Particle-in-cell simulation study of the interaction between a relativistically moving leptonic micro-cloud and ambient electrons

Abstract

Context. The jets of compact accreting objects are composed of electrons and a mixture of positrons and ions. These outflows impinge on the interstellar or intergalactic medium and both plasmas interact via collisionless processes. Filamentation (beam-Weibel) instabilities give rise to the growth of strong electromagnetic fields. These fields thermalize the interpenetrating plasmas. Aims. Hitherto, the effects imposed by a spatial non-uniformity on filamentation instabilities have remained unexplored. We examine the interaction between spatially uniform background electrons and a minuscule cloud of electrons and positrons. The cloud size is comparable to that created in recent laboratory experiments and such clouds may exist close to internal and external shocks of leptonic jets. The purpose of our study is to determine the prevalent instabilities, their ability to generate electromagnetic fields and the mechanism, by which the lepton micro-cloud transfers energy to the background plasma. Methods. A square micro-cloud of equally dense electrons and positrons impinges in our particle-in-cell (PIC) simulation on a spatially uniform plasma at rest. The latter consists of electrons with a temperature of 1 keV and immobile ions. The initially chargeand current neutral micro-cloud has a temperature of 100 keV and a side length of 2.5 plasma skin depths of the micro-cloud. The side length is given in the reference frame of the background plasma. The mean speed of the micro-cloud corresponds to a relativistic factor of 15, which is relevant for laboratory experiments and for relativistic astrophysical outflows. The spatial distributions of the leptons and of the electromagnetic fields are examined at several times. Results. A filamentation instability develops between the magnetic field carried by the micro-cloud and the background electrons. The electromagnetic fields, which grow from noise levels, redistribute the electrons and positrons within the cloud, which boosts the peak magnetic field amplitude. The current density and the moduli of the electromagnetic fields grow aperiodically in time and steadily along the direction that is anti-parallel to the cloud's velocity vector. The micro-cloud remains conjoined during the simulation. The instability induces an electrostatic wakefield in the background plasma. Conclusions. Relativistic clouds of leptons can generate and amplify magnetic fields even if they have a microscopic size, which implies that the underlying processes can be studied in the laboratory. The interaction of the localized magnetic field and high-energy leptons will give rise to synchrotron jitter radiation. The wakefield in the background plasma dissipates the kinetic energy of the lepton cloud. Even the fastest lepton micro-clouds can be slowed down by this collisionless mechanism. Moderately fast charge-and current neutralized lepton micro-clouds will deposit their energy close to relativistic shocks and hence they do not constitute an energy loss mechanism for the shock.

General features of experiments on the dynamics of laser-driven electron–positron beams

“…Several theoretical works reported in the literature (see, as possible examples, Ref. [14,19,20,21,22]) have shown how the propagation of an EPB in a background electron-ion plasma might trigger the onset of a series of instabilities, the most important ones namely being the oblique, the two-stream, and the filamentation (sometimes loosely referred to as Weibel) instabilities. The competition between these instabilities is ruled by a series of beam and background plasma parameters, with the dominant one arguably being the ratio between the beam density n b and background plasma density n p : α = n b /n p .…”

“…The competition between these instabilities is ruled by a series of beam and background plasma parameters, with the dominant one arguably being the ratio between the beam density n b and background plasma density n p : α = n b /n p . As a rule of thumb, oblique instabilities dominate for α 1 whilst the filamentation instability dominates for α ≥ 1 [14,19,20,21,22]. Two-stream instabilities are instead dominant for non-relativistic beams [20] and will not be considered here.…”

One-dimensional thermal pressure-driven expansion of a pair cloud into an electron-proton plasma

“…[2] ionized a background gas, which was contained in the experimental vessel prior to the laser shot ensuring the interaction with a pre-existing ambient plasma. The number of electronpositron pairs in this cloud was large enough to let the pairs behave as a plasma; a filamentation instability grew between the cloud and the ambient plasma [7,8]. The limited size of the cloud implied that the electromagnetic field it carried could interact only during a short time with the ambient plasma, which ruled out any significant acceleration of the ions in the ambient plasma.…”

Experimental Observation of a Current-Driven Instability in a Neutral Electron-Positron Beam

“…Weibel-mediated shocks in the jet could generate fields of sufficient strength, but are expected to decay rapidly, on timescales comparable to the inverse plasma frequency [13]. On the other hand, analytical [10] and numerical [21][22][23][24] studies give significant evidence that magnetic fields of sufficient strength and persistence might be generated by strong current filamentation of the EPB.To date, there is no direct evidence of these phenomena, either in the laboratory or in astrophysical observations. This lack of experimental data is ultimately due to the difficulty of generating neutral EPBs in the laboratory despite considerable dedicated efforts worldwide [25][26][27].…”

“…Weibel-mediated shocks in the jet could generate fields of sufficient strength, but are expected to decay rapidly, on timescales comparable to the inverse plasma frequency [13]. On the other hand, analytical [10] and numerical [21][22][23][24] studies give significant evidence that magnetic fields of sufficient strength and persistence might be generated by strong current filamentation of the EPB.…”