Linear modeling of plasmas in the proximity of a magnetic X-point

The process during which different magnetic field lines merge with a change in the magnetic topology is called magnetic reconnection; it is one of the most important but least understood phenomenon in plasma physics. On the sun, for example, reconnection is thought to be the key mechanism behind the corona heating via solar flares. In fusion devices such as tokamaks or reversed field pinches, fast relaxation phenomena occur that strongly influence the plasma confinement. Laboratory experiments and space observations both indicate that the characteristic time for reconnection is far too small to be explained by conventional models based on the resistive dissipation of a magneto-hydrodynamic (MHD) fluid.

To take the analysis further from the theoretical side, it is now opportune to characterize precisely the linear instability allowing for the non-linear reconnection to take place on a fast time scale. A detailed description of the interaction between charged particles with the global electromagnetic wavefield is then necessary to correctly model different wave branches which may interact with each other, such as the shear-Alfvén, the quasi-electrostatic and the drift waves.

For a master of science thesis, the project will begin with the analytical and numerical calculation of metric tensor elements describing the plasma equilibrium in a magnetic cusp field. Using this intermediate result with some additional knowledge of differential geometry, the Maxwell equations for small amplitude electromagnetic field perturbations will be formulated in magnetic coordinates, complete with boundary conditions and ready for discretization with bi-dimensional finite elements. Using an existing 2D code and some external help, an attempt will be made to implement first a simple two fluid model for the plasma and calculate numerically the growth rate of the instability.

This is a difficult and challenging project for a computational physics student with a serious potential for a continuation at the doctoral level. Depending on the outcome, comparisons can be carried out with measurements from the magnetic reconnection experiment built by the group of Prof. A. Fasoli (MIT), and the modeling of the plasma dynamics can be refined in collaboration with Prof. F. Porcelli (Polytechnico Turin). Both collaborations may ultimately lead to the understanding of a fundamental phenomenon, which is now at the cross-roads of astrophysics and fusion plasma physics.

For further information, contact André JAUN and consult http://www.fusion.kth.se/jaun.