Acceleration of nonthermal fast ions in an oblique magnetosonic shock wave is studied theoretically and numerically.
After the encounter with a shock wave, some of the fast ions begin to move with it. Because their speeds are higher than the shock speed v_sh, they can move back and forth between the shock and upstream regions owing to gyromotion. When they are in the shock region, they gain energy from the transverse electric field. Also, because of the magnetic structure, their momenta parallel to the magnetic field increase in these processes. After a few gyroperiods, these ions thus go away ahead of the shock wave, and the acceleration ceases.
However, fast ions can be incessantly accelerated because of the relativistic effect that velocity is limited by the speed of light while the momentum can grow indefinitely. This incessant acceleration occurs when v_sh ∼ c cos θ, where θ is the angle between the wave normal and the external magnetic field. Hybrid simulations show acceleration from γ ∼ 4 to γ ∼ 160, where γ is the Lorentz factor. (In this method, the field profiles of shock waves are obtained from particle simulations, and test particle trajectories are calculated by use of these fields.) Furthermore, the time variation of energy distribution function of the fast ions is investigated. The evolution of these ions in the momentum space is also discussed.