C. Wendland

Physics of the Density Limit in the W7-AS Stellarator

Density-limit discharges in the W7-AS stellarator, with constant line-integrated density and a duration of up to 2 s, were studied at three values of the toroidal magnetic field (B = 0.8, 1.25 and 2.5 T). The central factor governing the physics of the density limit in stellarators was demonstrated to be the decreasing net power to the plasma when the centrally peaked radiated power density profile exceeds that of the deposited power density. The process was further accelerated by the peaking of electron density under these conditions. In discharges with B = 2.5 T, simulations of the centrally peaked radiation power density profiles could be shown to be due to peaked impurity density profiles. Laser blow off measurements clearly inferred an inward pinch of the injected aluminium. These discharges had the electron density profile form found in the improved confinement H-NBI mode on W7-AS. The aim of producing steady-state discharges at the highest possible density in stellarators is naturally of special interest for reactor operation. Such a scenario has been best achieved in H-mode discharges, in which ELMs restricted the impurity influx to the plasma and an equilibrium in the plasma parameters with suitably low radiation power levels was possible. A density scan in ECRH discharges highlights the need to control impurity sources and choose electron densities well below the density limit in order that steady-state operation can be attempted in discharges without ELMs. A simple model of bulk radiation predicted that the limiting density should depend on the square root of heating power and this was experimentally confirmed. The magnetic field scaling of the limiting density found experimentally in this simple model will partly depend on the term concerning the radial profile of the impurity density, which in turn is a function of the diffusion coefficient and inward pinch of the impurity ions. Theoretical studies have shown that an assumption about the B dependence of the thermal conductivity leads to density limit scaling laws with an explicit B dependence.

Edge transport barrier formation and ELM phenomenology in the W7-AS stellarator

In NBI discharges with density ramps in W7-AS, the quiescent H-mode is restricted to the same ranges of the edge rotational transform as in ECRH discharges and occurs above threshold densities ≥ 10 20 m 3 which increase with heating power. Higher power needs higher density for stabilization. The approach to the quiescent H-mode often occurs, with increasing density and decreasing power flow through the edge, from grassy through dithering states to bursts of ELMs and, in a few cases, quasi-periodic ELMs. This goes parallel with increasing radial gradients of the plasma pressure and E-field at the edge. Higher heating power reduces in particular the T i gradients and hence the E-field gradients, which effect can be compensated by higher density. The correlations found are fairly consistent when an E x B flow shear decorrelation of the turbulent transport is assumed.

Radiation measurements and modeling of the density limit on the W7-AS stellarator

Density limit discharges in the W7-AS stellarator with a strong density ramp were compared to a series of discharges with constant line integrated density approaching the maximum value achieved in the density ramp. The physics of the density limit in stellarators was demonstrated to be consistent with the predictions of the two-point model, indicating that this model successfully describes the density limit process in both stellarators and tokamaks. The discharges with a strong density ramp were found to have broader density profiles than those discharges with constant line integrated density. The latter discharges had the electron density profile form found in the improved confinement H-NBI mode on W7-AS. Modeling of the radiation profile, to simultaneously match the measured bolometer and soft X-ray radial profiles of radiated power, implies that impurity density profiles were peaked and continuously increased during the discharge. The increase in radiated power decreased the net deposited power to the plasma and the diamagnetic energy fell. The aim of producing steady-state discharges at the highest possible density is aided by the reduction of impurity sources by helium glow discharge cleaning.

On the way to divertor detachment in the W7-AS stellarator

Abstract 3D modeling on W7-AS suggests that to obtain divertor plasma detachment, upstream separatrix densities nes in the range of 10 20 m −3 will be necessary. This paper investigates the ratio of nes to the line-averaged density n e under a variety of conditions – P heat ∼0.4–2 MW , n e ∼0.2–2.7×10 20 m −3 – for inner-limiter plasma configurations in preparation for the upcoming divertor phase. n es / n e ranges from 0.05 for the quiescent H-mode H* (Pecrh∼0.4 MW) up to ∼0.35 for high-power (Pnbi∼2 MW), heavily fueled discharges where nes approaches 1020 m−3 within a density ramp. For P nbi MW , n es / n e declines with increasing n e as the H-mode threshold density n e thr approaches. L–H–L switching transitions cause n es / n e to alternate between higher and lower values. The attainment of H* implies reduced n es / n e and incipient radiation collapse of the core plasma. n e thr and n es / n e both increase with heating power by which means detachment-relevant nes can be attained, albeit at n e close to the density limit. These phenomena in detail exhibit a sensitive dependence on ιa – even a 1% change results in evident and reproducible plasma behavior.

Peaked density profiles: evidence of inward transport in the W7-AS stellarator

Radially peaked density profiles were found in discharges heated purely with ECH in the currentless W7-AS stellarator. Changes in the central particle source are not significant and do not explain the density peaking. This is evidence for inward convection in W7-AS. The existence of the inward convection is confirmed with two independent transient transport studies. Flatness of the temperature profiles is essential for the density peaking, and an anti-correlation was found between the density and temperature gradients. The density peaks as the ECH-deposition is moved outwards. The density peaking parameter was found to decrease with increasing heating power. No clear density dependence was found. Strong gas puffing, or the corresponding high edge density prevents the formation of the peaked profiles.