Field dispersion in uniformly-excited radial parallel plate waveguides for a compact proton accelerator design

Proton therapy (PT) is a beneficial modality for treating certain cancers but remains under utilized due in part to the high cost of existing PT devices. Dielectric wall accelerators (DWAs) are a proposed class of coreless induction accelerators that may present a suitable option for compact and affordable PT. To realize a compact device, acceleration modules must be designed to achieve field strengths approaching 100 MV/m delivered as pulses on the order of nanoseconds.

Here, we examine pulse injection into radial parallel plate waveguides as a means of producing high-intensity, pulsed accelerating fields. We present an approach for understanding the impact of waveguide properties on electromagnetic dispersion as well as a means of accounting for this dispersion to produce suitable accelerating fields.

Geometric and material properties for a set of waveguides were identified based on existing literature and commonly available materials. An analytic model is presented to describe how waveguide geometry and material affect electromagnetic dispersion in a waveguide. Simulations performed in COMSOL Multiphysics are used to calculate a transfer function for the set of waveguides, which provide a means of determining the waveguides output for arbitrary inputs and vice versa. The simulation results are compared to the analytic solution and used to explore alternate matching conditions at the beampipe of the accelerator.

Overall, radial waveguides provide a passive enhancement of the injected pulse, with enhancement of high-frequency components found to be proportional to the square root of the ratio of outer radius to inner radius of the waveguide. Dispersion in the waveguide caused by the radial propagation of the pulse depends on multiple waveguide properties (outer radius, inner radius, material) and leads to reduced enhancement at lower frequencies. The field enhancement in the waveguides reduces the peak voltage required to achieve the desired accelerating field strength. However, dispersion alters the temporal profile of the applied pulse, resulting in a distorted field at the inner radius. Using the transfer function, it is possible to determine the shape of the pulse required to achieve a suitable accelerating field for a given waveguide design.

Passive field enhancement occurred in all waveguides and across all frequencies studied in this work. As such, radial parallel plate waveguides could help to reduce the high voltages required from upstream switching networks. The analytic model can be used to select waveguide parameters that provide a suitable enhancement of the upstream voltage pulse to achieve the high field strengths required for a compact accelerator. However, pulse dispersion must be accounted for. If upstream pulse shaping can be achieved to account for electromagnetic dispersion in the waveguide, pulse injection into radial parallel plate waveguides could be a suitable mechanism for field generation in a DWA.