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

Abstract

We study with a two-dimensional particle-in-cell simulation the stability of a discontinuity or piston, which separates an electron-positron cloud from a cooler electron-proton plasma. Such a piston might be present in the relativistic jets of accreting black holes separating the jet material from the surrounding ambient plasma and when pair clouds form during an x-ray flare and expand into the plasma of the accretion disk corona. We inject a pair plasma at a simulation boundary with a mildly relativistic temperature and mean speed. It flows across a spatially uniform electron-proton plasma, which is permeated by a background magnetic field. The magnetic field is aligned with one simulation direction and oriented orthogonally to the mean velocity vector of the pair cloud. The expanding pair cloud expels the magnetic field and piles it up at its front. It is amplified to a value large enough to trap ambient electrons. The current of the trapped electrons, which is carried with the expanding cloud front, drives an electric field that accelerates protons. A solitary wave grows and changes into a piston after it saturated. Our simulations show that this piston undergoes a collisionless instability similar to a Rayleigh-Taylor instability. The undular mode grows and we observe fingers in the proton density distribution. The effect of the instability is to deform the piston but it cannot destroy it.

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

“…In what follows we refer to this interface as the electromagnetic pulse (EMP). It separates positrons from protons and resembles the one observed previously 20 at early simulation times.…”

“…Hence, they tend to be more unstable and disruptive than the undular mode 25 studied in Ref. 20. We do not observe these interchange modes because the EMP is destroyed before the magnetic Rayleigh-Taylor instability can set in.…”

“…1 have not been explored to the same extent. Such a discontinuity has been observed in two-dimensional PIC simulations of a pair plasma that propagated through a magnetized electron-proton plasma 19,20 and studied in one spatial dimension 21 assuming that it is planar. In the two-dimensional simulation, 20 the discontinuity became unstable to a magnetic Rayleigh-Taylor-like instability.…”

“…Such a discontinuity has been observed in two-dimensional PIC simulations of a pair plasma that propagated through a magnetized electron-proton plasma 19,20 and studied in one spatial dimension 21 assuming that it is planar. In the two-dimensional simulation, 20 the discontinuity became unstable to a magnetic Rayleigh-Taylor-like instability. [22][23][24][25][26] The wave vector of the perturbation was parallel to the magnetic field and the instability increased magnetic tension, which eventually quenched the instability.…”

“…Its magnetic pressure matches the electron thermal pressure. We use the same plasma conditions as in a previous simulation 20 apart from a lower mean speed of the pair cloud and a magnetic field direction, which is now normal to the simulation plane. We obtain the following results.…”