Topological Concepts in Plasmas

Magnetized plasmas consist of a large collection of charged particles coupled together by long-range Lorentz forces and Maxwells equations. Plasmas are ubiquitous around the Universe, and are also harnessed for fusion power, space propulsion, semi-conductor technologies and other industrial applications. As opposed to fluid dynamics, the challenge in describing the dynamics of plasmas comes from complex fluid-like behaviour simultaneously affected by collisionless effects and single particle influences over a wide range of spatial and temporal scales. This seminar will present simple concepts of "helicity", taken from the mathematical subject of topology, and show how these concepts have been very successful in describing the dynamics of magnetized plasmas. From these topological concepts, the final state of a plasma can be predicted without needing to know all the detailed dynamics leading to that state. As an example, the seminar will present recent results on how two plasma configurations (known as spheromaks) can merge together to form one of two configurations (another spheromak or a field-reversed configuration) in the laboratory.