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A theory is developed to explain cascading bifurcations to chaos observed in a current-carrying ion sheath. The basic equation is derived to describe ion dynamics in an ion sheath which obeys the Child-Langmuir law for a large potential drop and is numerically solved to show the same bifurcation sequences as those in the experiments.

For initial plasma production, an induction electric field generated by applying voltage to a poloidal field (PF) coil system is used to produce a Townsend avalanche breakdown. When the avalanche margins are small, as for the International Thermonuclear Experimental Reactor (ITER) in which the induction electric field is about 0.3 V/m, the assistance of radio-frequency waves (RF) is provided to reduce the induction electric field required for reliable breakdown. However, the conditions of RF-assisted breakdown are not clear. Here, the effects of both RF and induction electric field on the RF-assisted breakdown are evaluated considering the electron loss. When traveling loss is the dominant loss, a simple model of an extended Townsend avalanche is proposed. In this model, the induction electric field required for RF-assisted breakdown can be decreased to half that required for induction breakdown.