Electromagnetic Field of the Dynamic Ergodic Divertor

The concept of the Dynamic Ergodic Divertor (DED) has been proposed by the Torus Experiment for Technology Oriented Research (TEXTOR) group as one of the advanced tokamak scenarios. External perturbation coils create at the edge a rotating helical field whose frequency can be changed from dc to a few tens kilohertz depending on the operational regime. In the low frequency operation the presence of the tokamak plasma does not have much effect and the heat conductivity of the resulting vacumm-like static ergodic configuration can be studied directly. For medium through high frequencies of operation, the presence of the plasma becomes increasingly important, in particular the plasma response to the magnetic perturbation near the resonant surface where the confining background field is parallel to the currents inside the DED field coils. In this regime one can expect on one hand a well developed ergodic transport which smears out the heat load and, other the other hand, because of the plasma response (skin effect), the perturbation fields will not penetrate too far into the core plasma thus reducing the confinement properties. Therefore, a consistent theory for the penetration and interaction of the perturbation field with the plasma is of prime interest. The linear and quasilinear properties of the field-plasma interactions are studied. For the linear problem, the equations are Fourier analyzed with respect to time, poloidal and toroidal direction (periodic cylinder model). The resulting set of ordinary differential equations for the Fourier amplitudes is to be integrated numerically where special care has to be given to the stiffness of the problem. From the solution of the linear problem the quadratic source terms of the quasilinear equation are to be obtained. This equation is of diffusive nature and has to be solved in order to generate the new background profiles. The solution of this problem can be used to study global stability and tranport properties.

Dynamic Ergodic Divertors (DED) had been proposed by the Torus Experiment for Technology Oriented Research (TEXTOR) group in order to obtain better control on the plasma recycling process and, at the same time, to reduce the heat load at the outer wall of a tokamak. In the concept of DED, external perturbation coils create at the edge a rotating helical field whose frequency can be changed from dc to a few kilohertz depending on the operational regime. When the corresponding wave propagation into the finite temperature plasma is studied, kinetic effects are important, in particular if the resonant magnetic surface (the local helical magnetic field lines are parallel to the external DED coils) is located inside the core plasma, where the plasma is essentially collisionless. Within the present project, the problem of the interaction of the rotating magnetic field with the tokamak plasma is studied in the linear and partly the quasilinear approximation. The nonlocal plasma conductivity operator is obtained within kinetic theory without the need of additional simplifying assumptions like quasineutrality and/or incompressibility as it is often made in MHD studies of this problem. A finite Larmor radius expansion is derived which ensures on one hand positive definiteness of the total absorbed energy in the plasma volume in case of a homogeneous Maxwellian distribution of plasma particles and, on the other hand, guarantees the invariance of the resonant part of the plasma response current with respect to Galilean coordinate transformations to moving frames. The results have been used to model the interaction between the DED field and a realistic TEXTOR plasma, i.e. experimental profiles of plasma density and temperature and also taking into account the toroidal plasma rotation. The modeling shows that plasma pressure gradients significantly effect the direction and value of the DED created torque which acts on the plasma. The modeling revealed that in the presence of an electron pressure gradient, the torque is always in the direction of the ion diamagnetic velocity (diamagnetic plasma current) independent of the rotation of the perturbation field, unless the perturbation field rotates in the electron diamagnetic direction and its frequency exceeds the electron diamagnetic frequency. In particular, the torque stays finite even for a nonrotating perturbation field. The results of the present project eventually contribute to the joint international effort to use fusion as a potential source for future energy production.