Motions of ultrarelativistic particles accelerated in an oblique plasma wave

The motion of ultrarelativistic particles in an oblique plasma wave is theoretically studied. Making use of the relation $vdγ/dt≫γdv/dt,$ where γ is the Lorentz factor, the zeroth-order velocity and energy increase rate are obtained. This solution is applicable to any particle species. The particle velocity is nearly parallel to the external magnetic field when $vsh∼c cos θ,$ where $vsh$ is the wave propagation speed and θ is the angle between the wave normal and the external magnetic field. The perturbed motions of ions and of positrons are then separately discussed. Their perturbations are both nearly perpendicular to the zeroth-order velocity. The ion perturbation is one dimensional with the frequency $ω∼Ωi0γ−1/2,$ while that of the positrons is elliptic with $ω∼Ωp0γ−1,$ where $Ωi0$ and $Ωp0$ are the nonrelativistic gyrofrequencies of ions and positrons, respectively.