Session Item

To computationally model electromagnetic distortion in radial parallel plate waveguides. This work is part of an effort to refine the design parameters of the electromagnetic field delivery modules for a compact dielectric wall accelerator for proton radiotherapy. The field delivery modules, composed of high-voltage pulse-generating circuits and parallel plate waveguides, are stacked along the beam axis and sequentially deliver short-lived (∼1 ns), high-gradient (∼100 MV/m) electric field pulses as the particle bunch transits the device. The high-gradient electric fields promise a compact accelerator (∼3 m), but pose design challenges, especially in the context of electrical breakdown. The proposed radial geometry offers a passive field amplification, which alleviates the electrical stress on upstream circuitry. However, temporal distortions of the waveform also occur, which can lead to undesirable characteristics in the accelerating field (mainly related to longitudinal stability of the particle bunch). Understanding the impact that waveguide geometry and composition have on the distortions is crucial to selecting a design that is both feasible to construct and suitable for the acceleration of a clinical proton beam.

COMSOL Multiphysics (2D Axisymmetric, Transient Electromagnetic Waves) was used to model radial parallel plate waveguides. The waveguide was uniformly excited at the outer radius with a Gaussian voltage pulse (f ), and the output pulse (h) at the inner radius was measured (Fig 1). The frequency response of the system (G, i.e., frequency-dependent amplification factor), was calculated numerically (Eq 1) and studied for various geometric (inner radius r_in , outer radius r_out , plate separation d) and material (relative permittivity ε_r ) parameters (Fig 1).

All simulated geometries exhibited non-uniform amplification across the bandwidth of f , with amplification factors approaching a plateau at higher frequencies (Fig 2). Decreasing r_in , increasing r_out, and increasing ε_r all increased amplification of the signal, although the frequency-dependence of this effect was unique to each parameter. Additional study is needed to understand the interplay between the parameters, and to further quantify the frequency-dependence of the responses. Changing d had no effect on G.

Decreasing the inner radius, increasing the outer radius, and increasing the relative permittivity of the waveguide all led to increased amplification across the frequencies studied. This information can be used in conjunction with external factors in the accelerator design (particle bunch stability, material cost/availability, size/weight of the device, etc.) to select an appropriate waveguide geometry and composition. These results also inform the power output and pulse shaping requirements of the upstream circuit design as they provide an important bridge between the strength and temporal profile of the injected pulses and those of the accelerating fields.