The neoclassical confinement and the bootstrap current are analysed in the configuration space of W7-X by self-consistent neoclassical transport simulations. Since the establishment of ...quasi-stationary operation is the most important goal for W7-X, the analysis concentrates on high-performance discharge scenarios in magnetic configurations which are adjusted so that bootstrap current vanishes, or, alternatively, on scenarios where the bootstrap current can be balanced by strong ECCD. Both scenarios lead to restrictions either in the configuration space or in plasma parameters and ECRH heating scenarios. Furthermore, the flexibility of the magnetic configuration space of W7-X is briefly described with emphasis on other physics topics of interest, for example, ballooning unstable configurations as well as configurations with a magnetic hill which might lead to interchange instability.
A significant improvement of plasma parameters in the optimized stellarator W7-X is found after injections of frozen hydrogen pellets. The ion temperature in the post-pellet phase exceeds 3 keV with ...5 MW of electron heating and the global energy confinement time surpasses the empirical ISS04-scaling. The plasma parameters realized in such experiments are significantly above those in comparable gas-fuelled discharges. In this paper, we present details of these pellet experiments and discuss the main plasma properties during the enhanced confinement phases. Local power balance is applied to show that the heat transport in post-pellet phases is close to the neoclassical level for the ion channel and is about a factor of two above that level for the combined losses. In comparable gas-fuelled discharges, the heat transport is by about ten times larger than the neoclassical level, and thus is largely anomalous. It is further observed that the improvement in the transport is related to the peaked density profiles that lead to a stabilization of the ion-scale turbulence.
The achievable efficiency for external current drive through electron-cyclotron waves in a demonstration tokamak reactor is investigated. Two possible reactor designs, one for steady state and one ...for pulsed operation, are considered. Beam propagation, absorption and current drive are modelled employing the beam-tracing technique and including momentum conservation in electron-electron collisions. It is found that for midplane injection the achievable current drive efficiency is limited by second-harmonic absorption at levels consistent with previous studies. Higher efficiencies can be achieved by injecting the beams from the top of the machine, exploiting wave absorption by more energetic (less collisional) electrons. Current drive efficiencies competitive with those usually obtained by neutral beam current drive are reported. These optimum efficiencies are found for frequencies around 230 GHz and 290 GHz for the steady-state and the pulsed DEMO, supposed to operate at a magnetic field B = 5.84 T and B = 7.45 T, respectively.
For strong central heating the interdependency of the particle and energy balances is invoked to show that the particle source required for steady-state conditions is related to the power deposition ...through the ratio of particle to energy fluxes. Consequences of this relationship for high-performance plasmas in the Wendelstein 7-X (W7-X) stellarator are investigated for long-pulse scenarios in which only electron cyclotron resonance heating is employed. If neoclassical transport is predominant in the core region, as is demonstrated to have been the case for comparable plasmas in the previous experiment, Wendelstein 7-AS, then hollow density profiles are shown to be inevitable in W7-X given the expected recycling properties of the device and the refueling capabilities of the present pellet-injection system.
The radial neoclassical fluxes of electrons in the 1/ν-regime are calculated with relativistic effects taken into account and compared with those in the non-relativistic approach. The treatment is ...based on the relativistic drift-kinetic equation with the thermodynamic equilibrium given by the relativistic Maxwell-Jüttner distribution function. It is found that for the range of fusion temperatures, Te < 100 keV, the relativistic effects produce a reduction of the radial fluxes which does not exceed 10%. This rather small effect is a consequence of the non-monotonic temperature dependence of the relativistic correction caused by two counteracting factors: a reduction of the contribution from the bulk and a significant broadening with the temperature growth of the energy range of electrons contributing to transport. The relativistic formulation for the radial fluxes given in this paper is expressed in terms of a set of relativistic thermodynamic forces which is not identical to the canonical set since it contains an additional relativistic correction term dependent on the temperature. At the same time, this formulation allows application of the non-relativistic solvers currently used for calculation of mono-energetic transport coefficients.
Fluctuations of electron cyclotron emission (ECE) signals are analyzed for differently heated Wendelstein 7-X plasmas. The fluctuations appear to travel predominantly on flux surfaces and are used as ...'tracers' in multivariate time series. Different statistical techniques are assessed to reveal the coupling and information entropy-based coupling analysis are conducted. All these techniques provide evidence that the fluctuation analysis allows one to check the consistency of magneto-hydrodynamic (MHD) equilibrium calculations. Expanding the suite of techniques applied in fusion data analysis, partial mutual information (PMI) analysis is introduced. PMI generalizes traditional partial correlation (Frenzel and Pompe Phys. Rev. Lett. 99 204101) and also Schreiber's transfer entropy (Schreiber 2000 Phys. Rev. Lett. 85 461). The main additional capability of PMI is to allow one to discount for specific spurious data. Since PMI analysis allows one to study the effect of common drivers, the influence of the electron cyclotron resonance heating on the mutual dependencies of simultaneous ECE measurements was assessed. Additionally, MHD mode activity was found to be coupled in a limited volume in the plasma core for different plasmas. The study reveals an experimental test for equilibrium calculations and ECE radiation transport.
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.
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BFBNIB, GIS, IJS, KISLJ, NUK, PNG, UL, UM, UPUK
A brief review of the theory contributions presented in the EC-18 Workshop is given. The covered spectrum of topics is quite broad including the electron cyclotron wave propagation physics as well ...the results of numerical modelling of transport and current drive.
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IZUM, KILJ, NUK, PILJ, PNG, SAZU, UL, UM, UPUK
To increase flexibility in ECRH experiments on the helically symmetric experiment (HSX), a second gyrotron and transmission line have been installed. The second antenna includes a steerable mirror ...for off-axis heating, and the launched power may be modulated for use in heat pulse propagation experiments. The extraordinary wave at the second harmonic of the electron gyrofrequency or the ordinary wave at the fundamental resonance are used for plasma start-up and heating on HSX. The tracing visualized ray tracing code (Marushchenko et al 2007 Plasma Fusion Res. 2 S1129) is used to estimate single-pass absorption and to model multi-pass wave damping in the three-dimensional HSX geometry. The single-pass absorption of the ordinary wave at the fundamental resonance is calculated to be as high as 30%, while measurements of the total absorption indicate that 45% of the launched power is absorbed. A multi-pass ray tracing model correctly predicts the experimental absorption and indicates that the launched power is absorbed within the plasma core ().
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