Cosmic plasma in a mathematical suit

Stephen Pankavich is an associate professor at the Colorado School of Mines, Golden, USA. Thanks to a grant from the Knut and Alice Wallenberg Foundation, he will be a visiting professor at the Department of Mathematical Sciences, Chalmers University of Technology, Gothenburg.

Together with Visiting Professor Stephen Pankavich, researchers at Chalmers will develop new methods for solving different mathematical problems in the kinetic theory of plasma dynamics. Kinetic theory is a mathematical theory that originated in the 19th-century work on gases by Ludvig Boltzmann and James C. Maxwell.

Plasma is a special kind of gas in which electrons are stripped from the atoms, making the gas electrically charged. Plasma is therefore of practical interest; for example, plasma engines have been developed to drive probes that are sent far out in space. Plasma is regarded as the fourth form of matter, after gases, liquids and solids, and is the most common state of matter in the universe. Galactic clouds, tails of comets and the solar wind, among many other things, consist of plasma’s electrically charged particles.

The motions of plasma are described by a number of complicated partial differential equations. The purpose of this project is to show that the equations have realistic solutions, and to determine the properties of these solutions, such as development over time, and calculate their sensitivity with respect to the plasma’s state, such as its mass, charge, or temperature.

Since the mathematical models always have physical counterparts, the challenge of analyzing a problem mathematically also becomes a challenge in understanding the physical phenomena it describes at a deeper level. Therefore, a discovery of a specific behavior in solutions to partial differential equations can be translated into real knowledge of problems in plasma physics or astrophysics.