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1.
Abstract

We study the problem of the coalescence of twisted flux tubes by assuming that the azimuthal field lines reconnect at a current sheet during the coalescence process and everywhere else the magnetic field is frozen in the fluid. We derive relations connecting the topology of the coalesced flux tube with the topologies of the initial flux tubes, and then obtain a structure equation for calculating the field configuration of the coalesced flux tube from the given topology. Some solutions for the two extreme cases of low-β plasma and high-β plasma are discussed. The coalesced flux tube has less twist than the initial flux tube. Magnetic helicity is found to be exactly conserved during the coalescence, but the assumptions in the model put a constraint on the energy dissipation so that we do not get a relaxation to the minimum-energy Taylor state in the low-β case. It is pointed out that the structure equation connecting the topology and the equilibrium configuration is quite general and can be of use in many two-dimensional flux tube problems.  相似文献   

2.
Abstract

Two open curves with fixed endpoints on a boundary surface can be topologically linked. However, the Gauss linkage integral applies only to closed curves and cannot measure their linkage. Here we employ the concept of relative helicity in order to define a linkage for open curves. For a magnetic field consisting of closed field lines, the magnetic helicity integral can be expressed as the sum of Gauss linkage integrals over pairs of lines. Relative helicity extends the helicity integral to volumes where field lines may cross the boundary surface. By analogy, linkages can be defined for open lines by requiring that their sum equal the relative helicity.

With this definition, the linkage of two lines which extend between two parallel planes simply equals the number of turns the lines take about each other. We obtain this result by first defining a gauge-invariant, one-dimensional helicity density, i.e. the relative helicity of an infinitesimally thin plane slab. This quantity has a physical interpretation in terms of the rate at which field lines lines wind about each other in the direction normal to the plane. A different method is employed for lines with both endpoints on one plane; this method expresses linkages in terms of a certain Gauss linkage integral plus a correction term. In general, the linkage number of two curves can be put in the form L=r + n, |r|≦1J2, where r depends only on the positions of the endpoints, and n is an integer which reflects the order of braiding of the curves.

Given fixed endpoints, the linkage numbers of a magnetic field are ideal magneto-hydrodynamic invariants. These numbers may be useful in the analysis of magnetic structures not bounded by magnetic surfaces, for example solar coronal fields rooted in the photosphere. Unfortunately, the set of linkage numbers for a field does not uniquely determine the field line topology. We briefly discuss the problem of providing a complete and economical classification of field topologies, using concepts from the theory of braid equivalence classes.  相似文献   

3.
The problem of coronal plasma heating is discussed based on coronal magnetic loop heating. The radiation loss in coronal plasma is very high; therefore, it is necessary that rather powerful heating sources exist in this plasma in order to maintain the corona in a quasistationary state. The existing heating mechanisms (current dissipation, magnetic reconnection, microflares, wave heating) are briefly considered from the standpoint of their effectiveness and elaboration. A conclusion has been drawn that heating by microflares and wave heating can be the most promising mechanisms from the standpoint of energy. The mechanism of heating by magnetic reconnection has not yet been studied in detail from the standpoint of its effectiveness and implementation conditions. Heating as a result of Joule dissipation of electric currents is only possible when current filamentation is strong, the presence of which cannot be verified since the equipment resolution is still insufficient.  相似文献   

4.

The behaviour of magnetic helicity in kinematic dynamos at large magnetic Reynolds number is considered. Hughes, et al . [ Phys. Lett. A 223 , 167-172 (1996)] observe that the relative helicity tends to zero in the limit of large magnetic Reynolds number. This paper gives upper bounds on the helicity, by relating the helicity spectrum to the energy spectrum. These bounds are confirmed by numerical simulation and the distribution of helicity over scales is considered. Although it is found that the total helicity becomes small in the limit of high conductivity, there can remain significant, but cancelling, helicity at large and small scales of the field. This is illustrated by considering the evolution of helicity in the stretch-twist-fold dynamo picture.  相似文献   

5.
In this article we present a review of some of the author's most recent results in topological magnetohydrodynamics (MHD), with an eye to possible applications to astrophysical flows and solar coronal structures. First, we briefly review basic work on magnetic helicity and linking numbers, and fundamental relations with magnetic energy and average crossing numbers of magnetic systems in ideal conditions. In the case of magnetic knots, we focus on the relation between their groundstate energy and topology, discussing the energy spectrum of tight knots in terms of ropelength. We compare this spectrum with the one given by considering the bending energy of such idealized knots, showing that curvature information provides a rather good indicator of magnetic energy contents. For loose knots far from equilibrium we show that inflexional states determine the transition to braid form. New lower bounds for tight knots and braids are then established. We conclude with results on energy-complexity relations for systems in presence of dissipation.  相似文献   

6.
This review presents some of the new developments in the understanding of coronal magnetic fields in flares and coronal mass ejections. The modelling of the coronal magnetic field based on observed photospheric field permits to understand the location of energy release. Various flare observations are consistent with a model where magnetic reconnection occurs between two magnetic fields of different connectivity. Because magnetic helicity is almost conserved, the stored energy cannot be fully released in confined flares. The corona gets rid of the helicity injected by the convection zone only by ejecting part of the magnetic field. A severe physical constraint (open-field limit) on these ejections has been firmly established for force-free fields. It is, however, possible to open partially the field or to eject a twisted flux-tube keeping the energy of the field behind the open-field limit. New results show that in simply connected fields this happen after a finite time without loss of equilibrium, while in more complex topology a loss of equilibrium can still be present.  相似文献   

7.
The magnetic helicity is often considered a quasi-invariant in the magnetohydrodynamic evolution of a plasma. While in general this is not the case, this invariance phenomenon occurs in many relevant situations, so that it is interesting to look for physical parameters that may detract from the maximum theoretical decay rate of helicity. The size of the Lorentz force is the main one: based on it, we find that several means of the magnetic energy, the transfer rate between kinetic and magnetic energies, and the variation of the angular momentum tend to slow down the evolution of magnetic helicity.  相似文献   

8.
Ultracool stars usually have active regions, which is confirmed by their high-power radiofrequency emission modulated by the star axial rotation. The interpretation of this emission is commonly based on the electron cyclotron maser mechanism realized in the active regions. A plasma mechanism of radiofrequency emission is not considered, because ultracool star atmospheres are tightly “pressed” against the star surface, and the plasma frequency is much lower than the electron gyrofrequency (fL ? fB) at the coronal levels. This paper explores active regions of ultracool stars for the possible existence of a system of coronal magnetic loops carrying electric current generated by photospheric convection. It is shown that current dissipation induces a temperature increase inside the loops to about 107 K, which causes an increase in the scale of height of the inhomogeneous atmosphere and, at the coronal levels, effectuates condition fL ? fB, at which the plasma mechanism of radiofrequency emission prevails over the electron cyclotron maser mechanism. The magnetic loop parameters, intensity of electric currents generated by the photospheric convection, and efficiency of plasma heating inside the magnetic loops are evaluated on the example of the brown dwarf TVLM513-46546. The scale of the height of the modified atmosphere, which appears to be comparable to the star radius, is calculated; it is shown that the soft X-ray flow created by the hot modified atmosphere inside a coronal magnetic loop is about equal to that observed for brown dwarf TVLM513-46546.  相似文献   

9.
Using a magnetic dynamo model, suggested by Kazantsev (J. Exp. Theor. Phys. 1968, vol. 26, p. 1031), we study the small-scale helicity generation in a turbulent electrically conducting fluid. We obtain the asymptotic dependencies of dynamo growth rate and magnetic correlation functions on magnetic Reynolds numbers. Special attention is devoted to the comparison of a longitudinal correlation function and a function of magnetic helicity for various conditions of asymmetric turbulent flows. We compare the analytical solutions on small scales with numerical results, calculated by an iterative algorithm on non-uniform grids. We show that the exponential growth of current helicity is simultaneous with the magnetic energy for Reynolds numbers larger than some critical value and estimate this value for various types of asymmetry.  相似文献   

10.
The turbulent cross helicity is directly related to the coupling coefficients for the mean vorticity in the electromotive force and for the mean magnetic-field strain in the Reynolds stress tensor. This suggests that the cross-helicity effects are important in the cases where global inhomogeneous flow and magnetic-field structures are present. Since such large-scale structures are ubiquitous in geo/astrophysical phenomena, the cross-helicity effect is expected to play an important role in geo/astrophysical flows. In the presence of turbulent cross helicity, the mean vortical motion contributes to the turbulent electromotive force. Magnetic-field generation due to this effect is called the cross-helicity dynamo. Several features of the cross-helicity dynamo are introduced. Alignment of the mean electric-current density J with the mean vorticity Ω , as well as the alignment between the mean magnetic field B and velocity U , is supposed to be one of the characteristic features of the dynamo. Unlike the case in the helicity or α effect, where J is aligned with B in the turbulent electromotive force, we in general have a finite mean-field Lorentz force J ?×? B in the cross-helicity dynamo. This gives a distinguished feature of the cross-helicity effect. By considering the effects of cross helicity in the momentum equation, we see several interesting consequences of the effect. Turbulent cross helicity coupled with the mean magnetic shear reduces the effect of turbulent or eddy viscosity. Flow induction is an important consequence of this effect. One key issue in the cross-helicity dynamo is to examine how and how much cross helicity can be present in turbulence. On the basis of the cross-helicity transport equation, its production mechanisms are discussed. Some recent developments in numerical validation of the basic notion of the cross-helicity dynamo are also presented.  相似文献   

11.
Abstract

The two dimensional incompressible MHD equations describing the decay of a random initial velocity field in the presence of a uniform magnetic background field are solved numerically by a Chebyshev spectral method. The nonlinear interactions of standing Alfvén-waves of a given energy are studied for various Reynolds numbers and field strengths of the magnetic background field. Small scale structures are generated by these interactions, which increase the energy dissipation, however, the uniform background field suppresses the production of arbitrary small scales. Thus energy dissipation is found to be insignificant at sufficiently high Reynolds numbers. Anisotropies of the fluctuating field components are also studied. In the temporal evolution they appear first in the magnetic field. This is explained by the conservation of mean square vector potential in the limit of infinite conductivity.  相似文献   

12.
Abstract

The relatively large resistivity in the solar photosphere and chromosphere softens the ideal tangential discontinuities of magnetostatic equilibrium into continuous transitions in field direction over scales of 0.1–10 km. This softening is communicated upward at the Alfvén speed into the active solar corona. The degree of softening is a vital part of the theory of magnetic heat input to the active X-ray corona, because the very low resistivity of the coronal gas provides effective dissipation only if the current sheets are reduced to a thickness of 10?2km.

A close examination of the problem shows that the Alfvén transit time up into the corona is large compared to the characteristic time of 1 sec in which the coronal tangential discontinutities are formed. It also shows that the principal effect of the resistivity is to create a thin surface layer of fluid on adjacent flux bundles, which causes a general drift of the flux but does not directly broaden the current sheets higher up in the field. In fact the motions of the surface layers do not extend upwards beyond the first winding pattern at each end of a coronal loop.

It appears that the photospheric and chromospheric resistivity is without striking consequences for magnetic heating in the corona.  相似文献   

13.
We consider an unforced, incompressible, turbulent magnetofluid constrained by concentric inner and outer spherical surfaces. We define a model system in which normal components of the velocity, magnetic field, vorticity, and electric current are zero on the boundaries. This choice allows us to find a set of Galerkin expansion functions that are common to both velocity and magnetic field, as well as vorticity and current. The model dynamical system represents magnetohydrodynamic (MHD) turbulence in a spherical domain and is analyzed by the methods similar to those applied to homogeneous MHD turbulence. We find a statistical theory of ideal (i.e. no dissipation) MHD turbulence analogous to that found in the homogeneous case, including the prediction of coherent structure in the form of a large-scale quasistationary magnetic field. This MHD dynamo depends on broken ergodicity, an effect that is enhanced when total magnetic helicity is increased relative to total energy. When dissipation is added and large scales are only weakly damped, quasiequilibrium may occur for long periods of time, so that the ideal theory is still pertinent on a global scale. Over longer periods of time, the selective decay of energy over magnetic helicity further enhances the effects of broken ergodicity. Thus, broken ergodicity is an essential mechanism and relative magnetic helicity is a critical parameter in this model MHD dynamo theory.  相似文献   

14.
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15.
Abstract

A magnetohydrodynamic, dynamo driven by convection in a rotating spherical shell is supposed to have averages that are independent of time. Two cases are considered, one driven by a fixed temperature difference R and the other by a given internal heating rate Q. It is found that when q, the ratio of thermal conductivity to magnetic diffusivity, is small, R must be of order q ?4/3 and Q of order q ?2 for dynamo action to be possible; q is small in the Earth's core, so it is hoped that the criteria will prove useful in practical as well as theoretical studies of dynamic dynamos. The criteria can be further strengthened when the ohmic dissipation of the field is significant in the energy balance. The development includes the derivation of two necessary conditions for dynamo action, both based on the viscous dissipation rate of the velocity field that drives the dynamo.  相似文献   

16.
Abstract

In Naeser (1979), later denoted N, it was shown that a frequency shift of a wave spectrum had to be expected as a result of dissipation of energy and conservation of spin of the waves. While time-dependency was treated in N, mainly space-dependency is treated here. In order to do this, the velocity of the spin of the waves is calculated. It is shown that this can be made equal to the group velocity by a second order coordinate transformation. In the limits of deep and shallow water the transformation becomes the identity, and leaves the Stokes drift at its usual value if the moment point is located at the mean water level.

By supposing that the dissipation is proportional to the molecular dissipation, and that the entire wind-wave interaction takes place at extremely high frequencies and at a constant rate, it is shown that the energy density at the high frequency slope of a fetch-dependent spectrum is inversely proportional to the fifth power of the frequency, while a spectrum which is only a function of the time for which the wind has blown is inversely proportional to the fourth power. The theory is compared with observations which it fits within the accuracy of the method. It is also compared with existing theories and reasons for the discrepancies are pointed out.  相似文献   

17.
In contrast to the way that the spreading of irregularities in a plasma is usually considered, the diffusion spreading of irregularities stretched along the geomagnetic field B is examined using a three-dimensional rigorous numerical model of quasi-neutral diffusion in the presence of a magnetic field, in conjunction with the actual height variations of the diffusion and conductivity tensors in the ionosphere. A comparison with the earlier constructed approximate model of unipolar diffusion was made. As in the previous case, the same peculiarities of irregularity spreading in the inhomogeneous background ionospheric plasma were observed. The accuracy of the approximate model for describing the process of spreading of anisotropic ionospheric irregularities is established. Time relaxation effects of real heating-induced ionospheric irregularities on their scale transverse to B are presented using the approximate analytical model for the case of a quasi-homogeneous ionospheric plasma. The calculated results have a vivid physical meaning and can be directly compared with experimental data on the radiophysical observations of artificial heating-induced irregularities created by powerful radio waves in the ionosphere.  相似文献   

18.
Abstract

A class of exact solutions to the steady, two-dimensional magnetohydrodynamic equations ina cylindrical geometry is presented. These may model both closed and open magnetic structures found in the solar atmosphere. For closed structures, it is found that increasing the flow speed causes the summit of the arcade of closed magnetic fieldlines to rise. Parameter ranges also exist where the solution has regions of open and closed field, and so the solutions may be relevant for modelling flows in solar magnetic structures such as coronal streamers, X-ray bright points coronal plumes and coronal holes.  相似文献   

19.
The behavior of the main magnetic field components during a polarity transition is investigated using the α2-dynamo model for magnetic field generation in a turbulent core. It is shown that rapid reversals of the dipole field occur when the helicity, a measure of correlation between turbulent velocity and vorticity, changes sign. Two classes of polarity transitions are possible. Within the first class, termed component reversals, the dipole field reverses but the toroidal field does not. Within the second class, termed full reversals, both dipole and toroidal fields reverse. Component reversals result from long term fluctuations in core helicity; full reversals result from short term fluctuations. A set of time-evolution equations are derived which govern the dipole field behavior during an idealized transition. Solutions to these equations exhibit transitions in which the dipole remains axial while its intensity decays rapidly toward zero, and is regenerated with reversed polarity. Assuming an electrical conductivity of 3 × 105 mho m?1 for the fluid core, the time interval required to complete the reversal process can be as short as 7500 years. This time scale is consistent with paleomagnetic observations of the duration of reversals. A possible explanation of the cause of reversals is proposed, in which the core's net helicity fluctuates in response to fluctuations in the level of turbulence produced by two competing energy sources—thermal convection and segregation of the inner core. Symmetry considerations indicate that, in each hemisphere, helicity generated by heat loss at the core-mantle boundary may have the opposite sign of helicity generated by energy release at the inner core boundary. Random variations in rates of energy release can cause the net helicity and the α-effect to change sign occasionally, provoking a field reversal. In this model, energy release by inner core formation tends to destabilize stationary dynamo action, causing polarity reversals.  相似文献   

20.
Abstract

The mean-field effects of cyclonic convection become increasingly complex when the cyclonic rotation exceeds ½-π. Net helicity is not required, with negative turbulent diffusion, for instance, appearing in mirror symmetric turbulence. This paper points out a new dynamo effect arising in convective cells with strong asymmetry in the rotation of updrafts as against downdrafts. The creation of new magnetic flux arises from the ejection of reserve flux through the open boundary of the dynamo region. It is unlike the familiar α-effect in that individual components of the field may be amplified independently. Several formal examples are provided to illustrate the effect. Occurrence in nature depends upon the existence of fluid rotations of the order of π in the convective updrafts. The flux ejection dynamo may possibly contribute to the generation of field in the convective core of Earth and in the convective zone of the sun and other stars.  相似文献   

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