D. Reiser

The European turbulence code benchmarking effort: turbulence driven by thermal gradients in magnetically confined plasmas

A cross-comparison and verification of state-of-the-art European codes describing gradient-driven plasma turbulence in the core and edge regions of tokamaks, carried out within the EFDA Task Force on Integrated Tokamak Modelling, is presented. In the case of core ion temperature gradient (ITG) driven turbulence with adiabatic electrons (neglecting trapped particles), good/reasonable agreement is found between various gyrokinetic/gyrofluid codes. The main physical reasons for some deviations observed in nonlocal simulations are discussed. The edge simulations agree very well on collisionality scaling and acceptably well on beta scaling (below the MHD boundary) for cold-ion cases, also in terms of the non-linear mode structure.

Localized recycling as a trigger of MARFE

An analytical model taking into account the plasma cooling due to localized hydrogen recycling is proposed to interpret the conditions of the MARFE onset above a critical plasma density in TEXTOR-94. Results of numerical modeling confirm that under conditions of a good plasma contact with the inner wall this mechanism of the MARFE triggering is more important than the usually considered cooling instability on impurity radiation.

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.

Improved kinetic test particle model for impurity transport in tokamaks

The expression for the Coulomb collision term in Fokker-Planck form is revised and generalized to the case of interaction of trace impurity ions with a fluid-like background plasma. The velocity distribution of the background ions is assumed as a Maxwellian in the 13 moment expansion, with parameters determined from a fluid consideration. The impurities are described in the framework of a linear drift kinetic test particle model. The new Coulomb term is suitable for linear Monte Carlo procedures and provides both a correct treatment of thermalization of the test particles and an accurate kinetic description of velocity distribution effects on the thermal and frictional forces. These features are missed out in existing codes for kinetic modelling of impurity transport, based on a reduced Coulomb term with these forces treated in the fluid approximation. Numerical results presented for TEXTOR specific edge plasma conditions emphasize the importance of the proposed more accurate treatment, in particular by consideration of the influence of thermal forces on low ionized impurities.

Observation of geodesic acoustic modes (GAMs) and their radial propagation at the edge of the TEXTOR tokamak

The electrostatic potential and density fluctuations have been measured at the edge of the TEXTOR tokamak by two toroidally distant Langmuir probe arrays. The geodesic acoustic mode (GAM) zonal flows (ZFs) are observed in potential fluctuations with a toroidal and poloidal symmetric structure. The GAM frequency, fGAM, changes monotonically with the local temperature and is close to the frequency-dispersion predicted by theories. Bispectral analysis shows clear nonlinear coupling between the GAM and broadband ambient turbulence. The GAM packet has a narrow radial extent with kr 0.5–0.7 cm−1 and exhibits explicitly a radially outward propagation. Furthermore, the radial correlation structure of GAMs and their radial propagation have been investigated in a wide range of parameters by varying plasma density and edge safety factor (5.0 ≤ q(a) ≤ 5.9). It is found that the magnitude of the GAM correlations reduces remarkably with the increase in the plasma density approaching the density limit, while the radial wavelength of GAMs only decreases slightly in higher density and larger q(a) discharges. With increasing plasma density, the radial propagating phase speed of GAMs is strongly reduced along with the drop in the local temperature. The results provide new evidence on the propagation properties of GAM ZFs.

Edge turbulence during the static dynamic ergodic divertor experiments in TEXTOR

The influence of the magnetic ergodization on edge turbulence and turbulence-induced transport has been investigated by Langmuir probes in TEXTOR under three different static DED configurations. Common features are observed. With DED, the edge equilibrium profiles are altered and the resultant positive Er is in agreement with modelling. In the ergodic zone, the potential fluctuations are strongly reduced and the local turbulent flux changes direction from radially outwards to inwards. In the same zone, the turbulence properties are profoundly modified by energy redistribution in frequency spectra, suppression of large-scale structures and reduction of the radial and poloidal correlation lengths for all frequencies. Meanwhile, the fluctuation poloidal phase velocity changes sign from the electron to ion diamagnetic drift, consistent with the change of the Er × B flow, whereas the slight radially outward propagation of fluctuations is hindered by the DED. In the laminar region, the turbulence correlation is found to react to the observed reduced flow shear. Before the DED the Reynolds stress displays a radial gradient at the plasma edge while during DED the profile is suppressed, suggesting a rearrangement by the DED on the flow momentum profile.

Impact of rotating resonant magnetic perturbation fields on plasma edge electron density and temperature

Rotating resonant magnetic perturbation (RMP) fields impose a characteristic modulation to the edge electron density ne(r, t) and temperature Te(r, t) fields, which depends on the relative rotation frel between external RMP field and plasma fluid. The ne(r, t) and Te(r, t) fields measured in the edge (r/a = 0.9–1.05) of TEXTOR L-mode plasmas are in close correlation with the local magnetic vacuum topology for low relative rotation frel = −0.2 kHz. In comparison with the 3D neutral and plasma transport code EMC3-Eirene, this provides substantial experimental evidence that for low relative rotation level and high resonant field amplitudes (normalized radial field strength ), a stochastic edge with a remnant island chain dominated by diffusive transport exists. Radially outside a helical scrape-off layer, the so-called laminar zone embedded into a stochastic domain is found to exist. In contrast for high relative rotation of frel = 1.8 kHz, the measured modulation of ne is shifted by π/2 toroidally with respect to the modelled vacuum topology. A pronounced flattening in Te(r) and a reduction in ne(r) is measured at the resonant flux surface and represents a clear signature for a magnetic island, which is phase shifted with respect to the vacuum island position. A correlated shift of the laminar zone radially outwards at the very plasma edge is observed suggesting that the actual near-field structure at the perturbation source is determined by the plasma response as well.

Three-dimensional modeling of plasma edge transport and divertor fluxes during application of resonant magnetic perturbations on ITER

Results from three-dimensional modeling of plasma edge transport and plasma–wall interactions during application of resonant magnetic perturbation (RMP) fields for control of edge-localized modes in the ITER standard 15 MA Q = 10 H-mode are presented. The full 3D plasma fluid and kinetic neutral transport code EMC3-EIRENE is used for the modeling. Four characteristic perturbed magnetic topologies are considered and discussed with reference to the axisymmetric case without RMP fields. Two perturbation field amplitudes at full and half of the ITER ELM control coil current capability using the vacuum approximation are compared to a case including a strongly screening plasma response. In addition, a vacuum field case at high q 95 = 4.2 featuring increased magnetic shear has been modeled. Formation of a three-dimensional plasma boundary is seen for all four perturbed magnetic topologies. The resonant field amplitudes and the effective radial magnetic field at the separatrix define the shape and extension of the 3D plasma boundary. Opening of the magnetic field lines from inside the separatrix establishes scrape-off layer-like channels of direct parallel particle and heat flux towards the divertor yielding a reduction of the main plasma thermal and particle confinement. This impact on confinement is most accentuated at full RMP current and is strongly reduced when screened RMP fields are considered, as well as for the reduced coil current cases. The divertor fluxes are redirected into a three-dimensional pattern of helical magnetic footprints on the divertor target tiles. At maximum perturbation strength, these fingers stretch out as far as 60 cm across the divertor targets, yielding heat flux spreading and the reduction of peak heat fluxes by 30%. However, at the same time substantial and highly localized heat fluxes reach divertor areas well outside of the axisymmetric heat flux decay profile. Reduced RMP amplitudes due to screening or reduced RMP coil current yield a reduction of the width of the divertor flux spreading to about 20–25 cm and cause increased peak heat fluxes back to values similar to those in the axisymmetric case. The dependencies of these features on the divertor recycling regime and the perpendicular transport assumptions, as well as toroidal averaged effects mimicking rotation of the RMP field, are discussed in the paper.

Modelling of the penetration process of externally applied helical magnetic perturbation of the DED on the TEXTOR tokamak

The error-field penetration process of the dynamic ergodic divertor (DED) on the TEXTOR tokamak has been investigated analytically in terms of a single fluid MHD model with a finite plasma resistivity and viscosity in a cylindrical geometry. The linear model produces a localization of the induced current at the resonance surface and predicts a vortex structure of the velocity field near the resonance layer. Moreover, effects of the Alfven resonance for the error-field penetration are identified by two peaks in the radial profiles of the perturbed toroidal current and the perturbed magnetic flux when the relative rotation velocity between the DED and the rotating tokamak plasma is set to large. Fine structures of the vorticity induced by the DED in the vicinity of the rational surface disappear by introducing a finite plasma perpendicular viscosity. In addition, it is shown that the two peaks of the perturbed toroidal current overlap by an anomalous plasma perpendicular viscosity. Likewise, a bifurcation of the penetration process from the suppressed to the excited state is obtained by a quasi-linear approach taking into account modifications of the radial profiles of the equilibrium current and the plasma rotation due to the DED. A comparison with real experimental results of the DED on the TEXTOR tokamak is shown.