Modelling of ECCD and ECRH in Toroidal Devices

The steady state operation of tokamak fusion devices relies upon the possibility of sustaining the plasma equilibrium and confining the plasma particles using auxiliary, non-inductive driven current. Due to its importance for fusion reactor development and operation, the demonstration of the feasibility of such a steady state operation has turned out to be an actual goal for different fusion machines such as Tore Supra (CEA Cadarache) or TCV (EPFL Lausanne). Among all the existing current drive methods, electron cyclotron current drive (ECCD) is the most suitable for driving the current in the center of the plasma volume and for controlling this current. As it is known for cyclotron resonance wave-particle interaction which is responsible for energy coupling from the wave to the plasma, non-linear effects can be important for high power experiments. Therefore, a traditional theoretical approach in description of wave absorption and ECCD (linear and quasi-linear theory) may become invalid. On the other hand, the theory of non-linear wave-particle interaction is not adequately developed to describe the real experimental situation. In a previous study, the electron distribution function has been modeled with the Monte Carlo method using the mapping technique which takes into account realistic orbits of electrons during their non-linear cyclotron interaction with the wave beam. The first results of the computation of the power absorption within this approach show a significant difference of this quantity and of the absorption coefficient from the prediction of the theories mentioned above. This is true for parameters which are typical for Tore Supra, TCV and ASDEX Upgrade (IPP Garching) (input power 400 kW). Therefore, the correct account of nonlinear interaction is necessary for future modelling experiments on these devices. A similar strong influence of nonlinear effects on the current drive efficiency is also observed in the computations. Within the proposed project we plan to improve our model in order to enable the treatment of current drive scenarii for realistic magnetic field geometries and to study the current drive efficiency for typical experimental conditions on ASDEX Upgrade, TCV and Tore Supra. To this end, the Stochastic Mapping code and the extended TORBEAM code should be combined with the ECCD/ECRH code. This combination will allow for the evaluation of supra-thermal electron fluxes whose convective transport can play a significant role in the radial flux balance of stellarators. In addition, a search for new current drive scenarii with improved efficieny is planned.

The steady state operation of tokamak fusion devices relies upon the possibility of sustaining the plasma equilibrium and confining the plasma particles using auxiliary, non-inductive driven current. Due to its importance for fusion reactor development and operation, the demonstration of the feasibility of such a steady state operation has turned out to be an actual goal for different fusion machines such as Tore Supra (CEA Cadarache) or TCV (EPFL Lausanne). Among all the existing current drive methods, electron cyclotron current drive (ECCD) is the most suitable for driving the current in the centre of the plasma volume and for controlling this current. As it is known for cyclotron resonance wave-particle interaction which is responsible for energy coupling from the wave to the plasma, non-linear effects can be important for high power experiments. The starting point of the current project was the model of non-linear wave-particle interaction developed within the FWF-Project P13495-TPH. The applicability of that model was limited to the case where the wave vector of the injected electron cyclotron wave beam is perpendicular to the main confining magnetic field of the fusion device. Therefore, in a first step, this model has been generalized to treat also the case of an arbitrary injection angle. This activities resulted in the development of the Fortran code ECNL. In a second step, the problem of beam propagation in the plasma has been addressed together with Dr. Emanuele Poli from IPP-Garching by combining ECNL with the Fortran code TORBEAM developed and used in Garching. TORBEAM solves the problem of beam propagation in the plasma consistently but approximates the power absorption linearly. In the frame of this combination, an important task has been the implementation of a realistic tokamak geometry within ECNL. The results of the combined codes have shown that, for ASDEX Upgrade parameters, non-linear effects of wave- particle interaction will always be important whenever the second harmonic X-Mode with a beam propagating perpendicularly to the main magnetic field is used for heating. It has been shown that non-linear effects lead to a consequent broadening and shift of the absorption profile as compared to the result of linear modelling (TORBEAM). Moreover, the modelling of ECCD for the 2nd harmonic X-mode has shown that, for ASDEX Upgrade parameters, the broadening of the power deposition profile and of the current density profile appears with increasing beam width. It has been found that, during ECCD with 2nd harmonic X-mode and mid-plane launch, power absorption and current generation are sensitive to rational magnetic surfaces. The observed reduction of power absorption and current generation around low-order magnetic surfaces could be explained as a result of a plateau formation on the distribution function of electrons on the particular surface due to their often re-entries in the wave beam. Performed detailed analysis has shown that the presence of a resulting dip on driven current profiles can change the sign of the tearing mode stability index in contrast to the profile resulting from a linear wave absorption model without such a dip. Hence, cocurrent drive shows a stabilizing effect and countercurrent drive shows a destabilizing effect on neoclassical tearing modes.