A Study of Current Filaments Generated by Electromagnetic Weibel and Filamentation Instabilities

Abstract

In this dissertation, collisionless electromagnetic instabilities, known as Weibel instability (WI) and Filamentation instability (FI), have been investigated. The WI appears in anisotropic temperature plasma media, whereas the FI appears when the plasma counterstreams. The properties, particle acceleration and magnetic field generations associated with the WI and the FI, have been studied theoretically and by means of Particle-in-cells (PIC) simulations.

A full comparison of the WI and the FI from the linear to fully saturated stages are made by using a 2D PIC KEMPO code. Under the comparable initial conditions, the linear growth rates of the WI and the FI are almost the same as the theory predicts, but in the nonlinear phase, the maximum and nonlinearly saturated magnetic fields generated by the WI are always smaller than those generated by the FI. It is found that during the initial linear growth phase, the WI and the FI both have center-filled currents, but in the nonlinear phase, the WI and the FI develop different types of current structures such that the WI maintains a center-filled current structure, whereas the FI develops a hollow current structure. Significant particle acceleration around the drift velocity is observed for the FI, whereas it is almost absent in the WI, which indicates that the enhanced velocity of the electron by particle acceleration is related to the occurrence of hollow current structure in the FI.

In addition to distinguishing the differences between the WI and the FI, a theoretical model of the FI triggered by cold electron/positron beam (e+b/e-b) injection is developed for a non-relativistic plasma. In this case, the e+b/e-􀀀b counterstreams with electron/positron or electron/ion ambient plasmas. Due to the FI, current filaments are formed. The theory developed predicts that on the evolution of the FI, particles are trapped inside the currents, where the acceleration/deceleration process takes place. When e+b/e-b is injected into the electron/ion plasma, the e+b particles are preferentially accelerated, while the e-􀀀b particles are preferentially decelerated. It is shown the preferential acceleration/deceleration is absent when the e+b/e-􀀀b is injected into the electron/positron plasma. The theory also predicts that the particle momentum in the beam direction is transferred to the the vector potential due the merging process, leading to the increase of the magnetic field energy. The 2D PIC KEMPO code has been employed for simulations, which confirms the theory. The finding results could be applied to a wide range of astrophysical objects which have e+b/e-b injection.

Since current filaments formed by the FI have been observed in all simulations, the final goal in this dissertation is to study the current filament types and their formation processes. It is shown that difference in the spacial distribution of Lorentz factor will produce different current filament types. When the Lorentz factor is homogeneously distributed in the space, the current filament is generated by the charge-neutrality condition. This is the case of non-relativistic counterstreaming plasma because the Lorentz factor is almost 1 everywhere in the space. In the relativistic regime, the variation in the spacial distribution of the Lorentz factor triggers the formation of space-charge filaments. Thus, in the relativistic counterstreaming plasma, the current filament can be created by the space-charge filament. Supporting results are provided by using the 1D PIC EPOCH code.