Generic magnetic field model in poloidal divertor tokamaks in the presence of resonant magnetic perturbations

Abstract

A generic analytical model for the description of magnetic field lines in poloidal divertor tokamaks in the presence of external resonant magnetic perturbations is proposed. It is based on the Hamiltonian description of magnetic field lines in tokamaks. The safety factor and the spectra of magnetic perturbations are chosen by the requirement to satisfy their generic behaviour near the magnetic separatrix and at the magnetic axis. The field line equations are integrated by the construction of two symplectic and computationally efficient mappings of field lines. The model for internal MHD modes is also proposed. The mapping procedure for field lines which includes the MHD modes is described. It is shown that the numerically calculated diffusion and convection coefficients of field lines are in close agreement with the quasilinear ones. It is found that in the presence of internal MHD modes at the plasma edge the convectional outward transport of field lines may reverse its direction to inward convectional transport.

Universal asymptotical behaviour of poloidal spectra of resonant magnetic perturbations created by a set of saddle coils in tokamaks

“…where A 3 (ψ) and C 3 (ψ) are functions similar to A j (ψ), C j (ψ), (j = 1, 2). The asymptotical forms of H (j ) m,n (ψ) (j = 1, 2) and H (3) mn = −(n/m)G mn (ψ) given by equations ( 29) and ( 30) are generalized versions of the model proposed in [31,32]. Below we will show that these formulae indeed describe well the asymptotical behaviour of poloidal spectra H mn for tokamak plasmas.…”

“…In this section we summarize the results on the perturbation magnetic field generated by the set consisting of N pairs of saddle coils. According to equations ( 17) and ( 25 ψ ns (ψ, ϑ) sin (n s ϕ) , (32) n s = (2s + 1)N,…”

“…where H j = 2A j /q, for j = 1, 2 and H 3 = 2nA 3 /m. Consider that the primary toroidal mode n = N = 3 in equation (32) gives the main contribution of the RMP field. mode number m for the odd (curve 1) and even (curve 2) parity configurations at the magnetic surface ψ N = 0.9.…”

Energetic electron transport in magnetic fields with island chains and stochastic regions

“…Possible mechanisms to consider include: (i) shift in the location of the island surface with respect to the ECH/ECCD pulses, (ii) formation of stochastic region in the edge plasma due to island overlap, (iii) opening of additional small islands throughout the plasma. Due to the Hamiltonian nature of the magnetic field lines (Abdullaev 2010), these three mechanisms are not independent of each other. For example, opening of additional small islands can lead to island overlap in the edge plasma, which in turn produces an edge stochastic region.…”

On collisional diffusion in a stochastic magnetic field

“…The Hamiltonian equation 1is integrated using the symplectic mapping procedure [29,32,33]. Let (ϑ k , ψ k ) be the values of the poloidal angle and the toroidal flux (ϑ, ψ) at the sections ϕ = ϕ k = (2π/N ) k, k = 0, ±1, ±2, • • • .…”