Force-free magnetic fields with singular current density surfaces and their stability

Starting from Bernstein's principle of magnetohydrodynamic energy, a general analysis is presented for the stability of a kind of 1-D force-free magnetic fields with singular current density surfaces and a single parameter in cylindrical coordinates. It is found that in the parameter space of this kind of force-free magnetic fields there simultaneously exist stable and unstable regions. Their stability is solely determined by the radial distribution of the magnetic pitch in the neighborhood of the cylinder axis, and is independent of the presence of singular current density surface at the boundary of the field.     

Kinetic Alfvén waves in preflare plasma

Low‐frequency instabilities of plasma waves in the arch structures in solar active regions have been investigated before a flare. In the framework of mechanism of “direct initiation” of instability by slowly increasing (quasi‐static) large‐scale electric field in a loop the dispersion relation has been studied for the perturbations which propagate almost perpendicularly to the magnetic field of the loop. The case has been considered, when amplitude of weak (“subdreicer”) electric field sharply increases before a flare, low‐frequency instability develops on the background of ion‐acoustic turbulence and thickness of this turbulent plasma layer plays the role of mean characteristic scale of inhomogeneity of plasma density. If the values of the main plasma parameters, i.e. temperature, density, magnetic field amplitude allow to neglect the influence of the shear of magnetic strength lines on the instability development, then two types of the waves can be generated in preflare plasma: the kinetic Alfvén waves and some new kind of the waves from the range of slowly magneto‐acoustic ones. Instability of kinetic Alfvén waves has clearly expressed threshold character with respect to the amplitude of “subdreicer” electric field. This fact seems to be useful for the short‐time prediction of a flare in arch structure. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The stability of dissipative magnetohydrodynamic shear flow in a parallel magnetic field

Abstract

Strong decay bounds are obtained for linearized perturbations to an unbounded, plane Couette flow in a parallel magnetic field. Finite conductivity and molecular viscosity are found to be stabilizing. Those modes decaying most slowly have the form of rolls aligned with the shear flow. The non-aligned rolls decay at an enhanced rate. Stability bounds at finite amplitude are obtained for flows bounded in one direction using energy methods.     

Magnetic reconnection in solar flares

Abstract

The magnetic energy stored in the corona is the only plausible source for the energy released during large solar flares. During the last 20 years most theoretical work has concentrated on models which store magnetic energy in the corona in the form of electrical currents, and a major goal of present day research is to understand how these currents are created, and then later dissipated during a flare. Another important goal is to find a flare model which can eject magnetic flux into interplanetary space. Although many flares do not eject magnetic flux, those which do are of special importance for solar-terrestrial relations since the ejected flux can have dramatic effects if it hits the Earth's magnetosphere. Three flare models which have been extensively investigated are the emerging-flux model, the sheared-arcade model, and the magnetic-flux-rope model. All of these models can store and release magnetic energy efficiently provided that rapid magnetic reconnection occurs. However, only the magnetic-flux-rope model appears to provide a plausible mechanism for ejecting magnetic flux into interplanetary space.     

Laboratory and numerical model studies of a negatively-buoyant jet discharged horizontally into a homogeneous rotating fluid

Abstract

The results of laboratory experiments and numerical model simulations are described in which the motion of a round, negatively-buoyant, turbulent jet discharged horizontally above a slope into a rotating homogeneous fluid has been investigated. For the laboratory study, flow visualisation data are presented to show the complex three-dimensional flow fields generated by the discharge. Analysis of the experimental data indicates that the spatial and temporal developments of the flow field are controlled primarily by the lateral and vertical discharge position of the jet (with respect to the bounding surfaces of the container of width W) and the specific momentum (M ₀) and buoyancy (B ₀) fluxes driving the jet. The flow is seen to be characterised by the formation of (i) a primary anticyclonic eddy (PCC) close to the source, (ii) an associated secondary cyclonic eddy (SCE) and (iii) a buoyancy-driven bottom boundary current along the right side boundary wall. For the parameter ranges studied, the size L _{p, s} and spatial location x _{p, s} of the PCC and SCE (and the nose velocity u _N of the boundary current) are shown to be only weakly-dependent upon the value of the mixed parameter M ₀Ω/B ₀, where Ω is the background rotation rate. Both L _p and x _p are shown to scale with the separation distance y?/W of the right side wall (y = 0) from the source (y = y?), both L _s and x _s scale satisfactorily with the length scale l _M (= M ₀ ^3/4/B ₀ ^½) and u _N is determined by the appropriate gravity current speed [(g']₀ H]^½ and the separation distance y?/W.

Numerical model results show good qualitative agreement with the laboratory data with regard to the generation of the PCC, SCE and boundary current as characteristic features of the flow in question. In addition, extension of the numerical model to

diagnose potential vorticity and plume thickness distributions for the laboratory cases allow the differences in momentum-and buoyancy-dominated flows to be clearly delineated. Specifically, the characteristic features of the SCE are shown to be strongly dependent upon the value of M ₀Ω/B ₀ for the buoyant jet flow; not least, the numerical model data are able to confirm the controlling role played by the boundary walls in the laboratory experiments. Quantitative agreement between the numerical and laboratory model data is fair; most significantly, the success of the former model in simulating the dominant flow features from the latter enables the reliable extension of the numerical model to be made to cases of direct oceanic interest.     

Mean electromotive force proportional to mean flow in MILD turbulence

In mean‐field magnetohydrodynamics the mean electromotive force due to velocity and magnetic‐field fluctuations plays a crucial role. In general it consists of two parts, one independent of and another one proportional to the mean magnetic field. The first part may be nonzero only in the presence of mhd turbulence, maintained, e.g., by small‐scale dynamo action. It corresponds to a battery, which lets a mean magnetic field grow from zero to a finite value. The second part, which covers, e.g., the α effect, is important for large‐scale dynamos. Only a few examples of the aforementioned first part of the mean electromotive force have been discussed so far. It is shown that a mean electromotive force proportional to the mean fluid velocity, but independent of the mean magnetic field, may occur in an originally homogeneous isotropic mhd turbulence if there are nonzero correlations of velocity and electric current fluctuations or, what is equivalent, of vorticity and magnetic field fluctuations. This goes beyond the Yoshizawa effect, which consists in the occurrence of mean electromotive forces proportional to the mean vorticity or to the angular velocity defining the Coriolis force in a rotating frame and depends on the cross‐helicity defined by the velocity and magnetic field fluctuations. Contributions to the mean electromotive force due to inhomogeneity of the turbulence are also considered. Possible consequences of the above findings for the generation of magnetic fields in cosmic bodies are discussed (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Convective dynamos in spherical wedge geometry

Self‐consistent convective dynamo simulations in wedge‐shaped spherical shells are presented. Differential rotation is generated by the interaction of convection with rotation. Equatorward acceleration and dynamo action are obtained only for sufficiently rapid rotation. The angular velocity tends to be constant along cylinders. Oscillatory large‐scale fields are found to migrate in the poleward direction. Comparison with earlier simulations in full spherical shells and Cartesian domains is made (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Direct measurement of effective electro conductivity of turbulent liquid metal

Direct measurement of effective electro conductivity are performed in a nonstationary turbulent flow of liquid gallium, generated in a closed toroidal channel. The peak level of the Reynolds number reached Re ≈ 10⁶, what corresponds to the magnetic Reynolds number Rm ≈ 1. The conductivity of the liquid metal was determined measuring the phase shift between sinusoidal voltage and current in the RLC‐circuit, the inductance of which was made by the toroidal coil embracing the channel. The maximal deviation of electrical conductivity from its ohmic value reaches about 1%. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The screw dynamo in a thick torus

The problem of magnetic field generation under screw motion in a toroidal channel is studied numerically. The screw dynamo in the cylinder with periodical boundary conditions was found to be a suitable approximation for generation of the magnetic field by a screw flow in a thin torus. For the thick torus, a principally new solution of the screw dynamo problem was obtained. In this case the growing global magnetic field mode has the scale of a maximal geometrical size of the torus and does not vanish on the axis of the torus (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)