeter)
centimeter) interaction
interaction length.
length. Output
Output power
power levels
levels in
in excess
excess of
of 100
100
large
MWare
are projected;
projected; experimental
experimental work
work isis currently
currently in
in progress.
progress.
MW
FIELD SIMULATIONS
SIMULATIONS
FIELD
Simulation of
of the
the slab
slab structure
structure was
was carried
carried out
out using
using the
the finite-difference
finite-difference code
code
Simulation
[14]. For
For simulation
simulation purposes,
purposes, magnetic
magnetic boundary
boundary conditions
conditions on
on x were
were used
used
DFIDL [14].
GGDFIDL
to obtain
obtain aa nearly
nearly constant
constant field
field in
in the
the wide
wide dimension
dimension without
without requiring
requiring aa
to
prohibitively large
large computational
computational volume.
volume.
prohibitively
Initially, eigensolutions
eigensolutions were
were found
found for
for aa segment
segment of
of the
the structure
structure in
in the absence of
Initially,
external couplers;
couplers; contour
contour plots
plots of
of the
the fields
fields for
for the
the accelerating
accelerating mode
mode are
are shown
shown in
in
external
Figure 3.
3. Note
Note the
the flatness
flatness of
of the
the wavefronts
wavefronts of
of the
the accelerating
accelerating component,
component, showing
showing
Figure
335
that acceleration in this mode is independent of the transverse location of the beam.
that acceleration in this mode is independent of the transverse location of the beam.
The fields decrease smoothly to zero in the dielectric.
The fields decrease smoothly to zero in the dielectric.
8.9.10 3
0.010 °8.91.0
5
0,0003
0.0001.
0
0,0001
0.0003
0.0001
0.0003
y
8.910
N 0,010 <M
8.910
0.0003
0.0001
0
FIGURE 3. Contour plots in the y-z plane from simulation, showing the fundamental accelerating
FIGURE
plotsininz.theLongitudinal
y-z plane from
showing
the negative
fundamental
accelerating
mode over3.oneContour
half-period
fieldsimulation,
(top) extends
in z from
to positive
field
mode
overtransverse
one half-period
in z. is
Longitudinal
(top)
extends in zatfrom
negativeboundary.
to positive field
maxima;
field (bottom)
zero along yfield
= 0 and
discontinuous
the dielectric
maxima; transverse field (bottom) is zero along y = 0 and discontinuous at the dielectric boundary.
Using a copper boundary with finite conductivity, the structure ohmic Q is
Using a tocopper
boundary with
conductivity,
the structure
Q is
calculated
be approximately
600,finite
and the
simulated fields
give riseohmic
to a shunt
calculated
to
be
approximately
600,
and
the
simulated
fields
give
rise
to
a
shunt
impedance for the structure of 15.3 MQ/m. This relatively low value is a consequence
impedance
the structure
15.3beMΩ/m.
This in
relatively
low value
is a consequence
of the slab for
geometry,
whichofmay
understood
this context
as a combination
of a
of
the
slab
geometry,
which
may
be
understood
in
this
context
as
a
combination
of a
large number of cylindrically-symmetric structures in parallel. For this reason, slab
large
number
of
cylindrically-symmetric
structures
in
parallel.
For
this
reason,
slab
structures are well suited for laser-powered accelerators, in which accelerating fields
structures
areby
well
suited for laser-powered
accelerators,
in which
are limited
breakdown
rather than available
power.
Fromaccelerating
this result,fields
the
are
limited
by
breakdown
rather
than
available
power.
From
thisMV/m
result,when
the
accelerating field gradient can be estimated to be approximately 50-100
accelerating
field
gradient
can
be
estimated
to
be
approximately
50–100
MV/m
when
the radiation power is 100 MW.
the To
radiation
power
is 100 MW.
simulate
the time-dependent
filling of the structure, the geometry was extended
To
simulate
the
time-dependent
filling
of the
the conducting
geometry was
extended
to create entry and exit waveguides
above
andstructure,
below the
walls,
with
to
create entry
and exit
waveguides
and below
the conducting
walls, with
boundary
conditions
adjusted
to give above
the correct
+z polarization
for the fields.
The
boundary
adjustedin toFigure
give the
correct shows
+z polarization
for thefields
fields.in The
geometry conditions
is demonstrated
4, which
the computed
the
geometry
is demonstrated
in Figureof4,course,
whichthe
shows
computed
fields in the
structure during
filling. In practice,
drivethe
radiation
will illuminate
an
structure
during
filling. In
the drive
radiation Coupling
will illuminate
area many
wavelengths
in practice,
diameter of
in course,
the correct
polarization.
slots an
of
area
in diameter
in the
Coupling
slots
of
widthmany
3 |umwavelengths
(visible in Fig.
4 as small
gapscorrect
on toppolarization.
of the conducting
walls)
were
width
µm
in Fig.
4 asstructure,
small gaps
on location
top of the
conductingpositive
walls) axial
were
located3 at
the(visible
upper edge
of the
at the
of maximum
located
at the upper
edge
the structure,
the location
of maximum
positive
axial
field. Symmetry
about
theofmidplane
is not at
enforced
a priori,
as both input
and output
field.
Symmetry
about the
midplane is
not enforced
a priori,
as both
output
couplers
are included.
Monitoring
power
flow from
the exit
side input
of theand
structure
couplers
included. ofMonitoring
power flowin from
the exit domain.
side of the structure
allows theare
computation
scattering parameters
the frequency
allows the computation of scattering parameters in the frequency domain.
336
Geometry for
for simulation
simulation of
of time-dependent
time-dependent fields,
fields, showing
showing aa slice
slice through
through the
the structure
structure
FIGURE 4. Geometry
one-half of an
an axial
axial period
period thick.
thick. The
The picture
picture includes
includes metal
metal boundaries
boundaries (dark),
(dark), dielectric
dielectric boundaries
boundaries
(grey mesh), and fields
fields (grey
(grey arrows),
arrows), with
with dimensions
dimensions in
in meters.
meters. The
The z-axis
z-axis isis vertical;
vertical; thus
thus the
the entire
entire
structure consists of
of aa vertical
vertical stack
stack of
of such
such slices.
slices. The
The open
open area
area inin the
the foreground
foreground isis the
the input
input
waveguide, containing
containing an
an exciting
exciting field
field traveling
traveling in
in the
the –y
—ydirection.
direction. Since
Since the
the conducting
conducting wall
wall
between waveguide and
and central
central gap
gap isis slightly
slightly lower
lower than
than the
the +z
+z boundary,
boundary, aa coupling
coupling slot
slot isis formed
formed
through
through which
which the
the fields
fields enter
enter the
the accelerator.
accelerator. Field
Field enhancement
enhancement within
within the
the gap
gap isis clearly
clearly visible.
visible. An
An
exit
exit coupling
coupling slot
slot and
and waveguide
waveguide are
are on
on the
the opposite
opposite side
side of
of the
the gap
gap (facing
(facing away
away from
from the
theviewer
viewerinin
this
this picture),
picture), with
with some
some transmitted
transmitted field
field shown.
shown.
1
E(t)/E
max
0.8
0.6
0.4
0.2
0
00
100
100
200
200
300
300 400
400
time
time(ps)
(ps)
500
500
600
600
FIGURE
FIGURE 5.
5. Plot
Plot of
of field
field amplitude
amplitude within
within the
the gap
gap as
as aa function
function of
oftime.
time. The
Thesolid
solidline
lineisisinterpolated
interpolated
from
from the
the calculated
calculated field
field values
values (circles).
(circles).
Figure
Figure 55 shows
shows aa plot
plot of
of the
the field
field amplitude
amplitude within
within the
the gap,
gap, normalized
normalized to
to its
its
steady-state
steady-state value,
value, as
as aa function
function of
of time.
time. The
The curve
curve shape
shape shows
shows the
the usual
usual response
response of
of
aa resonator
resonator being
being driven
driven near
near its
its resonant
resonant frequency.
frequency. Given
Givenaafill
fill time
timeof
of400
400ps
psfrom
from
the
the graph,
graph, the
the structure
structure Q
Q == ωτ
COT is
is calculated
calculated to
to be
be approximately
approximately 2000,
2000, aa relatively
relatively
high
high value
value for
for this
this planar
planar structure.
structure.
337
WAKEFIELD SIMULATIONS
Simulations of the wakefields produced by the passage of a line charge through
slab-symmetric structures were carried out using the two-dimensional particle-in-cell
code OOPIC [15]. Figure 6 is an illustrative example of the wakefields produced by a
relatively long bunch; the longitudinal wakefields are quite weak, and the transverse
wakefields vanish completely within the vacuum gap of the structure, as expected.
FIGURE 6. Surface plots of longitudinal (left) and transverse (right) wakefields in a slab geometry
with a = 0.58 mm, b = 1.44 mm, e = 3.9, Q = 200 pC, beam ar = 120 um, beam az = 4 ps. Beam travel
is left to right. The transverse wake is completely cancelled within the vacuum gap.
For the particular geometry under consideration here, the magnitudes of both
transverse and longitudinal wakefields are small. Figure 7 shows the longitudinal
wakefield behind the beam for two different beam lengths. When az = 1.2 mm, the
wakefields are almost entirely washed out. For much shorter bunches (az =120 |um),
one would still expect a retarding field of only 8 to 10 kV/m to be experienced by the
injected beam, so that with a structure length of a few centimeters the energy change
experienced would be impossible to observe. Note in both cases that the correct
wavelength (340 |um) was produced by the simulation. Fig. 7 also shows the
vanishing of the wakefield after about 8 periods, which could be due to destructive
interference between wake radiation and transition radiation from the beam's entry
into the structure. This topic has also been discussed by Park and Hirshfield [10].
Further simulations will be necessary to investigate wakefields in the case of beams
propagating at some small transverse angle to the z-axis. Such a misalignment would
break the symmetry which is responsible for the cancellation of the transverse wakes,
so that it might become possible to observe some transverse effect on a test beam.
Three-dimensional studies are also anticipated.
338
FIGURE 7. Lineouts of the longitudinal wakefield (in V/m) as a function of axial position (in cm) for
the design geometry, for a long (az =1.2 mm) bunch (left) and a short (az =120 um) bunch (right). In
both cases the leading edge of the driving beam is located at z = 0.87 cm, and ay = 25 um.
SUMMARY AND FUTURE PLANS
In this paper, we have described a slab-symmetric dielectric-loaded structure which
serves as a resonant laser-driven accelerator with advantageous transverse stability.
When such an accelerator is powered by a submillimeter-wave source at 340 |um, the
structure dimensions become ample for acceleration of a slab electron beam with
realistic transverse size.
Such structures have an intrinsically low shunt impedance, but when driven with
the high power levels available from optical and submillimeter radiation sources,
appreciable accelerating fields may be obtained. For the dimensions described here,
with available power levels of 100 MW or more, gradients of up to 100 Me V/m are
expected.
Experimental investigation of the slab-symmetric, dielectric-loaded structure is to
begin in fall 2002 at the UCLA Neptune facility. Planned measurements include
measurement of the wakefield radiation spectrum (which would enable checking the
theoretical dependence on gap spacing) and possible transverse beam disruption when
the pointing is deliberately misaligned; cold-testing of the structure by using the
output coupling slots to verify the resonant frequency is also envisioned. Breakdown
limitations are not clear at present and must also be tested experimentally as a function
of incident power density, e.g. by varying the laser spot size. A successful
demonstration of energy gain by a slab beam will depend on detailed knowledge of the
structure physics, as verified by experiment.
ACKNOWLEDGMENTS
This work was supported by US Dept. of Energy grant DE-FG03-92ER40693. We
thank S. Tochitsky for helpful conversations.
339
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