Some aspects of collisionless heating in inductive discharges

Considering a simple model of a spiral antenna inductive discharge in the collisionless heating regime, the basis of the equivalence of the stochastic and surface impedance methods is demonstrated. Formulae for the power per unit area, for each approach, are obtained in the regime of small normalized RF frequency, w, and shown to have the same functional dependence on w; the numerical coefficients agree to within a factor of 0.6. A study of the azimuthal electric field, E(theta), appropriate to the surface impedance method shows that although generally nonmonotonic, within the vicinity of the coil E(theta) falls exponentially. The decay length delta (c) very closely matches the skin depth of the stochastic method for a range of electron densities and RF frequencies. Thus the assumption that an exponential decay for E(theta) in the stochastic method is a very good approximation for the purpose of calculating the collisionless heating is confirmed.