Integral equation for electrostatic waves radiated by a point source in a spatially homogeneous magnetized plasma

TL;DR

This paper derives an integral equation describing the electric field radiated by a point source in a magnetized plasma, simplifying the mathematical form to facilitate numerical solutions for plasma response analysis.

Contribution

It presents a new integral equation formulation with a simplified kernel for electrostatic wave radiation in magnetized plasmas, enabling easier numerical computation.

Findings

Kernel involves elementary functions only

Equation suitable for numerical solutions

Applicable to plasma impulse response studies

Abstract

Solutions of the linearized Vlasov-Poisson equations for the electric field radiated by a time varying point charge in a three-dimensional, unbounded, spatially homogeneous plasma with a uniform background magnetic field and a uniform (static) flow velocity are expressed in terms of an equivalent integral equation in the time domain. For plasmas characterized by Maxwell distribution functions with isotropic temperatures, the kernel has a relatively simple mathematical form consisting only of elementary functions, exponential and trigonometric functions (sines and cosines), and no infinite sums of Bessel functions. Consequently, the integral equation is amenable to numerical solutions and may be useful for the study of the impulse response of magnetized plasmas and, more generally, the response to arbitrary waveforms.