Adiabatic theory of nonlinear electron-cyclotron resonance heating

Plasma heating at the electron-cyclotron frequency by an ordinary wave propagating at right-angles to a unidirectional magnetic field is considered. The injected microwave power is assumed to be sufficiently large that the relativistic change in electron gyrofrequency during one flight through the wave beam is much greater than inverse time of flight. The electron motion in the wave field is described using the Hamiltonian formalism in the adiabatic approximation. It is shown that energy coupling from the wave to electrons is due to a bifurcation of the electron trajectory, which results in a jump in the adiabatic invariant. The probability of a bifurcational transition from one trajectory to another is calculated analytically and used for the estimation of the beam power absorbed in the plasma.