S.S. Abdullaev

Identification and analysis of transport domains in the stochastic boundary of TEXTOR-DED for different mode spectra

At the TEXTOR tokamak an external resonant magnetic perturbation is applied with the dynamic ergodic divertor to control the edge transport properties. The approaches to analyse the impact of such a kind of edge stochastization on transport apply mostly a shell-like picture which includes a dependence of transport from magnetic field topology in the radial direction only. In this paper multiple experimental evidence is presented in contrast to these approaches the perturbation applied forms a poloidally heterogenous edge layer in which the transport characteristics are determined by the poloidally alternating field line behaviour. A thorough analysis of density and temperature profiles and their gradients for base mode spectra with poloidal/toroidal mode numbers of m/n = 12/4 and m/n = 6/2 is worked out in comparison with the modelled magnetic field topology and results from three dimensional transport modelling with EMC3/EIRENE. Hereby two poloidally adjacent transport domains are identified for the first time in such detail. A domain representing a helical scrape off layer is formed by field lines with short connection and therefore prevailing parallel transport to the wall elements. Here, the field lines are clustered into extended flux tubes embedded into a long connection length ergodic domain with diffusive transport characteristics and enhanced radial transport.

Modelling of the magnetic field structures and first measurements of heat fluxes for TEXTOR-DED operation

The dynamic ergodic divertor (DED) was recently installed at the TEXTOR tokamak. One of the aims of the DED is to control and study heat and particle deposition on a plasma wall via modification of the plasma edge by external perturbation coils. Sixteen perturbation coils are mounted on the high-field side of the torus. The external magnetic perturbation creates a zone of chaotic field lines at the plasma edge by destroying several resonant surfaces. These structures have the properties of an open chaotic system while the field lines intersect the tokamak vessel. In order to study the topology of the field lines in different regimes, a set of tools called Atlas was created. Atlas uses a symplectic mapping technique to trace the magnetic field lines. The thermographic set-up is used to measure characteristic temperature patterns on the divertor target plates. The first measurements show the relation of the observed patterns with the results from the modelling with the Atlas codes.

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.

Influence of the dynamic ergodic divertor on transport properties in TEXTOR

Experiments to investigate transport properties under the influence of the dynamic ergodic divertor (DED) on TEXTOR are discussed. Relativistic runaway electrons are applied for studying transport properties of ergodization such as enhanced runaway loss. The ergodization causes an enhanced loss rate; this loss is higher for low relativistic electrons than for highly relativistic ones, in good agreement with particle orbit mapping. Edge transport can be controlled by the DED perturbation: in limiter H-mode plasmas ELM-like particle and heat bursts associated with the formation of enhanced edge pressure gradients are mitigated in the 6/2 configuration on the expense of a reduced pedestal height. Finally, the plasma is driven back to L-mode under the influence of the magnetic perturbation. In the 3/1 configuration the onset of tearing modes limits the possibility to affect edge transport. A mode of spontaneous density built-up has been found for the TEXTOR-DED as well. This mode is in particular strong for an inward shifted plasma; the built-up has a resonant character with respect to q(a). Langmuir probe measurements with two probe arrays show a strong influence of the magnetic ergodization on both the edge plasma equilibrium and fluctuation parameters. In particular, in the ergodic zone the turbulence properties and turbulence-driven flux are profoundly modified.

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 .

Transport and divertor properties of the dynamic ergodic divertor

The concept of the dynamic ergodic divertor (DED) is based on plasma edge ergodization by a resonant perturbation. Such a divertor concept is closely related to helical or island divertors in stellerators. The base mode of the DED perturbation field can be m/n = 12/4, 6/2 or 3/1. The 3/1 base mode with its deep penetration of the perturbation field provides the excitation of tearing modes. This topic was presented elsewhere. In this contribution we concentrate on the divertor properties of the DED. We report on the characterization of the topology, transport properties in ergodic fields, impurity transport and density limit behaviour.The 12/4 base where the perturbation is restricted to the plasma edge is suitable for divertor operation. With increasing perturbation field island chains are built up at the resonance layers. Overlapping islands lead to ergodization. The plasma is guided in the laminar region via open field lines of short connection length to the divertor target. The magnetic topology is not only controlled by the coil current but especially by the edge safety factor. For appropriate edge safety factor we observe a strong temperature drop in the plasma edge, indicating an expansion of the laminar region, which is necessary to decouple the divertor plasma from the core plasma. The modifications of the magnetic topology can be directly seen, for example, from carbon emission lines. The magnetic structure is calculated by the ATLAS code and shows good agreement with the experimental findings.

Mappings of stochastic field lines in poloidal divertor tokamaks

Two mapping methods to study magnetic field lines near the separatrix of poloidal divertor tokamaks in the presence of external non-axisymmetric magnetic perturbations are proposed. The first mapping method is based on the Hamiltonian formulation of field line equations in the Boozer coordinates and solving it by the canonical transformation of variables (Abdullaev et al 1999 Phys. Plasmas 6 153). The second mapping is a canonical mapping near the separatrix which is constructed using the recently developed method (Abdullaev 2004 Phys. Rev. E 70 064202, Abdullaev 2005 Phys. Rev. E 72 064202). We construct the corresponding mappings for magnetic field lines in divertor tokamaks in the presence of non-axisymmetric magnetic perturbations. The mappings are applied to study the properties of open stochastic field lines near the separatrix for the wire model of the plasma. Poincare sections, the so-called laminar and magnetic footprint plot (a contour plot of wall to wall connections lengths) in the plasma region and on the divertor plates are obtained. The quasilinear diffusion coefficients of field lines are also estimated.

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.

Rotation dependence of a phase delay between plasma edge electron density and temperature fields due to a fast rotating, resonant magnetic perturbation field

Measurements of the plasma edge electron density ne and temperature Te fields during application of a fast rotating, resonant magnetic perturbation (RMP) field show a characteristic modulation of both, ne and Te coherent to the rotation frequency of the RMP field. A phase delay Φ between the ne(t) and Te(t) waveforms is observed and it is demonstrated that this phase delay Φ is a function of the radius with Φ(r) depending on the relative rotation of the RMP field and the toroidal plasma rotation. This provides for the first time direct experimental evidence for a rotation dependent damping of the external RMP field in the edge layer of a resistive high-temperature plasma which breaks down at low rotation and high resonant field amplitudes.

The dynamic ergodic divertor in the TEXTOR tokamak: plasma response to dynamic helical magnetic field perturbations

Recently, the dynamic ergodic divertor (DED) of TEXTOR has been studied in an m/n = 3/1 set-up which is characterized by a relatively deep penetration of the perturbation field. The perturbation field creates (a) a helical divertor, (b) an ergodic pattern and/or (c) excitation of tearing modes, depending on whether the DED current is static, rotating in the co-current direction or in the counter-current direction. Characteristic divertor properties such as the high recycling regime or enhanced shielding have been studied. A strong effect of the ergodization is spin up of the plasma rotation, possibly due to the electric field at the plasma edge. Tearing modes are excited in a rather reproducible way and their excitation threshold value, their motion and their reduction due to the ECRH/ECCD have been studied. The different scenarios are characterized by strong modifications of the toroidal velocity profile and by a reduced or enhanced radial transport.