H.-P. Zehrfeld

B2-EIRENE simulation of ASDEX and ASDEX-Upgrade scrape-off layer plasmas

The 2D multifluid edge code B2 coupled with the 3D neutral gas Monte Carlo code EIRENE is being used for edge interpretation and model validation on the axisymmetric poloidal divertor experiments ASDEX and ASDEX-Upgrade. For this purpose B2 was significantly improved especially by a fully implicit treatment of the topological cuts appearing in X-point configurations, and a reasonably accurate handling of inclined target plates. A fast, automatic grid generator has been developed, which allows direct implementation of experimental MHD equilibria into B2-EIRENE. Typical ASDEX and ASDEX-Upgrade simulations are presented and discussed.

Stationary toroidal equilibria at finite beta.

We investigate the effects of plasma flow on axisymmetric, self-consistent equilibria in toroidal geometry. The investigation is of considerable interest in relation to hot plasmas confined in toroidal systems with longitudinal current. On the basis of the one-fluid MHD plasma model, we use a concise formulation to elucidate important features of the equilibrium. In contrast to previous flow calculations which were treated almost exclusively in the low-beta approximation, we retain, together with flow, all beta effects.As in the treatment of the full flow problem at low beta, we find conditions for equilibrium. The form of our description allows a quite general discussion of its nature and existence for finite beta. This shows that there is a close relationship between the solvability conditions for equations arising from integrals of the system, and the nature of the characteristics of the partial differential equation describing the radial force balance. In the case of large aspect-ratio, these considerations lead to a generalized Bennett relation and to an expression for plasma displacement exhibiting beta and flow effects.

MHD Mode Structure and Propagation in the ASDEX Tokamak

The Mirnov oscillations observed in the ASDEX tokamak are analysed with regard to the generally accepted interpretation scheme according to which (1) Mirnov oscillations are caused by currents flowing parallel to the magnetic field on rational magnetic surfaces and (2) the field perturbation is frozen within the plasma. If the second statement holds, the frequency is obtained from the profiles of the electron density, the ion temperature and, if applicable, the toroidal or poloidal rotation velocity. It is shown that there are modes which are consistent with the above interpretation. On the other hand, mode coupling is observed. Mode coupling is also invoked to reconcile the experimental findings with the predictions of a theory based on statement (1); according to this theory, there is a poloidal variation of both the phase velocity and the amplitude of the Mirnov oscillations. While the observed phase velocity fits well into this picture, the poloidal variation of the amplitude cannot be ascribed to only one mode in the majority of cases. In addition, the possibility of coherent MHD activity due to currents in the scrape-off layer is discussed.

Numerical MHD stability studies: toroidal rotation, viscosity, resistive walls and current holes

The linear magnetohydrodynamic (MHD) stability of ideal and resistive, axisymmetric toroidal equilibria is investigated with respect to various physical effects, such as differential toroidal rotation, viscosity, ideal and resistive external walls and current holes. For this purpose, the CASTOR code has been comprehensively extended. Static equilibria, equilibria with toroidal flow and equilibria with current holes serve as input to this code called CASTOR_FLOW code. ASDEX Upgrade type equilibria with toroidal flow are computed up to a toroidal Mach number of Mta = 0.5, and compared with the static solution. Using these equilibria, the stabilizing effect of differential toroidal rotation on double tearing modes (DTMs) is investigated. The studies show that the computation of equilibria with flow is necessary for toroidally rotating plasma with Mta ≥ 0.2. The stability of DTMs is also studied for equilibria with current holes. Further, the stabilizing effect of a resistive wall on an external ideal kink mode is investigated.

Electric currents in the scrape-off layer in ASDEX Upgrade

Abstract Scrape-off layer (SOL) currents are measured by means of Langmuir probes and shunts in the divertor of ASDEX Upgrade. They consist of the overlayed contributions of thermoelectric and Pfirsch–Schluter (PS) currents. The SOL currents exhibit a drastic decrease when the line-averaged density approaches the Greenwald density in the H-mode. An analytical model is presented which reproduces the measured thermoelectric current quantitatively. Matching of the analytical model with the measured current scaling yields information about divertor temperatures and SOL e-folding lengths.

Effect of inertia on losses from a plasma in toroidal equilibrium

We investigate theoreticall y the MHD equilibrium of a resistive, low-density plasma in a model stellarator field. Th e effect of inertia on plasma motion is treated exactly and its influence on plasma loss determined. The results are valid for arbitrary aspect ratio. For the existence of a stationary equilibrium we show that there are two unconnected regions of solution, described in terms of the mass fluxes the long and the short way within a magnetic surface. For the region containing the case of the well-known classical resistive diffusion we argue that the increase in plasma loss due to inertia is strongly limited and does not appreciably exceed the classical diffusion rate.

ELM phenomenon as an interaction between bootstrap-current driven peeling modes and pressure-driven ballooning modes

An ELMy ASDEX Upgrade plasma equilibrium is reconstructed taking into account the bootstrap current. The peeling mode stability of the equilibrium is numerically analysed using the GATO [1] code, and it is found that the bootstrap current can drive the plasma peeling mode unstable. A high-n ballooning mode stability analysis of the equilibria revealed that, while destabilizing the peeling modes, the bootstrap current has a stabilizing effect on the ballooning modes. A combination of these two instabilities is a possible explanation for the type I ELM phenomenon. A triangularity scan showed that increasing triangularity stabilizes the peeling modes and can produce ELM-free periods observed in the experiments.

Resistive ballooning stability of ASDEX equilibria

Experiments on the maximum attainable beta values of ASDEX discharges show that the limits for this parameter lie in the range of theoretical predictions. In a previous publication a theoretical identification of the corresponding instabilities has been attempted. No significant correlation with global plasma instabilities could be found, but the two-dimensional MHD equilibria calculated on the basis of ASDEX experimental parameters turned out to be close to the marginal ideal ballooning limit. In the work presented here, the previous investigation on resistive ballooning modes is extended. Separatrix bounded as well as limiter controlled plasma equilibria are considered. Because of the small aspect ratio of ASDEX (A 4) all equilibrium as well as stability calculations are performed in full toroidal geometry. After the formulation of a system of four equations describing the resistive evolution of velocity and magnetic fields in the high-m stability limit in co-ordinate invariant form and its Fourier approximation in the neighbourhood of a localization field line, the resulting quasimode equations are solved, applying methods of finite-element discretization. Complex growth rates γ are found, with a positive real part for values of the toroidal mode number n below 100. Calculated values of Re {γ} ≤ 10−3/τA S−1 (with τA being the Alfven time) are small and therefore in agreement with the experimentally observed non-disruptive behaviour at the βp limit. Thus we believe that the characteristic signatures which govern ASDEX high βp discharges can be explained by resistive ballooning modes.

Local, ideal and resistive stability in tokamaks with non-circular cross-section

Recently, the conditions for stability of an arbitrarily shaped, finite-pressure toroidal plasma against localized ideal and resistive modes were presented. The characteristic time scale for local instability with respect to ideal modes is small compared with that for resistive modes so that an investigation of ideal local stability is a prerequisite for an assessment of non-ideal local stability. Here we consider the stability of a particular class of non-circular cross-section tokamak equilibria with respect to such modes. The equilibria are described analytically so that no ordering or expansion procedure is necessary, and both ideal and resistive stability are investigated over the whole plasma region. The effects of plasma shape (vertical elongation and triangularity), as well as aspect ratio are investigated and particular reference is made to next-generation tokamak designs (e.g. JET).