Multicarrier Multipactor Analysis Based on Branching Levy Walk Hypothesis

In this paper, we propose a stochastic approach for the analytical analysis of the multicarrier multipactor discharge occurring in high-power vacuum microwave devices, in which electric fields are not homogeneously distributed. We indicate that the statistical behavior of large amount of secondary electrons in the process of a multipactor discharge can be well described by the probabilistic random walk and Levy walk theory. Based on the derived probability density of the lateral diffusion of secondary electrons in homogeneous fields, the multicarrier multipaction in inhomogeneous fields can be analytically computed with significantly enhanced efficiency. As a demonstration, the accumulation of secondary electrons of a multicarrier multipaction in a rectangular waveguide supporting TEE) mode is given. The theoretical results comply well with the results achieved by the time-consuming particle simulation, the slope difference of which is less than 0.8%, while only costs one-order less computational time. To the best of our knowledge, this is the first time that the probability density of the lateral diffusion of secondary electrons during a multipaction is theoretically derived. This density depicts the physical picture of the statistical movement of secondary electrons during the process of a multicarrier multipactor, which can be widely used in the areas of high-power electronics and electromagnetism.