Map-Based Multipactor Theory for Cross-Field Devices

A novel theoretical model for multipactor discharge based on principles from nonlinear dynamics and chaos theory has been introduced and recently extended to two-surface multipactor in a parallel-plate geometry. A major advantage of this approach is that it is universal in that different systems can be studied by simply changing the underlying equations. In this paper, this is demonstrated for cross-field devices, where a dc magnetic field is transverse to the radio frequency (RF) electric field. As in the initial study, maps that relate the RF emission phase to the RF arrival phase are developed with no a priori assumptions on the electron trajectories (neglecting space-charge effects). By systematically applying the maps and scanning system parameters, bifurcation diagrams are constructed that summarize all possible multipactor modes. These scans recover conventional resonant multipactor in addition to high periodicity and nonresonant forms. By incorporating the secondary emission properties of the surface material and additionally scanning a realistic spread in the secondary emission energies and angles, the multipactor growth (or decay) rate is computed over a wide range of parameters. As in the initial study, it is found that the attractor form manifests in the exponential growth rate. These theoretical predictions are validated with particle-in-cell simulations.