Condition for parametric generation of high frequency field in crossed and time-depend electric and magnetic fields

Many works were devoted to the research of behavior of charged particles in crossed electric and magnetic fields, for example [1], but many topics are still remain untouched. Today we know generators built on devices with crossed fields, but generation in them occurs in the presence of a constant electric field. However, in [1] it was suggested that the generation is possible in the absence of a constant electric field. In this paper, the authors show that in the case of time-depend magnetic induction at parametric resonance (the equal frequencies of existing fields: electric field and magnetic induction) generation in crossed fields is possible in the absence of a constant electric field. The analysis was performed for a planar resonator system.