SLAB symmetric dielectric micron scale structures for high gradient electron acceleration. Page: 4 of 5
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introduction of a taper at the slot opening provides
improved coupling over the case of a rectangular slot
profile.
2 NUMERICAL RESULTS
In the study of these structures we have found it useful to
rely on numerical solution of the Maxwell equations in
slab geometry. We use a custom finite difference time
domain code to inject and propagate the laser fields into
the structure geomerty under study. The program
implements periodic boundary conditions in z (the beam
propagation direction) and absorbing boundary conditions
in y (the laser propagation direction) to handle any
reflected laser energy from the structure. The structure is
assumed to be of infinite extent in the x-view. For a given
structure geometry, the integration is continued until a
steady state condition is reached. The structure is "tuned"
numerically by adjusting one of its parameters (typically
the dielectric constant) until the asymptotic stored energy
is maximized. (In the laboratory one would tune the
structure by changing a geometrical parameter like the
vacuum gap size.)
We have analyzed a structure with dielectric thickness
(b-a) equal to the vacuum gap (a =1.6 gm), period of
10.6 pm (corresponding to a commone CO2 laser line),
and dielectric constant e =3.7. The conductive cladding
thickness in the simulation is 0.3 pm. The laser coupling
and field strengths in the structure were studied as a
function of the shape of the coupling slot. While not
exhaustive, these calculations indicate a promising
approach to the problem of coupling optimization. The
following results are normalized to a peak laser electric
field of 0.25 Statvolt/cm = 75 kV/m.4R
AS(k)
Figure 2. Pseudocolor contour map of E. in the comput-
ational area for the tapered aperture structure. Laser radia-
tion is incident from the top of the figure (y=0). The area
depicted in solid black is the conductive cladding, and the
thin black line indicates the dielectric-vacuum boundary.Y( 1,,aI
In reference[71, the fields of a similar structure having an
infinitesimally thick, sinusoidally modulated transmit-
tivity outer cladding were computed. While reasonable
coupling was achieved, it was also pointed out that the
surface electric field on the mirror-dielectric interface was
undesirably large, roughly twice the maximum field in the
vacuum gap. The case of a finite thickness mirror with a
rectangular aperture was studied for this paper. For a 2
pm slot width the corresponding peak surface field is 2.0
Statvolt/cm for a gap field amplitude of 1.06 Statvolt/cm.
The largest surface fields in this device occurred at the
exterior corners of the slot; this might be further improved
by rounding the corners. (The present version of the
simulation code cannot handle curved boundaries except
via a stairstep approximation.) An increase in the
coupling slot width to 3 pm produced slightly worse
results with a surface field/gap field ratio of 1.9/0.87.
The effect of tapering the aperture of the coupling slot
is shown in Figure 2. The surface field/gap field ratio is
relatively small, 1.56/1.23, while the gap field strength is
also a maximum for all similar device geometries. Stored
energy and gap field strengths vs time are shown in
Figure 3. From the energy history we can read off a fill
time of 0.57 ps, corresponding to Q=102. As we have
discussed previously[7], the fields in the vacuum gap are
a superposition of Fabry-Perot-like (zero phase shift per
period, providing no net acceleration) and accelerating
(forward wave componet resonant with an ultrarelativistic
particle) modes. The Fabry-Perot mode amplitude has
been diminished to 20% of the accelerating mode
amplitude in the present case, solely through through the
periodicity of the coupling. This proportion seems to be
about the most favorable we have been able to obtain.0A
04
020 '0 MO 300~ 400 !00 3 70 10 O L0 W *W0
Figure 3. Fill curves for the tapered aperture structure.
The fill time is 0.56 ps, corresponding to Q=102. The
stored energy is normalized to its maximum value, while
the accelerating and Fabry-Perot modes are shown
relative to the accelerating field amplitude./ I- Aob400
Iaa
'00
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Rosenzweig, J. B. & Schoessow, P. V. SLAB symmetric dielectric micron scale structures for high gradient electron acceleration., article, June 12, 1999; Illinois. (https://digital.library.unt.edu/ark:/67531/metadc621439/m1/4/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.