Cyclotron resonance in an inhomogeneous plasma†

The motion of a charged particle in a transverse wave of varying amplitude, wavelength and phase speed β_p, propagating along a uniform magnetic field, together with a longitudinal electric field, is investigated. The equations of motion, in Hamiltonian form, are reduced to a system with two degrees of freedom in which integrable cases appear naturally. It is shown that particles may be locked in resonance with the wave, and expressions are found for the energy and momentum of such particles in terms of β_p.