Wendelstein 7-AS was the first modular stellarator device to test some basic elements of stellarator optimization: a reduced Shafranov shift and improved stability properties resulted in β-values up to 3.4% (at 0.9 T). This operational limit was determined by power balance and impurity radiation without noticeable degradation of stability or a violent collapse. The partial reduction of neoclassical transport could be verified in agreement with calculations indicating the feasibility of the concept of drift optimization. A full neoclassical optimization, in particular a minimization of the bootstrap current was beyond the scope of this project. A variety of non-ohmic heating and current drive scenarios by ICRH, NBI and in particular, ECRH were tested and compared successfully with their theoretical predictions. Besides, new heating schemes of overdense plasmas were developed such as RF mode conversion heating—Ordinary mode, Extraordinary mode, Bernstein-wave (OXB) heating—or 2nd harmonic O-mode (O2) heating. The energy confinement was about a factor of 2 above ISS95 without degradation near operational boundaries. A number of improved confinement regimes such as core electron-root confinement with central Te ≤ 7 keV and regimes with strongly sheared radial electric field at the plasma edge resulting in Ti ≤ 1.7 keV were obtained. As the first non-tokamak device, W7-AS achieved the H-mode and moreover developed a high density H-mode regime (HDH) with strongly reduced impurity confinement that allowed quasi-steady-state operation (τ ≈ 65 · τE) at densities (at 2.5 T). The first island divertor was tested successfully and operated with stable partial detachment in agreement with numerical simulations. With these results W7-AS laid the physics background for operation of an optimized low-shear steady-state stellarator.

Major results from the stellarator Wendelstein 7-AS (Review Article)

The three-dimensional (3D) magnetohydrodynamic (MHD) equilibrium solver HINT is improved as a new HINT code, 'HINT2' having various useful features by introducing modern computing techniques. By using the algorithm inherent to HINT2, the treatment of the peripheral plasma corresponding to the experimental results is addressed in the Large Helical Device (LHD).

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Development and application of HINT2 to helical system plasmas

In the Large Helical Device (LHD), the highest operational averaged beta value has been expanded from 3.2% to 4% in the last 2 years by increasing the heating capability and exploring a new magnetic configuration with a high aspect ratio. Although the magneto-hydrodynamic (MHD) stability properties are considered to be unfavourable in the new high aspect configuration, the heating efficiency due to neutral beams and the transport properties are expected to be favourable in a high-beta range. In order to clarify the effect of the global ideal MHD unstable mode on the operational regimes in helical systems, especially the beta gradients in the peripheral region and the beta value, the MHD analysis and the transport analysis are performed in a high-beta range of up to 4% in LHD. In a high-beta range of more than 3%, the maxima of the observed thermal pressure gradients at a low order rational magnetic surface in the peripheral region are marginally unstable to the low-mode-number ideal MHD instability. Though a gradual degradation of the local transport in the region has been observed as beta increases, a disruptive degradation of the local transport does not appear in the beta range up to 4%.

https://iopscience.iop.org/article/10.1088/0029-5515/45/11/004/pdf

Effects of global MHD instability on operational high beta-regime in LHD

An energy principle is used to obtain the solution of the magnetohydrodynamic (MHD) equilibrium equation J×B−∇p=0 for nested magnetic flux surfaces that are expressed in the inverse coordinate representation x=x(ρ, θ, ζ). Here, θ are ζ are poloidal and toroidal flux coordinate angles, respectively, and p=p(ρ) labels a magnetic surface. Ordinary differential equations in ρ are obtained for the Fourier amplitudes (moments) in the doubly periodic spectral decomposition of x. A steepest‐descent iteration is developed for efficiently solving these nonlinear, coupled moment equations. The existence of a positive‐definite energy functional guarantees the monotonic convergence of this iteration toward an equilibrium solution (in the absence of magnetic island formation). A renormalization parameter λ is introduced to ensure the rapid convergence of the Fourier series for x, while simultaneously satisfying the MHD requirement that magnetic field lines are straight in flux coordinates. A descent iteration is also developed for determining the self‐consistent value for λ.

Steepest descent moment method for three-dimensional magnetohydrodynamic equilibria

The physical understanding of net-current free helical plasmas has progressed in the Large Helical Device (LHD) since the last Fusion Energy Conference in Geneva, 2008. The experimental results from LHD have promoted detailed physical documentation of features specific to net-current-free 3-D helical plasmas as well as complementary to the tokamak approach. The primary heating source is NBI with a heating power of 23 MW, and ECH with 3.7 MW plays an important role in local heating and power modulation in transport studies. The maximum central density has reached 1.2  10 21 m -3 due to the formation of an Internal Diffusion Barrier (IDB) at the magnetic field of 2.5 T. The IDB has been maintained for 3 s by refueling with repetitive pellet injection. The plasma with a central ion temperature reaching 5.6 keV exhibits the formation of an Internal Transport Barrier (ITB). The ion thermal diffusivity decreases to the level predicted by neoclassical transport. This ITB is accompanied by spontaneous toroidal rotation and an Impurity Hole which generates an impurity-free core. Impurity Hole is due to a large outward convection of impurities in spite of the negative radial electric field. The magnitude of the Impurity Hole is enhanced in the magnetic configuration with larger helical ripple and for higher Z impurities. Another mechanism to suppress impurity contamination has been identified at the plasma edge with a stochastic magnetic field. A helical system shares common physics issues with tokamaks such as 3-D equilibria, transport in a stochastic magnetic field, plasma response to a Resonant Magnetic Perturbation (RMP), divertor physics, and the role of radial electric field and meso-scale structure.

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Overview of results from the Large Helical Device

Recently, dramatic progress has been achieved in the study of helical systems with high-beta experiments. Discharges with more than 3% beta plasmas have been achieved in Large Helical Device (LHD) and Wendelstein 7-AS (W7-AS). Although magnetohydrodynamic (MHD) instabilities affect local pressure gradients, the global transport property does not seem to limit the achieved beta value in either device. We summarize the LHD high-beta properties in MHD stability, equilibrium, and transport, and we show the relationship between the experimentally achieved parameters and theoretical predictions. We contrast the LHD results with the W7-AS high-beta properties. In both devices, stationary discharges in the definitely MHD unstable region have not been observed. We mention the key issue for achievement of the beta values >5%.

Progress of High-Beta Experiments in Stellarator/Heliotron

Local Transport Property of Reactor-Relevant High-Beta Plasmas on LHD

We analyze the relationship between the experimentally observed pressure gradients at resonant rational surfaces and the theoretically predicted ideal magnetohydrodynamics (MHD) unstable region of global modes in the large helical device (LHD). According to the stability analysis of the ideal MHD modes with a low toroidal mode number, we find that the ideal MHD mode gives a constraint on the operational regime of the pressure gradients in the core. In the edge, a clear saturation of the pressure gradients due to the ideal MHD instability has not been observed up to the high beta regime around 3% as the volume-averaged toridal beta value, where global ideal MHD modes are predicted to be unstable.

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Kazumichi Narihara

Papers

Progress of High-Beta Experiments in Stellarator/Heliotron

Local Transport Property of Reactor-Relevant High-Beta Plasmas on LHD

Relationships between the Prediction of Linear MHD Stability Criteria and the Experiment in LHD

Configuration Dependence of Energetic Ion Driven Alfven Eigenmodes in the Large Helical Device