Internal electron transport barrier due to neoclassical ambipolarity in the Helically Symmetric Experiment

Abstract

Electron cyclotron heated plasmas in the Helically Symmetric Experiment (HSX) feature strongly peaked electron temperature profiles; central temperatures are 2.5 keV with 100 kW injected power. These measurements, coupled with neoclassical predictions of large “electron root” radial electric fields with strong radial shear, are evidence of a neoclassically driven thermal transport barrier. Neoclassical transport quantities are calculated using the PENTA code [D. A. Spong, Phys. Plasmas 12, 056114 (2005)], in which momentum is conserved and parallel flow is included. Unlike a conventional stellarator, which exhibits strong flow damping in all directions on a flux surface, quasisymmetric stellarators are free to rotate in the direction of symmetry, and the effect of momentum conservation in neoclassical calculations may therefore be significant. Momentum conservation is shown to modify the neoclassical ion flux and ambipolar ion root radial electric fields in the quasisymmetric configuration. The effect is much smaller in a HSX configuration where the symmetry is spoiled. In addition to neoclassical transport, a model of trapped electron mode turbulence is used to calculate the turbulent-driven electron thermal diffusivity. Turbulent transport quenching due to the neoclassically predicted radial electric field profile is needed in predictive transport simulations to reproduce the peaking of the measured electron temperature profile [Guttenfelder et al., Phys. Rev. Lett. 101, 215002 (2008)].

Helical modulation of the electrostatic plasma potential due to edge magnetic islands induced by resonant magnetic perturbation fields at TEXTOR

“…We will maintain this terminology here, although in our case the fluxes must be evaluated numerically, similarly to the modern stellarator literature [59,60,61,62]. In our simulations we find an unstable ion-root at E r < 0 (∼ −150 V ) and a stable electron-root at E r > 0 (∼ 120 V ), where the latter is found for a positive potential consistently with the experimental findings (see Fig.…”

“…We will use the algebraic determination of the ambipolar electric field, which is customary in the stellarator community: some examples include FORTEC-3D [59,60] and EUTERPE-GSRAKE [61], or the linearized drift-kinetic equation, such as in the case of DkesPenta [62]. In the chaotic transport calculations with Orbit it is easier to find a proper analytic form for Φ to stick into the GC equations of motion, Eqs (1,2).…”

Comparison of particle trajectories and collision operators for collisional transport in nonaxisymmetric plasmas

“…Once E r approaches the resonance, however, the three trajectory models yield substantially different results. This E r ∼ E res r regime can be relevant to experiments with high ratios T e /T i [23,45,48] and strong gradients [49]. In figure 3, we find that in the large-E r region anticipated for the edge of W7-X, the bootstrap current density in the full trajectory model is modestly reduced (by 8%) compared to an incompressible-E × B calculation, but should larger values of E * arise, we expect the deviation could grow more significant.…”

Edge ambipolar potential in toroidal fusion plasmas

“…37 Alternatively, one can use a linearized drift-kinetic equation, such as in the case of DKES-PENTA. 40 In the case of chaotic structures of the RFP, an optimal tool is the guiding-center code ORBIT, 18 recently validated against a volume-preserving field line tracer code (NEMATO) on the RFP topology. 26 ORBIT exploits a rather unique feature of the RFP: the precise knowledge of the radial structure (eigenfunction) of the saturated, almost stationary spectrum of tearing modes.…”