Evolution of the Weibel instability in relativistically hot electron–positron plasmas

Abstract

Analytical and numerical studies of the evolution of the Weibel instability in relativistically hot electron–positron plasmas are presented. Appropriate perturbations on the electromagnetic fields and the particle orbits, corresponding to a single unstable mode, are determined analytically and used as initial conditions in the numerical simulations to excite a single unstable mode. A simple estimate of the saturation amplitude is also obtained analytically. Numerical simulations are carried out when a single unstable mode is favorably excited. Comparisons of the simulation results with the analytical ones show very good agreement. Also observed in the simulations are mode competition, mode suppression, and the difference in the long-term evolution between the magnetized and unmagnetized plasmas. For relativistic unmagnetized plasmas, energy-like global constraints, which are conservation laws in addition to the conservation of energy and momentum, are derived. Numerical simulations of the multimode evolution are described. Simulation results show growth in electromagnetic energy in the early stage, a narrowing in the bandwidth and a shift in the peak of the spectrum to longer wavelength in the subsequent evolution, and a decrease in the temperature anisotropy. In a simulation for an unmagnetized plasma, it is observed that the system reaches a steady state halfway through the simulation. In contrast, the peak of the spectrum continues to shift to lower wave number k, and the temperature anisotropy continues to decrease during the entire simulation for a magnetized plasma.

Effects of filamentation instability on the divergence of relativistic electrons driven by ultraintense laser pulses

“…It is seen that the field becomes saturated nonlinearly with a magnitude of ∼ 1.5 × 10 4 T after t = 120fs. Such nonlinear saturation appears as the gyroradius of REs becomes of the order of the modulation wavelength, i.e., r L ∼ λ F , namely magnetic trapping 16,17 , leading to a saturation magnetic field amplitude…”

“…Fura) Electronic mail: xhyang@nudt.edu.cn b) Electronic mail: yanyunma@126.com thermore, the full divergence of REs including a regular radial beam deviation and a random angular dispersion is reported recently 15 , which are determined by the transverse component of the laser ponderomotive force and collisionless Weibel instability induced micro-magnetic fields, respectively. The Weible/filamentation instability induced magnetic field will be saturated after a rapid linear growth due to magnetic trapping [16][17][18] . In addition, magnetic field of 10 4 T magnitude generated by the reflected laser in preplasma can also deflect the laserdriven REs 19 .…”

Are Gamma‐Ray Burst Shocks Mediated by the Weibel Instability?

“…As a result of the instability, current filaments are formed along the direction of the proton motion. The magnetic field forms a sort of cocoon around these filaments and eventually traps protons within the filaments; then the instability stops ( Yang et al 1994;Wiersma & Achterberg 2004). The quiver motion of a proton within the current filament can be described by the linearized equation…”

Multidimensional electron beam-plasma instabilities in the relativistic regime

“…The cold distribution is the simplest possible choice, able to provide zero-order analytical estimates, whereas waterbag distributions are commonly employed as a first step to explore kinetic effects. 52,61,109,105,125,126 Owing to its smooth shape, the relativistic Maxwell-Jüttner distribution appears as a natural choice for a more realistic treatment of these effects, which, in addition, lends itself to tractable parametric numerical computations ͑see Sec. III E͒.…”