Emergence of MHD structures in a collisionless PIC simulation plasma

Abstract

The expansion of a dense plasma into a dilute plasma across an initially uniform perpendicular magnetic field is followed with a one-dimensional particle-in-cell (PIC) simulation over MHD time scales. The dense plasma expands in the form of a fast rarefaction wave. The accelerated dilute plasma becomes separated from the dense plasma by a tangential discontinuity at its back. A fast magnetosonic shock with the Mach number 1.5 forms at its front. Our simulation demonstrates how wave dispersion widens the shock transition layer into a train of nonlinear fast magnetosonic waves. A thermal pressure gradient in a magnetized plasma accelerates the dense plasma towards the dilute one and a rarefaction wave develops. The collision of the expanding plasma with the dilute plasma triggers shocks if the collision speed exceeds the phase velocity of the fastest ion wave. In the rest frame of the shock, the fast-moving upstream plasma is slowed down, compressed and heated as it crosses the shock and moves downstream. This net flux adds material to the downstream plasma, which lets the shock expand into the upstream direction.Shocks have been widely examined due to their key role in regulating the transfer of mass, momentum and energy in plasma. They are most easily described in a one-dimensional geometry. Shock tube experiments [1,2], which enforce such a geometry, examined shocks in partially magnetized and collisional plasma. Particle collisions equilibrate the plasma and macroscopic quantities like flow speed and temperature are uniquely defined. The time-evolution of these quantities is described well by the equations of single-fluid magnetohydrodynamics (MHD) if collisions are frequent enough to establish a thermal equilibrium between electrons and ions on the time scales of interest. Numerical shock tube experiments investigating the thermal expansion of plasma have also been performed in order to test single-fluid MHD codes, since the important MHD shocks emerge under such conditions [3,4].However, not all plasma shocks are collisional. The mean free path of the particles in the plasma, in which the Earth's bow shock [5] is immersed, is large compared to the thickness of its transition layer and it is sustained by electromagnetic fields. Collisionless plasmas support energetic structures that are not captured by a single-fluid MHD theory and that can play a vital role in the thermalization of plasma. Examples are magnetosonic solitons [6,7] and the beams of shock-reflected particles ahead of the bow shock [8], which enforce a non-stationarity of the shock [9-12]. Single-fluid MHD simulations are nevertheless used to solve problems in collisionless plasma based on the argument that they can describe the plasma dynamics on a large enough scale.Here we examine with the particle-in-cell (PIC) code EPOCH [13] the relaxation of a thermal pressure gradient in the presence of a perpendicular magnetic field. We thus perform a numerical shock tube experiment with collisionless plasma to test the hypothesis that the plasma evolut...

Expansion of a radially symmetric blast shell into a uniformly magnetized plasma

“…The subdivision of the plasma into a rarefaction wave, into a tangential discontinuity that separated the blast shell plasma from the shocked ambient plasma and a laminar forward shock observed in Ref. [9] closely followed the plasma distribution we would expect from a MHD model. The shock formed on time scales much shorter than an inverse ion gyro-frequency because it involved the high-frequency part of the fast magnetosonic mode.…”

“…Indeed it has been shown in the one-dimensional simulation in Ref. [9] that the shock, which propagates orthogonally to the magnetic field, becomes a fast magnetosonic one.…”

“…The shock speed in Ref. [9] equalled 1.5 times the fast magnetosonic speed. Shocks with such a low Mach number reflect only a small fraction of the inflowing upstream ions.…”

“…Reference [9] followed the plasma expansion over a longer time. The lower-hybrid shock changed into a fast magnetosonic shock on a time scale of the order of tens of inverse lower-hybrid frequencies.…”

Effects of radiative losses on the relativistic jets of high-mass microquasars

“…Some first steps towards the connection between kinetic and macroscopic scales have recently been made: Dieckmann et al (2019) show that, under even small magnetic guide fields, kinetic jets can develop a structure resembling the hydrodynamical structure of a jet over scales much larger than the kinetic scales. An electromagnetic piston-like structure is coherently formed, acting like the contact discontinuity between jet and ambient material in a hydrodynamical jet (see also Dieckmann et al 2017). We note that, in the same context, Dieckmann et al (2019) also show that a leptonic jet propagating into an ambient ion-electron plasma can accelerate positrons to speeds of several hundred of MeV.…”