Exact analytical calculation and numerical modelling by finite-difference time-domain method of the transient transmission of electromagnetic waves through cold plasmas

Research paper by Ivan V. Pavlenko, Igor O. Girka, Oleksandr V. Trush, Daria O. Melnyk

Indexed on: 11 Jun '20Published on: 01 Jun '20Published in: Journal of Plasma Physics


The transient transmission of an electromagnetic wave through cold, unmagnetized and collisionless plasmas is described both analytically and numerically for its normal incidence from vacuum upon a plasma half-space. Exact formulas for the electromagnetic field are written in integral forms, which are convenient for approximate analysis and comparison with the results of direct numerical simulations. The time when the plasma particle oscillations become self-consistent with the electromagnetic field can be calculated from the simplified formulas for an arbitrary distance from the plasma–vacuum interface. Special attention is paid to the formation of the electrostatic oscillation in the case when the frequency of the incident wave is equal to the plasma frequency. The amplitudes of the vanishing magnetic field and the forming electrostatic oscillation are calculated as functions of time and the distance from the plasma–vacuum interface. The formation of the electrostatic oscillation is a slow process because the electromagnetic power penetrating into the plasma tends to zero with time. The transmitted plasma electromagnetic field is also simulated by the a finite-difference time-domain (FDTD) code. The difficulties of the numerical simulation of the quasi-electrostatic field are discussed. The analytical results can be used for the validation of the FDTD codes for plasma waves.