An analytical model to evaluate the radiated power spectrum of a multipactor discharge in a parallel-plate region

This paper is aimed at studying the electromagnetic radiation pattern of a multipactor discharge occurring in a parallel-plate waveguide. The proposed method is based on the Fourier expansion of the multipactor current in terms of time-harmonic currents radiating in the parallel-plate region. Classical radiation theory combined with the frequency domain Green's function of the problem allows the calculation of both the electric and the magnetic radiated fields. A novel analytical formula for the total radiated power of each multipactor harmonic has been derived. This formula is suitable for predicting multipactor with the third-harmonic technique. The proposed formulation has been successfully tested with a particle-in-cell code.