Evolution of magnetic Kubo number of stochastic magnetic fields during the edge pedestal collapse simulation

Abstract

Using a statistical correlation analysis, we compute evolution of the magnetic Kubo number during an edge pedestal collapse in nonlinear reduced magnetohydrodynamic simulations. The kubo number is found not to exceed the unity in spite of performing the simulation with a highly unstable initial pressure profile to the ideal ballooning mode. During the edge pedestal collapse, the Kubo number is within the values of 0.2 and 0.6 suggesting that the quasilinear diffusion model is sufficient to explain the energy loss mechanism during the pedestal collapse. Temporal evolution of poloidal correlation lengths of pressure fluctuations resembles with that of the Chirikov parameter and the Kubo number; while radial correlation lengths of the pressure fluctuations are strongly correlated with the radial width of the magnetic stochastic layer.

Nonlinear energy transfer from low frequency electromagnetic fluctuations to broadband turbulence during edge localized mode crashes

“…Turbulence and open magnetic field lines are considered to be part of the major causes explaining the anomalous transport during ELM crashes [4]; for instance, non-linear simulations have predicted an enhanced ⃗ E × ⃗ B advective transport [15] contributing more than 50% of the total transport [16]. Numerous non-linear magnetohydrodynamics (MHD) simulations during pedestal collapses have indicated increased fluctuation levels for various physical quantities [17][18][19][20][21][22][23][24], which have also been observed in experiments on the density [25], temperature [26], floating potential [27] and magnetic fields [28] during ELM crashes. In addition to well-developed arguments based on the flow shear [10] and open magnetic fields [29] for explaining the increased fluctuation or transport levels during ELM crashes, non-linear MHD simulations [30][31][32] have predicted the existence of non-linear interactions between a low frequency dominant mode and background broadband fluctuations.…”

Theory of mean E × B shear in a stochastic magnetic field: ambipolarity breaking and radial current

“…The degree of stochastization can be quantified by the ratio of the autocorrelation length to the scattering length l ac /l c (l ac = 1/|∆k ∥ | and 1/l c = k 2 θ DM 3L 2 s 1/3 [15,16], where D M = k b2 r, k πδ k ∥ is the stochastic magnetic diffusivity, k ∥ and k θ are parallel and poloidal wavenumber, respectively, and L s is scale length of magnetic shear). The ratio l ac /l c is related to the Kubo number [17].…”

Interplay between fluctuation driven toroidal axisymmetric flows and resistive ballooning mode turbulence

“…One of the critical issues is therefore to understand the nonlinear dynamics underlying the ELM crash and resultant energy loss process. Several nonlinear MHD codes such as BOUT [6][7][8][9] , M3D 10 , NIMROD 11,12 , JOREK [13][14][15][16][17][18] , M3D-C1 19 and BOUT++ [20][21][22][23][24][25] have therefore been developed and provided qualitative understanding of the nonlinear dynamics of ELMs.…”

“…For nonlinear simulations, solving the (m ̸ = 0, 0) component of vorticity equation is important to obtain consistent n = 0 magnetic field evolution since the pedestal collapse gives a large deformation of zonal pressure, p (0,0) which is coupled with the toroidal curvature term in vorticity equation.In some previous BOUT++ simulations, only ZFs ϕ (0,0) were taken into account and the (m ̸ = 0, 0) component of vorticity equation was filtered out. This scheme was applied to an electrostatic turbulence collapse simulation36 and ELM crash simulations24,25 including the effect of the geodesic acoustic mode (GAM)37 . GAM is produced by the poloidal mode coupling between ϕ (0,0) and p (1,0) so that solving only the (0, 0) component of vorticity equation is enough for GAM physics.…”