Turbulence in fast-mode shocks as a triggering mechanism in a solar flare

If a solar flare originates from the dissipation of magnetic energy, available in abundance in a larger region, this dissipation must take place very rapidly. A local topological change in the magnetic field structure may be sufficient to start the dissipation process. Such a change in topology might be obtained by fast reconnection in a smaller region, such as e.g. in the Sweet-Parker model, as a result of current-driven microinstabilities.Among the candidates satisfying the requirements to obtain large enough currents, such as magnetically neutral or current sheets and MHD shocks, the latter are shown to be most probable. In a fast MHD shock the (thermal) results of turbulence do in fact destroy the conditions for turbulence. However, in this work we show numerically that the nonlinear steepening mechanism of such a shock is able to restore the driving current for a large range of parameters and over a long time. This is still true if the most difficult threshold for turbulence, being that for Langmuir turbulence, is to be achieved. The critical parameter, not only for the occurrence of turbulence but also for the restoration of the driving current, is the shock thickness.     

耀斑大尺度电流片的湍流耗散和能谱分析

磁重联在宇宙的许多动力学现象中都是非常核心的过程.磁流体动力学(MHD)数值模拟是研究磁重联过程以及相应物理图像的一种很有效的手段.通过不同的参数组合,来研究MHD数值模拟中磁雷诺数和空间分辨率对磁重联率、数值耗散和能谱分布的影响.对得到的数据进行分析后,发现磁雷诺数对磁重联率和能谱分布有一定的影响.磁雷诺数越大,磁重联过程进入非线性阶段所需的特征时间越短,磁重联率就越早发生跃升.磁雷诺数R_m对耗散开始发挥作用的Kolmogorov微观尺度l_ko有明显影响:R_m越大,l_ko就越小.研究了磁重联过程中包括数值耗散在内的额外耗散对重联过程的影响.结果表明,撕裂模不稳定性开始之前的额外耗散以纯数值耗散为主,撕裂模不稳定性出现之后,额外耗散出现同步跃升,说明不稳定性导致的湍流明显增强了耗散的效果,相当于在局部湍流区引入了超电阻.能谱分析进一步表明,大尺度电流片的l_ko完全可能出现在宏观的MHD尺度上.     

The impact of correlated noise on SuperWASP detection rates for transiting extrasolar planets

The evolution of the Alfvén turbulence due to three-wave interactions is discussed using kinetic theory for a collisionless, thermal plasma. There are three low-frequency modes, analogous to the three modes of compressible magnetohydrodynamics (MHD). When only Alfvén waves are considered, the known anisotropy of turbulence in incompressible MHD theory is reproduced. Inclusion of a fast mode wave leads to the separation of turbulence into two regimes: small wave numbers where three-wave processes involving a fast mode are dominant, and large wave numbers where the three Alfvén wave process is dominant. Possible application of the anisotropic Alfvén turbulence to the interstellar medium and dissipation of magnetic energy in magnetars are discussed.     

Compressible turbulence in Hall Magnetohydrodynamics

By direct numerical simulations we investigate the nonlinear dynamics of a compressible Hall Magnetohydrodynamic (MHD) plasma. At small scales, where the Hall effect dominates, we found an increase of the compressibility of the system and the breakdown of the strong link between velocity and magnetic fields, typical of usual MHD. Moreover, we find that small-scale fluctuations are characterized by an anti-correlation between density and magnetic field intensity. These features characterize the excitation of a quasi-perpendicular magnetosonic turbulence that can be interpreted as the small-scale signature of the break-down of the MHD nonlinear energy cascade due to Hall effect. Fluctuations with the same properties, based on measurements by Cluster spacecraft in space plasma turbulence during different magnetopause crossings, have been recently observed.     

Turbulence Diffusion and Energy Spectrum Analysis of Large-scale Current Sheets in Flares

Magnetic reconnection (MR) is one of the most important physical processes for many dynamical phenomena in the universe. Magnetohydrodynamical (MHD) simulation is an effective way to study the MR process and the physical pictures related to the MR. With different parameter setups, we investigate the influences of the Magnetic Reynolds number and spatial resolution on the reconnection rate, numerical dissipation, and energy spectrum distribution in the MHD simulation. We have found that the magnetic Reynolds number $R_m$ has definite impact on the reconnection rate and energy spectrum distribution. The characteristic time for entering into the non-linear phase will be earlier as the Reynolds number increases. When it comes to the tearing phase, the reconnection rate will increase rapidly. On the other hand, the magnetic Reynolds number affects significantly the Kolmogorov microscopic scale $l_{\mathit{ko}}$, which becomes smaller as $R_m$ increases. An extra dissipation is defined as the combined effect of the numerical diffusion and turbulence dissipation. It is shown that the extra dissipation is dominated by the numerical diffusion before the tearing mode instability takes place. After the instability develops, the extra dissipation rises vastly, which indicates that turbulence caused by the instability can enhance the diffusion obviously. Furthermore, the energy spectrum analysis indicates that $l_{\mathit{ko}}$ of the large-scale current sheet may appear at a macroscopic MHD scale very possibly.     

Alfvén waves and turbulence in quiescent prominences

In the dynamical model of quiescent prominences presented in this paper, it is assumed that the ever-changing velocity field and brightness of the fine structure is due to MHD turbulence driven by an Alfvén-wave flux from below. It is shown that these waves become highly non-linear and are dissipated over relatively short scales in prominence matter. For magnetic field strengths lower than those observed in quiescent prominences, no closed arch structure can exist with the physical parameters observed. For higher field strengths the conditions for the creation of turbulence are not fulfilled. The momentum gained by prominence matter in the dissipation process, is shown to be of the right order of magnitude to provide the supporting force against gravity. ‘Edge’ effects find a simple explanation within the framework of this hypothesis. In the upper regions of a prominence one result of the dissipation may be the formation of open magnetic configurations, in keeping with the presence of streamers connected with quiescent prominences. Observational tests are proposed and discussed.     

Dissipation in dynamos at low and high magnetic Prandtl numbers

Using simulations of helically driven turbulence, it is shown that the ratio of kinetic to magnetic energy dissipation scales with the magnetic Prandtl number in power law fashion with an exponent of approximately 0.6. Over six orders of magnitude in the magnetic Prandtl number the magnetic field is found tobe sustained by large‐scale dynamo action of alphasquared type. This work extends a similar finding for small magnetic Prandtl numbers to the regime of large magnetic Prandtl numbers. At large magnetic Prandtl numbers, most of the energy is dissipated viscously, lowering thus the amount of magnetic energy dissipation, which means that simulations can be performed at magnetic Reynolds numbers that are large compared to the usual limits imposed by a given resolution. This is analogous to an earlier finding that at small magnetic Prandtl numbers, most of the energy is dissipated resistively, lowering the amount of kinetic energy dissipation, so simulations can then be performed at much larger fluid Reynolds numbers than otherwise. The decrease in magnetic energy dissipation at large magnetic Prandtl numbers is discussed in the context of underluminous accretion found in some quasars (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Towards the circuit theory of solar flares

It has been shown that the main problems of the circuit theory of solar flares - unlikely huge current growth time and the origin of the current interruption - have been resolved considering the case of magnetic loop emergence and the correct application of Ohm's law. The generalized Ohm's law for solar flares is obtained. The conditions for flare energy release are as follows: large current value, > 10¹¹ A, nonsteady-state character of the process, and the existence of a neutral component in a flare plasma. As an example, the coalescence of a flare loop and a filament is considered. It has been shown that the current dissipation has increased drastically as compared with that in a completely ionized plasma. The current dissipation provides effective Joule heating of the plasma and particle acceleration in a solar flare. The ion-atom collisions play the decisive role in the energy release process. As a result the flare loop resistance can grow by 8–10 orders of magnitude. For this we do not need the anomalous resistivity driven by small-scale plasma turbulence. The energy release emerging from the upper part of a flare loop stimulates powerful energy release from the chromospheric level.     

Basic Properties of Compressible MHD Turbulence: Implications for Molecular Clouds

Recent advances in understanding of the basic properties of compressible Magnetohydrodynamic (MHD) turbulence call for revisions of some of the generally accepted concepts. First, the MHD turbulence is not so messy as it is usually believed. In fact, the notion of strong nonlinear coupling of compressible and incompressible motions is not tenable. Alfven, slow and fast modes of MHD turbulence follow their own cascades and exhibit degrees of anisotropy consistent with theoretical expectations. Second, the fast decay of turbulence is not related to the compressibility of fluid. Rates of decay of compressible and incompressible motions are very similar. Third, the viscosity by neutrals does not suppress MHD turbulence in a partially ionized gas. Instead, MHD turbulence develops magnetic cascade at scales below the scale at which neutrals damp ordinary hydrodynamic motions. The implications of those changes of MHD turbulence paradigm for molecular clouds require further studies. Those studies can benefit from testing of theoretical predictions using new statistical techniques that utilize spectroscopic data. We briefly discuss advances in development of tools using which the statistics of turbulent velocity can be recovered from observations.     

Viscous Energy Dissipation by Flux Pile-Up Merging in the Solar Corona

Magnetic field annihilation in resistive viscous incompressible plasmas is analyzed. Anisotropic viscous transport is modeled by the dominant terms in the Braginskii viscous stress tensor. An analytical solution for steady-state magnetic merging, driven by vortical plasma flows in two dimensions, is derived. Resistive and viscous energy dissipation rates are calculated. It is shown that, except in the limiting case of zero vorticity, viscous heating can significantly exceed Joule heating at the merging site. The results strongly suggest that viscous dissipation can provide a significant fraction of the total energy release in solar flares, which may have far-reaching implications for flare models.     

From Small-Scale Dynamo to Isotropic MHD Turbulence

We consider the problem of incompressible, forced, nonhelical, homogeneous, isotropic MHD turbulence with no mean magnetic field. This problem is essentially different from the case with externally imposed uniform mean field. There is no scale-by-scale equipartition between magnetic and kinetic energies as would be the case for the Alfvén-wave turbulence. The isotropic MHD turbulence is the end state of the turbulent dynamo which generates folded fields with small-scale direction reversals. We propose that the statistics seen in numerical simulations of isotropic MHD turbulence could be explained as a superposition of these folded fields and Alfvén-like waves that propagate along the folds.     

Spherical Magnetic Vortex in an External Potential Field: A Dissipative Contraction

We consider the dissipative evolution of a spherical magnetic vortex with a force-free internal structure, located in a resistive medium and held in equilibrium by the potential external field. The magnetic field inside the sphere is force-free (the model of Chandrasekhar in Proc. Natl. Acad. Sci. 42, 1, 1956). Topologically, it is a set of magnetic toroids enclosed in spherical layers. A new exact MHD solution has been derived, describing a slow, uniform, radial compression of a magnetic spheroid under the pressure of an ambient field, when the plasma density and pressure are growing inside it. There is no dissipation in the potential field outside the sphere, but inside the sphere, where the current density can be high enough, the magnetic energy is continuously converted into heat. Joule dissipation lowers the magnetic pressure inside the sphere, which balances the pressure of the ambient field. This results in radial contraction of the magnetic sphere with a speed defined by the conductivity of the plasma and the characteristic spatial scale of the magnetic field inside the sphere. Formally, the sphere shrinks to zero within a finite time interval (magnetic collapse). The time of compression can be relatively small, within a day, even for a sphere with a radius of about 1 Mm, if the magnetic helicity trapped initially in the sphere (which is proportional to the number of magnetic toroids in the sphere) is quite large. The magnetic system is open along its axis of symmetry. On this axis, the magnetic and electric fields are strictly radial and sign-variable along the radius, so the plasma will be ejected along the axis of magnetic sphere outwards in both directions (as jets) at a rate much higher than the diffusive one, and the charged particles will be accelerated unevenly, in spurts, creating quasi-regular X-ray spikes. The applications of the solution to solar flares are discussed.     

The effects on the flow field of retaining the Joule heating and viscous dissipation term in the energy equation for the hydromagnetic free-convective oscillatory flow past a porous limiting surface,I

With viscous dissipation and Joule heating taking into account the hydromagnetic two-dimensional oscillating free-convection flow, of a viscous, incompressible and electrically conducting fluid, past an infinite vertical porous limiting surface, is studied. For the solution of the problem it is considered that, the free-stream velocity, the plate temperature and the induced magnetic field are oscillating in the time about constant mean values. The flow is subjected to a constant suction velocity, through the porous surface, and a magnetic field of uniform strength is applied transversely to the direction of the flow. Analytical expressions for the flow field are obtained by solving the coupled non-linear system of equations which describe the flow. The influence of the various parameters entering into the problem is also extensively discussed signifying the importance of retaining the Joule heating and viscous dissipation term in the energy equation.     

Dynamo process governing solar wind-magnetosphere energy coupling

Based on the method of dimensional analysis, the energy transfer rate from the solar wind into the magnetosphere can be characterized by a magnetic coupling parameter α on open field lines and by a viscous coupling parameter β on closed field lines. By assuming that the energy transfer rate can be monitored by the total energy dissipation rate of the magnetosphere, the histogram of α is constructed and is found to peak around ?0.1 < α < 0.1. This result implies that the energy transfer is governed primarily by the MHD dynamo process on open field lines and indicates that the ? function obtained by Perreault and Akasofu is verified as the first approximation of the solar wind-magnetosphere energy coupling function.     

Cosmic ray scattering in compressible turbulence

We study the scattering of low-energy cosmic rays (CRs) in a turbulent, compressive magnetohydrodynamic (MHD) fluid. We show that compressible MHD modes – fast or slow waves with wavelengths smaller than CR mean free paths induce cyclotron instability in CRs. The instability feeds the new small-scale Alfvénic wave component with wavevectors mostly along magnetic field, which is not a part of the MHD turbulence cascade. This new component gives feedback on the instability through decreasing the CR mean free path. We show that the ambient turbulence fully suppresses the instability at large scales, while wave steepening constrains the amplitude of the waves at small scales. We provide the energy spectrum of the plane-parallel Alfvénic component and calculate mean free paths of CRs as a function of their energy. We find that for the typical parameters of turbulence in the interstellar medium and in the intercluster medium the new Alfvénic component provides the scattering of the low-energy CRs that exceeds the direct resonance scattering by MHD modes. This solves the problem of insufficient scattering of low-energy CRs in the turbulent interstellar or intracluster medium that was reported in the literature.     

Magnetic reconnection: flares and coronal heating in active galactic nuclei

A magnetically structured accretion disc corona, generated by buoyancy instability in the disc, can account for observations of flare-like events in active galactic nuclei. We examine how Petschek magnetic reconnection, associated with MHD turbulence, can result in a violent release of energy and heat the magnetically closed regions of the corona up to canonical X-ray emitting temperatures. X-ray magnetic flares, the after effect of the energy released in slow shocks, can account for the bulk of the X-ray luminosity from Seyfert galaxies and consistently explain the observed short-time-scale variability.     

The spontaneous magnetic field direction in an anisotropic MHD dynamo

The phenomenon of magnetic field generation in an astrophysical plasma in the frame of developed magnetohydrodynamic (MHD) turbulence is considered. The functional quantum field renormalization group approach is applied to helical anisotropic MHD developed turbulence which is stabilized by the self-generated homogeneous magnetic field. The purpose of the study is to calculate the value as well as direction of the magnetic field in the stochastic dynamo model. The generated magnetic field is determined by ignoring divergent rotor part of Green function of the magnetic field. It is shown that the magnetic field direction is connected with unique existing vector n describing the anisotropic turbulence forcing.