Evaluation of the toroidal torque driven by external non-resonant non-axisymmetric magnetic field perturbations in a tokamak

Abstract

The toroidal torque driven by external non-resonant magnetic perturbations (neoclassical toroidal viscosity) is an important momentum source affecting the toroidal plasma rotation in tokamaks. The well-known force-flux relation directly links this torque to the non-ambipolar neoclassical particle fluxes arising due to the violation of the toroidal symmetry of the magnetic field. Here, a quasilinear approach for the numerical computation of these fluxes is described, which reduces the dimension of a standard neoclassical transport problem by one without model simplifications of the linearized drift kinetic equation. The only limiting condition is that the non-axisymmetric perturbation field is small enough such that the effect of the perturbation field on particle motion within the flux surface is negligible. Therefore, in addition to most of the transport regimes described by the banana (bounce averaged) kinetic equation also such regimes as, e.g., ripple-plateau and resonant diffusion regimes are naturally included in this approach. Based on this approach, a quasilinear version of the code NEO-2 [W. Kernbichler et al., Plasma Fusion Res. 3, S1061 (2008).] has been developed and benchmarked against a few analytical and numerical models. Results from NEO-2 stay in good agreement with results from these models in their pertinent range of validity.

Effect of 3D magnetic perturbations on the plasma rotation in ASDEX Upgrade

“…In a tokamak plasma, charged particles and neutrals together with the electromagnetic field are represented by a coupled system, which can be characterized by the exact conservation law of the total toroidal momentum of particles and of the electromagnetic field. In a covariant notation this conservation law is given as (see, e.g., [8] for its toroidally averaged form),…”

“…Formally the contributions from all external non-axisymmetric electromagnetic perturbations, including besides the static or slowly varying magnetic perturbations also the contribution from RF heating and current drive, can be separated into the source term T NA ϕ . Generally, this separation is not so straightforward as (6), see, e.g., [8] for the case of non-resonant magnetic perturbations, and may even not always be meaningful in a general case (see discussion in Section 4). Thus, equation (5)…”

“…In case of non-resonant external magnetic perturbations, T NA ϕ is directly linked through the flux-force relation to the non-ambipolar neoclassical particle flux densities Γ NA α driven by these perturbations in a stationary radial electric field (see, e.g. [5,8]),…”

“…Torque produced by these thermal particle fluxes is called NTV torque. In presence of suprathermal particle losses, the torque density (8) should include also the flux of these fast particles (see, e.g., [23,24]). However, this type of flux cannot be described by the local neoclassical ansatz.…”

“…In particular, ϕ is not an exact symmetry variable anymore. This difference, however, is small for weakly perturbed equilibria and can be ignored in (7) (see [8]). For evaluation of the analytical expressions of Shaing [5] magnetic fields have been converted from Boozer coordinates to Hamada coordinates.…”