Experimental Evidence of Plasmoids in High-ß Magnetic Reconnection.

Magnetic reconnection is a ubiquitous and fundamental process in plasmas by which magnetic fields change their topology and release magnetic energy. Despite decades of research, the physics governing the reconnection process in many parameter regimes remains controversial. Contemporary reconnection theories predict that long, narrow current sheets are susceptible to the tearing instability and split into isolated magnetic islands (or plasmoids), resulting in an enhanced reconnection rate. While several experimental observations of plasmoids in the regime of low-to-intermediate ß (where ß is the ratio of plasma thermal pressure to magnetic pressure) have been made, there is a relative lack of experimental evidence for plasmoids in the high-ß reconnection environments which are typical in many space and astrophysical contexts. Here, we report strong experimental evidence for plasmoid formation in laser-driven high-ß reconnection experiments.

Theory of the Drift-Wave Instability at Arbitrary Collisionality.

A numerically efficient framework that takes into account the effect of the Coulomb collision operator at arbitrary collisionalities is introduced. Such a model is based on the expansion of the distribution function on a Hermite-Laguerre polynomial basis to study the effects of collisions on magnetized plasma instabilities at arbitrary mean-free path. Focusing on the drift-wave instability, we show that our framework allows retrieving established collisional and collisionless limits. At the intermediate collisionalities relevant for present and future magnetic nuclear fusion devices, deviations with respect to collision operators used in state-of-the-art turbulence simulation codes show the need for retaining the full Coulomb operator in order to obtain both the correct instability growth rate and eigenmode spectrum, which, for example, may significantly impact quantitative predictions of transport. The exponential convergence of the spectral representation that we propose makes the representation of the velocity space dependence, including the full collision operator, more efficient than standard finite difference methods.

Fully kinetic Biermann battery and associated generation of pressure anisotropy.

The dynamical evolution of a fully kinetic, collisionless system with imposed background density and temperature gradients is investigated analytically. The temperature gradient leads to the generation of temperature anisotropy, with the temperature along the gradient becoming larger than that in the direction perpendicular to it. This causes the system to become unstable to pressure anisotropy driven instabilities, dominantly to the electron Weibel instability. When both density and temperature gradients are present and nonparallel to each other, we obtain a Biermann-like linear-in-time magnetic field growth. Accompanying particle-in-cell numerical simulations are shown to confirm our analytical results.

Anomalous Heating and Plasmoid Formation in a Driven Magnetic Reconnection Experiment.

We present a detailed study of magnetic reconnection in a quasi-two-dimensional pulsed-power driven laboratory experiment. Oppositely directed magnetic fields (B=3 T), advected by supersonic, sub-Alfvénic carbon plasma flows (V_{in}=50 km/s), are brought together and mutually annihilate inside a thin current layer (δ=0.6 mm). Temporally and spatially resolved optical diagnostics, including interferometry, Faraday rotation imaging, and Thomson scattering, allow us to determine the structure and dynamics of this layer, the nature of the inflows and outflows, and the detailed energy partition during the reconnection process. We measure high electron and ion temperatures (T_{e}=100 eV, T_{i}=600 eV), far in excess of what can be attributed to classical (Spitzer) resistive and viscous dissipation. We observe the repeated formation and ejection of plasmoids, consistent with the predictions from semicollisional plasmoid theory.

Structure of a Magnetic Flux Annihilation Layer Formed by the Collision of Supersonic, Magnetized Plasma Flows.

We present experiments characterizing the detailed structure of a current layer, generated by the collision of two counterstreaming, supersonic and magnetized aluminum plasma flows. The antiparallel magnetic fields advected by the flows are found to be mutually annihilated inside the layer, giving rise to a bifurcated current structure-two narrow current sheets running along the outside surfaces of the layer. Measurements with Thomson scattering show a fast outflow of plasma along the layer and a high ion temperature (T_{i}∼Z[over ¯]T_{e}, with average ionization Z[over ¯]=7). Analysis of the spatially resolved plasma parameters indicates that the advection and subsequent annihilation of the inflowing magnetic flux determines the structure of the layer, while the ion heating could be due to the development of kinetic, current-driven instabilities.

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 magnetohydrodynamics 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.

Magnetic-field generation and amplification in an expanding plasma.

Particle-in-cell simulations are used to investigate the formation of magnetic fields B in plasmas with perpendicular electron density and temperature gradients. For system sizes L comparable to the ion skin depth d(i), it is shown that B ∼ d(i)/L, consistent with the Biermann battery effect. However, for large L/d(i), it is found that the Weibel instability (due to electron temperature anisotropy) supersedes the Biermann battery as the main producer of B. The Weibel-produced fields saturate at a finite amplitude (plasma ß ≈ 100), independent of L. The magnetic energy spectra below the electron Larmor radius scale are well fitted by the power law with slope -16/3, as predicted by Schekochihin et al. [Astrophys. J. Suppl. Ser. 182, 310 (2009)].

Fast collisionless reconnection and electron heating in strongly magnetized plasmas.

Magnetic reconnection in strongly magnetized (low-beta), weakly collisional plasmas is investigated by using a novel fluid-kinetic model [Zocco and Schekochihin, Phys. Plasmas 18, 102309 (2011)] which retains nonisothermal electron kinetics. It is shown that electron heating via Landau damping (linear phase mixing) is the dominant dissipation mechanism. In time, electron heating occurs after the peak of the reconnection rate; in space, it is concentrated along the separatrices of the magnetic island. For sufficiently large systems, the peak reconnection rate is cE(∥)(max) ≈ 0.2v(A)B(y,0), where v(A) is the Alfvén speed based on the reconnecting field B(y,0). The island saturation width is the same as in magnetohydrodynamics models except for small systems, when it becomes comparable to the kinetic scales.

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

A two-dimensional (2D) linear theory of the instability of Sweet-Parker (SP) current sheets is developed in the framework of reduced magnetohydrodynamics. 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 14, 100703 (2007)] is recovered, i.e., current sheets are unstable to the formation of a large-wave-number chain of plasmoids (k(max)L(CS)~S(3/8), where k(max) is the wave number of fastest growing mode, S=L(CS)V(A)/η is the Lundquist number, L(CS) is the length of the sheet, V(A) is the Alfvén speed, and η is the plasma resistivity), which grows super Alfvénically fast (γ(max)τ(A)~S(1/4), where γ(max) is the maximum growth rate, and τ(A)=L(CS)/V(A)). For typical background profiles, the growth rate and the wave number are found to 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 Alfvén speed associated with the upstream magnetic field. The KH instability grows even faster than the plasmoid instability γ(max)τ(A)~k(max)L(CS)~S(1/2). The effect of viscosity (ν) on the plasmoid instability is also addressed. In the limit of large magnetic Prandtl numbers Pm=ν/η, it is found that γ(max)~S(1/4)Pm(-5/8) and k(max)L(CS)~S(3/8)Pm(-3/16), leading to the prediction that the critical Lundquist number for plasmoid instability in the Pm>>1 regime is S(crit)~10(4)Pm(1/2). These results are verified via direct numerical simulation of the linearized equations, using an analytical 2D SP equilibrium solution.

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 the resistive magnetohydrodynamic to the collisionless regime is provided.

Formation of plasmoid chains in magnetic reconnection.

A detailed numerical study of magnetic reconnection in resistive MHD for very large, previously inaccessible, Lundquist numbers (10(4) 10(4).

X-point collapse and saturation in the nonlinear tearing mode reconnection.

We study the nonlinear evolution of the resistive tearing mode in slab geometry in two dimensions. We show that, in the strongly driven regime (large delta'), a collapse of the X point occurs once the island width exceeds a certain critical value approximately 1/delta'. A current sheet is formed and the reconnection is exponential in time with a growth rate proportional eta(1/2), where eta is the resistivity. If the aspect ratio of the current sheet is sufficiently large, the sheet can itself become tearing-mode unstable, giving rise to secondary islands, which then coalesce with the original island. The saturated state depends on the value of delta'. For small delta', the saturation amplitude is proportional delta' and quantitatively agrees with the theoretical prediction. If delta' is large enough for the X-point collapse to have occurred, the saturation amplitude increases noticeably and becomes independent of delta'.