Formation of plasmoids during sawtooth crashes

Abstract

The nonlinear growth of the internal kink mode is studied numerically using reduced magnetohydrodynamic equations in cylinder geometry. For low Lundquist numbers, S < 107, the already well-known results have been reproduced: a m/n = 1/1 magnetic island (m: poloidal, n: toroidal mode number) grows while the original core shrinks until full reconnection is achieved. For higher S values, however, the dynamics is found to be qualitatively different from the well-known Kadomtsev's model (Kadomtsev 1975 Sov. J. Plasma Phys. 1 389). The growth of the 1/1 island causes the development of a very thin current sheet which becomes tearing unstable. The current sheet is thus broken up and secondary islands (plasmoids) form. These plasmoids strongly speed up the reconnection and eventually coalesce into one secondary island. The formation of a large secondary island stops the fast reconnection process, leading even to a partial reversal of this process. The final state of sawtooth reconnection is thus no longer an axis-symmetric equilibrium as in the case of complete reconnection for low S values, but a helical equilibrium with two coexisting magnetic islands.

Non-monotonic growth rates of sawtooth precursors evidenced with a new method on ASDEX Upgrade

“…It is shown that the growth rate behaviour is not monotonic and can be approximated as a set of well-identified phases with quasi-constant growth rate. Also, all three cases show postcursor oscillations compatible with incomplete reconnection, itself compatible with both plasmoids [12] and stochasticity interpretations [15].…”

“Ideal” tearing and the transition to fast reconnection in the weakly collisional MHD and EMHD regimes

“…The above discussions demonstrate that the rescaling argument at the basis of ideal tearing may provide a fairly general paradigm to describe explosive growth rate increases. Consider now what is observed in the nonlinear stage of simulations of reconnection at L / a not much larger than unity [ Ali et al , ; Biancalani and Scott , ; Yu et al , ], when an X point collapses into two Y points and the current sheet between the two becomes tearing unstable, eventually leading to what has been interpreted as the plasmoid chain instability.…”

“…Moreover, numerical simulations of tearing mode instabilities have identified a secondary, nonlinear, increase of the reconnection rate that has been sometimes interpreted in terms of a nascent plasmoid-unstable SP regime [Loureiro et al, 2005;Ali et al, 2014] or generically a secondary "explosive reconnection" regime [Biancalani and Scott, 2012]. A nonlinear increase of the reconnection rate on ideal, Alfvénic time scales was also numerically measured by Yu et al [2014] in simulations of low mode number reconnection instabilities. Given the recent developments of the theory of large aspect ratio current sheet instabilities, it is important to understand whether such augmented fast reconnection rates may indeed be interpreted as fast secondary instabilities of the nonlinearly generated current sheets stemming from the primary reconnection event.…”

“…The present paper focuses on the extension of the IT scaling arguments to weakly collisional regimes where reconnection is mediated by electron inertia effects and on whether such generalized IT regimes might explain the nonlinear occurrence of fast exponentially growing reconnection rates. We will consider both the incompressible reduced MHD (RMHD) [see, e.g., Zank and Matthaeus, 1992] and electron MHD (EMHD ) [Kingsep et al, 1990] frequency ranges, where the perturbations are dominated by Alfvén and whistler modes, respectively. The formal similarity between RMHD and EMHD reconnection in slab geometry, previously discussed in [Del Sarto et al, 2003, 2006, allows a unified treatment for the onset of IT in an electron inertia-driven framework.…”

Plasmoids Formation During Simulations of Coaxial Helicity Injection in the National Spherical Torus Experiment

“…However, effects beyond MHD may also contribute to fast reconnection as the current sheet width (δ sp ) becomes smaller than the two-fluid or kinetic scales [18,19]. Secondary islands (plasmoids) have also been seen in reduced MHD simulations during the nonlinear evolution of the tearing instability in slab geometry [20] and during the nonlinear growth of an internal kink mode in cylindrical geometry [21,22]. In these studies it was concluded that for realistic fusion relevant parameters, it is the inclusion of two-fluid effects, not the plasmoid instability, that may lead to the fast sawtooth reconnection [22].…”