Reduced Plasma Frequency Calculation Based on Particle-in-Cell Simulations

We propose a scheme to calculate the reduced plasma frequency of a cylindrical-shaped electron beam flowing inside of a cylindrical tunnel, based on results obtained from particle-in-cell (PIC) simulations. In PIC simulations, we modulate the electron beam using two parallel, non-intercepting, closely spaced grids which are electrically connected together by a single-tone sinusoidal voltage source. The electron energy and the beam current distributions along the length of the tunnel are monitored after the system is operating at steady-state. We build a system matrix describing the beam’s dynamics, estimated by fitting a
$2\,\, {}\times {}2$
matrix that best agrees with the first-order differential equations that govern the physics-based system. Results are compared with the theoretical Branch and Mihran model, which is typically used to compute the plasma frequency reduction factor in such systems. Our method shows excellent agreement with the theoretical model, however, it is also general. Our method can be potentially utilized to determine the reduced plasma frequencies of electron beams propagating in longitudinally uniform beam tunnels (i.e., drift regions) of different transverse cross sections, such as the case of a cylindrical or elliptical electron beam propagating inside of a metallic beam tunnel of cylindrical, square, or elliptical cross section. It can be applied also to electron beams composed of multiple streams.