List of forthcoming papers

This paper is largely a reply to Cowling's review of the present status of cosmic dynamo theory and its alternatives of primordial or fossil field models. Central is the question of turbulent diffusion, without which plasma dynamos will not work but primordial magnetic fields are retained. Turbulence does not shred or divide fields into small-scale elements as claimed; instead it creates these elements in addition to the large-scale field which remains after Ohmic diffusion has destroyed the small fields. The significance of the existence of a terrestrial dynamo is stressed and various objections to the existence of a solar-type dynamo are discussed, including the steady divergence of theory and observational evidence over a quarter century. Cowling's criticisms of the primordial field theory are discussed; these include turbulent diffusion, the timing of the solar magnetic cycle, and the importance attached to observations in active and quiet magnetic regions.Since this paper was communicated, a personal communication from Professor Cowling has partially resolved the difference of opinion about turbulent diffusion and its effects. This is discussed in a letter to the Editor, at the end of this volume, p. 477.     

Predicting solar ‘climate’ by assimilating magnetic data into a flux-transport dynamo

Observational and theoretical knowledge about global-scale solar dynamo ingredients have reached the stage that it is possible to calibrate a flux-transport dynamo for the Sun by adjusting only a few tunable parameters. The important ingredients in this class of model are differential rotation (Omega-effect), helical turbulence (alpha-effect), meridional circulation and turbulent diffusion. The meridional circulation works as a conveyor belt and governs the dynamo cycle period. Meridional circulation and magnetic diffusivity together govern the memory of the Sun's past magnetic fields. After describing the physical processes involved in a flux-transport dynamo, we will show that a predictive tool can be built from it to predict mean solar cycle features by assimilating magnetic field data from previous cycles. We will discuss the theoretical and observational connections among various predictors, such as dynamo-generated toroidal flux integral, cross-equatorial flux, polar fields and geomagnetic indices. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Milestones in the Observations of Cosmic Magnetic Fields

Magnetic fields are observed everywhere in the universe. In this review, we concentrate on the observational aspects of the magnetic fields of Galactic and extragalactic objects. Readers can follow the milestones in the observations of cosmic magnetic fields obtained from the most important tracers of magnetic fields, namely, the star-light polarization, the Zeeman effect, the rotation measures (RMs, hereafter) of extragalactic radio sources, the pulsar RMs, radio polarization observations, as well as the newly implemented sub-mm and mm polarization capabilities. The magnetic field of the Galaxy was first discovered in 1949 by optical polarization observations. The local magnetic fields within one or two kpc have been well delineated by starlight polarization data. The polarization observations of diffuse Galactic radio background emission in 1962 confirmed unequivocally the existence of a Galactic magnetic field. The bulk of the present information about the magnetic fields in the Galaxy comes from anal     

The origin of our galactic magnetic field

A serious difficulty with the standard alpha‐omega theory of the origin of galactic magnetic fields involves the question of flux expulsion. This is intimately related to flux freezing. The alpha‐omega theory is shown in the context of the giant superbubble explosions that have a large impact on the physics of the interstellar medium. It is shown that superbubbles alone can duplicate the processes of the alpha‐omega dynamo and produce exponential growth of the galactic magnetic field. The possibility of the blow‐out of pieces of the magnetic field is discussed and it is shown that they have the potential to solve the flux‐expulsion problem. However, such an explanation must lead to apparent ‘gaps’ in the field in the galactic disc. These gaps are probably unavoidable in any dynamo theory and should have important observable consequences, one of which is an explanation for the escape of cosmic rays from the disc (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Kinematic Theory of Solar Dynamo

Generation of the Sun‘s magnetic fields by self-inductive processes in the solar electrically conducting interior, the solar dynamo theory, is a fundamentally important subject in astrophysics. The kinematic dynamo theory concerns how the magnetic fields are produced by kinematically possible flows without being constrained by the dynamic equation. We review a number of basic aspects of the kinematic dynamo theory, including the magnetohydrodynamic approximation for the dynamo equation, the impossibility of dynamo action with the solar differential rotation, the Cowling‘s anti-dynamo theorem in the solar context, the turbulent alpha effect and recently constructed three-dimensional interface dynamos controlled by the solar tachocline at the base of the convection zone.     

行星和太阳内部的磁流体力学

许多行星 (如木卫三 ,水星 ,地球 ,木星和土星 )和恒星 (如太阳 )具有内部磁场。对这些磁场的存在和变化的解释对行星科学家和天体物理学家是一个巨大的挑战。本文试图总结行星和恒星的导电流体内部磁流体力学研究的新近发展和困难。一般由热对流驱动的流动通过磁流体力学过程产生并维持在行星和恒星中的磁场。在行星中磁流体力学过程强烈地受到转动 ,磁场和球几何位型的综合影响。其动力学的关键方面涉及科里奥利力和洛伦兹力间的相互作用。在太阳中其流线 ,即处于对流层的薄的剪切流层在太阳的磁流体力学过程中扮演了一个基本的角色 ,并由之产生了 1 1年的太阳黑子周期。本文也给出了一个新的非线性三维太阳发电机模型。     

On self–killing and self–creating dynamos

Numerical studies with a spherical dynamo model have shown two remarkable phenomena. The model consists of a spherical body of an electrically conducting incompressible uid surrounded by free space. In addition to a rotation of the body an inner motion due to a given forcing is considered which satisfies a no–slip condition at the boundary. The full interaction of magnetic field and motion is taken into account. Starting from a fluid motion capable of dynamo action and a very weak magnetic field it was observed that the growing magnetic field destroys the dynamo property of the motion and then decays, and that the system ends up in a state with another motion incapable of dynamo action and zero magnetic field. In another case with a motion unable to prevent small magnetic fields from decay it proved to be possible that stronger magnetic fields deform it so that a dynamo starts to work which enables the system to approach a steady state with a finite magnetic field.     

Behavior of planetary dynamos under the influence of external magnetic fields: Application to Mercury and Ganymede

For planets with strong intrinsic magnetic fields such as Earth and Jupiter, an external magnetic field is unlikely to affect the internal dynamo, but for bodies with weak intrinsic fields in appropriate environments, such as Mercury and Ganymede, the interaction with nearby field sources may determine the internal dynamics and overall behavior of their liquid iron cores. On the basis of simulations of such interactions using numerical models for fluid flow and dynamo generation, the parameter regimes for stable dipolar and multipolar reversing dynamo magnetic fields established for isolated systems can be substantially changed by the action of external sources. Relatively weak external background fields (as low as 2% of the averaged undisturbed field at the core-mantle boundary) may change the energy balance and alter the regime over which natural isolated dynamos operate.     

Galactic magnetic fields and their interactions with the gas and cosmic rays

(i) The controversy of dynamo or primordial origin of galactic magnetic fields is summarized and extended to show that the dynamo theory appears to fail. However, much more important than their origin are the characteristics of the fields and their interactions with the gas and cosmic rays. (ii) A passive magnetic field frozen into a turbulent plasma is not dissipated like a cloud of smoke (turbulent or eddy diffusion) as believed previously. On the contrary it is amplified exponentially until, within a few eddy periods, either the growing magnetic stresses halt the turbulence or the field becomes chaotic. Even if the Petschek reconnection mechanism operates, the field is always disordered to a scale <0.1L, whereL is the eddy dimension. The investigation may at last provide a semi-quantitative deductive theory of hydromagnetic eddies. (iii) It is concluded that the gas motions observed in our Galaxy are not convective but are mainly hydromagnetic waves or oscillations, with the magnetic field in control. The significance of this result is discussed in connection with the overall gas velocity field, the creation of stars and stellar systems, and with the origin and distribution of cosmic rays.     

The dynamo theory of plasma turbulence wave in rotating celestial bodies

The various modes of plasma turbulence waves (including MHD waves) are easily excited under cosmic circumstances. In this paper, if we consider that the celestial bodies rotate, there is a source term generated for the magnetic induced equation by the excited plasma turbulence waves. If we expand the turbulent field in the Fourier series and include rotation velocity, the dynamo equation for turbulent waves is obtained. We have also obtained the solutions of various wave forms corresponding to different rotation velocities and then we significantly discuss the magnetic fields in the Sun, planets, and other celestial bodies.     

Magnetism and thermal evolution of the terrestrial planets

Of the terrestrial planets, Earth and probably Mercury possess substantial intrinsic magnetic fields generated by core dynamos, while Venus and Mars apparently lack such fields. Thermal histories are calculated for these planets and are found to admit several possible present states, including those which suggest simple explanations for the observations; whule the cores of Earth and Mercury are continuing to freeze, the cores of Venus and Mars may still be completely liquid. The models assume whole mantle convection, which is parameterized by a simple Nusselt-Rayleigh number relation and dictates the rate at which heat escapes from the core. It is found that completely fluid cores, devoid of intrinsic heat sources, are not likely to sustain thermal convection for the age of the solar system but cool to a subadiabatic, conductive state that can not maintain a dynamo. Planets which nucleate an inner core continue to sustain a dynamo because of the gravitational energy release and chemically driven convection that accompany inner core growth. The absence of a significant inner core can arise in Venus because of its slightly higher temperature and lower central pressure relative to Earth, while a Martian core avoids the onset of freezing if the abundance of sulfur in the core is ?15% by mass. All of the models presented assume that (I) core dynamos are driven by thermal and/or chemical convection; (ii) radiogenic heat production is confined to the mantle; (iii) mantle and core cool from initially hot states which are at the solidus and superliquidus, respectively; and (iv) any inner core excludes the light alloying material (sulfur or oxygen) which then mixes uniformly upward through the outer core. The models include realistic pressure and composition-dependent freezing curves for the core, and material parameters are chosen so that the correct present-day values of heat outflow, upper mantle temperature and viscosity, and inner core radius are obtained for the earth. It is found that Venus and Mars may have once had dynamos maintained by thermal convection alone. Earth may have had a completely fluid core and a dynamo maintained by thermal convection for the first 2 to 3 by, but an inner core nucleates and the dynamo energetics are subsequently dominated by gravitational energy release. Complete freezing of the Mercurian core is prohibited if it contains even a small amount of sulfur, and a dynamo can be maintained by chemical convection in a thin, fluid shell.     

Planetary magnetism

The origin and maintenance of planetary magnetic fields are discussed. The discussion is not limited to dynamo theories although these are almost universally favored. Thermoelectric currents are found to be a possible alternative for Jupiter. Two energy sources for dynamos are considered: convection and precessionally induced fluid flow. The earth is the most favorabl planet for a precessionally driven dynamo, although Neptune is a possibility. Jupiter is likely to have a convectionally driven dynamo, as may Saturn, but the relevant properties of Saturn are not yet well known. Conclusions for each planet are given.     

Dynamo mechanism for turbulent wave in celestial bodies

It is well known that under cosmic conditions the various modes of plasma turbulence waves (including MHD waves) are easily excited. In this paper we are trying to show that the turbulent wave also generates a source-term for the magnetic induced equations as does the turbulent fluid with nonzero helicity. By expanding the turbulent field in Fourier series, we have obtained dynamo equation for turbulent wave and a reasonable solution which indicates that the poloidal field may be built-up in the turbulent source region. Perhaps, we may think that the poloidal field of Equation (9) is the analytical form of the magnetic field in a turbulent source region of celestial bodies.     

Meridional circulation and the period of the solar dynamo cycle

We consider the conditions in the transition from the tachocline to the solar convective zone with changing diffusion coefficient. The topology of the magnetic fields involved in the solar dynamo is revised under the assumption that intermediate fields (of the order of 10 mT) have a dominant role in generating the fields in new cycle. The inclusion of meridional circulation is found to increase the dynamo wave period in comparison to the observed period. This suggests that the αΩ-effects are unimportant in calculating the solar cycle period but hold significance in determining the cycle amplitude.     

Dynamo action in an ambient field

The origin of global magnetic fields in celestial bodies is generally ascribed to dynamo action by fluid motions in their electrically conducting interiors. Some objects – e.g. close‐in extra‐solar planets or the moons of some giant planets – are embedded in ambient magnetic fields which modify the generation of the internal field in these bodies. Recently, the feedback of the magnetospheric field by Chapman‐Ferraro currents in the magnetopause onto the interior dynamo has been proposed to explain the observed weakness of the intrinsic magnetic field of planet Mercury. We study a simplified mean‐field dynamo model which allows us to analytically address various issues like positive and negative feedback situations, stationary versus time‐dependent solutions, and the stability of weak and strong field branches. We discuss the influence of the response function on the solutions when the external field depends on the strength of the intrinsic field like in the situation of the feedback dynamo of Mercury. We find that the feedback mechanism works only for a narrow range of dynamo numbers in the case of Mercury which makes him unique in our solar system. We conclude with some implications for extra‐solar planets (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Magnetohydrodynamic instabilities and turbulence in accretion disks

In this paper we review the possibilities for magnetohydrodynamic processes to handle the angular momentum transport in accretion disks. Traditionally the angular momentum transport has been considered to be the result of turbulent viscosity in the disk, although the Keplerian flow in accretion disks is linearly stable towards hydrodynamic perturbations. It is on the other hand linearly unstable to some magnetohydrodynamic (MHD) instabilities. The most important instabilities are the Parker and Balbus-Hawley instabilities that are related to the magnetic buoyancy and the shear flow, respectively. We discuss these instabilities not only in the traditional MHD framework, but also in the context of slender flux tubes, that reduce the complexity of the problem while keeping most of the stability properties of the complete problem. In the non-linear regime the instabilities produce turbulence. Recent numerical simulations describe the generation of magnetic fields by a dynamo in the resulting turbulent flow. Eventually such a dynamo may generate a global magnetic field in the disk. The relation of the MHD-turbulence to observations of accretion disks is still obscure. It is commonly believed that magnetic fields can be highly efficient in transporting the angular momentum, but emission lines, short-time scale variability and non-thermal radiation, which a stellar astronomer would take as signs of magnetic variability, are more commonly observed during periods of low accretion rates. Received October 12, 1995 / Accepted November 16, 1995     

Nonhelical mean‐field dynamos in a sheared turbulence

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 shearcurrent 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., when Pm < Pm^cr < 1). The threshold in the magnetic Prandtl number, Pm^cr = 0.24, is determined using second order correlation approximation (or first‐order smoothing approximation) for a background random flow with a scale‐dependent viscous correlation time τ_c = (νk 2)^–1 (where ν is the kinematic viscosity of the fluid and k is the wave number). For turbulent flows with large Reynolds numbers shear‐current dynamo occurs for arbitrary magnetic Prandtl numbers. This dynamo effect represents a very generic mechanism for generating large‐scale magnetic fields in a broad class of astrophysical turbulent systems with large‐scale shear. On the other hand, mean‐field dynamo due to homogeneous kinetic helicity fluctuations alone in a sheared turbulence is not realistic for a broad class of astrophysical systems because it requires a very specific random forcing of kinetic helicity fluctuations that contains, e.g., low‐frequency oscillations. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

星系盘中的磁重平衡:星系贮留原初磁场的观测证据

邻近旋涡星系中观测到的磁场被理论学家解释为发电机作用的结果.而我们发现,在邻近的星系中,磁场的强度与中性氢的柱密度紧密相关.星系盘中的磁场处于磁重平衡状态.这一结果与发电机放大机制相悖,从而支持星系磁场是原初起源的假说.     

Axisymmetric field generation within an ambient axial field

The generation of magnetic field in a homogeneous, electrically conducting fluid – as required for the dynamo generation of the fields of many astrophysical bodies – is normally a threshold process; the dynamo mechanism, applicable to such bodies in unmagnetised environments, requires motions of sufficient strength to overcome the innate magnetic diffusion. In the presence of an ambient field, however, the critical nature of the field generation process is relaxed. Motions can distort and amplify the ambient field for all amplitudes of flow. For motions with appropriate geometries, an internal ‘dynamo‐like’ field of appreciable strength can be generated, even for relatively weak flows. At least a minority of planets, moons and other bodies exist within significant external astrophysical fields. For these bodies, the ambient field problem is more relevant than the classical dynamo problem, yet it remains relatively little studied. In this paper we consider the effect of an axial ambient field on a spherical mean‐field α ²ω dynamo model, through nonlinear calculations with α ‐quenching feedback. Ambient fields of varying strengths, and both stationary and oscillatory in time, are imposed. Particular focus is placed on the effects of these fields on the equatorial symmetry and the time dependence of the preferred solutions. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the interaction between differential rotation and magnetic fields in the Sun

We have performed 3-D numerical simulations of compressible convection under the influence of rotation and magnetic fields in spherical shells. They aim at understanding the subtle coupling between convection, rotation and magnetic fields in the solar convection zone. We show that as the magnetic Reynolds number is increased in the simulations, the magnetic energy saturates via nonlinear dynamo action, to a value smaller but comparable to the kinetic energy contained in the shell, leading to increasingly strong Maxwell stresses that tend to weaken the differential rotation driven by the convection. These simulations also indicate that the mean toroidal and poloidal magnetic fields are small compared to their fluctuating counterparts, most of the magnetic energy being contained in the non-axisymmetric fields. The intermittent nature of the magnetic fields generated by such a turbulent convective dynamo confirms that in the Sun the large-scale ordered dynamo responsible for the 22-year cycle of activity can hardly be located in the solar convective envelope.