Coalescence instability in chromospheric partially ionized plasmas

Standard magnetohydrodynamic (MHD) theory predicts reconnection rate that is far too slow to account for a wide variety of reconnection events observed in space and laboratory plasmas. Therefore, it was commonly accepted that some non-MHD (kinetic) effects play a crucial role in fast reconnection. A recently renewed interest in simple MHD models is associated with the so-called plasmoid instability of reconnecting current sheets. Although it is now evident that this effect can significantly enhance the rate of reconnection, many details of the underlying multiple-plasmoid process still remain controversial. Here, we report results of a high-resolution computer simulation which demonstrate that fast albeit intermittent magnetic reconnection is sustained by numerous small-scale Petschek-type shocks spontaneously formed in the current sheet due to its plasmoid instability.

Magnetic reconnection is widely believed to be involved in dynamical phenomena such as solar flares or magnetospheric substorms. The Sweet–Parker model of magnetic reconnection in a Y-type geometry predicts a characteristic time scale proportional to S1/2 (where S is the Lundquist number), which is too slow to account for the observed time scales. The Petschek model, in contrast, predicts a time scale proportional to ln S in an X-point geometry. Numerical magnetohydrodynamic (MHD) simulations in the high-S regime generally validate the Sweet–Parker model, unless the resistivity is enhanced in the diffusion region to large values (such that typically S<103). It is demonstrated in this paper that nonlinear reconnection dynamics in a Harris sheet driven by inward boundary flows occurs on a nonlinear time scale that is proportional to S1/5 and thus has a weaker dependence on resistivity than the Sweet–Parker time scale. The current sheet amplitude at the separatrix (spanning Y points) grows algebraically in the linear regime but is suddenly enhanced after it makes a transition to the nonlinear regime. An analytical calculation is given for both the linear and the nonlinear regimes, and supported by two-dimensional resistive MHD simulations. The features of sudden current sheet enhancement and fast reconnection, controlled by boundary flows, are relevant to the phenomena of substorm onset or the impulsive phase of flares.

Observations of interplanetary scintillation (IPS) provide a set of data that is used in estimating the solar wind parameters with reasonably good accuracy. Various tomography techniques have been developed to deconvolve the line‐of‐sight integration effects ingrained in observations of IPS to improve the accuracy of solar wind reconstructions. Among those, the time‐dependent tomography developed at the University of California, San Diego (UCSD) is well known for its remarkable accuracy in reproducing the solar wind speed and density at Earth by iteratively fitting a kinematic solar wind model to observations of IPS and near‐Earth spacecraft measurements. However, the kinematic model gradually breaks down as the distance from the Sun increases beyond the orbit of Earth. Therefore, it would be appropriate to use a more sophisticated model, such as a magnetohydrodynamics (MHD) model, to extend the kinematic solar wind reconstruction beyond the Earth's orbit and to the outer heliosphere. To test the suitability of this approach, we use boundary conditions provided by the UCSD time‐dependent tomography to propagate the solar wind outward in a MHD model and compare the simulation results with in situ measurements and also with the corresponding kinematic solution. Interestingly, we find notable differences in proton radial velocity and number density at Earth and various locations in the inner heliosphere between the MHD results and both the in situ data and the kinematic solution. For example, at 1 AU, the MHD velocities are generally larger than the spacecraft data by up to 150 km s−1, and the amplitude of density fluctuations is also markedly larger in the MHD solution. We show that the MHD model can deliver more reasonable results at Earth with an ad hoc adjustment of the inner boundary values. However, we conclude that the MHD model using the inner boundary conditions derived from kinematic simulations has little chance to match IPS and in situ data as well as the kinematic model does unless it too is iteratively fit to the observational data and measurements.

The combined effects of the imposed vertical mean magnetic field ( $B_0$ , scaled as the Alfvèn velocity) and rotation on the heat transfer phenomenon driven by the Rayleigh–Taylor (RT) instability are investigated using direct numerical simulations. In the hydrodynamic (HD) case, as the strength of the Coriolis frequency ( $f$ ) increases, the Coriolis force enhances the mixing of fluids that dampens the growth of the mixing layer height ( $h$ ) and reversible exchanges between the fluids, leading to a reduction in the heat transport, characterised by the Nusselt number ( $Nu$ ). In non-rotating magnetohydrodynamic (MHD) cases, we find a significant delay in the onset of RT instability with increasing $B_0$ , consistent with the linear theory in the literature. The imposed $B_0$ forms vertically elongated thermal plumes that exhibit a larger reversible buoyancy flux due to limited mixing, enabling them to transport heat efficiently between the bottom hot fluid and the upper cold fluid. This leads to enhanced heat transfer in the initial regime of unbroken elongated plumes in non-rotating MHD cases compared to the corresponding HD case. In the turbulent regime of broken small-scale structures, the imposed $B_0$ collimates the flow along the vertical magnetic field lines, reducing vertical velocity fluctuations ( $u_3^{\prime }$ ) and increasing the growth of $h$ . The increased $h$ primarily drives the heat transfer enhancement in the turbulent regime of non-rotating MHD over the corresponding HD case. When rotation is added along with the imposed $B_0$ , the growth and breakdown of vertically elongated plumes are inhibited by the instability-damping effect of the Coriolis force. Consequently, heat transfer is also reduced in the rotating MHD cases compared to the corresponding non-rotating MHD cases. Interestingly, heat transport in rotating MHD cases is enhanced compared to the corresponding rotating HD cases because $B_0$ reduces mixing and mitigates the instability-damping effect of the Coriolis force. The presence of the ultimate state regime $Nu\simeq Ra^{1/2}Pr^{1/2}$ , where $Ra$ is the Rayleigh number and $Pr$ is the Prandtl number, is observed in the non-rotating HD and MHD cases. However, the rotating HD and MHD cases depart from this ultimate state scaling. Furthermore, the dynamic balance between different forces is analysed to understand the behaviour of the thermal plumes. The turbulent kinetic energy budget reveals the conversion of the turbulent kinetic energy, generated by the buoyancy flux, into turbulent magnetic energy.

Dissipation processes responsible for fast magnetic reconnection in collisionless plasmas are investigated using 3D electromagnetic particle-in-cell simulations. The present study revisits the two simulation runs performed in the previous study (Fujimoto, Phys. Plasmas 16, 042103 (2009)); one with small system size in the current density direction, and the other with larger system size. In the case with small system size, the reconnection processes are almost the same as those in 2D reconnection, while in the other case a kink mode evolves along the current density and deforms the current sheet structure drastically. Although fast reconnection is achieved in both the cases, the dissipation mechanism is very different between them. In the case without kink mode, the electrons transit the electron diffusion region without thermalization, so that the magnetic dissipation is supported by the inertia resistivity alone. On the other hand, in the kinked current sheet, the electrons are not only accelerated in bulk, but they are also partly scattered and thermalized by the kink mode, which results in the anomalous resistivity in addition to the inertia resistivity. It is demonstrated that in 3D reconnection the thickness of the electron current sheet becomes larger than the local electron inertia length, consistent with the theoretical prediction in Fujimoto and Sydora (Phys. Plasmas 16, 112309 (2009)).

The present paper studies the basic physics of the spontaneous fast reconnection model in a three-dimensional (3D) situation for different resistivity parameter values, where the threshold for occurrence of current-driven anomalous resistivity is allowed to increase with the thermal velocity (T), and the initial plasma density notably changes in space with the plasma pressure in the current sheet system. For any case, once the anomalous resistivity is ignited, the 3D fast reconnection mechanism explosively evolves as a nonlinear instability by the positive feedback between the anomalous resistivity and the reconnection flow, even if the threshold significantly increases with the thermal velocity; for the larger threshold values, the fast reconnection evolution becomes more drastic and the reconnection rate, finally attained on the nonlinear saturation phase, becomes larger. In the resulting 3D fast reconnection configuration, slow shocks stand and extend outwards in the finite extent; also, ahead of the fast reconnection jet, a large-scale 3D plasmoid swells and propagates in the central current sheet, and a vortex flow is formed near the plasmoid side boundary. In the wide range of parameter values, the basic physics of the 3D spontaneous fast reconnection evolution in the finite extent is found to be, qualitatively, consistent with the well-known two-dimensional one.

<p>Near-Earth solar wind conditions, including disturbances generated by coronal mass ejections (CMEs), are routinely forecast using 3-dimensional, numerical magnetohydrodynamic (MHD) models of the heliosphere. The resulting forecast errors are largely the result of uncertainty in the near-Sun boundary conditions, rather than heliospheric model physics or numerics. Thus ensembles of heliospheric model runs with perturbed initial conditions are used to estimate forecast uncertainty. MHD heliospheric models are relatively cheap in computational terms, requiring tens of minutes to an hour to simulate CME propagation from the Sun to Earth. Thus such ensembles can be run operationally. However, ensemble size is typically limited to ~10<sup>1</sup>-10<sup>2</sup>, which may be inadequate to sample the relevant high-dimensional parameter space. Here, we describe a simplified solar wind model that can estimate CME arrival time in approximately 0.01 seconds on a modest desktop computer and thus enables significantly larger ensembles. It is a 1-dimensional, incompressible, hydrodynamic model, which has previously been used for the steady-state solar wind, but is here used in time-dependent form. This approach is shown to adequately emulate the MHD solutions to the same boundary conditions for both steady-state solar wind and CME-like disturbances. We suggest it could serve as a “surrogate” model for the full 3-dimensional MHD models. For example, ensembles of ~10<sup>5</sup>-10<sup>6</sup> members can be used to identify regions of parameter space for more detailed investigation by the MHD models. Similarly, the simplicity of the model means it can be rewritten as an adjoint model, enabling variational data assimilation with MHD models without the need to alter their code. Model code is available as an Open Source download in the Python language.</p>

In this study, we simulate the Solar Wind Charge Exchange (SWCX) soft X‐ray emissions at dayside magnetosheath and cusps by using magnetohydrodynamic (MHD) and LAtmos TEst Particle (LaTeP) models. MHD models are unable to resolve the particle kinetic effects, such as the different behaviors of ions with different q/m, or distinguish the magnetospheric plasma from the solar wind plasma. We investigate these effects with the LaTeP model. As the LaTeP model does not self‐compute magnetic and electric field, the magnetic and electric field data obtained from Open Geospace General Circulation Model (OpenGGCM) and Lagrangian version of the piecewise parabolic method (PPMLR) MHD model are used as the input to LaTeP model. The soft X‐ray emissivity maps simulated from pure OpenGGCM and PPMLR MHD approaches and from LaTeP‐OpenGGCM and LaTeP‐PPMLR approaches are presented and compared. The results indicate that the LaTeP model can well resolve the kinetic effects and can be used to investigate the individual spectral characteristics. Therefore, the LaTeP model is a complementary approach for simulating the X‐ray emissions near the dayside magnetopause. We also calculate the ratio of integrated OVII/OVIII line intensities, produced by charge exchange of O7+ ions and O8+ ions, respectively. We find a relatively higher ratio at the bow shock compared to the surrounding areas, suggesting that this ratio can be an effective parameter to identify the bow shock location.

Fast magnetic reconnection mechanism triggered by current sheet ejection is studied in plasma merging laboratory experiment with a strong guide field. The current sheet is hardly compressed in the presence of the guide field and slow steady reconnection evolves in the early phase. It then transits to impulsively fast magnetic reconnection when the current sheet is ejected from the X point region. Behavior of the current sheet is investigated in detail by comparison with the fast reconnection case provided by anomalous resistivity.

MHD simulations of fast reconnection spontaneously developing in a current sheet

We consider a general family of regularized Navier-Stokes and Magnetohydrodynamics (MHD) models on n-dimensional smooth compact Riemannian manifolds with or without boundary, with n greater than or equal to 2. This family captures most of the specific regularized models that have been proposed and analyzed in the literature, including the Navier-Stokes equations, the Navier-Stokes-alpha model, the Leray-alpha model, the Modified Leray-alpha model, the Simplified Bardina model, the Navier-Stokes-Voight model, the Navier-Stokes-alpha-like models, and certain MHD models, in addition to representing a larger 3-parameter family of models not previously analyzed. We give a unified analysis of the entire three-parameter family using only abstract mapping properties of the principle dissipation and smoothing operators, and then use specific parameterizations to obtain the sharpest results. We first establish existence and regularity results, and under appropriate assumptions show uniqueness and stability. We then establish results for singular perturbations, including the inviscid and alpha limits. Next we show existence of a global attractor for the general model, and give estimates for its dimension. We finish by establishing some results on determining operators for subfamilies of dissipative and non-dissipative models. In addition to establishing a number of results for all models in this general family, the framework recovers most of the previous results on existence, regularity, uniqueness, stability, attractor existence and dimension, and determining operators for well-known members of this family.

Three major cusp models are systematically compared with low-resolution (large-scale) and high-resolution (fine-scale) low-altitude observations. Those models are (a) global magnetohydrodynamics (MHD) models (including MHD+drift models), (b) turbulent/diffusive entry models, and (c) direct flowing entry models. Although low-resolution data are mostly consistent with MHD models, high-resolution data mostly contradicts them. The data instead supports the other models in which the cusp is considered as a local `extra' open region. This is a good lesson to us: past supportive `tests' of MHD cusp models might have essential flaws in the methodology, and high-resolution data is necessary even for large-scale modelings.

This work investigates the interaction between high current vacuum arc (HCVA) and the macroparticle (MP) generated from the cathode spots (CS) in the small-size vacuum trigatron. Magnetohydrodynamic (MHD) model is used to describe the arc column. MPs are added into MHD model, which are described by discrete phase model (DPM). The control equations of MPs include charging equation, motion equation and heat transfer equation, in which the evaporation of MPs is also considered. Based on the above model, the effects of MP diameter and arc current on the characteristics of MPs are studied. Simulation results show that MPs leave the interelectrode gap with a deflection angle larger than the initial angle under the influence of plasma. The motion of MPs is similar to that of projectiles. MPs with smaller diameter are influenced by the arc plasma more significantly. MPs can act as a source of the plasma, but these influences are not obvious in HCVA. What may be more harmful to the trigatron is the charging process of MPs during post-arc process.

The dawn‐dusk asymmetry of the magnetopause radial distance under the Parker (and ortho‐Parker) configuration of the interplanetary magnetic field (IMF) is investigated. An extensive data set of about 50,000 magnetopause crossings identified in the data from the THEMIS A‐E, Magion 4, Geotail, and Interball‐1 satellites is used for this purpose. It is shown that the magnetopause radial distances are larger at the side where the IMF is quasi‐parallel to the bow shock normal than at the side where IMF is quasi‐perpendicular to the bow shock normal. The effect is more significant at the flanks than close to the subsolar point. This introduces a significant asymmetry of the magnetopause shape, with the difference in the magnetopause radial distances being as large as about one Earth radius beyond the terminator. The experimental results are confirmed by a global magnetohydrodynamic (MHD) model, demonstrating that the asymmetry can be explained by MHD effects, without considering foreshock transients. This MHD model is further used to investigate the evolution of individual pressure components across the magnetopause and contrast them in quasi‐parallel and quasi‐perpendicular cases.

Ion heating during a substorm on 15 February 2008, starting at 0348 UT, is studied with a new approach recently described in Ashour‐Abdalla et al. (2015). The general conditions of the magnetotail are obtained from a global magnetohydrodynamic (MHD) model and are used to drive a full kinetic particle‐in‐cell (PIC) simulation of a 3‐D region of the tail. Within the kinetic box, the ions, the electrons, and the fields evolve self‐consistently. The large scales are captured by the MHD model and the small scales by the PIC model based on the MHD state. This approach is used to study ion heating. Different heating mechanisms were analyzed by examining the velocity distributions at different locations. In the x direction heating occurs as the reconnection‐generated ion jet interacts with the environment in which it propagates. The heating is found mostly in the separatrices and increases downstream of the reconnection region. In the y direction the heating is less intense and is found near the dipolarization fronts. It occurs as ions become magnetized and gyrotropize the distribution function. In addition, ions can be heated in the y direction by the reconnection electric field near the reconnection site. In the z direction the ions are heated by the formation of beams moving along z between the separatrices.