Theory of electron cyclotron resonance heating. II. Long time and stochastic effects

For pt. I see abstr. A4666 of 1973. The theory of single particle electron cyclotron resonance heating in a magnetic mirror is treated analytically and numerically, from the viewpoint of (a) an impulsive heating approximation and (b) a stochastic approximation, using a Fokker-Planck equation. Using (a), numerical calculations of particle heating are performed for 105 half-bounce times tau b. Numerically and analytically from (a), for a given r.f. field strength, are obtained two limiting energies Ws and Wb, with Wb approximately=5Ws. For the transverse particle energy at resonance Wperpendicular to R Wb, invariant curves exist which form a barrier to further particle heating. For a parabolic mirror B(z)=B0 (1+z2/L2) with cyclotron resonance at z=+or-l, Wb=2.88eEL(1+l2/L2)12/( tau b/ tau s)23/, where e is the electronic charge, E the r.f. electric field, and tau s is the period for the cyclotron phase to slip 2 pi with respect to the r.f. field.