The effect of an electrostatic field on particle acceleration at cyclotron resonance

The effect of an electrostatic field parallel to a static magnetic field on the cyclotron resonance acceleration of electrons is studied. Exact relativistic calculations show that for electrostatic field strengths below a certain limit, which depends on the field strength of the e.m. wave and the index of refraction, a steady average energy gain occurs. At this limit the energy of the particle increases steadily without any oscillation, while above the limit a stepwise energy gain occurs. Sufficiently far above, an analytical nonrelativistic approximation yields a simple expression for the energy gain of electrons with an initially isotropic transverse velocity distributio