Viscosity effect on the m=1 internal kink mode in a tokamak

Linear and nonlinear simulations of the visco-resistive internal kink mode using the M3D code

“…Another problem in comparing the results in this article with experimental observations is related to the fact that the large values of viscosity used in our simulations may be difficult to justify. However, as argued in section 1, viscosity may be enhanced by neoclassical effects [26] and, perhaps more importantly for the purposes of the present analysis, as soon as toroidal symmetry is violated [27], which indeed is the case as soon as an m/n = 1 magnetic island is formed. Therefore, a quantitative evaluation of the actual viscosity in experiments with observable m/n = 1 magnetic islands will allow a more direct comparison with the theoretical results obtained in this article.…”

“…However, there is ample evidence that Braginskii's transverse ion viscosity coefficient does underestimate the actual viscosity in tokamak experiments for two main reasons: firstly, neoclassical ion viscosity tends to dominate over Braginskii's viscosity coefficient; in particular, parallel ion viscosity tends to dominate in the socalled banana regime, giving rise to effective neoclassical values of V that can be an order of magnitude larger than the values inferred by Braginskii's analysis. A nice discussion of neoclassical viscosity effects on internal kink modes can be found, for instance, in [26]. Secondly, and perhaps more importantly, as soon as toroidal symmetry is violated by the growth of an m/n = 1 magnetic island, neither Braginskii's nor neoclassical analyses are no longer applicable [27]; then, the effective viscosity during the growth of a symmetry-breaking m = n = 1 magnetic islands may be significantly larger, as discussed in [27].…”

Identification of Mercier instabilities in Alcator C-Mod tokamak

“…In the context of a two fluid analysis of internal kink modes, Porcelli and Migliuolo 18 showed that with the addition of resistivity the ω − solution is destabilized and the ω + solution damped, while perpendicular ion viscosity has the reverse effect. Lakhin and Mikhailovskii 19 have found that longitudinal neo-classical viscosity is similar to perpendicular viscosity in driving ω + and damping ω − .…”

“…In fact, ω * i /2 ∼ 2.9 × 10 4 , while γ I ∼ 1.5 × 10 4 [rad/sec]. It is well known, [18][19][20] however, that FLR stabilization is not robust. Addition of any plasma dissipation or Landau resonance results in destabilization of one of the oscillatory modes and damping of the other.…”