Research

Plasma turbulence is the chaotic and irregular behavior of charged particles in a plasma, which can affect many phenomena such as fusion energy, astrophysics, and space weather. One way to study plasma turbulence is through continuum simulations, which are numerical methods that solve the equations of motion for the plasma fluid as a whole. Continuum simulations can capture the complex dynamics of plasma turbulence at different scales and reveal its underlying mechanisms. 

The Weibel instability is a plasma instability that occurs when two streams of charged particles, such as electrons, move in opposite directions with a relative velocity greater than their thermal velocity. This instability can generate magnetic fields perpendicular to the streaming direction, which can grow exponentially until they reach a nonlinear saturation stage.

We are trying to study the non-linear saturation using numerical simulations and applications of this instability in astrophysics and laboratory plasmas.

The Weibel instability can be understood as a result of the current filamentation effect. When two counter-streaming electron beams interact, they tend to form current filaments due to small perturbations in their density or velocity. These current filaments produce magnetic fields that act back on the electrons, deflecting them and enhancing the filamentation. This positive feedback loop leads to an exponential growth of the magnetic field until it becomes comparable to the kinetic energy of the electrons.

The linear growth rate of the Weibel instability depends on the parameters of the electron beams, such as their density, temperature, and relative velocity. The linear theory can be derived from the Vlasov-Maxwell equations, which describe the evolution of the distribution function of the electrons and the electromagnetic fields. The linear theory predicts that the fastest growing mode has a wavelength of the order of the electron skin depth, which is the characteristic length scale for plasma oscillations.

The nonlinear saturation of the Weibel instability is more complicated and involves several physical processes. One of them is magnetic trapping, which occurs when the electrons are confined by the magnetic field and cannot escape from their filaments. This reduces the effective current and slows down the growth of the magnetic field. Another process is electrostatic potential formation, which happens when transverse flows induced by the magnetic field create charge separation and electric fields. These electric fields can also trap or scatter the electrons and affect their dynamics.

Numerical simulations are essential tools to study the nonlinear saturation of the Weibel instability, as they can capture the full kinetic effects and complex interactions between the electrons and the fields. We are using Gkeyll framework which uses discontinous galerkin method. Gkeyll simulations can reproduce the linear growth and nonlinear saturation of the Weibel instability for different beam parameters and initial conditions.

The Weibel instability has many applications in astrophysics and laboratory plasmas, where it can play a role in generating or amplifying magnetic fields, accelerating particles, or producing shocks. For example, it has been proposed that the Weibel instability is responsible for creating the magnetic fields in gamma-ray burst jets, which are powerful relativistic outflows from massive stellar explosions or mergers. It has also been suggested that the Weibel instability can mediate collisionless shocks in supernova remnants, where it can facilitate particle acceleration and cosmic ray production. In laboratory plasmas, the Weibel instability has been observed in experiments with intense laser beams or particle beams interacting with plasmas, where it can affect energy transport, plasma heating, or radiation emission.

The Weibel instability is a fascinating phenomenon that occurs in plasmas with an anisotropy in velocity space. This means that the plasma particles have different temperatures or velocities in different directions. The Weibel instability can generate strong magnetic fields from an initially unmagnetized plasma, which can have important applications in laboratory and astrophysical settings. For example, the Weibel instability is believed to play a role in the formation of collisionless shocks in supernova remnants and gamma-ray bursts.

In this work, I reproduced the results of the paper "Temperature-dependent Saturation of Weibel-type Instabilities in Counter-streaming Plasmas" Here we will focus on a simple case of the Weibel instability, where two counter-streaming beams of electrons collide with each other. It has been showed how it leads to magnetic field growth and saturation.