Adiabatic theory of current generation by non-linear waves in a Vlasov plasma

The one-dimensional Vlasov distribution function in terms of the adiabatic invariants of the Vlasov equation for a single, non-linear, large-amplitude travelling wave excited by an external source is derived. The result takes into account the adiabatic turn-on of the pump and is valid to all orders in the electric field amplitude everywhere in phase-space, except for a narrow region near the separatrix. All electrons, including the trapped ones, are adiabatic and the processes are reversible. The non-linearity is found to lead to the generation of a steady-state current whose properties are examined. The theory is applied to study the steady-state currents that could be driven by the lower hybrid wave in present-day tokamak experiments. The trapped electrons play a very significant role in determining the nature of this current. (author)