Numerical results for the three mono-energetic transport coefficients required for a complete neoclassical description of stellarator plasmas have been benchmarked within an international collaboration. These transport coefficients are flux-surface-averaged moments of solutions to the linearised drift kinetic equation which have been determined using field-line-integration techniques, Monte Carlo simulations, a variational method employing Fourier-Legendre test functions and a finite difference scheme. The benchmarking has been successfully carried out for past, present and future devices which represent different optimisation strategies within the extensive configuration space available to stellarators.A qualitative comparison of the results with theoretical expectations for simple model fields is provided. The behaviour of the results for the mono-energetic radial and parallel transport coefficients can be largely understood from such theoretical considerations but the mono-energetic bootstrap current coefficient exhibits characteristics which have not been predicted.

Using an analytic solution of the kinetic equation in the 1/ regime, a new formula for the neoclassical transport coefficients is obtained which takes into account all classes of trapped particles. This formula holds in any coordinate system and no simplifying assumptions about the magnetic field are needed. Therefore it is also applicable to complex magnetic fields given in real space coordinates. The method and the results can be used to optimize magnetic field configurations with respect to the 1/ regime. The method is bench-marked against Monte Carlo calculation both for the lϭ3 classical stellarator model and also for the original Helias configuration ͓J. Nührenberg and R. Zille, Phys. Lett. A 114, 129 ͑1986͔͒ with a more complex magnetic field structure. Some features of transport for Helias are clarified by analyzing the bounce-averaged drift velocity.

Effects of linear plasma response currents on non-axisymmetric magnetic field perturbations from the I-coil used for Edge Localized Mode mitigation in DIII-D tokamak are analyzed with the help of a kinetic plasma response model developed for cylindrical geometry. It is shown that these currents eliminate the ergodization of the magnetic field in the core plasma and reduce the size of the ergodic layer at the edge. A simple balance model is proposed which qualitatively reproduces the evolution of the plasma parameters in the pedestal region with the onset of the perturbation.It is suggested that the experimentally observed density pump-out effect in the long mean free path regime is the result of a combined action of ion orbit losses and magnetic field ergodization at the edge.

The heat balance equation is derived and solved for fusion edge plasma conditions with ͑partially developed͒ ergodic magnetic-field structures. For this purpose, a three-dimensional ͑3D͒ Monte Carlo code, ''E3D,'' based upon the ''multiple local magnetic coordinate system approach'' has been developed. Parameters typical for the Dynamic Ergodic Divertor ͑DED͒ of TEXTOR-94 ͑Torus Experiment for the Technology Oriented Research͒ ͓K. H. Finken et al., Fusion Eng. Des. 37, 1 ͑1997͔͒ are chosen in the applications. The plasma temperature fields and the profiles of the radial component of heat flux due to the classical parallel and anomalous perpendicular diffusion are calculated. Because of magnetic-field ergodization and diversion of field lines, parallel conduction also can contribute to this radial flux. The results are compared with theoretical predictions for two limiting cases: With the Rechester-Rosenbluth model of ergodization-induced transport and with a ''laminar flow model'' proposed in the present paper. This latter model describes the effects of field line diversion. The diversion effect is shown to be dominant for TEXTOR-DED conditions.

First experiments on edge-localized mode (ELM) mitigation with the help of ITER-like coils on ASDEX Upgrade are analysed using linear and quasilinear kinetic models to describe the interaction of resonant magnetic field perturbations (RMP) with the plasma. The gyrokinetic derivation of RMP-driven transport coefficients is given in detail. The role of fluid resonances is studied, in particular the role of the resonance associated with the equilibrium electric field reversal point Er = 0. Like the electron fluid resonance associated with the zero of the total perpendicular electron fluid velocity, the Er = 0 resonance may lead to enhanced transport due to the reduction of RMP shielding in the pedestal region where the RMP field can even be amplified by this resonance. The conditions on the RMP coil spectrum resulting from the analysis are discussed.