Kinetic Modelling of Radio Frequenz Heting in Toroidal Confinement Devices

Radio frequency (rf) heating of electrons and ions is a basic heating mechanism in fusion devices. The theoretical frame work for the physical description of rf heating is the kinetic plasma theory. After averaging over the fast gyro motion of the particles one is left with particle distribution functions in 5D phase space. Regular methods, i.e., all methods not based on stochastic steps, can only be applied if sufficient symmetries exist which can be used to reduce the dimensionality of the problem. Stochastic methods like Monte Carlo (MC) are therefore preferable if a reduction of dimensionality is not possible. MC methods are simply to apply but in order to obtain a good resolution, millions of stochastic trajectories have to be followed. Even on present-day fast parallel computers time becomes a severe constraint. On the other hand, in circumstances where the typical collision time is large compared to he typical bounce time in a toroidal or ripple magnetic well, a tremendous amount of computer time is wasted in re-computing again and again the drift orbits which are only slightly perturbed by collisions. To overcome the numerical stiffness in these time scales, a stochastic mapping technique had been developed. A code utilising this technique should be worked out in detail and applied to data from Wendelstein stellarator W7-AS and later also to W7-X. An interesting aspect would be to study then the new confinement regime (the electron root feature) of W7-AS. It shows good confinement times and can be triggered by localised electron cyclotron radio frequency heating.

Within the framework of kinetic theory a numerical code has been developed in order to study heating and transport in very general magnetic traps. At the same time, the nonlinear dynamics of plasma particles inside the electromagnetic field of a radio frequency beam and the implication on the energy absorption has been treated. The heating of a hot fusion plasma with radio frequency waves is a prime mechanism to provide the additional heating needed to run a fusion reactor device. Kinetic theory is necessary to describe the physics of wave propagation and wave particle interaction inside the practically collisionless plasma. In addition, Coulomb interactions within the plasma as well as the nonlinear particle dynamics play an essential role when heating a plasma by electromagnetic waves. While passing through the wave beam, the plasma particles interact resonantly with the wave field. Subsequently, the gained energy is lost again to the background plasma by Coulomb collisions. The novel aspect of the developed numerical code is the combination of Monte Carlo methods with a special Poincaré mapping technique. With the help of this Stochastic Mapping Technique, the drift kinetic equation is solved in the long mean free path regime and in application to stellarators with few symmetries in the magnetic field geometries. Even island chains and ergodic magnetic field layers can be present. From the theoretical investigation of the nonlinear electron dynamics the reduction of the energy absorption during heating with radio frequency waves has been obtained quantitatively.