Stabilisation of BGK modes by relativistic effects

Abstract

Context. We examine plasma thermalisation processes in the foreshock region of astrophysical shocks within a fully kinetic and self-consistent treatment. We concentrate on proton beam driven electrostatic processes, which are thought to play a key role in the beam relaxation and the particle acceleration. Our results have implications for the effectiveness of electron surfing acceleration and the creation of the required energetic seed population for first order Fermi acceleration at the shock front. Aims. We investigate the acceleration of electrons via their interaction with electrostatic waves, driven by the relativistic Buneman instability, in a system dominated by counter-propagating proton beams. Methods. We adopt a kinetic Vlasov-Poisson description of the plasma on a fixed Eulerian grid and observe the growth and saturation of electrostatic waves for a range of proton beam velocities, from 0.15c to 0.9c. Results. We can report a reduced stability of the electrostatic wave (ESW) with increasing non-relativistic beam velocities and an improved wave stability for increasing relativistic beam velocities, both in accordance with previous findings. At the highest beam speeds, we find the system to be stable again for a period of ≈160 plasma periods. Furthermore, the high phase space resolution of the Eulerian Vlasov approach reveals processes that could not be seen previously with PIC simulations. We observe a, to our knowledge, previously unreported secondary electron acceleration mechanism at low beam speeds. We believe that it is the result of parametric couplings to produce high phase velocity ESW's which then trap electrons, accelerating them to higher energies. This allows electrons in our simulation study to achieve the injection energy required for Fermi acceleration, for beam speeds as low as 0.15c in unmagnetised plasma.

VALIS: A split-conservative scheme for the relativistic 2D Vlasov–Maxwell system

“…The approach taken in the development of VALIS is to build on an existing [21], and proven [37,4,38,39,11] 1D1P algorithm and write the code in a parallelised domain decomposed form in order that it can scale onto current, and future, massively parallel machines. The update of the particle distributions is based on a split-Eulerian scheme.…”

Particle-in-cell simulation of a mildly relativistic collision of an electron-ion plasma carrying a quasi-parallel magnetic field

“…Such an acceleration is needed for their injection (Cargill & Papadopoulos 1988;Kirk & Dendy 2001;Kuramitsu & Krasnoselskikh 2005a,b) into the diffusive shock acceleration process (See Drury (1983)) so that they can cross the shock transition layer repeatedly. Electrostatic instabilities dominate for nonrelativistic flows in unmagnetized plasmas (Bret et al 2008;Bret 2009) and they can neither accelerate the electrons to highly relativistic speeds (Sircombe et al 2006) nor amplify the magnetic fields.…”

Numerical Simulation of the Bump-on-Tail Instability

“…(29b), the acceleration of the particles in the tail is higher with respect to the first case in Fig.(11a). The low frequencies associated with the dominant longer wavelengths result in higher phase velocities of the different modes, which are accelerating trapped particles to higher velocities in the tail of the distribution function, with kinetic energies above the initial energy of the beam (see the recent work in Sircombe et al, 2006Sircombe et al, , 2008. The trapped accelerated population is adjusting in return in order to provide the distribution function with a zero slope at the phase velocities of the waves, allowing the different modes to oscillate at a constant amplitude (modulated by the oscillation of the trapped particles).…”