Collisionless tangential discontinuity between pair plasma and electron–proton plasma

Abstract

We study with a one-dimensional particle-in-cell (PIC) simulation the expansion of a pair cloud into a magnetized electron-proton plasma as well as the formation and subsequent propagation of a tangential discontinuity that separates both plasmas. Its propagation speed takes the value that balances the magnetic pressure of the discontinuity against the thermal pressure of the pair cloud and the ram pressure of the protons. Protons are accelerated by the discontinuity to a speed that exceeds the fast magnetosonic speed by the factor 10. A supercritical fast magnetosonic shock forms at the front of this beam. An increasing proton temperature downstream of the shock and ahead of the discontinuity leaves the latter intact. We create the discontinuity by injecting a pair cloud at a simulation boundary into a uniform electron-proton plasma, which is permeated by a perpendicular magnetic field. Collisionless tangential discontinuities in the relativistic pair jets of X-ray binaries (microquasars) are in permanent contact with the relativistic leptons of its inner cocoon and they become sources of radio synchrotron emissions.Filamentation instabilities between colliding unmagnetized or magnetized pair clouds 1-6 and between initially unmagnetized counterstreaming clouds of electrons and ions 7,8 have been studied widely with particle-in-cell (PIC) simulations. These simulations showed that a filamentation instability rapidly thermalizes the interpenetrating plasma clouds. Strong electromagnetic fields exist only in a layer that is close to the boundary that separates the inflowing upstream plasma from the thermalized one; this layer corresponds to a shock if the collision speed is high enough. See 9 for a review of such shocks.Mechanisms, that can enforce the separation of a fast plasma flow from an ambient plasma at rest rather than their thermalization, are interesting in the context of relativistic astrophysical jets 10,11 . Their plasma is dilute, which implies that binary (Coulomb) collisions between particles are rare on the time scales of interest. We call a plasma collisionless if its dynamics is determined by the electromagnetic fields generated by the collective of the particles rather than by binary collisions.Black hole X-ray binaries can emit such jets, in which case they are called microquasars 12 . Material from the companion star is attracted by the black hole and forced onto an accretion disk. Instabilities transform some of the inner disk's kinetic and magnetic energies into thermal energy heating up the disk's corona to MeV temperatures. Large clouds of electrons and positrons form (See 13 for a review and 14 for an observation of pair annihilation lines). If we assume that the temperature of this pair cloud is relativistic at its source then its initial expansion speed should be at least mildly relativistic. Open magnetic field lines that start at the inner disk allow the pair cloud to escape from the black hole's vicinity. It flows through an ambient plasma, which is initially that of the corona foll...

Collisionless Rayleigh–Taylor-like instability of the boundary between a hot pair plasma and an electron–proton plasma: The undular mode

“…It arises because the injected cloud particles experience a loss of energy when they are reflected by the moving piston in the interval x > 0. 14…”

“…We would have to extend the simulation time by an order of magnitude to observe such a shock. 14 Finally, we want to test if Rayleigh-Taylor-type instabilities can grow fast enough to explain the observed fingers in the proton density. We assume for simplicity that the piston could maintain a separation of positrons and protons at all times and that the spatial oscillation of the piston grew from a sinusoidal seed perturbation.…”

“…Pair plasma propagated along the magnetic field of the piston in that simulation. A PIC simulation, 14 which resolved only the direction perpendicular to the piston and did not give any particle species a net drift along its magnetic field, demonstrated that this drift was not important for stabilizing the piston. However, the process that caused the piston to oscillate in space 4 could not be determined due to the geometrical constraints.…”

“…Here, we present data from a simulation with the same initial conditions as in our previous one 14 but with a second dimension that is aligned with the background magnetic field. Kelvin-Helmholtz type instabilities cannot develop because the particles are injected in the direction orthogonal to the magnetic field of the piston.…”

Collisionless Rayleigh-Taylor-like instability of the boundary between a hot pair plasma and an electron-proton plasma: the undular mode

“…We would have to extend the simulation time by an order of magnitude to observe such a shock. 14 Finally, we want to test if Rayleigh-Taylor-type instabilities can grow fast enough to explain the observed fin- gers in the proton density. We assume for simplicity that the piston could maintain a separation of positrons and protons at all times and that the spatial oscillation of the piston grew from a sinusoidal seed perturbation.…”