Relativistic electron motion in the presence of cyclotron resonant electromagnetic waves

The relativistic collisionless motion of magnetically trapped electrons under the influence of rf wave with frequency near an integral multiple of their ambient synchrotron frequency is studied analytically. A Hamiltonian formalism is used to determine the phenomena of losing or maintaining local resonance and the accumulation or dispersion of the electrons in the magnetic well as they heat. Sustenance of resonance is shown to be markedly dependent on the index of refraction of the wave; it is also shown that the inherently relativistic detrapping effect can be important even for low energies and can be enhanced by low energy collisions