Edge ambipolar potential in toroidal fusion plasmas

Abstract

A series of issues with toroidally confined fusion plasmas are related to the generation of 3D flow patterns by means of edge magnetic islands, embedded in a chaotic field and interacting with the wall. These issues include the Greenwald limit in Tokamaks and reversed-field pinches, the collisionality window for ELM mitigation with the resonant magnetic perturbations (RMPs) in Tokamaks, and edge islands interacting with the bootstrap current in stellarators. Measurements of the 2D map of the edge electric field E r ðr ¼ a; h; /Þ in the RFX reversed-field pinch show that E r has the same helicity of the magnetic islands generated by a m/n perturbation: in fact, defining the helical angle u ¼ mh À n/ þ xt, maps show a sinusoidal dependence as a function of u, E r ¼Ẽ r sin u. The associated E Â B flow displays a huge convective cell with vðaÞ 6 ¼ 0 which, in RFX and near the Greenwald limit, determines a stagnation point for density and a reversal of the sign of E r . From a theoretical point of view, the question is how a perturbed toroidal flux of symmetry m/n gives rise to an ambipolar potential U ¼Ũsin u. On the basis of a model developed with the guiding center code ORBIT and applied to RFX and the TEXTOR tokamak, we will show that the presence of an m/n perturbation in any kind of device breaks the toroidal symmetry with a drift proportional to the gyroradius q, thus larger for ions (q i ) q e ). Immediately, an ambipolar potential arises to balance the drifts, with the same symmetry as the original perturbation.

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

“…This potential is the response of the plasma to non-ambipolar fluxes, generated through the breaking of the toroidal symmetry by the 3D fields. Similar results have been obtained in the RFX-mod RFP, where a model of electrostatic potential was built up for the island resonating with poloidal/toroidal mode number m/n = 0/1 at the edge of RFX-mod [47]. This model reproduces the main features of E r , such as amplitude and geometry along the toroidal angle ϕ.…”

“…Our results have been obtained in the case of a static RMP: this solution is valid even in the case of slowly rotating islands, as in the case of RFX [47]. In the case of fast rotating islands (in TEXTOR, with frequency ω > 3 kHz), it is necessary to account for an inductive correction for Φ, due to the term ∂ t α B that adds to the expression of Eq.…”

“…In particular, the correlation is very strong in the region outside the LCFS, while inside V p does not follow exactly the flux surfaces. On the basis of the simulations of D and the measured V p map, we find good reason to assume that the ambipolar potential Φ should possess the same geometry as the 4/1 island, similarly to the 0/1 and 1/7 island cases in RFX-mod [17,47].…”

“…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). To do that, we need to mix an experimental radial profile and simulation observations along θ, as previously done on RFX-mod [47]. In this way,…”

“…In Ref. [47] we presented the calculation of the particle diffusion coefficients, D, in between fixed points, O and X (OP and XP in the remainder of the paper). Here, we propose again the result as it is instrumental to the measurements of plasma potential and the modeled ambipolar potential, that we present below.…”