Exact Relativistic Kinetic Theory of an Electron-Beam–Plasma System: Hierarchy of the Competing Modes in the System-Parameter Space

Abstract

The stability analysis of an electron-beam-plasma system is of critical relevance in many areas of physics. Surprisingly, decades of extensive investigation have not yet resulted in a realistic unified picture of the multidimensional unstable spectrum within a fully relativistic and kinetic framework. All attempts made so far in this direction were indeed restricted to simplistic distribution functions and/or did not aim at a complete mapping of the beam-plasma parameter space. The present Letter comprehensively tackles this problem by implementing an exact linear model. Three kinds of modes compete in the linear phase, which can be classified according to the direction of their wave number with respect to the beam. We determine their respective domain of preponderance in a three-dimensional parameter space and support our results with multidimensional particle-in-cell simulations.

Multidimensional electron beam-plasma instabilities in the relativistic regime

“…20 within the Maxwell-Jüttner model. 18 In Figs. 37͑a͒ and 37͑b͒ are plotted the beam and plasma profiles obtained around the end of the linear phase for n b / n p =1, ␥ b =3, T b = 1000 keV, and T p = 5 keV.…”

“…The reason is that the electrostatic two-stream instability does govern the spectrum under the nonrelativistic conditions characteristic of these early experiments. 18,24 Despite the multidimensional character of the spectrum, beam-aligned modes then grow much faster than the nonparallel ones and determine the onset of the beam evolution. For decades following Fried's and Weibel's seminal papers, nonparallel instabilities hardly received academic attention due to the relative scarcity of physical applications wherein they may have been relevant.…”

“…Studies related to these topics have spurred most of the theoretical advances in beam-plasma instabilities over the past 15 years, much effort being put into revisiting, and elaborating, the long-known result 8,9 that, within an extended parameter range, nonparallel modes may initially govern the system evolution. 18,28 Although this review focuses on FIS and GRB physics, it is worth mentioning that beam-plasma instabilities in the relativistic regime are also relevant for solar flares physics, 29 cosmic magnetic fields generation, 30 magnetic reconnection, 31,32 or even quantum chromodynamics. 33,34 …”

“…Simple fluid models, whether covariant 12 or not, 13,14 were subsequently worked out, before comprehensive kinetic treatments [15][16][17][18] managed to provide a unified vision of the entire unstable spectrum, further confirmed by particle-in-cell simulations. [19][20][21][22][23] Given the potentially broad unstable spectrum of beamplasma system, one may wonder why early results on gas discharge fluctuations were so readily attributed to a single class of instability, namely, the two-stream one.…”

“…The temperature-dependent analysis 18,110 brings in at least two additional parameters, namely, the beam and plasma temperatures. The introduction of both transverse and parallel thermal spreads would lead to a daunting sixdimensional parameter space.…”