D. Biskamp

Magnetic reconnection via current sheets

A general picture of magnetic reconnection in the framework of 2‐D incompressible resistive magnetohydrodynamic theory is presented. Numerical studies of (quasi‐) steady‐state driven reconnection reveal current sheet formation for Mach numbers M=u/vA exceeding the Sweet–Parker reconnection rate MSP=(η/LvA)1/2. Since the thickness δ of the current sheet is found to be invariant to a change of the resistivity η, its length Δ increases rapidly with decreasing η or increasing M, which can be written in the form Δ∼(M/MSP)4, so that Δ reaches the global system size L within a short range of the parameter M/MSP. The results are rather insensitive to the particular choice of boundary conditions. Because of the presence of a current sheet, the overall reconnection process is quite slow. This picture essentially agrees with Syrovatsky’s [Sov. Phys. JETP 33, 933 (1971)] theory and disproves Petschek’s [AAS/NASA Symposium on the Physics of Solar Flares, (NASA, Washington, DC, 1964) p. 425] mechanism of fast magnetic ...

Structure of the dissipation region during collisionless magnetic reconnection

Collisionless magnetic reconnection is studied using a 2 1/2-dimensional hybrid code including Hall dynamics and electron inertia. The simulations reveal that the dissipation region develops a two-scale structure: an inner electron region and an outer ion region. Close to the X line is a region with a scale of c/ωpe, the electron collisionless skin depth, where the electron flows completely dominate those of the ions and the frozen-in magnetic flux constraint is broken. Outside of this region and encompassing the rest of the dissipation region, which scales like c/ωpi, the ion inertial length, is the Hall region where the electrons are frozen-in to the magnetic field but the ions are not, allowing the two species to flow at different velocities. The decoupling of electron and ion motion in the dissipation region has important implications for the rate of magnetic reconnection in collisionless plasma: the ions are not constrained to flow through the very narrow region where the frozen-in constraint is broken so that ion flux into the dissipation region is large. For the simulations which have been completed to date, the resulting rate of reconnection is a substantial fraction of the Alfven velocity and is controlled by the ions, not the electrons. The dynamics of the ions is found to be inherently nonfluid-like, with multiple ion beams present both at the X line and at the downstream boundary between the inflow and outflow plasma. The reconnection rate is only slightly affected by the temperature of the inflowing ions and in particular the structure of the dissipation region is controlled by the ion inertial length c/ωpi and not the ion Larmor radius based on the incoming ion temperature.

Two-fluid theory of collisionless magnetic reconnection

Theoretical studies of collisionless reconnection in the framework of two-fluid theory are presented. In the high-β case (β≳1) reconnection is controlled by the whistler mode, leading to decoupling of ions from electrons on scales <c/ωpi. Though reconnection requires electron inertia, the reconnection rate is independent thereof, controlled only by ion inertia. Reconnection is hence much faster than in the absence of the Hall term. In the opposite limit of small β the strong axial field suppresses the whistler mode. Hence ions have to follow the electrons in the narrow reconnection layer δ∼c/ωpe, forming a macroscopic current sheet which strongly reduces the reconnection rate. Theoretical scaling laws are confirmed by numerical simulations.

Scaling properties of three-dimensional magnetohydrodynamic turbulence

The scaling properties of three-dimensional magnetohydrodynamic turbulence with finite magnetic helicity are obtained from direct numerical simulations using 512(3) modes. The results indicate that the turbulence does not follow the Iroshnikov-Kraichnan phenomenology. The scaling exponents of the structure functions can be described by a modified She-Leveque model zeta(p) = p/9+1-(1/3)(p/3), corresponding to basic Kolmogorov scaling and sheetlike dissipative structures. In particular, we find zeta(2) approximately 0.7, consistent with the energy spectrum E(k) approximately k(-5/3) as observed in the solar wind, and zeta(3) approximately 1, confirming a recent analytical result.

Collisionless Shock Waves in Plasmas

A review is given of recent developments in collisionless-shock-wave research. Theoretical concepts are compared with both numerical simulation results and experimental observations. Particular emphasis is put on the analysis of collisionless dissipation processes, anomalous resistivity and viscosity.

Scaling properties of three-dimensional isotropic magnetohydrodynamic turbulence

A comprehensive picture of three-dimensional (3D) isotropic magnetohydrodynamic (MHD) turbulence is presented based on the first 5123-mode numerical simulations performed. Both temporal and spatial scaling properties are studied. For finite magnetic helicity H the energy decay is governed by the constancy of H and the decrease of the ratio of kinetic and magnetic energy Γ=EK/EM. A simple model consistent with a series of simulation runs predicts the asymptotic decay laws E∼t−1/2, EK∼t−1. For nonhelical MHD turbulence, H≃0, the energy decays faster, E∼t−1. The energy spectrum follows a k−5/3 law, clearly steeper than k−3/2 previously found in 2D MHD turbulence. The scaling exponents of the structure functions are consistent with a modified She–Leveque model ζpMHD=p/9+1−(1/3)p/3, which corresponds to a basic Kolmogorov scaling and sheet-like dissipative structures. The difference between the 3D and the 2D behavior can be related to the eddy dynamics in 3D and 2D hydrodynamic turbulence.

Numerical Studies of Magnetosonic Collisionless Shock Waves

Supercritical collisionless shock waves propagating perpendicularly to a magnetic field are studied by means of numerical simulation computations. When ion gyration is neglected, the ion temperature increase through the shock is only due to adiabatic compression. Anomalous ion heating is caused by dissipation of the reflected ions which occurs if ion gyration is included.

Electron magnetohydrodynamic turbulence

Electron magnetohydrodynamic (EMHD) turbulence is studied in two- and three-dimensional (2D and 3D) systems. Results in 2D are particularly noteworthy. Energy dissipation rates are found to be independent of the diffusion coefficients. The energy spectrum follows a k−5/3 law for kde>1 and k−7/3 for kde<1, which is consistent with a local spectral energy transfer independent of the linear wave properties, contrary to magnetohydrodynamic (MHD) turbulence, where the Alfven effect dominates the transfer dynamics. In 3D spectral properties are similar to those in 2D.

Transport Control by Coherent Zonal Flows in the Core/Edge Transitional Regime

3D Braginskii turbulence simulations show that the energy flux in the core/edge transition region of a tokamak is strongly modulated-locally and on average-by radially propagating, nearly coherent sinusoidal or solitary zonal flows. Their primary drive is the anomalous transport together with the Stringer-Winsor term. The transport modulation and the flow excitation are due to wave-kinetic effects studied for the first time in turbulence simulations. The flow amplitudes and the transport sensitively depend on the magnetic curvature acting on the flows, which can be influenced, e.g., by shaping the plasma cross section.

Statistical anisotropy of magnetohydrodynamic turbulence.

Direct numerical simulations of decaying and forced magnetohydrodynamic (MHD) turbulence without and with mean magnetic field are analyzed by higher-order two-point statistics. The turbulence exhibits statistical anisotropy with respect to the direction of the local magnetic field even in the case of global isotropy. A mean magnetic field reduces the parallel-field dynamics while in the perpendicular direction a gradual transition towards two-dimensional MHD turbulence is observed with k(-3/2) inertial-range scaling of the perpendicular energy spectrum. An intermittency model based on the log-Poisson approach, zeta(p)=p/g(2)+1-(1/g)(p/g), is able to describe the observed structure function scalings.