Electron surfing acceleration by mildly relativistic beams: wave magnetic field effects

Electron surfing acceleration (ESA) is based on the trapping of electrons by a wave and the transport of the trapped electrons across a perpendicular magnetic field. ESA can accelerate electrons to relativistic speeds and it may thus produce hot electrons in plasmas supporting fast ion beams, like close to astrophysical shocks. One-dimensional (1D) particle-in-cell (PIC) simulations have demonstrated that trapped electron structures ( phase space holes) are stabilized by relativistic phase speeds of the waves, by which ESA can accelerate electrons to ultrarelativistic speeds. The 2( 1) 2) D electromagnetic and relativistic PIC simulations performed in the present paper model proton beam driven instabilities in the presence of a magnetic field perpendicular to the simulation plane. This configuration represents the partially electromagnetic mixed modes and the filamentation modes, in addition to the Buneman waves. The waves are found to become predominantly electromagnetic and nonplanar for beam speeds that would result in stable trapped electron structures. The relativistic boost of ESA reported previously is cancelled by this effect. For proton beam speeds of 0.6 and 0.8c, the electrons reach only million electron volt energies. The system with the slower beam is followed sufficiently long in time to reveal the development of a secondary filamentation instability. The instability forms a channel in the simulation domain that is void of any magnetic field. Proton beams may thereby cross perpendicular magnetic fields for distances beyond their gyroradius.