From Fermi acceleration to collisionless discharge heating

The heating of electrons by time-varying fields is fundamental to the operation of radio frequency (RF) and microwave discharges. Ohmic heating, in which the phase of the electron oscillation motion in the field is randomized locally by interparticle collisions, can dominate at high pressures. Phase randomization can also occur due to electron thermal motion in spatially inhomogeneous RF fields, even in the absence of collisions, leading to collisionless or stochastic heating, which can dominate at low pressures. Generally, electrons are heated collisionlessly by repeated interaction with fields that are localized within a sheath, skin depth layer, or resonance layer inside the discharge. This suggests the simple heating model of a ball bouncing elastically back and forth between a fixed and an oscillating wall, Such a model was proposed originally by Fermi to explain the origin of cosmic rays. In this review, Fermi acceleration is used as a paradigm to describe collisionless heating and phase randomization in capacitive, inductive, and electron cyclotron resonance (ECR) discharges. Mapping models for Fermi acceleration are introduced, and the Fokker-Planck description of the heating and the effects of phase correlations are described, The collisionless heating rates are determined in capacitive and inductive discharges and compared with self-consistent (kinetic) calculations where available. Experimental measurements and computer simulations are reviewed and compared to theoretical calculations. Recent measurements and calculations of nonlocal heating effects, such as negative electron power absorption, are described. Incomplete phase randomization and adiabatic barriers are shown to modify the heating in low pressure ECR discharges.