Plasmoid and Kelvin-Helmholtz instabilities in Sweet-Parker current sheets

A 2D linear theory of the instability of Sweet-Parker (SP) current sheets is developed in the framework of Reduced MHD. A local analysis is performed taking into account the dependence of a generic equilibrium profile on the outflow coordinate. The plasmoid instability [Loureiro et al, Phys. Plasmas {\bf 14}, 100703 (2007)] is recovered, i.e., current sheets are unstable to the formation of a large-wave-number chain of plasmoids (k_{\rm max}\Lsheet \sim S^{3/8}, where $k_{\rm max}$ is the wave-number of fastest growing mode, S=\Lsheet V_A/\eta is the Lundquist number, \Lsheet is the length of the sheet, $V_A$ is the Alfv\'en speed and $\eta$ is the plasma resistivity), which grows super-Alfv\'enically fast (\gmax\tau_A\sim S^{1/4}, where \gmax is the maximum growth rate, and \tau_A=\Lsheet/V_A). For typical background profiles, the growth rate and the wave-number are found to {\it increase} in the outflow direction. This is due to the presence of another mode, the Kelvin-Helmholtz (KH) instability, which is triggered at the periphery of the layer, where the outflow velocity exceeds the Alfv\'en speed associated with the upstream magnetic field. The KH instability grows even faster than the plasmoid instability, \gmax \tau_A \sim k_{\rm max} \Lsheet\sim S^{1/2}. The effect of viscosity ($\nu$) on the plasmoid instability is also addressed. In the limit of large magnetic Prandtl numbers, $Pm=\nu/\eta$, it is found that \gmax\sim S^{1/4}Pm^{-5/8} and k_{\rm max} \Lsheet\sim S^{3/8}Pm^{-3/16}, leading to the prediction that the critical Lundquist number for plasmoid instability in the $Pm\gg1$ regime is \Scrit\sim 10^4Pm^{1/2}. These results are verified via direct numerical simulation of the linearized equations, using a new, analytical 2D SP equilibrium solution.Comment: 21 pages, 9 figures, submitted to Phys. Rev.

Magnetic Reconnection Onset via Disruption of a Forming Current Sheet by the Tearing Instability

The recent realization that Sweet-Parker current sheets are violently unstable to the secondary tearing (plasmoid) instability implies that such current sheets cannot occur in real systems. This suggests that, in order to understand the onset of magnetic reconnection, one needs to consider the growth of the tearing instability in a current layer as it is being formed. Such an analysis is performed here in the context of nonlinear resistive MHD for a generic time-dependent equilibrium representing a gradually forming current sheet. It is shown that two onset regimes, single-island and multi-island, are possible, depending on the rate of current sheet formation. A simple model is used to compute the criterion for transition between these two regimes, as well as the reconnection onset time and the current sheet parameters at that moment. For typical solar corona parameters this model yields results consistent with observations.Comment: 5 pages, no figures; accepted for publication in Physical Review Letter

Magnetic reconnection and stochastic plasmoid chains in high-Lundquist-number plasmas

A numerical study of magnetic reconnection in the large-Lundquist-number ($S$), plasmoid-dominated regime is carried out for $S$ up to $10^7$. The theoretical model of Uzdensky {\it et al.} [Phys. Rev. Lett. {\bf 105}, 235002 (2010)] is confirmed and partially amended. The normalized reconnection rate is \normEeff\sim 0.02 independently of $S$ for $S\gg10^4$. The plasmoid flux ($\Psi$) and half-width ($w_x$) distribution functions scale as $f(\Psi)\sim \Psi^{-2}$ and $f(w_x)\sim w_x^{-2}$. The joint distribution of $\Psi$ and $w_x$ shows that plasmoids populate a triangular region $w_x\gtrsim\Psi/B_0$, where $B_0$ is the reconnecting field. It is argued that this feature is due to plasmoid coalescence. Macroscopic "monster" plasmoids with $w_x\sim 10$% of the system size are shown to emerge in just a few Alfv\'en times, independently of $S$, suggesting that large disruptive events are an inevitable feature of large-$S$ reconnection.Comment: 5 pages, 6 figures, submitted for publicatio

FDI, income inequality and poverty : a time series analysis of Portugal, 1973–2016

Using time series data for Portugal between 1973 and 2016, this paper examines to what extent, inward FDI contributes to income inequality and poverty in the long-run. It was found that increased flows of inward FDI are associated with a less unequal income distribution and lower poverty rates. The results further suggest that, in the Portuguese case there is mutual causality between inward FDI and poverty in the long run, i.e., FDI significantly reduces poverty, and lower levels of poverty lead to higher inward FDI flows. In the case of inequality, the evidence shows that FDI does not contribute to higher (or lower) income inequality. Instead, more unequal income distributions significantly and negatively impact on inward FDI in the long run. Finally, human capital emerged as a key determinant to mitigate income inequality and circumvent poverty, contributing, indirectly, to fostering additional FDI inflows. Such results call for integrated public policy interventions that emphasize social and institu- tional dimensions.info:eu-repo/semantics/publishedVersio

Fast magnetic reconnection in the plasmoid-dominated regime

A conceptual model of resistive magnetic reconnection via a stochastic plasmoid chain is proposed. The global reconnection rate is shown to be independent of the Lundquist number. The distribution of fluxes in the plasmoids is shown to be an inverse square law. It is argued that there is a finite probability of emergence of abnormally large plasmoids, which can disrupt the chain (and may be responsible for observable large abrupt events in solar flares and sawtooth crashes). A criterion for the transition from magnetohydrodynamic to collisionless regime is provided.Comment: 4 pages, 1 figur

Viriato: a Fourier-Hermite spectral code for strongly magnetised fluid-kinetic plasma dynamics

We report on the algorithms and numerical methods used in Viriato, a novel fluid-kinetic code that solves two distinct sets of equations: (i) the Kinetic Reduced Electron Heating Model (KREHM) equations [Zocco & Schekochihin, Phys. Plasmas 18, 102309 (2011)] (which reduce to the standard Reduced-MHD equations in the appropriate limit) and (ii) the kinetic reduced MHD (KRMHD) equations [Schekochihin et al., Astrophys. J. Suppl. 182:310 (2009)]. Two main applications of these equations are magnetised (Alfvenic) plasma turbulence and magnetic reconnection. Viriato uses operator splitting (Strang or Godunov) to separate the dynamics parallel and perpendicular to the ambient magnetic field (assumed strong). Along the magnetic field, Viriato allows for either a second-order accurate MacCormack method or, for higher accuracy, a spectral-like scheme composed of the combination of a total variation diminishing (TVD) third order Runge-Kutta method for the time derivative with a 7th order upwind scheme for the fluxes. Perpendicular to the field Viriato is pseudo-spectral, and the time integration is performed by means of an iterative predictor-corrector scheme. In addition, a distinctive feature of Viriato is its spectral representation of the parallel velocity-space dependence, achieved by means of a Hermite representation of the perturbed distribution function. A series of linear and nonlinear benchmarks and tests are presented, including a detailed analysis of 2D and 3D Orszag-Tang-type decaying turbulence, both in fluid and kinetic regimes.Comment: 42 pages, 15 figures, submitted to J. Comp. Phy