Improved algorithm for a two-dimensional Darwin particle-in-cell code

TL;DR

This paper introduces an improved two-dimensional particle-in-cell code for simulating low-frequency electromagnetic processes in plasmas, utilizing a novel, faster algorithm based on the Darwin method that separates electric fields into solenoidal and irrotational components.

Contribution

The paper presents a new algorithm for calculating the solenoidal electric field in a Darwin particle-in-cell code, enhancing speed and reliability over previous methods.

Findings

The new algorithm is faster than previous formulations.

The code effectively simulates inductively coupled plasmas.

The iterative method improves solution reliability.

Abstract

A two-dimensional particle-in-cell code for simulation of low-frequency electromagnetic processes in laboratory plasmas has been developed. The code uses the Darwin method omitting the electromagnetic wave propagation. The Darwin method separates the electric field into solenoidal and irrotational parts. The irrotational electric field is the electrostatic field calculated with the direct implicit algorithm. The solenoidal electric field is calculated with a new algorithm based on the equation for the electric field vorticity. The new algorithm is faster and more reliable than the Streamlined Darwin Field Formulation introduced decades ago. The system of linear equations in the new algorithm is solved using a standard iterative method. The code is applied to simulate an inductively coupled plasma with the driving current flowing around the plasma region.