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 simulations in five-dimensional phase space are presented, clearly indicating that the additional “convective” electron fluxes driven by the ECRH are of the same order as the ambipolar neoclassical prediction for the “ion root” at much lower Er. For the predicted “electron root,” the ion fluxes calculated based on the traditional neoclassical ordering are much too small; shortcomings of the usual approach are indentified and a new ordering scheme is proposed.
The electron energy balance is analyzed for equivalent low-density electron cyclotron resonance heated (ECRH) discharges with highly peaked central power deposition in the stellarators W7-A [Plasma Phys. Controlled Fusion 28, 43 (1986)], L-2 [Proceedings of the 6th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Berchtesgaden, 1976 (International Atomic Energy Agency, Vienna, 1977), Vol. 2, p. 115] and W7-AS [Proceedings of the 9th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Baltimore, 1982 (International Atomic Energy Agency, Vienna, 1983), Vol. 3, p. 141]. Within the long mean-free path (LMFP) collisionality regime in stellarators, the neoclassical electron heat diffusivity χe can overcome the ‘‘anomalous’’ one. The neoclassical transport coefficients are calculated by the dkes code (Drift Kinetic Equation Solver) [Phys. Fluids 29, 2951 (1986); Phys. Fluids B 1, 563 (1989)] for these configurations, and the particle and energy fluxes are estimated based on measured density and temperature profiles. Neoclassical transport in the LMFP regime is minimum in W7-A and maximum in L-2, the standard configurations in W7-AS are in between. The radial electric field is estimated from the ambipolarity condition of only neoclassical particle fluxes. For these types of discharges in the quite different stellarator configurations, only the ‘‘electron root’’ exists in the innermost region, and, at the outer radii, only the ‘‘ion root.’’ In the region where both roots are found, a rather narrow shear layer in the poloidal plasma rotation is expected. Especially for W7-AS, a significant improvement of the neoclassical confinement is predicted in the ‘‘electron root’’ region. On the ‘‘ion root’’ side of the predicted ‘‘shear layer,’’ both the neoclassical energy and particle fluxes agree quite well with the experimental findings. At outer radii, the neoclassical fluxes are much lower. The predicted improvement for the ‘‘electron root’’ region is not found experimentally.
The ion current collected by a probe in a magnetized plasma is sensitive to the angle between its surface and the flow streamlines. This intuitive concept is the basis of the Gundestrup probe, a polar array of planar collectors mounted around an insulating housing. Probe theory for measuring flows has been developed on two fronts: Recent kinetic and fluid models, reviewed here, give similar predictions for the collected current within the range of applicability of the model assumptions. A comparison with measurements by a rotating Mach probe in the CASTOR tokamak (Czech Academy of Sciences Torus) [J. Stöckel, J. Badalec, I. Ďuran et al., Plasma Phys. Controlled Fusion, 41, 577 (1999)] highlights the role of magnetization in ion collection at grazing angles of incidence between the probe surface and the magnetic field lines.
A direct comparison of the electric potential and its fluctuations in the T-10 tokamak and the TJ-II stellarator is presented for similar plasma conditions in the two machines, using the heavy ion beam probe diagnostic. We observed the following similarities: (i) plasma potentials of several hundred volts, resulting in a radial electric field E r of several tens of V cm−1; (ii) a negative sign for the plasma potential at central line-averaged electron densities larger than , with comparable values in both machines, even when using different heating methods; (iii) with increasing electron density n e or energy confinement time τ E , the potential evolves in the negative direction; (iv) with electron cyclotron resonance heating and associated increase in the electron temperature T e, τ E degrades and the plasma potential evolves in the positive direction. We generally find that the more negative potential and E r values correspond to higher values of τ E . Modelling indicates that basic neoclassical mechanisms contribute significantly to the formation of the electric potential in the core. Broadband turbulence is suppressed at spontaneous and biased transitions to improved confinement regimes and is always accompanied by characteristic changes in plasma potential profiles. Various types of quasi-coherent potential oscillations are observed, among them geodesic acoustic modes in T-10 and Alfvén eigenmodes in TJ-II.
New experimental observations of the plasma potential using the heavy ion beam probe diagnostic are presented together with a theoretical description of the formation of the electric field E r in the T-10 circular tokamak (B 0 = 1.5-2.5 T, R = 1.5 m, a = 0.3 m). Ohmically heated (OH) deuterium plasmas with main plasma parameters ne = (0.6-4.7) × 10 19 m −3 , T e (0) < 1.3 keV, T i (0) < 0.6 keV are characterized by a negative potential ϕ(ρ) with maximum negative values of ϕ(6 cm) = −1400 V with respect to the wall. The potential profile monotonically increases towards the plasma edge. A density rise due to gas puff is accompanied by a plasma potential that becomes increasingly negative. When the density approaches values in the range ne = (2.5-3.5) × 10 19 m −3 , the value of the plasma potential saturates, while the energy confinement time still increases up to a saturation value that is obtained at a slightly higher density. With auxiliary heating by electron cyclotron resonance heating (ECRH) up to 1.2 MW, T e (0) increases (up to 3 keV) and the absolute value of the plasma potential decreases. In some cases the plasma potential changes its sign and becomes positive at the edge. The radial profile of E r and its dependence on n e and T i are qualitatively explained by a neoclassical model in the core, and a turbulent dynamic model (Braginskij magnetohydrodynamic equations) in the edge.
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