S. V. Kasilov

Evaluation of 1/ν neoclassical transport in stellarators

Using an analytic solution of the kinetic equation in the 1/ν 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/ν regime. The method is bench-marked against Monte Carlo calculation both for the l=3 classical stellarator model and also for the original Helias configuration [J. Nuhrenberg and R. Zille, Phys. Lett. A 114, 129 (1986)] with a more complex magnetic field structure. Some features of transport for Helias are clarified by analyzing the bounce-averaged drift velocity.

Kinetic estimate of the shielding of resonant magnetic field perturbations by the plasma in DIII-D

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 analysed 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.

Benchmarking of the mono-energetic transport coefficients—results from the International Collaboration on Neoclassical Transport in Stellarators (ICNTS)

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 linearized 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 optimization 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.

Calculation of stochastic thermal transport due to resonant magnetic perturbations in DIII-D

The effect of resonant magnetic perturbations on heat transport in DIII-D H-mode plasmas has been calculated by combining the TRIP3D field line tracing code with the E3D two-fluid transport code. Simulations show that the divertor heat flux distribution becomes non-axisymmetric because heat flux is efficiently guided to the divertor along the three-dimensional invariant manifolds of the magnetic field. Calculations demonstrate that heat flux is spread over a wider area of the divertor target, thereby reducing the peak heat flux delivered during steady-state operation. Filtered optical cameras have observed non-axisymmetric particle fluxes at the strike point and Langmuir probes have observed non-axisymmetric floating potentials. On the other hand, the predicted magnitude of stochastic thermal transport is too large to match the pedestal plasma profiles measured by Thomson scattering and charge exchange recombination spectroscopy. The Braginskii thermal conductivity overestimates the experimental heat transport in the pedestal because the mean free paths of both species are longer than estimates of the parallel thermal correlation lengths, and collisionless transport models are probably required for accurate description. However, even the collisionless estimates for electron thermal transport are too large by one to two orders of magnitude. Thus, it is likely that another mechanism such as rotational screening of resonant perturbations limits the stochastic region and reduces transport inside of the pedestal.

Monte Carlo study of heat conductivity in stochastic boundaries: Application to the TEXTOR ergodic divertor

The heat balance equation is derived and solved for fusion edge plasma conditions with (partially developed) ergodic magnetic-field structures. For this purpose, a three-dimensional (3D) Monte Carlo code, “E3D,” based upon the “multiple local magnetic coordinate system approach” has been developed. Parameters typical for the Dynamic Ergodic Divertor (DED) of TEXTOR-94 (Torus Experiment for the Technology Oriented Research) [K. H. Finken et al., Fusion Eng. Des. 37, 1 (1997)] 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.

Integrated physics optimization of a quasi-isodynamic stellarator with poloidally closed contours of the magnetic field strength

A quasi-isodynamic stellarator with poloidally closed contours of the magnetic field strength B (Mikhailov 2002 Nucl. Fusion 42 L23) has been obtained by an integrated physics optimization comprising MHD and neoclassical theory. For a configuration with six periods and aspect ratio approximately 12, a main result is the attainability of an essentially MHD-stable high-beta ([beta] approximate to 0.085) plasma with low neoclassical transport, approximately vanishing bootstrap current in the long-mean-free-path regime and excellent a-particle confinement.

Overview of magnetic structure induced by the TEXTOR-DED and the related transport

The dynamic ergodic divertor (DED), a new concept of the ergodic divertor, is presently installed for the TEXTOR tokamak. Beside the conventional ergodic divertor operation the DED also permits the operation with a rotating magnetic field which allows, in particular, to broaden the heat deposition pattern on the divertor plates. Since its first proposal of the DED in 1996 the structure of magnetic field, especially, the onset of ergodic zone of field lines and related transport in the DED-operation has been extensively studied using different theoretical and numerical methods. New methods to study the magnetic field, in particular, the field line mapping have been developed. The presentation gives the overview of the studies on the structure of magnetic field in the DED, the formation of the ergodic and laminar zones of field lines at the plasma edge. It also includes studies on the modelling efforts of the transport of heat and particles in the ergodic and laminar zones.

Evaluation of the toroidal torque driven by external non-resonant non-axisymmetric magnetic field perturbations in a tokamak

The toroidal torque driven by external non-resonant magnetic perturbations (neoclassical toroidal viscosity) is an important momentum source affecting the toroidal plasma rotation in tokamaks. The well-known force-flux relation directly links this torque to the non-ambipolar neoclassical particle fluxes arising due to the violation of the toroidal symmetry of the magnetic field. Here, a quasilinear approach for the numerical computation of these fluxes is described, which reduces the dimension of a standard neoclassical transport problem by one without model simplifications of the linearized drift kinetic equation. The only limiting condition is that the non-axisymmetric perturbation field is small enough such that the effect of the perturbation field on particle motion within the flux surface is negligible. Therefore, in addition to most of the transport regimes described by the banana (bounce averaged) kinetic equation also such regimes as, e.g., ripple-plateau and resonant diffusion regimes are naturally included in this approach. Based on this approach, a quasilinear version of the code NEO-2 [W. Kernbichler et al., Plasma Fusion Res. 3, S1061 (2008).] has been developed and benchmarked against a few analytical and numerical models. Results from NEO-2 stay in good agreement with results from these models in their pertinent range of validity.

Passive cyclotron current drive efficiency for relativistic toroidal plasmas

In this paper we present results of analytical and numerical studies of the passive cyclotron current drive efficiency in mildly relativistic toroidal plasmas. The problem of linearization and separation of the electron and photon balance equations becomes nontrivial for high‐temperature plasmas (e.g., D–3He) with low electron pressure (βe<0.1) due to the increased effect of radiation friction. The conditions under which this separation is possible is derived in this paper. The linearized problem for the electron distribution is formulated in the form of a standard variational principle, which includes both Coulomb collisions and ‘‘collisions’’ due to cyclotron radiation. The reduced variational principle for the current drive efficiency (generalized Spitzer–Harm function) is derived, as well as its bounce‐averaged form for toroidal plasmas. Finally, a convenient form of the passive cyclotron current drive efficiency is introduced, which can be used for a self‐consistent modeling of passive cyclotron curr...

Electron cyclotron current drive in low collisionality limit: On parallel momentum conservation

A comprehensive treatment of the models used in ray- and beam-tracing codes to calculate the electron cyclotron current drive (ECCD) by means of the adjoint technique, based on the adjoint properties of the collision and Vlasov operators appearing in the drift-kinetic equation, is presented. Particular attention is focused on carefully solving the adjoint drift-kinetic equation (generalized Spitzer problem) with parallel momentum conservation in the like-particle collisions. The formulation of the problem is valid for an arbitrary magnetic configuration. Only the limit of low collisionality is considered here, which is of relevance for high-temperature plasmas. It is shown that the accurate solution of the adjoint drift-kinetic equation with parallel momentum conservation significantly differs (apart from the suprathermal electron portion) from that calculated in the high-speed-limit, which is most commonly used in the literature. For high-temperature plasmas with significant relativistic effects, the accuracy of the resulting numerical models is demonstrated by ray-tracing calculations and benchmark results are presented. It is found that the ECCD efficiency calculated for ITER with parallel momentum conservation significantly exceeds the predictions obtained with the high-speed-limit model.