Two-dimensional particle simulation of the boundary between a hot pair plasma and magnetized electrons and protons: Out-of-plane magnetic field

Abstract

By means of a particle-in-cell (PIC) simulation, we study the interaction between a uniform magnetized ambient electron–proton plasma at rest and an unmagnetized pair plasma, which we inject at one simulation boundary with a mildly relativistic mean speed and temperature. The magnetic field points out of the simulation plane. The injected pair plasma expels the magnetic field and piles it up at its front. It traps ambient electrons and drags them across the protons. An electric field grows, which accelerates protons into the pair cloud's expansion direction. This electromagnetic pulse separates the pair cloud from the ambient plasma. Electrons and positrons, which drift in the pulse's nonuniform field, trigger an instability that disrupts the current sheet ahead of the pulse. The wave vector of the growing perturbation is orthogonal to the magnetic field direction and magnetic tension cannot stabilize it. The electromagnetic pulse becomes permeable for pair plasma, which forms new electromagnetic pulses ahead of the initial one. A transition layer develops with a thickness of a few proton skin depths, in which protons and positrons are accelerated by strong electromagnetic fields. Protons form dense clumps surrounded by a strong magnetic field. The thickness of the transition layer grows less rapidly than we would expect from the typical speeds of the pair plasma particles and the latter transfer momentum to protons; hence, the transition layer acts as a discontinuity, separating the pair plasma from the ambient plasma. Such a discontinuity is an important building block for astrophysical pair plasma jets.

Three-dimensional structure and stability of discontinuities between unmagnetized pair plasma and magnetized electron-proton plasma

“…This layer is thus capable of slowing down and compressing a pair plasma outflow, which is what we require from a discontinuity. Its width grew to a few proton skin depths at the end of the simulation, which was also observed in the 2D simulations [32,33].…”

“…This direction was not resolved in the 2D simulation in [32] and the ambient electrons remained cool. Resolving this direction heated the ambient electrons to a relativistic temperature and gave them an exponentially decreasing energy spectrum like the one we observe here [33].…”

“…In contrast, the initial EMP ahead of the injected pair cloud collapsed almost instantly and gave way to a transition layer filled with several EMPs. This transition layer developed as fast as the one ahead of the injected pair cloud in the 2D simulation that resolved the interchange mode [33]. We may attribute this collapse, which progressed faster than expected from theory [31] to the spatially non-uniform pressure of the injected pair cloud.…”

“…The undular mode deformed the boundary but it could not destroy it. When the background magnetic field pointed out of the simulation plane, the EMP collapsed on a time scale that was short compared to the growth time of the interchange mode [33]. The EMP was replaced by a broad transition layer that was nevertheless capable of confining the pair plasma and accelerating protons in the expansion direction of the pair plasma.…”