D. Borgogno

Recent advances in collisionless magnetic reconnection

One of the recurring problems in magnetic reconnection is the identification of the appropriate generalized Ohms law. In weakly collisional plasmas with a strong magnetic guide field component, a fluid model may be adopted, where electron inertia and the electron pressure gradient play important roles. In the absence of collisions, electron inertia provides the mechanism for magnetic field-line breaking. Electron compressibility alters significantly the structure of the reconnection region and allows for faster reconnection rates, which are consistent with the fast relaxation times of sawtooth oscillations in tokamak plasmas. The Hall term may also become important when the guide field is weak. The very possibility of nonlinear, irreversible magnetic reconnection in the absence of dissipation is addressed. We show that in a collisionless plasma, magnetic islands can grow and reach a saturated state in a coarse-grained sense. Magnetic energy is transferred to kinetic energy in smaller and smaller spatial scale lengths through a phase mixing process. The same model is then applied to the interpretation of driven reconnection events in the vicinity of a magnetic X-line observed in the VTF experiment at MIT. The reconnection is driven by externally induced plasma flows in a background magnetic configuration that has a hyperbolic null in the reconnection plane and a magnetic guide field component perpendicular to that plane. In the limit where the guide field is strong, assuming the external drive to be sufficiently weak for a linear approximation to hold, a dynamic evolution of the system is obtained which does not reach a stationary state. The reconnection process develops in two phases: an initial phase, whose characteristic rate is a fraction of the Alfven frequency, and a later one, whose rate is determined by the electron collision frequency.

Aspects of three-dimensional magnetic reconnection

The nonlinear behavior of reconnecting modes in three spatial dimensions (3D) is investigated, on the basis of a collisionless fluid model in slab geometry, assuming a strong constant guide field in one direction. Unstable modes in the so-called large Δ′ regime are considered. Single helicity modes, i.e., modes with the same orientation with respect to the guide field, depending on all three spatial coordinates correspond to “oblique” modes with, in general, mixed parity around the corresponding resonant magnetic surface, giving rise to a nonlinear drift of the magnetic island X point. The nonlinear coupling of initial perturbations with different helicities introduces additional helicities that evolve in time in agreement with quasilinear estimates, as long as their amplitudes remain relatively small. Magnetic field lines become stochastic when islands with different helicities are present. Basic questions such as the proper definition of the reconnection rate in 3D are addressed.

Gyro-induced acceleration of magnetic reconnection

The linear and nonlinear evolution of magnetic reconnection in collisionless high-temperature plasmas with a strong guide field is analyzed on the basis of a two-dimensional gyrofluid model. The linear growth rate of the reconnecting instability is compared to analytical calculations over the whole spectrum of linearly unstable wave numbers. In the strongly unstable regime (large Δ′), the nonlinear evolution of the reconnecting instability is found to undergo two distinctive acceleration phases separated by a stall phase in which the instantaneous growth rate decreases. The first acceleration phase is caused by the formation of strong electric fields close to the X-point due to ion gyration, while the second acceleration phase is driven by the development of an open Petschek-like configuration due to both ion and electron temperature effects. Furthermore, the maximum instantaneous growth rate is found to increase dramatically over its linear value for decreasing diffusion layers. This is a consequence of the fact that the peak instantaneous growth rate becomes weakly dependent on the microscopic plasma parameters if the diffusion region thickness is sufficiently smaller than the equilibrium magnetic field scale length. When this condition is satisfied, the peak reconnection rate asymptotes to a constant value.

Secondary instabilities in two-and three-dimensional magnetic reconnection in fusion relevant plasmas

The fast collisionless reconnection process typical of fusion relevant plasma regimes is analyzed with both two-dimensional and three-dimensional models. The vorticity and current density layers, which typically form in these regimes, are followed during all the phases of their dynamical evolution. Here, these structures are shown to be unstable in the cold electron case to secondary Kelvin-Helmholtz-like instabilities not only in the two-dimensional approximation but also in the full three-dimensional setting.

REDUCTION OF COMPRESSIBILITY AND PARALLEL TRANSFER BY LANDAU DAMPING IN TURBULENT MAGNETIZED PLASMAS

Three-dimensional numerical simulations of decaying turbulence in a magnetized plasma are performed using a so-called finite Larmor radius (FLR)-Landau fluid model which incorporates linear Landau damping and FLR corrections. It is shown that compared to simulations of compressible Hall-MHD, linear Landau damping is responsible for significant damping of magnetosonic waves, which is consistent with the linear kinetic theory. Compressibility of the fluid and parallel energy cascade along the ambient magnetic field are also significantly inhibited when the beta parameter is not too small. In contrast with Hall-MHD, the FLR-Landau fluid model can therefore correctly describe turbulence in collisionless plasmas such as solar wind, providing an interpretation for its nearly incompressible behavior.

INFLUENCE OF THE NONLINEARITY PARAMETER ON THE SOLAR WIND SUB-ION MAGNETIC ENERGY SPECTRUM: FLR–LANDAU FLUID SIMULATIONS

The cascade of kinetic Alfven waves (KAWs) at sub-ion scales in the solar wind is simulated numerically using a fluid approach that retains ion and electron Landau damping, together with ion finite Larmor radius (FLR) corrections. Assuming initially equal and isotropic ion and electron temperatures, and an ion beta equal to unity, different simulations are performed by varying the propagation direction and the amplitude of KAWs that are randomly driven at a transverse wavenumber k0 such that (where di is the proton inertial length), in order to maintain a prescribed level of turbulent fluctuations. The resulting turbulent regimes are characterized by the nonlinearity parameter, defined as the ratio of the characteristic times of Alfven wave propagation and of the transverse nonlinear dynamics. The corresponding transverse magnetic energy spectra display power laws with exponents spanning a range of values consistent with spacecraft observations. The meandering of the magnetic field lines and the homogenization of ion temperature along these lines are shown to be related to the strength of the turbulence, measured by the nonlinearity parameter. The results are interpreted in terms of a recently proposed phenomenological model where the homogenization process along field lines induced by Landau damping plays a central role.

Barriers in the transition to global chaos in collisionless magnetic reconnection. I. Ridges of the finite time Lyapunov exponent field

The transitional phase from local to global chaos in the magnetic field of a reconnecting current layer is investigated. Regions where the magnetic field is stochastic exist next to regions where the field is more regular. In regions between stochastic layers and between a stochastic layer and an island structure, the field of the finite time Lyapunov exponent (FTLE) shows a structure with ridges. These ridges, which are special gradient lines that are transverse to the direction of minimum curvature of this field, are approximate Lagrangian coherent structures (LCS) that act as barriers for the transport of field lines.

Asymmetric tearing mode in the presence of viscosity

The linear stability of the tearing mode (TM) in a plasma column is investigated in the presence of viscosity and finite equilibrium current density gradients (i.e., asymmetries). It is shown that for low β, both effects are essential in order to properly describe the mode behaviour close to marginality. In particular, the theory introduces a critical threshold for the destabilization, such that the perturbation grows only if Δ′>Δ′cr. The value of Δ′cr depends on the equilibrium configuration and on the plasma parameters. Most importantly, Δ′cr can take negative values, thus allowing unstable tearing modes for Δ′ < 0 (even in the absence of bootstrap current).

Barriers in the transition to global chaos in collisionless magnetic reconnection. II. Field line spectroscopy

The transitional phase from local to global chaos in the magnetic field of a reconnecting current layer is investigated. The identification of the ridges in the field of the finite time Lyapunov exponent as barriers to the field line motion is carried out adopting the technique of field line spectroscopy to analyze the radial position of a field line while it winds its way through partial stochastic layers and to compare the frequencies of the field line motion with the corresponding frequencies of the distinguished hyperbolic field lines that are the nonlinear generalizations of linear X-lines.

Predicting the behaviour of magnetic reconnection processes in fusion burning plasma experiments

Critical stability issues involving magnetic reconnection that are likely to influence the successful operation of burning plasma experiments are addressed. In particular, we discuss: (1) the stabilization of drift-tearing modes in weakly collisional regimes, with particular reference to nonlinear stability, including neo-classical effects; (2) the present understanding of sawtooth oscillations, in particular the interpretation of peculiar sawtooth features in FTU experiments with pellet injection; (3) reconnection near the X-points of magnetic separatrices.