Experimental and neoclassical electron heat transport in the LMFP regime for the stellarators W7-A, L-2, and W7-AS

Abstract

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.

Core electron-root confinement (CERC) in helical plasmas

“…8) is obtained from the diffusion equation for E r [36]. The bifurcation nature of the ambipolar E r is confirmed in other devices as well (cf., Fig.…”

Momentum correction techniques for neoclassical transport in stellarators

“…At the low collisionalities, an additional "electron-root" is obtained (the unstable root in between is not shown) which, by evaluating the thermodynamic principle described in Refs. [32,33], however, is not realised. For these W7-X configurations, the bootstrap current density is positive (tokamak-like) at low collisionalities and becomes negative at higher ones (the bootstrap current densities are always negative in a helically symmetric configuration).…”

Neoclassical transport simulations for stellarators

“…This equation follows from the thermodynamic approach [20][21][22] by minimizing the total heat production (A1) due to both the poloidal sheared rotation and the neoclassical transport; see Appendix A for more detail. An equation similar to (7) can be derived using the higher order expansion of the distribution function within the neoclassical theory [23].…”

“…With the assumption of a very narrow transition layer, the criterion for the position is obtained [22] from the variation of the generalized heat production with respect to the radial position:…”