Particle acceleration by a wave in a strong magnetic field: Regular and stochastic motion

Abstract

A general theory for the acceleration of a charged particle by a coherent wave of arbitrary polarization, propagation angle, and phase velocity in the presence of a uniform and strong magnetic field is presented. It is shown that the Hamiltonian surfaces are topologically open for waves with parallel phase velocity, ω/k∥, equal to or larger than the speed of light. The trapping width is found to be a strong function of the index of refraction (N), and for N=1 the trapping width increases as a function of the harmonic number. Particular emphasis is put on waves with N∥ ≡ck∥/ ω=1, and it is demonstrated that the physics of such waves is the relativistic counterpart of the nonrelativistic particle acceleration by a perpendicularly propagating wave. It is found that even at small wave amplitudes particles can be accelerated coherently to very large energies (relativistic factor γ>8) in the presence of such waves. The autoresonance acceleration mechanism [Sov. Phys. JETP 16, 629 (1963); Phys. Rev. A 135, 381 (1964)] is shown to be a special case of particle acceleration by waves with N∥ =1. A detailed analysis of the dispersion properties of these waves in a cold plasma is given. Finally, a novel mechanism for coherently accelerating particles to unlimited energies is presented. This new mechanism requires waves with N∥ ≲1 and wave amplitudes large enough so that the zeroth-order particle motion is the trapping due to the wave (‘‘weak’’ magnetic field limit) rather than the Larmor gyration which was the case for the autoresonance mechanism. This new mechanism is somewhat similar to the surfatron mechanism [Phys. Rev. Lett. 51, 392 (1983)] but can operate even if the wave amplitude is smaller than the magnetic field as a result of the oblique propagation angle of the wave.