Nonlinear Development of Electromagnetic Instabilities in Anisotropic Plasmas

Abstract

Theory and simulation experiment are presented for a wide variety of transverse electromagnetic instabilities in plasmas with different sources and degrees of anisotropy. In each of the electron bi-Maxwellian, electron-pinch, and ion-pinch experiments, the bulk response of the system during the initial stages of instability is in good agreement with the predictions of quasilinear theory. Furthermore, the two independent energy constants which derive from the fully nonlinear Vlasov-Maxwell equations are found to remain constant to very good accuracy, even when the magnetic field energy reaches a substantial fraction of the total system energy. In each simulation experiment it is found that the magnetic energy saturates once the magnetic bounce frequency has increased to a value comparable to the linear growth rate prior to saturation, i.e., when ω¯B∼γ¯k. It is concluded that amplitude limitation for Weibel instabilities is a result of magnetic trapping for a broad range of system parameters. In many experiments a large remnant anisotropy in kinetic energy persists long after saturation.

Electron streams formation and secondary two stream instability onset in the post-saturation regime of the classical Weibel instability

“…In particular, it is possible to divide them into classes according to their initial perpendicular velocity (here, classes with Dv y0 =c ¼ 0:06 for both simulations) and to follow the evolution of the effective potential field for each class during the simulations. This approach not only allows one to recover the well-known results of Morse and Nielson 21 with regards to the magnetic trapping 23 but also to go beyond and understand the origin of the secondary two stream instability, which develops after the saturation of the Weibel instability.…”

“…Plasmas 18, 052104 (2011) consequence of the progressive isotropization of the electron temperatures. 23 Notice finally that, as also, for example, in Stockem, Dieckmann, and Schlickeiser 16 and in Palodhi, Califano, and Pegoraro, 17 the box dimensions are chosen to have a limited number of unstable modes for the sake of clarity of exposition. Control runs with larger simulation boxes have shown behaviors qualitatively similar to the ones here presented also in presence of a higher number of unstable modes.…”

“…In Sec. V, first, the results of Morse and Nielson 21 regarding the saturation of the instability through magnetic trapping 23 are extended, and then new insights are obtained as regards the origin of the streams. Finally, in Sec.…”

Weibel instabilities in dense quantum plasmas

“…The purely growing Weibel instability in a non-Maxwellian plasma is excited by the anisotropy of the electron distribution function. The linear and nonlinear aspects of the Weibel instability in classical electron-ion plasmas are fully understood [4].…”

“…The purely growing Weibel instability in a non-Maxwellian plasma is excited by the anisotropy of the electron distribution function. The linear and nonlinear aspects of the Weibel instability in classical electron-ion plasmas are fully understood [4].However, in dense plasmas, such as those in compact astrophysical objects (e.g. the interior of the white dwarfs, neutron stars/magnetars, supernovae), as well as in the next-generation intense laser-solid density plasma experiments [5], in nanowires and in micromechanical systems, one notices the importance of quantum electron tunneling effects [6] at nanoscales.…”