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

Abstract

The electrostatic activity in the post-saturation regime of the velocity anisotropy driven Weibel instability is investigated by means of 1D 3V particle in cell simulations. Two different initial simulation configurations have been chosen to characterize the electrostatic activity in the post-saturation stage. A secondary two stream instability arises in both cases. However, significant differences occur in the thickness of the electron streams, in their initial locations, and in their effects on the bulk electron phase space distribution. An Hamiltonian description of particle motion in a 1D setting explains these differences in terms of the effective potential experienced by particles as a function of their initial perpendicular velocity. The different roles of the longitudinal electric field and the Lorentz force in the formation of electron streams are discussed.

On the multistream approach of relativistic Weibel instability. III. Comparison with full-kinetic Vlasov simulations

“…Such an instability is usually referred as the electrostatic two-stream instability as in Ref. 5, which begins with a symmetry-breaking instability of pair-wise merging of holes, …”

Electron temperature anisotropy instabilities represented by superposition of streams

“…by the self-generated magnetic field, leads to the formation of local bumps and thus to the set up of a secondary bump on tail instability responsible for the growth of resonant electrostatic modes (ESs) on scales now smaller than the instability length scale. 4 More recently, using a Hamiltonian description of particle motion and 1D3V PIC simulation, Innocenti et al 7 in a similar regime have identified the role of such electrostatic activity as a result of "a two-stream" like instability, leading to the formation of phase space electron holes. These 1D3V PIC simulations show that the Hamiltonian description of particle motion in the 1D limit is a valuable tool to understand the plasma dynamics as described in terms of particle bunches, each bunch having the same perpendicular canonical momentum.…”

Introduction of temporal sub-stepping in the Multi-Level Multi-Domain semi-implicit Particle-In-Cell code Parsek2D-MLMD

“…In Innocenti et al [23], the basics of the method are discussed (Sections [3][4][5]. It is proved that the physics of the simulation is preserved in the MLMD system: the growth rates of instabilities, such as the two stream [24] and the Weibel instability [25,26], are the ones expected from theory, electron structures in phase space develop correctly and the coarse grid is able to effectively drive the refined grid evolution (Section 6). In Beck et al [27], Parsek2D-MLMD, a pure MPI [28], C++ [29], Object Oriented [30] parallel code is presented.…”