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We analyze a 9 hr sequence of simultaneous, high-resolution, high-cadence G-band and K-line solar filtergrams plus magnetograms of lower cadence and resolution. Images include both network and internetwork. The magnetic and filtergram intensities, their fluctuations, and relative phases change with progressive strengthening of local magnetic field. At increased flux levels, sudden photospheric downflows create long-lived magnetic elements. For weak magnetic fields the K-line and G-band intensities include an oscillatory component with period 4 minutes. For stronger fields, the K-line period shifts to 5 minutes, while the G-band fluctuations fade due to dissociation of their source, the CH radical. These K-line and G-band fluctuations, whose periods are longer than the acoustic cutoff, are coherent and in phase. They also are coherent with fluctuations of the magnetic field. Weak-field magnetic fluctuations lead the intensity fluctuations by a phase shift of 90°. Strong-field magnetic fluctuations trail the intensities by 100°. These are interpreted as standing waves in the photosphere and low chromosphere. Another class of G-band fluctuations, with periods shorter than the acoustic cutoff, is associated both with stronger magnetic fields and with enhanced K-line emission with fluctuations longer than the cutoff period. This suggests waves excited by rapid photospheric perturbations and propagating up along magnetic flux tubes.

We analyze a unique 9 hr sequence of near-simultaneous, high-resolution and high-cadence G-band and K-line solar filtergrams, together with magnetograms of lower cadence and resolution. Our focus is on the phenomena surrounding discrete photospheric darkening events in internetwork G-band intensities. 72% of the darkenings are followed after 2 minutes by K-line brightenings. In the remaining cases, the darkenings are instead preceded by K-line brightenings 2 minutes earlier. Equivalent results are found when reference is shifted to K-line brightening events, although these two sets overlap by no more than 15%. The timing and coupling of the photospheric darkenings and chromospheric brightenings appear to be regulated by a preexisting 4 minute oscillation of the solar atmosphere. Other oscillations with periods in the range 1-8 minutes also are present, and in general the wave power is doubled at the time of an event. Our results favor an acoustic source for enhanced amplitudes of K-line intensity oscillations. The magnetic field acts as a passive tracer of horizontal photospheric flows that converge on the photospheric darkening events and then rebound.

We use a three-dimensional Cartesian resistive MHD code to investigate three-dimensional aspects of the interaction of magnetic flux tubes as observed in the solar atmosphere and studied in laboratory experiments. We present here the first results from modeling the reconnection of two Gold-Hoyle magnetic flux tubes that follow the system evolution to a final steady state. The energy evolution and reconnection rate for flux tubes with both parallel and antiparallel axial fields and with equal and nonequal strengths are studied. For the first time, we calculate a gauge-invariant relative magnetic helicity of the system and compare its evolution for all the above cases. We observed that the rate at which helicity is dissipated may vary significantly for different cases, and it may be comparable with the energy dissipation rate. The footpoints of the interacting flux tubes were held fixed or allowed to move to simulate different conditions in the solar photosphere. The cases with fixed footpoints had lower magnetic energy release and reached a steady state faster than cases with moving footpoints. For all computed cases the magnetic energy was released mostly through work done on the plasma by the electromagnetic forces rather than through resistive dissipation. The reconnection rate of the poloidal magnetic field is faster for the case with antiparallel flux tubes than for the case with parallel flux tubes, consistent with laboratory experiments. We find that during reconnection supersonic (but sub-Alfvenic) flows develop, and it may take a considerably longer time for the system to reach a steady state than for magnetic flux to reconnect. It is necessary to retain the pressure gradient in the momentum equation; the plasma pressure may be significant for the final equilibrium steady state even with low-β initial conditions, and the work done on the plasma by compression is important in energy exchange.

We study the characteristic scales of quiet-Sun photospheric velocity fields along with their temperature and magnetic markers in Doppler images from the Michelson Doppler Imager aboard the SOHO satellite (SOHO/MDI) in simultaneous, Doppler, magnetic, and intensity images from the San Fernando Observatory and in full-disk magnetograms and an intensity image from National Solar Observatory (Kitt Peak). Wavelet flatness spectra show that velocity fluctuations are normally distributed (Gaussian). This is often assumed in stochastic models of turbulence but had not yet been verified observationally for the Sun. Temperature fluctuations also are Gaussian distributed, but magnetic fields are intermittent and are gathered into patterns related to flow structures. Wavelet basis functions designed to detect characteristic convection cell-flow topologies in acoustically filtered SOHO/MDI Doppler images reveal granulation scales of 0.7-2.2 Mm and supergranulation scales of 28-40 Mm. Mesogranular flows are weakly but significantly detected in the range 4-8 Mm. The systematic flows account for only 30% of the image variances at granular and supergranular scales and much less in between. The main flows for the intermediate range of 2-15 Mm are self-similar, i.e., chaotic or turbulent.

Observations show that newly emerging flux tends to appear on the solar surface at sites where there is flux already; this results in clustering of solar activity. Standard dynamo theories do not predict this effect, and the mean field estimated by the theories is too weak to emerge at the surface of the Sun at all. Here a solution of the problem is suggested that involves strong fluctuating fields generated by the dynamo. The magnetic field emerges at the solar surface when the total field (the mean field plus fluctuations) exceeds the threshold for buoyancy. A slowly changing enhancement of the mean field provides a long-living basis ('hump') for emergence of fluctuating fields. The enhancements are gradually destroyed by the solar differential rotation, the stretching time scale of which defines the lifetime of clusters of activity. A simple 2-dimensional model explaining the appearance of persistent clusters of emerging flux is presented.

Constant-density electrically conducting fluid is confined to a rapidly rotating spherical shell and is permeated by an axisymmetric potential magnetic field with dipole parity; the regions outside the shell are rigid insulators. Slow steady axisymmetric motion is driven by rotating the inner sphere at a slightly slower rate. Linear solutions of the governing magnetohydrodynamic equations are derived in the small Ekman number E -limit for values of the Elsasser number Λ less than order unity. Attention is restricted to the mainstream outside the Ekman–Hartmann layers adjacent to the inner and outer boundaries.

Evolution of magnetic loops associated with filaments and coronal mass ejections involves a redistribution of solar magnetic helicity. Two mechanisms of the helicity redistribution are discussed. The first one involves magnetic reconnections among magnetic loops and can introduce helicity into an erupting magnetic field accompanied with an encapture of helicity by the Sun. The second one involves the MHD helicity redistribution in the Sun and indicates that the magnetic helicity of each hemisphere of the Sun oscillates about a mean with the half-period of the solar cycle (11 years), but does not change sign from one 11 year period to the next.

An asymptotic solution of the magnetic induction equation in a given velocity field is constructed for large magnetic Reynolds numbers. Initially localized distributions of the magnetic field are considered. The leading term of the asymptotics is found. The expansions are proved to be rigorously valid over a finite time interval. Estimates for the residuals are given. The results are illustrated by some examples: the Hubble flow with a linear dependence of the velocity on coordinates, and ABC type flows. The solutions in these cases are expressed in terms of elementary functions.

By using a nonlinear model of an axisymmetricα – Ω dynamo, an analytical expression which gives the magnitude of the mean magnetic field as a function of rotation and other parameters for a solar-type convective zone is obtained. The mean magnetic field varies as the\(\frac{3}{4}\) power of the rotation rate. The resulting theoretical relationship of the X-ray luminosity as a function of the angular velocity is in agreement with observations by Fleming, Gioia, and Maccacaro (1989).

Properties of the second‐order topological invariant (the helicity) and the third‐order topological invariant for ‘‘the Borromean rings’’ (three linked rings no two of which link each other) are discussed. A fourth‐order topological invariant of ideal magnetohydrodynamics is constructed in an integral form. This invariant is determined by the properties of Seifert surfaces bounded by two coupled flux tubes. In particular, for the Whitehead link, it represents the fourth‐order Sato–Levine invariant. The effect of reconnections on the topological invariants in the limit of small diffusivity is considered. In this limit the helicity is approximately conserved and the higher‐order invariants decay rapidly under the action of diffusivity. The destruction of the higher‐order invariants, however, creates helicity fluctuations.

A simple numerical model of the self-excitation of the magnetic field by chaotic motion of a highly conductive fluid is being developed. It is based on the following approach to simulating the turbulent dynamo generation of magnetic fields: the fluid is divided into cells and each cell acts as a machine that can randomly amplify or destroy a given magnetic field. The random amplification models the effects of a chaotic fast dynamo and the random destruction models the effects of reconnection. Uncorrelated and correlated processes are considered. Effects of non-linearity, diffusion, and correlation between cells in time and space are also included. Numerical results are presented from one- and two-dimensional models and possible applications to the generation and spatial-temporal distribution of solar, planetary and interplanetary magnetic fields are discussed.

A time series of the interplanetary magnetic field measured near 1.3 AU by Phobos 2 is analyzed as a fractal. The fractal dimension of the curves corresponding to the components and to the strength of the magnetic field are found to be close to 5/3. The corresponding spatial spectra are interpreted in the framework of MHD turbulence.

The Uranus and Neptune magnetic fields discovered by Voyager 2 can be explained by a dynamo acting in a thin conductive convective shell existing at the bottom of the icy oceans of the planets. The main helicity and differential rotation are the source for the dynamo which effectively excites nonaxisymmetric modes of the mean magnetic field. Estimates of the magnetic field amplitude in the nonlinear regime and of the inclination between the magnetic moment and the rotation axis are given.

Mars has a well-conducting core composed of a mixture of iron and sulphur. It is probably liquid and differentially rotating. The main problem is whether the core is stably stratified or convective. About 10–15% of sulphur is enough to drive a compositional convection over a great part of Martian evolution if an inner solid solid core was formed. Convection in a liquid rotating stratified core results in a mean helicity, which, together with differential rotation and turbulent magnetic diffusivity, is a source for mean field dynamo. The magnitude of the magnetic field generated can explain the origin of magnetization of the shergottie, nakhlite and chassignite meteorites. However, the dynamo probably does not work at present, in accordance with a weak large-scale magnetic field on the Martian surface estimated from the Mars-2, -3, -5, and Phobos mission results. This field is interpreted as an external product of the magnetized mantle having a slightly elliptical form. Some other possible explanations for the outer magnetic field are discussed.

We discuss the methods and results of analysis of nonlinear mean-field dynamo models based on a-quenching in two asymptotic regimes, namely for weakly and highly supercritical excitation. In the former case the spatial distribution of the steady-state magnetic field is close to that given by the neutrally stable eigenfunction of the corresponding kinematic dynamo. In the latter case the magnetic field distribution within the main part of the dynamo volume is presumably determined by the balance between the Lorentz and Coriolis forces while near the boundaries boundary layers arise in which the field adjusts itself to the boundary conditions. The asymptotic behaviour of the highly supercritical aw-dynamos is sensitive to the particular form of dependence of the mean helicity on magnetic field while α2-dynamos are less sensitive to this dependence.

Mutual quasi-periodicities near the solar-rotation period appear in time series based on the Earth's magnetic field, the interplanetary magnetic field, and signed solar-magnetic fields. Dominant among these is one at 27.03 +/- 0.02 days that has been highlighted by Neugebauer, et al. 2000, J. Geophys. Res., 105, 2315. Extension of their study in time and to different data reveals decadal epochs during which the ~ 27.0 day, a ~ 28.3 day, or other quasi-periods dominate the signal. Space-time eigenvalue analyses of time series in 30 solar latitude bands, based on synoptic maps of unsigned photospheric fields, lead to two maximally independent modes that account for almost 30% of the data variance. One mode spans 45 degrees of latitude in the northern hemisphere and the other one in the southern. The modes rotate around the Sun rigidly, not differentially, suggesting connection with the subsurface dynamo. Spectral analyses yield familiar dominant quasi periods 27.04 +/- 0.03 days in the North and at 28.24 +/- 0.03 days in the South. These are replaced during cycle 23 by one at 26.45 +/- 0.03 days in the North. The modes show no tendency for preferred longitudes separated by ~ 180 degrees., 22 pages including 10 figures

Kinematic models of galactic dynamo in axisymmetric disk show remarkable agreement with observations. We argue that nonlinear effects are relatively weak in galactic dynamos and consider the properties of linear dynamo models inherited by global magnetic configurations in spiral galaxies as well as nonlinear distortions of the linear solutions.

The fast dynamo acting in a turbulent flow explains the origin of magnetic fields in astrophysical objects. Stellar cycles and large-scale magnetic fields in spiral galaxies reflect the behaviour of a mean magnetic field. Intermittent magnetic structures in clusters of galaxies are associated with random magnetic field.

Observations show that solar activity is distributed non-axisymmetrically, concentrating at "preferred longitudes". This indicates the important role of non-axisymmetric magnetic fields in the origin of solar activity. We investigate the generation of the non-axisymmetric fields and their coupling with axisymmetric solar magnetic field. Our kinematic generation (dynamo) model operating in a sphere includes solar differential rotation, which approximates the differential rotation obtained by inversion of helioseismic data, modelled distributions of the turbulent resistivity, non-axisymmetric mean helicity, and meridional circulation in the convection zone. We find that (1) the non-axisymmetric modes are localised near the base of the convection zone, where the formation of active regions starts, and at latitudes around $30^{\circ}$; (2) the coupling of non-axisymmetric and axisymmetric modes causes the non-axisymmetric mode to follow the solar cycle; the phase relations between the modes are found. (3) The rate of rotation of the first non-axisymmetric mode is close to that determined in the interplanetary space., Comment: 22 pages, 18 figures. Accepted for publication in the Astrophysical Journal

The Sun is a natural site for a dynamo. In fact, the dynamo concept was introduced by Larmor in his 1919 report to the British Association for Advanced Science entitled”How could a rotating body as the Sun become magnetic?” Cowling’s famous anti-dynamo theorem appeared in his paper ”Magnetic fields of sunspots” (MNRAS. 94, 39 ,1934). Yet the origin of the Sun’s magnetic field is not well understood. Some scientists still challenge the dynamo as the source of solar magnetic field [7].

The spatial distribution of magnetic fields on the solar surface and the temporal distribution of solar magnetic activity each show the dual properties of intermittence and scaling symmetry. Both distributions therefore define measures amenable to multifractal and wavelet analyses (Cadavid, et al 1994; Lawrence, et al 1993, 1995a, 1995b, 1996). We present examples of applications of these techniques to the monthly Wolf Sunspot Number from 1749 to 1993, to global temperature fluctuations of the Earth, and to a high-resolution (~ 2″), digital, polarimetric image of line-of-sight magnetic field in quiet solar photosphere made with the San Fernando Observatory vacuum solar telescope and video spectra-spectroheliograph system.

A model of magnetic field generation by the turbulent motions of a highly conducting fluid is constructed. It is assumed that the field is generated in individual cells of space in a statistically independent manner. A coupling between the cells is realized by magnetic diffusion. The rates of growth of the field and its moments are calculated. The field distribution generated by this mechanism possesses an intermittent nature in both time and space.

The generation of magnetic fields by dynamo action of cosmic turbulent plasmas is considered. Three levels of the consideration are discussed: (1) the mean field behaviour, (2) deviations from the mean field, i.e. magnetic fluctuations, and (3) the generation and distribution of random magnetic field in the random flow of a conducting plasma. Examples of magnetic fields generated in the Uranus and Neptune interiors, in the Sun, and in the clusters of galaxies are presented.

We analyze high-resolution, digital, photoelectric images of solar photospheric magnetic fields. The line-of-sight fields are found to scale in a self-similar way with resolution and thus can be expressed in the form of a signed multifractal measure. The scaling properties of the measure are used to extrapolate field integrals, such as moments of the magnetic field, below resolvable limits. The scaling of the field moments is characteristic of highly intermittent fields. We suggest that the quiet-Sun photospheric fields are generated by local dynamo action based on random convective motions at high magnetic Reynolds number. The properties of active region images are determined by the presence of fields generated by the global, mean field dynamo

In accordance with the data on the Faraday rotation, angular coordinates, and dispersion measurements and distances of 38 pulsars, the strengthB=2.1±1.1 μG and directionl=99°±24°,b≅0° of the large-scale galactic magnetic field and the mean electron density in the galactic discNe=0.03±0.01 cm−3 are determined. A comparison with the results of a study of the measures of rotation of extragalactic radio sources enabled us to estimate the characteristic half-width of the distribution of the electron density on the Z-coordinate (h≅400 ps). The characteristic size of galactic magnetic field flucturations is shown to be ℒ=100–150 ps.

The turbulent dynamo equation with non-uniform mean helicity is solved in an approximation, which is similar to the quasi-classical approximation of quantum mechanics. We evaluate the rate of growth of the magnetic field and obtain a condition for dynamo action. The generated magnetic field is concentrated in the vicinity of an extremum of mean helicity, but in general vanishes at the point of extremum itself. The field is asymptotically force-free. The results obtained here clarify the fact, known from numerical calculations, that the threshold values of the dynamo-number for excitation of dipole and quadrupole modes are very close to each other.

The kinematic dynamo equations for the mean magnetic field are solved with an asymptotic method of the WKB type. The excitation conditions and main characteristics of the non-axially symmetric modes for a given distribution of the sources are obtained. Utilization of the helioseismologic data on the Sun's internal rotation permits an explanation, within the framework of dynamo theory, of the excitation of the main non-axially symmetric modes revealed in the Sun's magnetic field sector structure.

A magnetic field is shown to be asymptotically (t → ∞) decaying in a flow of finite conductivity with v = Cr, where C = Cζ(t) is a random matrix. The decay is exponential, and its rate does not depend on the conductivity. However, the magnetic energy increases exponentially owing to growth of the domain occupied by the field. The spatial distribution of the magnetic field is a set of thin ropes and (or) layers.

The turbulent mean-field dynamo of αω-type with a mean helicity quadratically dependent on the magnetic field is investigated. A nonlinear system of ordinary differential equation is derived for the amplitudes of the magnetic field expansion over the eigenvectors of the linear problem. In a one-mode approximation the non-linear supercritical solution is stable when dγ/d D > 0, where γ is the growth rate of the linear solution and D is the dynamo number. Non-linear interation between two modes of dipole and quadrupole symmetry is considered. The conditions are found for the synchronization and beats of these modes under the assumption that the quadrupole mode is weaker than the dipole one. Es werden Dynamos von αω-Typ untersucht, bei denen α eine Funktion zweiten Grades der magnetischen Feldstarke ist. Die Magnetfelder werden nach den Eigenvektoren des linearen Problems entwickelt, und eine System gewohnlicher Differentialgleichungen fur die Amplituden abgeleitet. In der “one-mode” Naherung ist die uberkritische Losung stabil falls dγ/dD > 0, wobei γ die Wachstumsrate der linearen Losung und D die Dynamozahl bezeichnen. Weiterhin wird die nichtlineare Wechselwirkung zwischen Moden von Dipoltyp und von Quadrupoltyp betrachtet. Unter der Annahme eines im Vergliech zum Dipol schwacheren Quadrupols wurden die Bedingungen fur eine Synchronisation und fur das Auftreten von Schwebungen gefunden.

It is shown that the frozen-in magnetic field in a given random homogeneous flow of an incompressible fluid which is renewed after a finite characteristic time grows exponentially. The rate-of-growth is positive in the limit of small magnetic diffusivity and continuous in v m . The increase of the rates-of-growth for successive field moments is revealed by the intermittent distribution of the magnetic field generated. The results are obtained by reducing the kinematic dynamo problem to the evaluation of the product of a large number of independent random operators.

Models for the generation of the magnetic field depending on one and two Cartesian coordinates in an anisotropically conducting fluid are constructed. A similarity between the solutions and the known homopolar disk dynamo is noted.

The simplest αω dynamo in a thin disk is analysed. It the antisymmetric helicity function α(z) (wherez is a coordinate perpendicular to the disk plane) is smooth and limited, then the conditions for generating a magnetic field and the symmetry of the resulting solutions depend only on the form of α at the segment (0,h) — whereh is the half-thickness of the disk — and the value of the dimensionless dynamo numberD. When α(z) does not change its sign at this segment andD>D c (the critical dynamo number), the excitation of non-oscillating even (quadrupole) and oscillating odd (dipole) fields are possible. When α(z) changes its sign at the segment indicated, non-oscillating odd magnetic fields can also be excited.

We consider evolution of the regular magnetic field in turbulent astrophysical jets. The observed lateral expansion of a jet is approximately described by a linear in coordinates regular velocity field (the Hubble flow). It is shown that in expanding turbulent jets with non-vanishing mean helicity of the turbulence temporal amplification and effective realignment of the regular magnetic field occurs with the field changing orientation from the transverse to the longitudinal one along the jet axis. The distance at which the realiggment occurs depends on parameters of the jet, in particular, on the power of the central source. Estimates for the jet in a weak source 3C 31 favourably agree with observations.

We propose and analyze a possible mechanism of amplification and variations in alignment of magnetic fields in astrophysical jets. We associate these processes with combined action of helical turbulent plasma motions and large-scale velocity within a jet which stretch and distort a seed magnetic field.