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[en] A new paradigm is emerging for 3D magnetic reconnection where the interaction of reconnection processes with current aligned instabilities plays an important role. According to the new paradigm, the initial equilibrium is rendered unstable by current aligned instabilities (lower-hybrid drift instability first, drift-kink instability later) and the non-uniform development of kinking modes leads to a compression of magnetic field lines in certain locations and a rarefaction in others. The areas where the flow is compressional are subjected to a driven reconnection process on the time scale of the driving mechanism (the kink mode). In the present paper we illustrate this series of event with a selection of simulation results.
[en] We report a new particle in cell (PIC) method based on the semi-implicit approach. The novelty of the new method is that unlike any of its semi-implicit predecessors at the same time it retains the explicit computational cycle and conserves energy exactly. Recent research has presented fully implicit methods where energy conservation is obtained as part of a non-linear iteration procedure. The new method (referred to as Energy Conserving Semi-Implicit Method, ECSIM), instead, does not require any non-linear iteration and its computational cycle is similar to that of explicit PIC. The properties of the new method are: i) it conserves energy exactly to round-off for any time step or grid spacing; ii) it is unconditionally stable in time, freeing the user from the need to resolve the electron plasma frequency and allowing the user to select any desired time step; iii) it eliminates the constraint of the finite grid instability, allowing the user to select any desired resolution without being forced to resolve the Debye length; iv) the particle mover has a computational complexity identical to that of the explicit PIC, only the field solver has an increased computational cost. The new ECSIM is tested in a number of benchmarks where accuracy and computational performance are tested. - Highlights: • We present a new fully energy conserving semi-implicit particle in cell (PIC) method based on the implicit moment method (IMM). The new method is called Energy Conserving Implicit Moment Method (ECIMM). • The novelty of the new method is that unlike any of its predecessors at the same time it retains the explicit computational cycle and conserves energy exactly. • The new method is unconditionally stable in time, freeing the user from the need to resolve the electron plasma frequency. • The new method eliminates the constraint of the finite grid instability, allowing the user to select any desired resolution without being forced to resolve the Debye length. • These features are achieved at a reduced cost compared with either previous IMM or fully implicit implementation of PIC.
[en] Here, the discovery of electrostatic fields playing a crucial role in establishing plasma motion in the flux conversion and dynamo processes in reversed field pinches is revisited. In order to further elucidate the role of the electrostatic fields, a flux rope configuration susceptible to the kink instability is numerically studied with anMHDcode. Simulated nonlinear evolution of the kink instability is found to confirm the crucial role of the electrostatic fields. Anew insight is gained on the special function of the electrostatic fields: they lead the plasma towards the reconnection site at the mode resonant surface. Without this step the plasma column could not relax to its nonlinear state, since no other agent is present to perform this role. While the inductive field generated directly by the kink instability is the dominant flow driver, the electrostatic field is found to allow the motion in the vicinity of the reconnection region.
[en] The growth of the lower hybrid drift instability (LHDI) in unstable current sheets induces a fluid velocity shear that drives a Kelvin-Helmholtz instability (KHI). The KHI results in kinking of the current sheet, so that any subsequent magnetic reconnection across the current sheet must occur in three dimensions. While this increases the complexity of modeling reconnection, it is of interest for its possible resolution of the stability to tearing of current sheets with a perpendicular magnetic field. Identification of the role of the LHDI in current sheet kinking required advances in simulation technique that allowed simulations at more realistic mass ratio and long time and length scales. Confidence in the results is strongly enhanced by confirmation with a standard plasma simulation using massively parallel computation. The results of this study have obvious relevance not only to magnetic reconnection and substorms in the Earth's magnetotail, where the LHDI has been observed, but also where thin current sheets occur, such as the solar corona
[en] A new paradigm is considered for 3D magnetic reconnection where the interaction of reconnection processes with current aligned instabilities plays an important role. According to the new paradigm, the initial equilibrium is rendered unstable by current aligned instabilities (lower-hybrid drift instability first, drift-kink instability later) and the non-uniform development of kinking modes leads to compression of magnetic field lines in certain locations and rarefaction in others. The areas where the flow is compressional undergo driven reconnection on the time scale of the driving mechanism (the kink mode). In the present paper we illustrate this series of events with a selection of simulation results
[en] Through numerical plasma simulations using the implicit code CELESTE3D [G. Lapenta and J. U. Brackbill, Nonlinear Processes Geophys. 7, 151 (2000)], the development of kink modes in a Harris current sheet is investigated, and their possible nonlinear interaction with the lower hybrid drift instability (LHDI) is considered. Consistent with earlier work, the rapid development of a short wavelength LHDI is observed, followed by the slow development of long wavelength current sheet kinking. The growth of kink modes is in agreement with the linear theory for the drift kink instability only at very small mass ratios (mi/me=16). At more realistic mass ratios, the growth rate exceeds that predicted by linear theory. A thorough investigation of the dependence of current sheet kinking on ion/electron mass and temperature ratios, and current sheet thickness reveals that the growth of kink modes is unaffected by current sheet thinning, but is strongly dependent on the ion/electron temperature ratio. The saturation amplitude of the LHDI increases with decreasing electron temperature, as do the nonlinear modifications of the initial equilibrium. In particular, the ion diamagnetic drift velocity of the ions decreases sufficiently on the flanks of the current sheet to support a Kelvin-Helmholtz instability, especially with cold electrons, whose properties are completely consistent with the kink modes observed in the simulations
[en] A two-dimensional reconnecting current sheet is studied numerically in the magnetohydrodynamic approach. Different simulation setups are employed in order to follow the evolution of the formed current sheet in diverse configurations: two types of initial equilibria, Harris and force-free, two types of boundary conditions, periodic and open, with uniform and nonuniform grid set, respectively. All the simulated cases are found to exhibit qualitatively the same behavior in which a current sheet evolves slowly through a series of quasiequilibria; eventually it fragments and enters a phase of fast impulsive bursty reconnection. In order to gain more insight on the nature and characteristics of the instability taking place, physical characteristics of the simulated current sheet are related to its geometrical properties. At the adopted Lundquist number of S=104 and Reynolds number R=104, the ratio of the length to width (aspect ratio) of the formed current sheet is observed to increase slowly in time up to a maximum value at which it fragments. Moreover, additional turbulence applied to the system is shown to exhibit the same qualitative steps, but with the sooner onset of the fragmentation and at smaller aspect ratio.
[en] Particle acceleration is a process of great importance in all areas of plasma physics. In most cases, kinetic effects are dominant and require a full kinetic treatment, such as the particle in cell (PIC) method. PIC methods are widely used in all aspects of plasma physics, proving to be a precious and irreplaceable tool. Yet all methods in use and published conserve energy to a good approximation, but not exactly. A well known property of PIC methods, documented extensively in all textbooks, is that energy is not conserved exactly. In fact, the particle noise is a unphysical source of energy that, when insufficient resolution is used, can make the simulations go unstable. In the present paper, we apply a new exactly energy conserving scheme and demonstrate that indeed exact energy conservation plays a key role in determining the correct spectrum of the accelerated particles.
[en] Within a MHD approach we find magnetic reconnection to progress in two entirely different ways. The first is well known: the laminar Sweet-Parker process. But a second, completely different and chaotic reconnection process is possible. This regime has properties of immediate practical relevance: (i) it is much faster, developing on scales of the order of the Alfven time, and (ii) the areas of reconnection become distributed chaotically over a macroscopic region. The onset of the faster process is the formation of closed-circulation patterns where the jets going out of the reconnection regions turn around and force their way back in, carrying along copious amounts of magnetic flux
[en] Based on a recent theory (Coppi 2002 Nucl. Fusion 42 1) of spontaneous toroidal rotation in tokamaks (Lee et al 2003 Phys. Rev. Lett. 91 205003) and in astrophysical accretion disks, we propose that an analogous process could be at play also in the Earth space environment. We use fully kinetic particle-in-cell simulations to study the evolution of drift instabilities. We show that indeed a macroscopic velocity shear is generated spontaneously in the plasma. As in tokamaks, the microscopic fluctuations remain limited to the edge of the plasma channel but the momentum spreads over the whole macroscopic system.