H. Maaßberg

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...

Benchmarking of the mono-energetic transport coefficients—results from the International Collaboration on Neoclassical Transport in Stellarators (ICNTS)

Numerical results for the three mono-energetic transport coefficients required for a complete neoclassical description of stellarator plasmas have been benchmarked within an international collaboration. These transport coefficients are flux-surface-averaged moments of solutions to the linearized drift kinetic equation which have been determined using field-line-integration techniques, Monte Carlo simulations, a variational method employing Fourier–Legendre test functions and a finite-difference scheme. The benchmarking has been successfully carried out for past, present and future devices which represent different optimization strategies within the extensive configuration space available to stellarators. A qualitative comparison of the results with theoretical expectations for simple model fields is provided. The behaviour of the results for the mono-energetic radial and parallel transport coefficients can be largely understood from such theoretical considerations but the mono-energetic bootstrap current coefficient exhibits characteristics which have not been predicted.

Neoclassical transport simulations for stellarators

The benchmarking of the thermal neoclassical transport coefficients is described using examples of the Large Helical Device (LHD) and TJ-II stellarators. The thermal coefficients are evaluated by energy convolution of the monoenergetic coefficients obtained by direct interpolation or neural network techniques from the databases precalculated by different codes. The temperature profiles are calculated by a predictive transport code from the energy balance equations with the ambipolar radial electric field estimated from a diffusion equation to guarantee a unique and smooth solution, although several solutions of the ambipolarity condition may exist when root-finding is invoked; the density profiles are fixed. The thermal transport coefficients as well as the ambipolar radial electric field are compared and very reasonable agreement is found for both configurations. Together with an additional W7-X case, these configurations represent very different degrees of neoclassical confinement at low collisionalities. The impact of the neoclassical optimization on the energy confinement time is evaluated and the confinement times for different devices predicted by transport modeling are compared with the standard scaling for stellarators. Finally, all configurations are scaled to the same volume for a direct comparison of the volume-averaged pressure and the neoclassical degree of optimization.

Momentum correction techniques for neoclassical transport in stellarators

In the traditional neoclassical ordering for stellarators, monoenergetic transport coefficients are evaluated using the simplified Lorentz form of the pitch-angle collision operator which violates momentum conservation. In this paper, the parallel momentum balance with radial parallel momentum transport and viscosity terms is analyzed, in particular, with respect to the radial electric field. Next, the impact of momentum conservation in the stellarator long-mean-free-path regime is estimated for the radial transport and the parallel electric conductivity. Two different momentum correction techniques are described based on monoenergetic transport coefficients calculated by the DKES code [W. I. van Rij and S. P. Hirshman, Phys. Fluids B 1, 563 (1989)]. The benchmarking of the parallel electric conductivity and of the bootstrap current is presented for a tokamak as well as for two W7-X stellarator configurations [G. Grieger et al., Phys. Fluids B 4, 2081 (1992)]. Finally, the impact of the momentum correctio...

Performance and properties of the first plasmas of Wendelstein 7-X

The optimized, superconducting stellarator Wendelstein 7-X went into operation and delivered first measurement data after 15 years of construction and one year commissioning. Errors in the magnet assembly were confirmend to be small. Plasma operation was started with 5 MW electron cyclotron resonance heating (ECRH) power and five inboard limiters. Core plasma values of keV, keV at line-integrated densities were achieved, exceeding the original expectations by about a factor of two. Indications for a core-electron-root were found. The energy confinement times are in line with the international stellarator scaling, despite unfavourable wall conditions, i.e. large areas of metal surfaces and particle sources from the limiter close to the plasma volume. Well controlled shorter hydrogen discharges at higher power (4 MW ECRH power for 1 s) and longer discharges at lower power (0.7 MW ECRH power for 6 s) could be routinely established after proper wall conditioning. The fairly large set of diagnostic systems running in the end of the 10 weeks operation campaign provided first insights into expected and unexpected physics of optimized stellarators.

Physical model assessment of the energy confinement time scaling in stellarators

The International Stellarator Confinement Database (ISCDB) is a joint effort of the helical device community. It is publicly available at http://www.ipp.mpg.de/ISS and http://iscdb.nifs.ac.jp. The validity of physics models is investigated employing ISCDB data. Bayesian model comparison shows differences in the confinement scaling of data subgroups. Theory-based assessment of pure neoclassical transport regimes, however, indicates scalability which is supported by experimental results in specific W7-AS scenarios. Therefore, neoclassical simulations are employed for predictive purposes in W7-X, accounting for effects due to power deposition, plasma profiles and the ambipolar radial electric field. Neoclassical case studies for W7-X are presented as examples for the neoclassical predictions to be considered as an upper limit of plasma performance.

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.

Aspects of steady-state operation of the Wendelstein 7-X stellarator

The objective of Wendelstein 7-X is to demonstrate steady-state operation at β -values of up to 5%, at ion temperatures of several keV and plasma densities of up to 2 × 1020 m−3. The second operational phase foresees a fully steady-state high heat flux (HHF) divertor. Preparations are underway to cope with residual bootstrap currents, either by electron cyclotron current drive or by HHF protection elements. The main steady-state heating system is an electron cyclotron resonance heating facility. Various technical improvements of the gyrotrons have been implemented recently. They enable a reliable operation at the 1 MW power level. Some of the technical issues preparing plasma diagnostics for steady-state operation are exemplified. This includes the protection against non-absorbed microwave radiation.

On the bootstrap current in stellarators and tokamaks

The expression for the long-mean-free-path limit of the bootstrap current in stellarators is rederived in such a way that the expansion procedure is identical to that used in the corresponding calculation for a tokamak. In addition, the first correction due to finite collisionality is calculated and shown to vanish in quasi-isodynamic configurations without net current. This correction, which is proportional to the square root of the collisionality, is found to compare well with a numerical solution of the first-order drift kinetic equation in spherical tokamak geometry. Numerically, it appears that there is a similar correction in general stellarator geometry, which however depends on the strength of the radial electric field.

Electron cyclotron current drive in low collisionality limit: On parallel momentum conservation

A comprehensive treatment of the models used in ray- and beam-tracing codes to calculate the electron cyclotron current drive (ECCD) by means of the adjoint technique, based on the adjoint properties of the collision and Vlasov operators appearing in the drift-kinetic equation, is presented. Particular attention is focused on carefully solving the adjoint drift-kinetic equation (generalized Spitzer problem) with parallel momentum conservation in the like-particle collisions. The formulation of the problem is valid for an arbitrary magnetic configuration. Only the limit of low collisionality is considered here, which is of relevance for high-temperature plasmas. It is shown that the accurate solution of the adjoint drift-kinetic equation with parallel momentum conservation significantly differs (apart from the suprathermal electron portion) from that calculated in the high-speed-limit, which is most commonly used in the literature. For high-temperature plasmas with significant relativistic effects, the accuracy of the resulting numerical models is demonstrated by ray-tracing calculations and benchmark results are presented. It is found that the ECCD efficiency calculated for ITER with parallel momentum conservation significantly exceeds the predictions obtained with the high-speed-limit model.