First Experiments on 3D Plasma Calculations Using Positive Maxwellian Operator

¹ Institute of Plasma Physics, National Science Center “Kharkiv Institute of Physics and Technology”, 61108, Kharkiv, Ukraine
² Uppsala University, S-75108 Uppsala, Sweden

^* Corresponding author: volodymyr.moiseyenko@angstrom.uu.se

Published online: 7 January 2026

Abstract

A new form of time-harmonic Maxwell’s equations [1] based on the standard formulation is used for the numerical modelling of RF fields in non-uniform plasmas without an external magnetic field. This formulation expresses the equations in terms of magnetic field strength, electric displacement, the vector and scalar potential. It offers several advantages. First, the differential operators act directly on these quantities with positive definiteness. Second, curl operators are absent in the leading-order terms of the equations. The Laplacian appears as the leading-order operator in the equations for potentials and magnetic field, while the gradient of a divergence is the leading-order operator for the electric displacement. Third, the absence of spatially varying coefficients in the leading-order differential operators ensures diagonal dominance of the discretized matrix. Following the approach of [1], the computational domain is chosen as a rectangular parallelepiped. A lowest-order 3D finite-difference method is applied for discretization. The antenna model is represented by a divergence-free electric current directed along the y axis. The plasma is treated as three-dimensional, non-uniform, and unmagnetized.