A. Wingen

High resolution numerical studies of separatrix splitting due to non-axisymmetric perturbation in DIII-D

In DIII-D the splitting and deformation of the separatrix due to externally applied resonant magnetic perturbations is calculated using a vacuum field line integration code (TRIP3D–MAFOT). The resulting footprint pattern on the divertor target plates is shown in high resolution by contour plots of the connection lengths and penetration depths of the magnetic field lines. Substructures inside the divertor footprint stripes are discovered. Regions of deep penetrating long connecting field lines, which are related to the internal resonances by their manifolds, alternate with regions of regular short connecting field lines. The latter are identified as compact laminar flux tubes, which perforate the perturbed plasma region close to the x-point. The properties and consequences of such flux tubes are investigated in detail. The interaction of different resonant magnetic perturbations is analysed considering the separatrix manifolds. Constructive and destructive interference of the manifolds is discovered and studied.

Measurement of plasma boundary displacement by n = 2 magnetic perturbations using imaging beam emission spectroscopy

Imaging beam emission spectroscopy has been used to study the displacement of the plasma boundary in ELMing H-mode discharges with a 10 Hz rotating n = 2 external magnetic field perturbation in DIII-D. The rotating magnetic field creates a helical displacement of the beam emission profile of ~2 cm on the low-field-side (LFS) midplane which rotates with the applied resonant magnetic perturbation. This shift in the beam emission profile is due primarily to a shift in the electron density profile, which is independently measured to be 1.9 cm on the LFS midplane. These boundary displacements exceed calculations for the displacement of the stable and unstable manifolds formed by the interaction of the magnetic perturbation with the divertor separatrix by a factor of 4–5, suggesting that the vacuum field model does not correctly model the effect of the magnetic perturbations even near the separatrix. The measured displacements are suggestive of a non-resonant kink response.

Traces of stable and unstable manifolds in heat flux patterns

Experimental observations of heat fluxes on divertor plates of tokamaks show typical structures (boomerang wings) for varying edge safety factors. The heat flux patterns follow from general principles of nonlinear dynamics. The pattern selection is due to the unstable and stable manifolds of the hyperbolic fixed points of the last intact island chain. Based on the manifold analysis, the experimental observations can be explained in full detail. Quantitative results are presented in terms of the penetration depths of field lines.

Runaway losses in ergodized plasmas

New results from the generation of runaways and the loss of runaway electrons in an ergodized magnetic field are presented. For the generation process, a clear difference between a ‘normal’ and a clean, freshly boronized wall condition has been found. Under clean wall conditions, one observes at low densities not only the runaway electrons with energies up to 30 MeV and at discharges with even lower electron density one finds more runaway electrons but at an energy in the low-MeV regime. The runaway electrons are utilized as test particles for revealing the ergodized magnetic field line structure. For the measurements the m/n = 6/2 base mode configuration of the dynamic ergodic divertor (DED), has been applied. One observes a clear modification of the radial runaway profile with preferential losses in the ergodized zone. From the loss rate of the runaway electrons due to ergodization and from the redistribution of the runaways after the DED phase, the diffusion rate is estimated to be of the order of 0.1 m 2 s −1 .

Mapping of drift surfaces in toroidal systems with chaotic magnetic fields

Drift orbits of test particles are studied using a recently proposed Hamiltonian theory of guiding-center motion in toroidal systems. A symplectic mapping procedure in symmetric form is developed which allows a fast and accurate characterization of the Poincare plots in poloidal cross sections. It is shown that the stochastic magnetic field acts differently on the onset of chaotic motion for co- and counterpassing particles, respectively. Resonant drift surfaces are shifted inward for the co-passing particles, and are shifted outward for the counterpassing particles, when compared with resonant magnetic surfaces. The overall result is an inward (outward) shift of chaotic zones of co-passing (counterpassing) particles with respect to the magnetic ergodic zone. The influence of a stationary radial electric field is discussed. It shifts the orbits farther inward for the co-passing particles and outward for the counterpassing particles, respectively. The shifts increase with the energies of the particles. A r...

Influence of stochastic magnetic fields on relativistic electrons

The relativistic motion of test particles in stochastic magnetic fields is investigated. Guiding-centre motion is analysed in relativistic invariant form for toroidal geometry. Including stochastic magnetic field components, a symmetric Hamiltonian mapping technique, leading to a 4-dimensional iteration procedure, is developed. In general, an external electric field and a time-dependence of the magnetic field perturbations are allowed for. Break-up of drift surfaces is demonstrated via Poincare plots. The latter are analysed in detail for increasing (relativistic) kinetic energies of the particles. The dependence of the escape rates on the kinetic energy is calculated and compared with the escape rates for field lines. The non-relativistic limit of the model is derived. Quantitative results for the magnetic perturbations in a dynamic ergodic divertor of the TEXTOR experiment are shown, and predictions for runaway electrons are compared with experiments.

Fast ion transport during applied 3D magnetic perturbations on DIII-D

Measurements show fast ion losses correlated with applied three-dimensional (3D) fields in a variety of plasmas ranging from L-mode to resonant magnetic perturbation (RMP) edge localized mode (ELM) suppressed H-mode discharges. In DIII-D L-mode discharges with a slowly rotating magnetic perturbation, scintillator detector loss signals synchronized with the applied fields are observed to decay within one poloidal transit time after beam turn-off indicating they arise predominantly from prompt loss orbits. Full orbit following using M3D-C1 calculations of the perturbed fields and kinetic profiles reproduce many features of the measured losses and points to the importance of the applied 3D field phase with respect to the beam injection location in determining the overall impact on prompt beam ion loss. Modeling of these results includes a self-consistent calculation of the 3D perturbed beam ion birth profiles and scrape-off-layer ionization, a factor found to be essential to reproducing the experimental measurements. Extension of the simulations to full slowing down timescales, including fueling and the effects of drag and pitch angle scattering, show the applied RMPs in ELM suppressed H-mode plasmas can induce a significant loss of energetic particles from the core. With the applied fields, up to 8.4% of the injected beam power is predicted to be lost, compared to 2.7% with axisymmetric fields only. These fast ions, originating from minor radii , are predicted to be primarily passing particles lost to the divertor region, consistent with wide field-of-view infrared periscope measurements of wall heating in RMP ELM suppressed plasmas. Edge fast ion (FIDA) measurements also confirm a large change in edge fast ion profile due to the fields, where the effect was isolated by using short 50 ms RMP-off periods during which ELM suppression was maintained yet the fast ion profile was allowed to recover. The role of resonances between fast ion drift motion and the applied 3D fields in the context of selectively targeting regions of fast ion phase space is also discussed.

Ambipolar stochastic particle diffusion and plasma rotation

The motion of electrons and ions in stochastic magnetic fields is considered. The analysis starts from a Hamiltonian formulation of the drift motion including electric fields. For an efficient statistical evaluation of the resulting particle transport, a symplectic mapping technique is applied. Compared to previous considerations, the ion and electron test particle motion are investigated simultaneously, allowing calculations of the ambipolar electric field and its influence on stochastic transport. The predictions based on the relativistic drift model are applied to the magnetic perturbations in the TEXTOR-DED [A. Wingen et al., Nucl. Fusion 46, 941 (2006)]. The influence of the magnetic coil arrangement on the poloidal plasma rotation, caused by the generated radial electric field, is discussed.

Influence of different DED base mode configurations on the radial electric field at the plasma edge of TEXTOR

The influences of resonant magnetic perturbations (RMPs) on the poloidal rotation at the edge of a tokamak are investigated. Specific results are displayed for the tokamak TEXTOR with the dynamic ergodic divertor (DED). The latter can be operated in three different base mode configurations, namely 12/4, 6/2 and 3/1. The base mode configurations distinguish themselves by resonating with different island chains and having distinctly different penetration depths. Calculations predict a strong influence of the DED base mode configurations on the strength of the poloidal plasma rotation. The interpretation of the results emanates from the electron and ion drift motions in partially stochastic magnetic fields. Generally, RMPs cause incomplete magnetic chaos; the latter influences the drift motion of electrons and ions differently. By virtue of the formed ambipolar electric field, the poloidal plasma rotation is directly connected via the radial force balance. With increasing current in the DED perturbation coils the electron and ion last closed drift surfaces as well as internal drift surfaces break up differently for each species. These break-ups, as well as the changes in the poloidal rotation in dependence on the electron and ion temperatures, are investigated in detail.

Dependence of a current driven ELM self-amplification process on the plasma shape

The numerical model of the non-linear evolution of edge-localized modes (ELMs) in tokamaks being used in this paper assumes that thermoelectric currents flow in short connection length flux tubes, initially established by error fields or other non-axisymmetric magnetic perturbations. The additional magnetic perturbation of the current filaments changes the magnetic topology. In a self-amplification process, more flux tubes are created which eventually allow more thermoelectric current to flow through the plasma edge. The process of flux tube formation is highly sensitive to the position of the secondary X-point in typical single null discharges in DIII-D. A new scenario for cases with large distances Δs between the secondary X-point and the primary separatrix is presented. In the numerical simulations, as Δs is increased the current evolution through short connection length flux tubes changes significantly. Ultimately, a final state with large stripe structures is found that results in footprints on the vessel wall which are similar to those found when Δs is small (Wingen et al 2010 Phys. Rev. Lett. 104 175001).