Particle acceleration by counter-propagating circularly polarized Alfv\'en waves

Counterpropagating Alfv\'en waves are ubiquitously observed in many astrophysical environments, such as a star surface and a planetary foreshock. We discuss an efficient particle acceleration mechanism in two counterpropagating circularly polarized Alfv\'en waves. Phase transitions of particle behavior occur when wave amplitudes exceed two critical values. Above the critical amplitudes, the numerical simulation shows that any particles irreversibly gain relativistic energy within a short time regardless of their initial position and energy once the coherent waveform is formed. The accelerated particles have spatial coherence. Higher wave phase velocity requires smaller critical amplitudes, while the maximum attainable energy increases as the wavenumber and the frequency decrease. The results may be applicable in some astrophysical phenomena, as well as a future laboratory experiment using high-power lasers.