Particle wave interaction using cavity modal expansion with an application on simulation of virtual cathode oscillator

Summary form only given. Simulation of high power microwave sources with high fidelity is very challenging. Usually it is either implemented using some averaging technique, or using particle in cell technique (PIC) which can simulate the interaction in general for any device but with a high computational cost. In this study, a new technique to simulate the interaction between the electromagnetic fields and charged particles in such devices is presented. The technique is based on considering the region of wave-particle interaction as a closed fictitious cavity region and expanding the electromagnetic fields inside it in terms of the solenoidal and irrotational modes^1-3, which form a complete set for the fields in that region. The electromagnetic radiation is leaked from the cavity through waveguide port mounted on one of the cavity walls. Those expansions are plugged in Maxwell´s equations, resulting in a number of first-order time derivatives of those mode coefficients, describing their time-evolution. These equations together with the particle equations of motion are integrated numerically, to obtain the time behavior of the electric and magnetic fields both inside the fictitious cavity and leaked out radiation through the waveguide port. Similar expansion technique has been previously used to solve cold electromagnetic scattering inside waveguides⁴ and even in free space5. In this study the technique is employed to solve the interaction of the charged particles with the different modes that expands the fields inside the interaction fictitious cavity giving the evolution with time of the mode coefficients interacting with particles. Hence, the technique is named particle in mode (PIM).