N. B. Marushchenko

Electron Cyclotron Heating for W7-X: Physics and Technology

The Wendelstein 7X (W7-X) stellarator (R = 5.5 m, a = 0.55 m, B < 3.0 T), which at present is being built at Max-Planck-Institut für Plasmaphysik, Greifswald, aims at demonstrating the inherent steady-state capability of stellarators at reactor-relevant plasma parameters. A 10-MW electron cyclotron resonance heating (ECRH) plant with continuous-wave (cw) capability is under construction to meet the scientific objectives. The physics background of the different heating and current drive scenarios is presented. The expected plasma parameters are calculated for different transport assumptions. A newly developed ray-tracing code is used to calculate selected reference scenarios and optimize the electron cyclotron launcher and in-vessel structure. Examples are discussed, and the technological solutions for optimum wave coupling are presented. The ECRH plant consists of ten radio-frequency (rf) modules with 1 MW of power each at 140 GHz. The rf beams are transmitted to the W7-X torus (typically 60 m) via two open multibeam mirror lines with a power-handling capability, which would already satisfy the ITER requirements (24 MW). Integrated full-power, cw tests of two rf modules (gyrotrons and the related transmission line sections) are reported, and the key features of the gyrotron and transmission line technology are presented. As the physics and technology of ECRH for both W7-X and ITER have many similarities, test results from the W7-X ECRH may provide valuable input for the ITER-ECRH plant.

The neoclassical “Electron Root” feature in the Wendelstein-7-AS stellarator

The neoclassical prediction of the “electron root,” i.e., a strongly positive radial electric field, Er (being the solution of the ambipolarity condition of the particle fluxes), is analyzed for low-density discharges in Wendelstein-7-AS [G. Grieger, W. Lotz, P. Merkel, et al., Phys. Fluids B 4, 2081 (1992)]. In these electron cyclotron resonance heated (ECRH) discharges with highly localized central power deposition, peaked Te profiles [with Te(0) up to 6 keV and with Ti≪Te] and strongly positive Er in the central region are measured. It is shown that this “electron root” feature at W7-AS is driven by ripple-trapped suprathermal electrons generated by the ECRH. The fraction of ripple-trapped particles in the ECRH launching plane, which can be varied at W7-AS, is found to be the most important. After switching off the heating the “electron root” feature disappears nearly immediately, i.e., two different time scales for the electron temperature decay in the central region are observed. Monte Carlo simulati...

Current Control by ECCD for W7-X

Abstract The magnetic configuration of the Wendelstein 7-X (W7-X) stellarator is optimized following a set of criteria including a rotational transform profile with low shear and minimized bootstrap current that must be controlled for proper functioning of the island divertor. This paper studies the compensation of residual bootstrap current by using electron cyclotron current drive (ECCD). The modeling shows that the loop voltage induced by ECCD leads to a redistribution of the current density with a diffusion time of ~2 s. The relaxation time of the total current is much longer, however - for W7-X plasma parameters the total toroidal current reaches steady state after several L/R times requiring hundreds of seconds. In order to keep the toroidal current and its profile in the acceptable range, a feed-forward or predictive control method using ECCD as actuator is proposed. The main steps are as follows: (a) calculate the bootstrap current distribution using plasma parameters measured in the online transport analysis and (b) determine and apply ECCD as needed. For the current control to work properly and to avoid long relaxation times, the reaction time of the control loop must be less than the current skin time.

On the heating mix of ITER

This paper considers the heating mix of ITER for the two main scenarios. Presently, 73 MW of absorbed power are foreseen in the mix 20/33/20 for ECH, NBI and ICH. Given a sufficient edge stability, Q = 10-the goal of scenario 2-can be reached with 40MW power irrespective of the heating method but depends sensitively inter alia on the H-mode pedestal temperature, the density profile shape and on the characteristics of impurity transport. ICH preferentially heats the ions and would contribute specifically with Delta Q 0.5, and strong off-axis current drive (CD). The findings presented here are based on revised CD efficiencies gamma for ECCD and a detailed benchmark of several CD codes. With ECCD alone, the goals of scenario 4 can hardly be reached. Efficient off-axis CD is only possible with NBI. With beams, inductive discharges with f(ni) > 0.8 can be maintained for 3000 s. The conclusion of this study is that the present heating mix of ITER is appropriate. It provides the necessary actuators to induce in a flexible way the best possible scenarios. The development risks of NBI at 1 MeV can be reduced by operation at 0.85 MeV.

The European Integrated Tokamak Modelling (ITM) effort: achievements and first physics results

A selection of achievements and first physics results are presented of the European Integrated Tokamak Modelling Task Force (EFDA ITM-TF) simulation framework, which aims to provide a standardized platform and an integrated modelling suite of validated numerical codes for the simulation and prediction of a complete plasma discharge of an arbitrary tokamak. The framework developed by the ITM-TF, based on a generic data structure including both simulated and experimental data, allows for the development of sophisticated integrated simulations (workflows) for physics application.The equilibrium reconstruction and linear magnetohydrodynamic (MHD) stability simulation chain was applied, in particular, to the analysis of the edgeMHDstability of ASDEX Upgrade type-I ELMy H-mode discharges and ITER hybrid scenario, demonstrating the stabilizing effect of an increased Shafranov shift on edge modes. Interpretive simulations of a JET hybrid discharge were performed with two electromagnetic turbulence codes within ITM infrastructure showing the signature of trapped-electron assisted ITG turbulence. A successful benchmark among five EC beam/ray-tracing codes was performed in the ITM framework for an ITER inductive scenario for different launching conditions from the equatorial and upper launcher, showing good agreement of the computed absorbed power and driven current. Selected achievements and scientific workflow applications targeting key modelling topics and physics problems are also presented, showing the current status of the ITM-TF modelling suite.

Kinetic modelling of the ECRH power deposition in W7-AS

Kinetic effects are important in low-density high-power ECRH discharges, and the electron distribution function can significantly deviate from Maxwellian. The ECRH power deposition is analysed for perpendicular on-axis heating in W7-AS, with different magnetic configurations characterized by either a minimum or a maximum of B on the plasma axis in the RF injection plane. The different heating scenarios are modelled by means of a new bounce- averaged Fokker-Planck code, well suited for the magnetic field geometry close to the plasma axis of W7-AS. The power deposition profile is estimated from the analysis of heat wave propagation stimulated by ECRH power modulation. In general, peaked deposition profiles as predicted from a ray-tracing code are obtained, but with an additional much broader contribution. The broadening of the thermal power deposition profile is assumed to be related to the radial transport by the rB drift of locally trapped suprathermal electrons. This is simulated by means of a simple convective Fokker-Planck model. The theoretical predictions are shown to be consistent with the experimental findings. Kinetic effects on the determination of the temperature both by Thomson scattering and by ECE diagnostics are briefly discussed.

Electron cyclotron current drive calculated for ITER conditions using different models

The current drive efficiency for the ITER reference scenario 2 has been calculated by the newly developed ray-tracing code TRAVIS for both the upper and the equatorial launchers. For comparison, two adjoint approach models are applied, the high-speed-limit model and a model with the parallel momentum conservation taken into account. It is shown that in the angle range expected as optimal launch angles the momentum conservation correction produces a non-negligible contribution in ECCD, leading to the necessity to revise the previous predictions carefully. Additionally, the scenario with reduced magnetic field is checked. It is shown that the ECCD efficiency (as well as the deposition profile) for the equatorial launcher may be significantly changed due to unwanted absorption at the higher (parasitic) harmonics.

Ray-tracing code TRAVIS for ECR heating, EC current drive and ECE diagnostic

A description of the recently developed ray-tracing code TRAVIS is given together with the theoretical background, results of benchmarking and examples of application. The code is written for electron cyclotron studies with emphasis on heating, current drive and ECE diagnostic. The code works with an arbitrary 3D magnetic equilibrium being applicable for both stellarators and tokamaks. The equations for ray tracing are taken in the weakly relativistic approach, i.e. with thermal eects taken into account, while the absorption, current drive and emissivity are calculated in the fully relativistic approach. For the calculation of ECCD, an adjoint technique with parallel momentum conservation is applied. The code is controlled through a specially designed graphical user interface, which allows the preparation of the input parameters and viewing the results in convenient (2D and 3D) form.

Current Drive Calculations with an Advanced Adjoint Approach

Abstract The advanced adjoint approach for arbitrary collisionalities with momentum conservation in the like-particle collision is considered. The results are generally applicable for the parallel conductivity as well as for current drive calculations. In addition, the weakly relativistic extension of the variational principle for the Spitzer function with momentum conservation in the electron-electron collision is described. The models developed are well suited to ray-tracing calculations.

20 years of ECRH at W7-A and W7-AS

Basic research on high-power ECRH started 20 years ago at IPP using 28 GHz pulses with 200 kW for 40 ms at the W7-A stellarator. These pilot experiments triggered a strong activity of exploration of the unique capabilities of localized heating and current drive. The achievements in physics were strongly linked with progress in source and transmission line technology. The capability and versatility of ECRH are reviewed using W7-A and W7-AS as example experiments; the latter was shut down on July 31, 2002. The milestone achievements are discussed. Standard heating scenarios such as O-mode and X-mode as well as advanced scenarios like mode-conversion heating via the O–X–B process at different harmonics were investigated and selected results are presented. First experiments with current drive by Bernstein-waves are reported. The physics of wave interaction with stellarator-specific trapped particle populations is discussed. The results from W7-A and W7-AS establish the experimental and technological bases for the 10 MW, CW ECRH system at W7-X, which aims to demonstrate the inherent steady-state capability of stellarators.