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

Abstract

Numerical simulations of visco-resistive internal kink modes with dominant poloidal and toroidal mode numbers m/n = 1 in tokamak plasma configurations have been carried out using the M3D code. The numerical scaling of the growth rate of linear visco-resistive internal kink is found to agree reasonably well with the analytical theory. The impact of toroidal effects is assessed. Nonlinear simulations show that when viscosity increases, the nonlinear evolution of resistive internal kinks transits from cyclic, Kadomtsev-like sawtooth oscillations at relatively low values of the viscosity parameter, to pulsating m/n = 1 magnetic islands at intermediate viscosity, to steady state islands at high viscosity. For the pulsating and steady state scenarios, the safety factor profile is nearly flat and almost equals to unity in the core region. Regimes with pulsating or steady state islands may be relevant to the interpretation of partial sawteeth and of the so-called snake phenomenon sometimes observed in tokamak experiments.

A new explanation of the sawtooth phenomena in tokamaks

“…At some point, when q 0 is low 2 enough, a (m, n) = (1, 1) (where m and n are poloidal and toroidal mode numbers) resistive reconnection event occurs, flattening the temperature and density profiles interior to the q = 1 surface and returning q 0 to 1. This process has been shown to occur in 3D resistive MHD and 2-fluid MHD simulations [5,[7][8][9][10][11][12] for tokamaks with sufficiently low values of pressure or β = 2µ 0 p /B 2 : β << 1 and/or sufficiently low values of Lundquist number S = τ R /τ A < 10 5 , where τ R and τ A are the resistive diffusion time and Alfvén transit time, respectively. However, these low-β , low temperature simulations do not exhibit the fast, ideal MHD timescale, temperature drops during the sawtooth cycle that are observed experimentally [13].…”

“…We compute the slopes of the 2 lines in Fig. (12) as 0.302 (before) and 0.306 (after). Using the boundary ellipticity of κ = 1 and evaluating Eq.…”

Nonlinear magnetohydrodynamic modeling of current-drive-induced sawtooth-like crashes in the W7-X stellarator

“…In the simulation the outer crash takes 1 ms whereas typical experimental values are 100 µs. This is not surprising since it is well documented that purely resistive reconnection cannot account for the fast sawtooth crash [7][8][9][10], and here the relatively large viscosity likely slows it down further. To reproduce the experimentally measured timescale, some sort of fast-reconnection mechanism may be needed, such as two-fluid effects [24] or the plasmoid instability [25].…”

“…This phenomenon is actually fairly common in tokamak simulations and related to the so-called "magnetic flux pumping" mechanism [8]. The formation or not of such structures can be sensitive to the transport parameters [9][10][11], and of particular importance in this case is the resistivity, to which the strength of the ECCD is proportional. We find that the (1,1) structure does not form if the ECCD is turned off during the crash, suggesting that a smaller resistivity may help.…”

“…A leading theory is the Kadomtsev model of magnetic reconnection driven by the (m, n) = (1, 1) internal kink mode due to the central safety factor falling below unity [6] (here m and n are the poloidal and toroidal mode numbers, respectively). Such repetitive reconnection events are routinely seen in nonlinear MHD simulations at low plasma beta [7][8][9][10][11] but seem elusive at high beta, where the Wesson model based on the pressure-driven interchange mode might be more applicable [12,13]. The sawtooth-like crashes in W7-X occur * yao.zhou@sjtu.edu.cn at low beta and ray-tracing modeling predicts near-axis ECCD deposition, which sets up a 'humped' rotational transform profile with two ι = 1 resonances.…”