Runaway electrons and Alfvén eigenmodes in tokamaks

Doctoral thesis, 2006

Runaway electrons can be generated as a consequence of the rapid thermal quench of the plasma in a tokamak disruption. If the time scale of this cooling is short compared to the collision time in the tail of the electron velocity distribution, incomplete thermalisation of this tail leads to a burst of runaway production. This phenomenon is investigated in the present thesis and simple criteria for whether it produces more runaways than the ordinary Dreicer runaway generation mechanism are derived. In tokamak disruptions a large part of the pre-disruption Ohmic current can be converted into a runaway current. A simple model for the current dynamics is presented and analysed analytically and numerically. The radial profile of the runaway current is found to become significantly more peaked on the magnetic axis than the pre-disruption profile in tokamaks with a large current. Furthermore, the effects of synchrotron radiation in the high energy runaway tail of the steady-state electron distribution function are studied and the governing kinetic equation is found to be of a two-way diffusion form. A general analytic scheme for solving two-way diffusion equations is developed. The theory of localisation of compressional Alfvén eigenmodes to the edge of a tokamak plasma is extended to the case of spherical tokamaks, which have elliptic cross section and aspect ratio of order unity. Another theory is developed in order to explain experimentally observed second harmonic density perturbations of Alfvén cascade eigenmodes. The second harmonic perturbation is generated as a nonlinear sideband of the Alfvén cascade through quadratic terms in the magnetohydrodynamic equations.