Particle methods for plasma physics

Summary

A plasma is an ionized gas with positively and negatively charged particles (ions and electrons). One promising method of generating electricity with nuclear fusion uses tokamak reactors filled with an extremely hot plasma, similar to what happens inside the Sun. A strong magnetic field keeps the plasma away from the reactor walls. This shows the importance of simulating a plasma in an electromagnetic field.

One approach is to use particle methods: write down the equations of motion of the particles inside the plasma and couple them to Maxwell's equations for the electromagnetic field. The standard method for this has only moderate accuracy (it is second order). Past research on numerical methods for solving these differential equations established that it is possible to improve the accuracy in time, but that to get maximal benefit from this, the accuracy in space should also be improved.

The aim of this project is to implement a method with high spatial accuracy, combine it with our accurate time stepper, and test the combined algorithm to see in what circumstances the improved accuracy is beneficial. This project requires some prior knowledge of numerical methods for both ordinary and partial differential equations and solid programming skills. An interest in plasma physics and high-performance computing are also needed.

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