STOCHASTIC METHODS IN TRANSPORT-THEORY

The methods of modern theory of stochastic processes appear to provide a useful tool for transport theory in magnetized plasmas. The Langevi n equation formalism provides important, but limited information about diffusive processes. A quite promising new approach to modelling comp lex situations, such as transport in incompletely destroyed magnetic s urfaces, is provided by the theory of Continuous Time Random Walks (CT RW), which is presented in some detail. A test problem is discussed in detail: transport of particles in a fluctuating magnetic field, in th e limit of infinite perpendicular correlation length. The well-known s ubdiffusive behavior of the Mean Square Displacement (MSD), proportion al to t(1/2), is recovered by a CTRW, but the complete density profile is only recovered under some additional conditions. The quasilinear a pproximation of the kinetic equation has the form of a non-markovian d iffusion equation and can thus be generated by a CTRW. Finally, a new iterative map, called ''tokamap'' is presented and its relation to tra nsport and CTRW is displayed.