Particle-in-cell simulation of a mildly relativistic collision of an electron-ion plasma carrying a quasi-parallel magnetic field*
Electron acceleration and magnetic field amplification at supernova shocks
Department of Science and Technology,
Linkoping University, 60174 Norrkoping, Sweden e-mail: Mark.E.Dieckmann@itn.liu.se
2 Dublin Institute for Advanced Studies, 31 Fitzwilliam Place, Dublin 2, Ireland
3 Center for Astroparticle Physics, Friedrich-Alexander-University Erlangen-Nuremberg, 91058 Erlangen, Germany
Accepted: 14 September 2009
Context. Plasma processes close to supernova remnant shocks result in the amplification of magnetic fields and in the acceleration of electrons, injecting them into the diffusive acceleration mechanism.
Aims. The acceleration of electrons and the magnetic field amplification by the collision of two plasma clouds, each consisting of electrons and ions, at a speed of 0.5c is investigated. A quasi-parallel guiding magnetic field, a cloud density ratio of 10 and a plasma temperature of 25 keV are considered.
Methods. A relativistic and electromagnetic particle-in-cell simulation models the plasma in two spatial dimensions employing an ion-to-electron mass ratio of 400.
Results. A quasi-planar shock forms at the front of the dense plasma cloud. It is mediated by a circularly left-hand polarized electromagnetic wave with an electric field component along the guiding magnetic field. Its propagation direction is close to that of the guiding field and orthogonal to the collision boundary. It has a frequency too low to be determined during the simulation time and a wavelength that equals several times the ion inertial length. These properties would be indicative of a dispersive Alfvén wave close to the ion cyclotron resonance frequency of the left-handed mode, known as the ion whistler, provided that the frequency is appropriate. However, it moves with the super-alfvénic plasma collision speed, suggesting that it is an Alfvén precursor or a nonlinear MHD wave such as a Short Large-Amplitude Magnetic Structure (SLAMS). The growth of the magnetic amplitude of this wave to values well in excess of those of the quasi-parallel guiding field and of the filamentation modes results in a quasi-perpendicular shock. We present evidence for the instability of this mode to a four wave interaction. The waves developing upstream of the dense cloud give rise to electron acceleration ahead of the collision boundary. Energy equipartition between the ions and the electrons is established at the shock and the electrons are accelerated to relativistic speeds.
Conclusions. The magnetic fields in the foreshock of supernova remnant shocks can be amplified substantially and electrons can be injected into the diffusive acceleration, if strongly magnetised plasma subshells are present in the foreshock, with velocities an order of magnitude faster than the main shell.
Key words: plasmas / acceleration of particles / magnetic fields / shock waves / methods: numerical / ISM: supernova remnants
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