Particle acceleration using laser-driven field-shaping structures, while an obvious extension of current microwave-based acceleration techniques, is fundamentally limited by both electric breakdown due to high power densities and by the deleterious effects of particle wakefields. One possible method for avoiding these issues in a laser-driven structure is the use of dielectric-loaded structures having slab symmetry. This idea has been investigated theoretically and computationally at UCLA since 1995 and experimental verification of the concept is being planned. This proposed experiment will complement the PBPL’s other laser-driven accelerator experiments (the ongoing IFEL and plasma beat-wave studies).
Slab-symmetric structures include any device which is very large in one transverse direction, so that the system has translational symmetry in that dimension. To be specific, consider a structure made up of two slabs of dielectric material separated by a vacuum gap and bounded by a thin conducting layer on their outer surfaces. (The first figure on the right shows a schematic drawing of such a structure.) If the vacuum gap width is, say, two orders of magnitude smaller than the transverse width of the slabs, and if a "ribbon-shaped"? Electron beam with the same aspect ratio propagates through this gap, the symmetry of the structure forces transverse (dipole-mode) wakefields to be zero even if the beam is not perfectly centered in the gap. Furthermore, accelerating field within the gap is independent of transverse position, and the use of dielectric materials in regions of high electric field raises the breakdown limitation to more than 1 GV/m for short pulses, allowing acceleration gradients of hundreds of MeV/m.
An experimental demonstration of the slab-symmetric accelerator concept would be difficult at optical frequencies, since the small transverse dimension of both structure and beam must be on the order of an optical wavelength. The proposed UCLA experiment is inspired by current work on a multimegawatt radiation source at terahertz frequencies, which uses non-collinear mixing of two CO2 laser lines in a nonlinear crystal to generate high power at a wavelength of 340 microns. Such a structure dimension allows electron beams of realistic size to be easily injected into the structure for initial tests of the concept.
The structure geometry is shown schematically in Figure 1. It consists of two mirror surfaces, taken to be (nearly) infinite in the x and z dimensions, displaced from each other in the y direction so as to create a narrow gap. The gap is lined on each side by a layer of dielectric material having relative permittivity epsilon. The distance between the conducting boundaries is 2b, 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) is incident 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.
In the absence of the coupling slots there would be no axial periodicity in the device at all. If the conducting boundaries were uniform partially transmitting mirrors, the structure would resemble a Fabry-Perot mirror pair, and would have resonant fields that were invariant in z. Such fields, of course, cannot accelerate particles. The coupling slots here enforce the correct field periodicity, and for a given drive frequency we can choose the structure and dielectric dimensions such that the axial wavefronts are synchronous with the particle beam, i.e. we can set the axial phase velocity equal to c.
The fundamental accelerating mode must have a sinusoidal dependence on z in order to satisfy the wave equation; thus we can solve for this mode by assuming an axial electric field of the form
E(y) cos(kzz) cos(omega t),
there being no x-dependence since the structure is translationally invariant in x. The synchronism condition then requires that the fields are constant in y within the gap. This symmetry is comparable to that of a rotationally-symmetric dielectric structure such as the dielectric wakefield accelerator, but with the advantage that misalignment does not destroy the symmetry.
Using the Maxwell equations and applying conducting boundary conditions at the metallic boundaries while enforcing field continuity at the vacuum/dielectric interface, one can solve for the rest of the fields and derive a transcendental equation for the allowed resonant wavenumbers kz as a function of the structure geometry and epsilon. In general, of course, we generate radiation at a fixed frequency and adjust the values of a and b for resonance. Field strength within the dielectric increases roughly proportionately to mode number, meaning that operation in the lowest mode is preferred, corresponding to the smallest possible resonant value for the gap spacing.
A physically realizable structure is of course finite rather than infinite, with fields that are not exactly constant in the x dimension. This could arise through a boundary or discontinuity at some (large) value of x, or because of the intrinsic field profile of an incident Gaussian laser pulse with some large but finite width. In either case, the result will be a small but nonzero wavenumber kx, and in order for the fields to remain synchronous (with speed-of-light phase fronts) we obtain a hyperbolic form for the field dependence on y--in other words, Ez is proportional to cosh(kx y) rather than constant in y--but if kx is sufficiently small, meaning that the x-dimension is large enough, the degree of field variation across the vacuum gap can be kept arbitrarily small.
The coupling slots also affect the field solutions. Unlike standard RF coupling apertures, they are extremely wide compared to a wavelength and hence are not cut off for any radiation frequency. They therefore fill with field, with two consequences: they are the most likely location for field breakdown, and they will perturb the structure resonant frequency. The extra energy stored in the slot fields is mostly electric, and the Slater pertubation theorem implies a downward frequency shift for the eigenmodes. The precise effect must be found through simulation.
To simulate the slab structure, we use the three-dimensional finite-difference code GdfidL for field eigensolutions, a custom 2D finite-difference time-domain code for structure filling calculations, and the 2D particle-in-cell code OOPICPro for checking wakefields.
A contour plot of the lowest eigenmode for the ideal, infinite structure without coupling slots is shown in Figure 2. Note the flatness of the wavefronts, as predicted by theory for the speed-of-light mode. The fields decrease smoothly to zero in the dielectric.
Typical electron bunch lengths at Neptune are several times larger than a radiation wavelength, so that longitudinal wakefields would be very small. To illustrate the suppression of transverse wakefields in simulation, we use a bunch length of 120 microns. The plots in Figure 3 show the longitudinal and transverse wakefields for this short-bunch case, demonstrating the cancellation of transverse wakes within the vacuum gap.
Figure 4 shows fields during filling, calculated using the 2D finite difference code. In this example, the length of the coupling slot is about one quarter of the radiation wavelength, which gives a matching condition such that the slot fields are zero at the inner aperture, and the acceleration fields and frequency are unperturbed. This result verifies our theoretical expectations, but is impractical for experimental use since the coupling Q factor becomes unacceptably large in this case. For shorter slots, one must compensate for the frequency detuning of the structure, but final accelerating field amplitudes are from 10 to 14 times larger than the amplitude of the drive laser.
Different construction methods for these structures are currently being investigated. Since the structure is to be built from a dielectric material which could be silicon or germanium, we can use layered deposition methods common in the semiconductor industry. Decisions still to be finalized include the exact materials to be used and whether the device should be constructed in one piece or in two pieces that are then micropositioned. Construction of a prototype will allow "cold testing" at low power, wth the spectral response of the output slots used as a diagnostic for filling the structure. An electron bunch can also be injected into the structure in order to measure the wakefield radiation frequency, and perhaps to investigate beam response to angular misalignment. Finally, structure prototypes will need to be tested at high power to establish dielectric breakdown limits and hence the maximum obtainable field gradient. Successful completion of these stages enables a full-scale test of the slab-symmetric resonant dielectric accelerator, to our knowledge the first such experiment.