Hysteresis and the E-to-H transition in radiofrequency inductive discharges

Typical inductive discharges, such as are used for plasma processing, exhibit two modes of operation: the true inductive discharge known as the H mode, and a weak capacitive discharge known as the E mode. Experimentally, the transition between these modes as the coil current is increased is clear and is marked by a large increase in discharge power, plasma density and optical emission occurring as the H mode appears. According to simple theory, this transition and the reverse transition occur at a single well defined current. In practice, this is usually not the case. The E-to-H transition occurs at a larger coil current than the H-to-E transition, and a range of currents between these values supports either E or H mode. This effect is called hysteresis. In this paper we show that hysteresis can be understood to arise from nonlinear effects, most notably in the electron power balance equation. We survey various mechanisms that can produce hysteresis and attempt to provide quantitative estimates of their significance.