Confinement Properties in Magnetized Plasmas

In order to model and determine properties of plasmas such as magnetosphere or fusion devices a consistent mathematical model is required. The goal of this project, among other open problems, is to prove long time uniqueness and existence of the Relativistic Vlasov Maxwell system. In the process, determine estimates on the electromagnetic field intensities, the kinetic distribution functions and their derivatives in hot and cold magnetized plasma regimes. A better understanding of plasma behaviors can prove advantageous in many applications such as space travel, or clean fusion devices. Computational challenges arise due to the non-linearity of the system. An original mathematic approach to such problems is being developed and implemented. So far it as been successful for cold plasmas, but one goal would be to extend these results to hot, relativistic plasmas. In the process help us to understand some of the turbulent structures which form. Richard Feynman is quoted with saying that the understanding of turbulence is the greatest problem in classical mechanics. Thus any advancements will be of highly invaluable to the field.

Faculty Supervisor:

Slim Ibrahim

Student:

Partner:

Université de Haute Bretagne Rennes 2

Discipline:

Mathematics

Sector:

Education

University:

University of Victoria

Program: