Local and nonlocal anisotropic transport in reversed shear magnetic fields: Shearless Cantori and nondiffusive transport

Abstract

A study of anisotropic heat transport in reversed shear (nonmonotonic q-profile) magnetic fields is presented. The approach is based on a recently proposed Lagrangian-Green's function method that allows an efficient and accurate integration of the parallel (i.e., along the magnetic field) heat transport equation. The magnetic field lines are described by a nontwist Hamiltonian system, known to exhibit separatrix reconnection and robust shearless (dq/dr=0) transport barriers. The changes in the magnetic field topology due to separatrix reconnection lead to bifurcations in the equilibrium temperature distribution. For perturbations of moderate amplitudes, magnetic chaos is restricted to bands flanking the shearless region. As a result, the temperature flattens in the chaotic bands and develops a very sharp radial gradient at the shearless region. For perturbations with larger amplitude, shearless Cantori (i.e., critical magnetic surfaces located at the minimum of the q profile) give rise to anomalous temperature relaxation involving widely different time scales. The first stage consists of the relatively fast flattening of the radial temperature profile in the chaotic bands with negligible flux across the shearless region that, for practical purposes, on a short time scale acts as an effective transport barrier despite the lack of magnetic flux surfaces. In the long-time scale, heat starts to flow across the shearless region, albeit at a comparatively low rate. The transport of a narrow temperature pulse centered at the reversed shear region exhibits weak self-similar scaling with non-Gaussian scaling functions indicating that transport at this scale cannot be modeled as a diffusive process with a constant diffusivity. Evidence of nonlocal effective radial transport is provided by the existence of regions with nonzero heat flux and zero temperature gradient. Parametric flux-gradient plots exhibit multivalued loops that question the applicability of the Fourier-Fick's prescription even in the presence of a finite pinch velocity.

Modulated heat pulse propagation and partial transport barriers in chaotic magnetic fields

“…[16]. More recently, the role of Cantori on anisotropic heat transport in plasmas has been studied in the context of steady state solutions [17] and time dependent solutions in monotonic and reversed shear magnetic configurations [3,4]. The basic idea is that although invariant closed curves (which correspond to flux surfaces in the Hamiltonian description of magnetic fields) present impenetrable transport barriers, regions without such curves (e.g., the region around R 2 ψ ≈ 0.275 in (1/2πL) L 0 dz 2π 0 dθ T (r, t), where L = 2πR is the length of the periodic cylindrical domain, and the plots in Fig.…”

“…[14]. In previous publications, this method was applied to study transport in different magnetic field configurations [2][3][4] but limiting attention to cases in which the heat source was either absent or time independent. Going beyond these previous studies, we consider heat transport in the presence of time modulated sources, and present in this section a re-formulation of the LG method in Fourier space to deal with this problem efficiently.…”

“…In previous publications we considered some aspects of this problem including a study of the break-down of the standard diffusive model in the case of full magnetic field stochasticity [1,2] and the role of partial transport barriers in monotonic and reversed shear configurations [3,4]. Going beyond these works, in the present paper we study electron heat pulse propagation driven by power modulation in three dimensional chaotic magnetic fields.…”

“…To study the propagation of modulated heat pulses in the presence of fully stochastic fields we consider a perturbation consisting of twenty overlapping modes (m, n) = {(5, 4), (9, 7), (4, 3), (7,5), (3,2), (5, 3), (7,4), (11,6), (2, 1), (9, 4), (7,3), (5,2), (14,5) This is the same magnetic field used in Ref. [4] to study freely decaying (i.e., without power modulation) heat pulses in fully stochastic fields.…”

Electron heat flow due to magnetic field fluctuations

“…In practical applications, it is ambiguous to distinguish between high and low stochasticity. It is also demonstrated that the RR transport is incompatible with integral (nonlocal) closures [18,19].…”