Model for relaxation oscillations in a helicon discharge

Abstract

Relaxation oscillations observed in the large-volume, helicon plasma experiment WOMBAT (Waves on Magnetized Beams and Turbulence) [R. W. Boswell and R. K. Porteous, Appl. Phys. Lett. 50, 1130 (1987)] are modeled. These oscillations have a period of several milliseconds and have been identified as transitions between a low-density, inductive discharge and a high-density, helicon-wave discharge. In the model, it is assumed that the mode transitions are triggered by variations in the neutral density in the source region. The neutral density decreases due to ionization augmented by ion pumping and increases due to refilling of the source chamber from the much larger diffusion chamber. The system is modeled using two, coupled, nonlinear, ordinary differential equations that describe the neutral and plasma densities in the source chamber. Ionization by inductively-coupled fields and ionization due to electrons accelerated by helicon waves with phase velocities near the threshold electron velocity for ionization are considered. The model is found to reproduce experimentally measured variations of the plasma density and helicon wave phase velocity with rf power, neutral pressure and magnetic field. The negative impedance needed for the existence of a relaxation oscillation is provided by the helicon-wave coupling mechanism.