Variations of the sunspot number are important indicators of the solar activity cycles. The sunspot formation is a result of a dynamo process inside the Sun, which is far from being understood. We use simple dynamical models of the dynamo process to simulate the magnetic field evolution and investigate general properties of the sunspot number variations during the solar cycles. We have found that the classical Parker's model with a standard kinetic helicity quenching cannot represent the typical profiles of the solar-cycle variations of the sunspot number, and also does not give chaotic solutions. For modeling of the solar cycle properties we use a nonlinear dynamo model of Kleeorin and Ruzmaikin (1982), which takes into account dynamics of the turbulent magnetic helicity. We have obtained a series of periodic and chaotic solutions for different layers of the convective zone. The solutions qualitatively reproduce some basic observational features of the solar cycle properties, in particular, the relationship between the growth time and the cycle amplitude. Also, on the longer time scale the dynamo model with the magnetic helicity has intermittent solutions, which may be important for modeling long-term variations of the solar cycles.
A simple explicit example of a Roberts-type dynamo is given in which the alpha-effect of mean-field electrodynamics exists in spite of point-wise vanishing kinetic helicity of the fluid flow. In this way it is shown that alpha-effect dynamos do not necessarily require non-zero kinetic helicity. A mean-field theory of Roberts-type dynamos is established within the framework of the second-order correlation approximation. In addition numerical solutions of the original dynamo equations are given, that are independent of any approximation of that kind. Both theory and numerical results demonstrate…
Nonlinear behaviour of galactic dynamos is studied, allowing for magnetic helicity removal by the galactic fountain flow. A suitable advection speed is estimated, and a one-dimensional mean-field dynamo model with dynamic alpha-effect is explored. It is shown that the galactic fountain flow is efficient in removing magnetic helicity from galactic discs. This alleviates the constraint on the galactic mean-field dynamo resulting from magnetic helicity conservation and thereby allows the mean magnetic field to saturate at a strength comparable to equipartition with the turbulent kinetic energy.
Magnetic fields correlated on kiloparsec scales are seen in spiral galaxies. Their origin could be due to amplification of a small seed field by a turbulent galactic dynamo. We review the current status of the galactic dynamo, especially the constraints imposed by magnetic helicity conservation. We estimate the minimal strength of the large-scale magnetic field which could arise inspite of the helicity constraint.
Large scale dynamos produce small scale current helicity as a waste product that quenches the large scale dynamo process (alpha effect). This quenching can be catastrophic (i.e.intensify with magnetic Reynolds number) unless one has fluxes of small scale magnetic (or current) helicity out of the system. We derive the form of helicity fluxes in turbulent dynamos, taking also into account the nonlinear effects of Lorentz forces due to fluctuating fields. We confirm the form of an earlier derived magnetic helicity flux term, and also show that it is not renormalized by the small scale magnetic fi…
We demonstrate that the inclusion of the helicity flux in the magnetic helicity balance in the nonlinear stage of galactic dynamo action results in a radical change in the magnetic field dynamics. The equilibrium value of the large-scale magnetic field is then approximately the equipartition level. This is in contrast to the situation without the flux of helicity, when the magnetic helicity is conserved locally, which leads to substantially subequipartition values for the equilibrium large-scale magnetic field.
Magnetic helicity effects are discussed in laboratory and astrophysical settings. First, dynamo action in Taylor-Green flows is discussed for different boundary conditions. However, because of the lack of scale separation with respect to the container, no large scale field is being produced and there is no resistively slow saturation phase as otherwise expected. Second, the build-up of a large scale field is demonstrated in a simulation where a localized magnetic eddy produces field on a larger scale if the eddy possesses a swirl. Such a set-up might be realizable experimentally through coils.…
We study a simple model for the solar dynamo in the framework of the Parker migratory dynamo, with a nonlinear dynamo saturation mechanism based on magnetic helicity conservation arguments. We find a parameter range in which the model demonstrates a cyclic behaviour with properties similar to that of Parker dynamo with the simplest form of algebraic alpha-quenching. We compare the nonlinear current helicity evolution in this model with data for the current helicity evolution obtained during 10 years of observations at the Huairou Solar Station of China. On one hand, our simulated data demonstr…
The motivation for considering distributed large scale dynamos in the solar context is reviewed in connection with the magnetic helicity constraint. Preliminary accounts of 3-dimensional direct numerical simulations (in spherical shell segments) and simulations of 2-dimensional mean field models (in spherical shells) are presented. Interesting similarities as well as some differences are noted.
Magnetic helicity is nearly conserved and its evolution equation provides a dynamical feedback on the alpha effect that is distinct from the conventional algebraic alpha quenching. The seriousness of this dynamical alpha quenching is particularly evident in the case of closed or periodic boxes. The explicit connection with catastrophic alpha quenching is reviewed and the alleviating effects of magnetic and current helicity fluxes are discussed.
We study effects of kinetic helicity fluctuations in a turbulence with large-scale shear using two different approaches: the spectral tau-approximation and the second order correlation approximation (or first-order smoothing approximation). These two approaches demonstrate that homogeneous kinetic helicity fluctuations alone with zero mean value in a sheared homogeneous turbulence cannot cause large-scale dynamo. Mean-field dynamo can be possible when kinetic helicity fluctuations are inhomogeneous which cause a nonzero mean alpha effect in a sheared turbulence. On the other hand, shear-curren…
Dynamo action is investigated in simulations of locally isotropic and homogeneous turbulence in a slab between open boundaries. It is found that a `pseudo-vacuum' boundary condition (where the field is vertical) leads to strong helicity fluxes which significantly reduce the amplitude of the resulting large scale field. On the other hand, if there is a conducting halo outside the dynamo-active region the large scale field amplitude can reach larger values, but the time scale after which this field is reached increases linearly with the magnetic Reynolds number. In both cases most of the helicit…
We present a simple semi-analytical model of nonlinear, mean-field galactic dynamos and use it to study the effects of various magnetic helicity fluxes. The dynamo equations are reduced using the `no-$z$' approximation to a nonlinear system of ordinary differential equations in time; we demonstrate that the model reproduces accurately earlier results, including those where nonlinear behaviour is driven by a magnetic helicity flux. We discuss the implications and interplay of two types of magnetic helicity flux, one produced by advection (e.g., due to the galactic fountain or wind) and the othe…
Several one and two dimensional mean field models are analyzed where the effects of current helicity fluxes and boundaries are included within the framework of the dynamical quenching model. In contrast to the case with periodic boundary conditions, the final saturation energy of the mean field decreases inversely proportional to the magnetic Reynolds number. If a nondimensional scaling factor in the current helicity flux exceeds a certain critical value, the dynamo can operate even without kinetic helicity, i.e. it is based only on shear and current helicity fluxes, as first suggested by Vish…
We consider the magnetic helicity balance for the galactic dynamo in the framework of the local dynamo problem, as well as in the no-z model (which includes explicitly the radial distribution of the magnetic fields). When calculating the magnetic helicity balance we take into account the redistribution of the small-scale and large-scale magnetic fields between the magnetic helicities, as well as magnetic helicity transport and diffusion due to small-scale turbulence. We demonstrate that the magnetic helicity flux through the galactic disc boundaries leads to a steady-state magnetic field with …
We show that the presence of a steady $\ao$ dynamo in astrophysical rotators likely leads to an outflow of relative magnetic helicity and thus magnetic energy available for particle acceleration in a corona. The connection between energy and magnetic helicity arises because the generation of large scale field is linked to a generation of large scale magnetic helicity. In a steady state, the relative magnetic helicity associated with the large scale field can escape, accompanied by an equal and opposite small scale contribution from the field, since the total magnetic helicity in large magnetic…
Some common properties of helical magnetic fields in decaying and driven turbulence are discussed. These include mainly the inverse cascade that produces fields on progressively larger scales. Magnetic helicity also restricts the evolution of the large scale field: the field decays less rapidly than a non-helical field, but it also saturates more slowly, i.e. on a resistive time scale if there are no magnetic helicity fluxes. The former effect is utilized in primordial field scenarios, while the latter is important for successfully explaining astrophysical dynamos that saturate faster than res…
The connection between helically isotropic MHD turbulence and mean-field dynamo theory is reviewed. The nonlinearity in the mean-field theory is not yet well established, but detailed comparison with simulations begin to help select viable forms of the nonlinearity. The crucial discriminant is the magnetic helicity, which is known to evolve only on a slow resistive time scale in the limit of large magnetic Reynolds number. Particular emphasis is put on the possibility of memory effects, which means that an additional explicitly time-dependent equation for the nonlinearity is solved simultaneou…
There is mounting evidence that the ejection of magnetic helicity from the solar surface is important for the solar dynamo. Observations suggest that in the northern hemisphere the magnetic helicity flux is negative. We propose that this magnetic helicity flux is mostly due to small scale magnetic fields; in contrast to the more systematic large scale field of the 11 year cycle, whose helicity flux may be of opposite sign, and may be excluded from the observational interpretation. Using idealized simulations of MHD turbulence as well as a simple two-scale model, we show that shedding small sca…
We continue our attempt to connect observational data on current helicity in solar active regions with solar dynamo models. In addition to our previous results about temporal and latitudinal distributions of current helicity (Kleeorin et al. 2003), we argue that some information concerning the radial profile of the current helicity averaged over time and latitude can be extracted from the available observations. The main feature of this distribution can be presented as follows. Both shallow and deep active regions demonstrate a clear dominance of one sign of current helicity in a given hemisph…
Dynamos in astrophysical disks are usually explained in terms of the standard alpha-omega mean field dynamo model where the local helicity generates a radial field component from an azimuthal field. The subsequent shearing of the radial field gives rise to exponentially growing dynamo modes. There are several problems with this model. The exponentiation time for the galactic dynamo is hard to calculate, but is probably uncomfortably long. Moreover, numerical simulations of magnetic fields in shearing flows indicate that the presence of a dynamo does not depend on a non-zero average helicity. H…
It is shown that the turbulent dynamo $α$-effect converts magnetic helicity from the turbulent field to the mean field when the turbulence is electromagnetic while the magnetic helicity of the mean-field is transported across space when the turbulence is electrostatic or due to the electron diamagnetic effect. In all cases, however, the dynamo effect strictly conserves the total helicity except for resistive effects and a small battery effect. Implications for astrophysical situations, especially for the solar dynamo, are discussed.
The nonlinear mean-field dynamo due to a shear-current effect in a nonhelical homogeneous turbulence with a mean velocity shear is discussed. The transport of magnetic helicity as a dynamical nonlinearity is taken into account. The shear-current effect is associated with the ${\bf W} {\bf \times} {\bf J}$ term in the mean electromotive force, where ${\bf W}$ is the mean vorticity due to the large-scale shear motions and ${\bf J}$ is the mean electric current. This effect causes the generation of large-scale magnetic field in a turbulence with large hydrodynamic and magnetic Reynolds numbers. T…
Dynamical studies of MHD turbulence on the one hand, and arguments based upon magnetic helicity on the other, have yielded seemingly contradictory estimates for the $α$ parameter in turbulent dynamo theory. Here we show, with direct numerical simulation of three-dimensional magnetohydrodynamic turbulence with a mean magnetic field, $\OB$, that the constraint on the dynamo $α$-effect set by the magnetic helicity is time-dependent. A time-scale $t_c$ is introduced such that for $t<t_c$, the $α$-coefficient calculated from the simulation is close to the result of Pouquet et al and Field et al, $-…
We have extended our previous mean-field galactic dynamo model which included algebraic and dynamic alpha nonlinearities (Kleeorin et al., A&A, v. 387, 453, 2002), to include also a quenching of turbulent diffusivity. We readily obtain equilibrium states for the large-scale magnetic field in the local disc dynamo model, and these fields have strengths that are comparable to the equipartition field strength. We find that the algebraic nonlinearity alone (i.e. quenching of both the alpha effect and turbulent magnetic diffusion) cannot saturate the growth of the mean magnetic field; only the comb…
The theory of large scale dynamos is reviewed with particular emphasis on the magnetic helicity constraint in the presence of closed and open boundaries. In the presence of closed or periodic boundaries, helical dynamos respond to the helicity constraint by developing small scale separation in the kinematic regime, and by showing long time scales in the nonlinear regime where the scale separation has grown to the maximum possible value. A resistively limited evolution towards saturation is also found at intermediate scales before the largest scale of the system is reached. Larger aspect ratios…
Mean field dynamo theory is a leading candidate to explain the observed large scale magnetic fields of galaxies and stars. However, controversy arises over the extent of premature quenching by the backreaction of the growing field. We distinguish between rapid mean field dynamo action, which is required by astrophysical systems, and resistively limited action. We show how the flow of magnetic helicity is important for rapid action. Existing numerical and analytic work suggesting that mean field dynamos are prematurely quenched and resistively limited include approximations or boundary conditio…
Large scale dynamo-generated fields are a combination of interlocked poloidal and toroidal fields. Such fields possess magnetic helicity that needs to be regenerated and destroyed during each cycle. A number of numerical experiments now suggests that stars may do this by shedding magnetic helicity. In addition to plain bulk motions, a favorite mechanism involves magnetic helicity flux along lines of constant rotation. We also know that the sun does shed the required amount of magnetic helicity mostly in the form of coronal mass ejections. Solar-like stars without cycles do not face such strong…
Magnetic field amplification in astrophysics ultimately requires an understanding of magnetohydrodynamic turbulence. Kinetic helicity has long been known to be important for large scale field growth in forced MHD turbulence, and has been recently demonstrated numerically to be asymptotically consistent with slow mean field dynamo action in a periodic box. Here we show numerically that the magnetic spectrum at and below the forcing scale is also strongly influenced by kinetic helicity. We identify a critical value, $f_{h,crit}$ above which the magnetic spectrum develops maxima at wavenumber $= …
The evolution of magnetic fields is studied using simulations of forced helical turbulence with strong imposed shear. After some initial exponential growth, the magnetic field develops a large scale travelling wave pattern. The resulting field structure possesses magnetic helicity, which is conserved in a periodic box by the ideal MHD equations and can hence only change on a resistive time scale. This constrains strongly the growth time of the large scale magnetic field, but less strongly the length of the cycle period. Comparing with the case without shear, the time scale for large scale fiel…
The effect of shear on the growth of large scale magnetic fields in helical turbulence is investigated. The resulting large-scale magnetic field is also helical and continues to evolve, after saturation of the small scale field, on a slow resistive time scale. This is a consequence of magnetic helicity conservation. Because of shear, the time scale needed to reach an equipartition-strength large scale field is shortened proportionally to the ratio of the resulting toroidal to poloidal large scale fields.
The possibility of non-helical large scale dynamo action is investigated using three-dimensional simulations of global accretion discs as well as idealized local simulations without rotation and only shear. Particular emphasis is placed on a certain correlation between vorticity and azimuthal velocity gradient which has been predicted to drive large scale dynamo action, independent of the presence or absence of kinetic helicity. In the global disc simulations two types of behaviours are found: those which do show this type of velocity correlation and those which do not. The former ones are typ…
Dynamo action owing to helically forced turbulence and large-scale shear is studied using direct numerical simulations. The resulting magnetic field displays propagating wave-like behavior. This behavior can be modelled in terms of an αΩdynamo. In most cases super-equipartition fields are generated. By varying the fraction of helicity of the turbulence the regeneration of poloidal fields via the helicity effect (corresponding to the α-effect) is regulated. The saturation level of the magnetic field in the numerical models is consistent with a linear dependence on the ratio of the fractional he…
The term ``dynamo'' means different things to the laboratory fusion plasma and astrophysical plasma communities. To alleviate the resulting confusion and to facilitate interdisciplinary progress, we pinpoint conceptual differences and similarities between laboratory plasma dynamos and astrophysical dynamos. We can divide dynamos into three types: 1. magnetically dominated helical dynamos which sustain a large scale magnetic field against resistive decay and drive the magnetic geometry toward the lowest energy state, 2. flow-driven helical dynamos which amplify or sustain large scale magnetic f…
A non-linear, time-dependent, magnetically driven dynamo theory which shows how magnetically dominated configurations can relax to become helical on the largest scale available is presented. Coupled time-dependent differential equations for large scale magnetic helicity, small scale magnetic helicity, velocity, and the electromotive force are solved. The magnetic helicity on small scales relaxes to drive significant large scale helical field growth on dynamical (Alfvén crossing) time scales, independent of the magnitude of finite microphysical transport coefficients, after which the growing ki…
We generalize the derivation of dynamo coefficient $α$ of Field et al (1999) to include the following two aspects: first, the de-correlation times of velocity field and magnetic field are different; second, the magnetic Prandtl number can be arbitrary. We find that the contributions of velocity field and magnetic field to the $α$ effect are not equal, but affected by their different statistical properties. In the limit of large kinetic Reynolds number and large magnetic Reynolds number, $α$-coefficient may not be small if the de-correlation times of velocity field and magnetic field are shorte…
Three closely related stumbling blocks of solar mean field dynamo theory are discussed: how dominant are the small scale fields, how is the alpha effect quenched, and whether magnetic and current helicity fluxes alleviate the quenching? It is shown that even at the largest currently available resolution there is no clear evidence of power law scaling of the magnetic and kinetic energy spectra in turbulence. However, using subgrid scale modeling, some indications of asymptotic equipartition can be found. The frequently used first order smoothing approach to calculate the alpha effect and other …
A number of problems of solar and stellar dynamo theory are briefly reviewed and the current status of possible solutions is discussed. Results of direct numerical simulations are described in view of mean-field dynamo theory and the relation between the alpha-effect and the inverse cascade of magnetic helicity is highlighted. The possibility of `catastrophic' quenching of the alpha-effect is explained in terms of the constraint placed by the conservation of magnetic helicity.
We construct a magnetic helicity conserving dynamo theory which incorporates a calculated magnetic helicity current. In this model the fluid helicity plays a small role in large scale magnetic field generation. Instead, the dynamo process is dominated by a new quantity, derived from asymmetries in the second derivative of the velocity correlation function, closely related to the `twist and fold' dynamo model. The turbulent damping term is, as expected, almost unchanged. Numerical simulations with a spatially constant fluid helicity and vanishing resistivity are not expected to generate large s…
The emergence of a large scale magnetic field from randomly forced isotropic strongly helical flows is discussed in terms of the inverse cascade of magnetic helicity and the alpha-effect. In simulations of such flows the maximum field strength exceeds the equipartition field strength for large scale separation. However, helicity conservation controls the speed at which this final state is reached. In the presence of open boundaries magnetic helicity fluxes out of the domain are possible. This reduces the timescales of the field growth, but it also tends to reduce the maximum attainable field s…
Mechanisms of nonhelical large-scale dynamos (shear-current dynamo and effect of homogeneous kinetic helicity fluctuations with zero mean) in a homogeneous turbulence with large-scale shear are discussed. We have found that the shear-current dynamo can act even in random flows with small Reynolds numbers. However, in this case mean-field dynamo requires small magnetic Prandtl numbers (i.e., ${\rm Pm} < {\rm Pm}^{\rm cr}<1$). The threshold in the magnetic Prandtl number, ${\rm Pm}^{\rm cr} = 0.24$, is determined using second order correlation approximation (or first-order smoothing approximatio…
Astrophysical objects with negligible resistivity are often threaded by large scale magnetic fields. The generation of these fields is somewhat mysterious, since a magnetic field in a perfectly conducting fluid cannot change the flux threading a fluid element, or the field topology. Classical dynamo theory evades this limit by assuming that magnetic reconnection is fast, even for vanishing resistivity, and that the large scale field can be generated by the action of kinetic helicity. Both these claims have been severely criticized, and the latter appears to conflict with strong theoretical arg…
Two questions about the solar magnetic field might be answered together once their connection is identified. The first is important for large scale dynamo theory: what prevents the magnetic backreaction forces from shutting down the dynamo cycle? The second question is: what determines the handedness of twist and writhe in magnetized coronal ejecta? Magnetic helicity conservation is important for answering both questions. Conservation implies that dynamo generation of large scale writhed structures is accompanied by the oppositely signed twist along these structures. The latter is associated w…
The magnetic helicity has paramount significance in nonlinear saturation of galactic dynamo. We argue that the magnetic helicity conservation is violated at the lepton stage in the evolution of early Universe. As a result, a cosmological magnetic field which can be a seed for the galactic dynamo obtains from the beginning a substantial magnetic helicity which has to be taken into account in the magnetic helicity balance at the later stage of galactic dynamo.
We supplement the mean field dynamo growth equation with the total magnetic helicity evolution equation. This provides an explicitly time dependent model for alpha quenching in dynamo theory. For dynamos without shear, this approach accounts for the observed large scale field growth and saturation in numerical simulations. After a significant kinematic phase, the dynamo is resistively quenched, i.e. the saturation time depends on the microscopic resistivity. This is independent of whether or not the turbulent diffusivity is resistively quenched. We find that the approach is also successful for…
Most large scale dynamo research for astrophysical rotators focuses on interior flow driven helical dynamos (FDHDs), but larger scale coronal fields most directly influence observations. It is thus important to understand the relationship between coronal and interior fields. Coronal field relaxation is actually a type of magnetically dominated helical dynamo (MDHD). MDHDs also occur in fusion plasma devices where they drive a system toward its relaxed state in response to magnetic helicity injection that otherwise drives the system away from this state. Global scale fields of astrophysical rot…
Stretching solar dynamos from differential rotation in a Riemannian manifold setting is presented. The spherical model follows closely a twisted magnetic flux tube Riemannian geometrical model or flux rope in solar physics, presented previously by Ricca [Solar Physics (1997)]. The spherical model presented here present new and interesting feature concerning its connection with spherical steady solar dynamos. One of this new feature is represented by the fact that the by considering poloidal magnetic field component much weaker than its toroidal counterpart, one obtains a stretch dynamo action …
Whether the upcoming cycle 24 of solar activity will be strong or not is being hotly debated. The solar cycle is produced by a complex dynamo mechanism. We model the last few solar cycles by `feeding' observational data of the Sun's polar magnetic field into our solar dynamo model. Our results fit the observed sunspot numbers of cycles 21-23 extremely well and predict that cycle~24 will be about 35% weaker than cycle~23.
We revisit the possible turbulent sources of the solar dynamo. Studying axisymmetric mean-field dynamo models, we find that the large-scale poloidal magnetic field could be generated not only by the famous alpha effect, but also by the Omega x J and shear-current effects. The inclusion of these additional turbulent sources alleviates several of the known problems of solar mean-field dynamo models.
Using a periodic box calculation it is shown that, owing to helicity conservation, a large scale field can only develop on a resistive timescale. This behaviour can be reproduced by a mean-field dynamo with alpha and eta_t quenchings that are equally strong and `catastrophic'.
We report our first results on comparing the variations of the solar internal rotation with solar activity, as predicted by non-linear solar dynamo modelling, with helioseismic measurements using the SOHO MDI data.
The location of the solar dynamo is discussed in the context of new insights into the theory of nonlinear turbulent dynamos. It is argued that, from a dynamo-theoretic point of view, the bottom of the convection zone is not a likely location and that the solar dynamo may be distributed over the convection zone. The near surface shear layer produces not only east-west field alignment, but it also helps the dynamo disposing of its excess small scale magnetic helicity.
In numerical studies of turbulence, hyperviscosity is often used as a tool to extend the inertial subrange and to reduce the dissipative subrange. By analogy, hyperdiffusivity (or hyperresistivity) is sometimes used in magnetohydrodynamics. The underlying assumption is that only the small scales are affected by this manipulation. In the present paper, possible side effects on the evolution of the large scale magnetic field are investigated. It is found that for turbulent flows with helicity, hyperdiffusivity causes the dynamo-generated magnetic field to saturate at a higher level than normal d…
(abridged) Aims: Three-dimensional numerical simulations of penetrative compressible convection with uniform horizontal shear are used to study dynamo action and the generation of large-scale magnetic fields. Methods: We consider cases where the magnetic Reynolds number is either marginal or moderately supercritical with respect to small-scale dynamo action in the absence of shear and rotation. The effects of magnetic helicity fluxes are studied by comparing results for the magnetic field with open and closed boundaries. Results: Without shear no large-scale dynamos are found even if the ingre…
The origin and sustenance of large scale galactic magnetic fields has been a long standing and controversial astrophysical problem. Here an alternative to the ``standard'' $\a-Ω$ mean field dynamo and primordial theories is pursued. The steady supply of supernovae induced turbulence exponentiates the total field energy, providing a significant seed mean field that can be linearly stretched by shear. The observed micro-Gauss fields would be produced primarily within one vertical diffusion time since it is only during this time that linear stretching can compete with diffusion. This approach doe…
A two-layer spherical $α^2$-dynamo model consisting of an inner electrically conducting core (magnetic diffusivity $λ_i$ and radius $r_i$) with $α= 0$ surrounded by an electrically conducting spherical shell (magnetic diffusivity $λ_o$ and radius $r_o$) with a constant $α$ is shown to exhibit oscillatory behavior for values of $β= λ_i/λ_o$ and $r_i/r_o$ relevant to the solar dynamo. Time-dependent dynamo solutions require $r_i/r_o \geq 0.55$ and $β\leq O(1)$. For the Sun, $r_i/r_o$ is about 0.8 and $β\approx 10^{-3}$. The time scale of the oscillations matches the 22 year period of the sunspot…
The sunspot solar cycle has been usually explained as the result of a dynamo process operating in the sun. This is a classical problem in Astrophysics that until the present is not fully solved. Here we discuss current problems and limitations with the solar dynamo modeling and their possible solutions using a kinematic dynamo model within the Babcock-Leighton approximation as a tool. In particular, we discuss the importance of the turbulent magnetic pumping versus the meridional flow circulation in the dynamo operation.
The spatio-temporal relationship between the sign of the observed radial component of the magnetic field at the solar surface and the sign of the toroidal field as inferred from Hale's polarity rules for sunspots is usually interpreted as signifying the phase relation between the poloidal and the toroidal magnetic field components involved in the solar dynamo process. This has been taken as a constraint for models of the solar dynamo. This note draws attention to the fact that the observed phase relation is naturally and inevitably produced by the emergence of tilted bipolar regions and flux t…
Turbulence with a large magnetic Reyonolds number, generically leads to rapidly growing magnetic noise over and above any mean field. We revisit the dynamics of this fluctuating field, in homogeneous, isotropic, helical turbulence. Assuming the turbulence to be Markovian, we first rederive, in a fairly transparent manner, the equation for the mean field, and corrected Fokker-Plank type equations for the magnetic correlations. In these equations, we also incorporate the effects of ambipolar drift which would obtain if the turbulent medium has a significant neutral component. We apply these equa…
We investigate the growth and structure of magnetic fields amplified by kinematic dynamo action in turbulence with non-zero kinetic helicity. We assume a simple Gaussian velocity correlation tensor, which allows us to consider very large magnetic Reynolds numbers, up to one trillion. We use the kinematic Kazantsev-Kraichnan model of dynamo and find a complete numerical solution for the correlation functions of growing magnetic fields.
