This thesis presents a theory for investigating streaming instabilities in converging geometries in warm and cold plasmas. We address the number density inhomogeneity by approximating the perturbed components with the Wentzel-Kramers-Brillouin (WKB) approximation. In the case of a warm plasma, an isotropic temperature is added to the set of coupled ordinary differential equations and their wavenumbers are obtained. The temporal growth rates are determined by mapping the wavenumbers to the frequency and obtained saddle points. Particle-in-cell (PIC) simulations are performed to support the semi analytical theory. The PIC simulations demonstrate an agreement to within an order of magnitude of the theoretical predictions for the cold plasma case. The PIC simulations for varying temperature and a fixed mode are performed and demonstrated to be in good agreement of less than an order of magnitude with the theoretical predictions. PIC simulations for fixed temperature and varying azimuthal mode number have been performed and demonstrate to be in good agreement within an order of magnitude with small qualitative differences.
PIC simulations are performed to replicate recent experiments. The simulations demonstrated that electrons are ejected transversely to the laser’s propagation direction. They are known as “side electrons”. We then describe the differences between the simulations and experiments. A theory for the mechanism responsible for the azimuthal modulations in the “side electrons” is proposed. Electrons converge on the axis of propagation and are mostly reflected by the large fields given the on-axis charge concentration. Electrons that diverge and then counter-stream with electrons that are converging on-axis. As a result, an electric field co-moves with the back of the bubble thus perpetuating an instability. PIC simulations are performed for two colliding electron flows with an inphase azimuthal sinusoidal modulation for converging geometry. The obtained change of phase in one of the annuli demonstrates the presence of an instability. Further slab geometry simulations are performed for two counter-streaming slabs with in phase modulations with an asymmetric strength, symmetric strength, a reverse momenta and a reflective boundary. All the simulations demonstrate the growth of the waves. The instabilities considered are the two-stream instability and the current filamentation instability.
|Date of Award||29 Jul 2022|
- University Of Strathclyde
|Sponsors||University of Strathclyde|
|Supervisor||Dino Jaroszynski (Supervisor) & Bernhard Ersfeld (Supervisor)|