Analysis of the Kolmogorov model with an asymptotic-preserving method

Fedele, Baptiste; Negulescu, Claudia; Ottaviani, M.

doi:10.1016/j.physleta.2021.127522

Cited by 1 publication

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“…In this context, the Alfvén theorem of magnetic flux conservation in an ideal MHD plasma is the mirror correspondent of the Helmholtz-Kelvin theorem of vorticity conservation in ideal hydrodynamics (Batchelor 1950;Elsasser 1950b;Truesdell 1950;Axford 1984;Greene 1993). We incidentally note that some formal similarities can be also recognised in the eigenmode analysis of resistive tearing modes and of ideal instabilities in presence of viscosity in a Kolmogorov hydrodynamic flow (Fedele, Negulescu & Ottaviani 2021). In terms of the RMHD equations above, the Lagrangian invariance of magnetic lines is expressed by the ideal limit (d e = ρ s = S −1 = 0) of (2.1), although a finite ρ s alone allows preservation of the ideal MHD topological conservation, provided a redefinition of the stream function of the velocity field U according to ϕ → ϕ − ρ 2 s ∇ 2 ϕ ).…”

Section: Magnetic Reconnection In Tearing Modes and Formation Of Magn...mentioning

confidence: 78%

Microscopic scales of linear tearing modes: a tutorial on boundary layer theory for magnetic reconnection

et al. 2022

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We revise in detail and in a pedagogical way the analysis of the boundary layer theory of warm tearing modes in slab, reduced magnetohydrodynamics (MHD), when magnetic reconnection is driven by electron inertia and/or resistivity, and ion-sound Larmor radius effects are included. By comparison with the numerical solution of the corresponding eigenvalue problem, we interpret these results by means of a heuristic approach, which in the warm-electron regime, we show to be in general not feasible without knowledge of the scaling of the gradient of the magnetic flux function, differently from what happens in the cold-electron regimes. We put in evidence for a non-trivial relation between the first derivative of the magnetic flux function and of the velocity parallel to the neutral line, evaluated in its proximity, by thus providing insight to the multiple boundary layer analysis that Pegoraro & Schep (Plasma Phys. Control. Fusion, vol. 28, 1986, p. 647) first showed to be required in warm-tearing regimes. In this way, we also suggest and justify a general operational definition of the reconnecting layer width and we discuss the linear appearance of microscopic scales related to the gradients of the eigenfunctions of the tearing modes.

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Section: Magnetic Reconnection In Tearing Modes and Formation Of Magn...mentioning

confidence: 78%