A phenomenological model for the description of rotating spokes in HiPIMS discharges

TL;DR

This paper presents a phenomenological model describing the rotating spokes in HiPIMS discharges, capturing their steady-state behavior and sensitivity to physical parameters through analytical solutions of coupled PDEs.

Contribution

It introduces a simplified, analytical phenomenological model for rotating spokes in HiPIMS discharges, linking plasma dynamics to neutral and electron densities.

Findings

Steady-state neutral and plasma densities are derived analytically.

The model explains the sustained rotation of spokes in HiPIMS.

Sensitivity analysis shows how physical parameters influence plasma behavior.

Abstract

In the ionization region above circular planar magnetrons well defined regions of high emissivity are observed, when the discharge is driven in the HiPIMS regime. Once their mode is stabilized, these structures rotate in the E x B direction with a constant rotation frequency in the hundreds of kHz range. A phenomenological model of the phenomenon is developed, in the form of a system of nonlinear coupled partial differential equations. The system is solved analytically in a frame co-moving with the structure, and its solution gives the neutral density and the plasma density once the electron density shape is imposed. From the balance of the mechanisms of ionization, electron loss and constant neutral refilling, a steady state configuration in the rotating frame is achieved for the electron and neutral densities. Therefore, the spoke experimentally observed can be sustained simply by the combination of this highly reduced number of phenomena. Finally, a study of the sensitivity of neutral and plasma densities to the physical parameters is also given.