Fermi acceleration revisited-from cosmic rays to discharge heating

Summary form only given, as follows. The motion of a ball bouncing between a fixed and an oscillating wall was originally proposed by Fermi in 1949 as a model for cosmic ray acceleration. Expectations that the ball could be heated to very high energies gave way to the realization that while the motion is chaotic at low energies, the phase space has an intricate fractal structure and there is an adiabatic limit to the heating. Adding a small dissipation changes the steady state chaos to a transient phenomenon, but a larger dissipation restores steady state chaos on a new fractal structure-a strange attractor. The application of these ideas to the "collisionless" or "stochastic" heating of charged particles in plasma discharges by time-periodic fields has been very fruitful. However, the purely dynamical phase randomization is here replaced by a (interparticle) collisional randomization at all but the lowest gas pressures. In both cases, a phase-averaged Fokker-Planck description of the motion can be used to determine the heating rate. Especially at low pressures, collisionless heating has been found to be important in RF-driven capacitive discharges, in microwave-driven electron cyclotron resonance discharges, and, more recently, in RF-driven inductive discharges. The latter application harks back to the discovery by Pippard, also in 1949, of the anomalous high frequency skin resistance in metals at low temperatures.