Nonlinear Viscosity in the Interchangeable Module Stellarator

Abstract

The experimental observation of nonlinear parallel viscosity in the Interchangeable Module Stellarator is reported. The damping of plasma flows, by poloidal viscosity and ion-neutral collisions, is determined from the dependence of the radial current on the radial electric field in the plasma. At low neutral density, the radial current drops and a jump in the radial electric field occurs at a poloidal Mach number in the range 210 to 215, in reasonable agreement with a model based on nonlinear viscosity. The nonlinearity of viscosity diminishes as the neutral density is increased. [S0031-9007(98)05995-X] PACS numbers: 52.55.Hc, 52.25.Fi Improving the confinement in toroidal magnetic devices has been a central focus of the fusion program since the discovery of the L-H transition in ASDEX [1] in the early 1980s to the more recent dramatic reduction in core turbulent transport with reverse magnetic shear in the TFTR [2] and DIII-D [3] tokamaks. In the past few years, spontaneous L-H transitions have also been reported in the Wendelstein VII-AS [4] and CHS [5] stellarators, and recently in the H-1 heliac [6]. Pioneering efforts to improve confinement in toroidal machines using biased electrodes dates back to 1966 and the B-3 stellarator [7]. Biased electrode experiments in tokamaks [8-10], meanwhile, have shown that there is a sudden jump in the radial electric field during the L-H transition about a poloidal Mach number (M p 2E r ͞B p n t where E r is the radial electric field, B p is poloidal magnetic field, and n t is the thermal velocity of ions) of unity. It has been suggested that the jump in the radial electric field is a result of the nonlinearity of viscosity at high E 3 B flow speeds [11].In this Letter, we show the first results of a sudden jump in the radial electric field at a poloidal Mach number much greater than one, in reasonable agreement with an expression by Shaing for the parallel viscosity in stellarators [12]. The unity poloidal Mach number in tokamaks occurs because of the purely toroidal modulation of the magnetic field; the higher poloidal Mach number in stellarators occurs because of the additional helical modulation of the magnetic field. Furthermore, we show that the bifurcation of the radial electric field due to the nonlinear viscosity can be suppressed by an increase in the neutral density. The competition between neoclassical parallel viscosity and ion-neutral collisions in a stellarator has been described theoretically for low speed [13] when the viscosity is linear with the flow, and for high rotation speed [12] when the viscosity becomes nonlinear. Previous experiments [14] in the Interchangeable Module Stellarator (IMS) [15] measuring the radial conductivity, flow speed, and damping rate confirmed the neoclassical model at low rotation speeds. The work described here confirms the model at high rotation speed. A higher power plasma source, higher plasma densities, and larger bias voltages contributed to the higher rotation speeds observed in this paper compared to previous experi...

Effects of plasma parameters on viscosity

“…With respect to the prediction 1): a drop in the bias current due to the helical peak is observed. A more accurate determination of the radial electric field based on the measurement of plasma potential profile at kW (not shown here) indicates that the peak of viscosity due to the helical ripple is at in reasonable agreement with the numerical calculation [11]. No drop in the radial current due to the toroidal peak in the viscosity has been observed.…”

“…Spontaneous L-H transitions have also been reported in the Wendelstein VII-AS [8], compact helical system (CHS) [9], and H-1 [10] stellarators. The experimental results from the interchangeable module stellarator (IMS), presented previously [11], indicate that viscosity in a stellarator is nonlinear too.…”

Metamorphosis of plasma turbulence–shear-flow dynamics through a transcritical bifurcation

“…A régime in which density fluctuation amplitudes are reduced continuously was also observed in [37]. In [38] a discontinuous bifurcation of the electric field in a stellarator was reported for conditions of low neutral density, where the charge-exchange damping rate is low. The change in the electric field became gradual for conditions of high neutral density, because the charge-exchange damping rate increases.…”

LH transition by a biased hot cathode in the Tohoku University Heliac

“…However, the driving force for plasma rotation was not controlled continuously with this set-up. On the other hand, plasma viscosity non-linearity was investigated in the interchangeable module stellarator (IMS), using a cold electrode with a triangular voltage-sweep biasing [16]. Non-linearity of the plasma viscosity at −M p in the range 10-15, determined from the radial current dependence on the radial electric field, was clearly shown.…”