Theory of electron cyclotron resonance heating. I. Short time and adiabatic effects

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Abstract
The theory of single particle electron cyclotron resonance heating in a magnetic mirror is treated analytically and numerically, using the techniques of (a) integration of the Lorentz force equation and (b) transformation to a Hamiltonian approximation, to study both short time scale and adiabatic effects. The force equation is analytically integrated in the vicinity of the resonance plane to obtain the energy dependence of the effective time spent in resonance per bounce te. For electrons passing through the resonant zone at constant parallel velocity vzR, te varies as vzR-12/. For electrons which turn in or near the resonant zone, te varies as vperpendicular to R, P=2/3, where vperpendicular to R is the transverse velocity at resonance. These results agree with the exact numerical integration of the force equation, for which P approximately=0.5-0.7.