Evidence for Convective Inward Particle Transport in a Stellarator

Abstract

Radially peaked density profiles were observed in the stellarator W7-AS in discharges with small central particle sources. Particle balance analyses and density modulation experiments revealed the existence of a convective inward particle flux. The peaked density profiles appear only in discharges with flat central electron temperature profiles. In discharges with peaked temperature profiles the convective inward flux is canceled by outward directed thermodiffusion. [S0031-9007(98)08292-1] PACS numbers: 52.55. Hc, 52.25.Fi Clear evidence exists that transport of particles and energy across magnetic flux surfaces of magnetically confined high-temperature plasmas is caused by turbulent processes. This is true for most of the accessible collisionality regimes in stellarators and tokamaks [1]. Progress in recent years with the numerical simulation of turbulent transport processes allows one now to account at least in the plasma edge for the magnitude of the observed losses [2,3]. It remains, however, difficult to understand how transport can be directed opposite to the corresponding thermodynamic force [4,5], as is reported in this Letter for the particle transport in the W7-AS stellarator. Evidence is presented for the fact that a fraction of the particle transport is (inward) convected up the density gradients. Under standard discharge conditions, a radially peaked temperature profile counteracts this inward component. Only when flat temperature profiles are generated by noncentral plasma heating, does this component become visible. In the edge of stellarators and tokamaks or in the core of low density and temperature discharges, probe measurements show that the fluctuation induced transport has intermittent character. The direction of transport due to these fluctuations depends on the phase shift between density and potential fluctuations. It is observed that most of the transport is outward directed but there exists a fraction where the phase shift results in inward-directed transport [6]. The observed inward convection could be related to these events and it was observed in the H-1 Heliac that the phase shift between density and potential fluctuations can change during a discharge leading to an increase of the inward directed fraction of particle transport [7].The radial particle flux through a magnetic flux surface is governed by the continuity equation. The electron particle flux G e is given bywith n e , the electron density, and S, the sum of all particle sources and sinks. The effective plasma radius r labels the magnetic flux surfaces. In collisional transport theory, radial electron density and temperature gradients drive the particle flux, which can be written as G e 2n e √ D 11 = r n e n e 1 D 12 = r T e

Up-gradient particle flux in a drift wave-zonal flow system

“…As noted earlier, tokamak experiments have sometimes shown evidence for an inward turbulent flux that are usually coincident with strong edge pressure gradients and E Â B shear flows found in improved confinement regimes [16][17][18][19] and space plasma observations also indicate up-gradient transport processes with simultaneous density gradient and E Â B shear regions. [4][5][6][7][8] These earlier observations are reminiscent of the results reported here, suggesting similar mechanisms could be at work in both cases (although theory shows magnetic shear to be effective at quenching the linear transverse KH instability 39 ).…”

“…[10][11][12][13][14][15] For fusion systems, inferred transport fluxes are often decomposed into an inward-directed turbulent pinch and down-gradient diffusive transport components (both of which are attributed to a combination of density and temperature gradients) that then compete to form the plasma equilibrium. In a few cases, direct measurements of net inward turbulent particle fluxes have been reported during or shortly after the formation of transport barriers associated with the formation of a suitably strong E Â B shear layer [16][17][18][19] or during the application of an externally forced E Â B shear flow. 20 However, the cause of the net inward flux in these latter works was never identified, nor has velocity shear ever been considered as a possible mechanism to drive inward pinches in confinement experiments.…”

Multi-Dimensional Structure of the Electric Field in Tokamak H-Mode

“…The origin of the inward pinch has yet to be unresolved. Ware pinch driven by the toroidal electric fi eld [12] alone cannot account for the peaked density profi le, because the inward pinch is observed even in helical systems [13,14] and noninductively current driven tokamaks [15]. In addition, the enhancement of the pinch velocity is observed after the L/H transition [16].…”

“…(11) remains. The pressure anisotropy, deduced from the drift kinetic equation with mass fl ow velocity, is as follows [40]: (12) The integral I ps is (13) where ν T is the characteristic collision frequency defi ned in Ref. [41], and G r is a geometric factor, taken to be G r = 1 in this paper.…”

Experimental test of the radial force balance equation in the compact helical system

“…The radial profile of electron density becomes more flattened during the ECH pulse and this flattening of the electron density is due to the outward directed thermodiffusion driven by a sharp electron temperature gradient. 13 On the other hand, the radial profile of carbon is even more hollow during the ECH pulse and more peaked than that of electron density after the ECH pulse. These results show that the accumulation ͑exhaust͒ of carbon impurity during the NBI (NBIϩECH) phase is more significant than that of the bulk ions.…”