Simulations of electromagnetic effects in high frequency capacitively coupled discharges using the Darwin approximation

TL;DR

This paper explores the use of the Darwin approximation for efficient simulation of electromagnetic effects in high frequency capacitively coupled discharges, demonstrating its validity and advantages over traditional methods.

Contribution

It introduces a simplified, fast electromagnetic simulation approach using the Darwin approximation applicable to fluid and kinetic plasma models.

Findings

Darwin approximation accurately models standing wave and skin effects.

The approach removes the Courant condition, enabling larger time steps.

The method is computationally efficient and easy to implement.

Abstract

The Darwin approximation is investigated for its possible use in simulation of electromagnetic effects in large size, high frequency capacitively coupled discharges. The approximation is utilized within the framework of two different fluid models which are applied to typical cases showing pronounced standing wave and skin effects. With the first model it is demonstrated that Darwin approximation is valid for treatment of such effects in the range of parameters under consideration. The second approach, a reduced nonlinear Darwin approximation-based model, shows that the electromagnetic phenomena persist in a more realistic setting. The Darwin approximation offers a simple and efficient way of carrying out electromagnetic simulations as it removes the Courant condition plaguing explicit electromagnetic algorithms and can be implemented as a straightforward modification of electrostatic algorithms. The algorithm described here avoids iterative schemes needed for the divergence cleaning and represents a fast and efficient solver, which can be used in fluid and kinetic models for self-consistent description of technical plasmas exhibiting certain electromagnetic activity.