Global MHD modeling of Mercury's magnetosphere with applications to the MESSENGER mission and dynamo theory

We use a global magnetohydrodynamic (MHD) model to simulate Mercury's space environment for several solar wind and interplanetary magnetic field (IMF) conditions in anticipation of the magnetic field measurements by the MESSENGER spacecraft. The main goal of our study is to assess what characteristics of the internally generated field of Mercury can be inferred from the MESSENGER observations, and to what extent they will be able to constrain various models of Mercury's magnetic field generation. Based on the results of our simulations, we argue that it should be possible to infer not only the dipole component, but also the quadrupole and possibly even higher harmonics of the Mercury's planetary magnetic field. We furthermore expect that some of the crucial measurements for specifying the Hermean internal field will be acquired during the initial fly-bys of the planet, before MESSENGER goes into orbit around Mercury.     

Mathematical theory of the ionospheric dynamo

A mathematical theory of the three-dimensional ionospheric dynamo is described, which is exact within the context of the assumption that the magnetic field lines are perfectly conducting.Explicit formulae are obtained for the electric fields, and hence for the current systems, which are excited by the dynamo e.m.f. associated with an arbitrary given wind field.They can also be applied to determine the fields arising from an external source of e.m.f., originating for example in the magnetosphere.The convergence properties of the solution are investigated for a simple symmetric wind field; it is found that inclusion of spherical harmonics up to degree 80 is sufficient to yield the features of the electrojet region, now fully coupled to the global current system.     

Some recent developments in solar dynamo theory

We discuss the current status of solar dynamo theory and describe the dynamo model developed by our group. The toroidal magnetic field is generated in the tachocline by the strong differential rotation and rises to the solar surface due to magnetic buoyancy to create active regions. The decay of these active regions at the surface gives rise to the poloidal magnetic field by the Babcock-Leighton mechanism. This poloidal field is advected by the meridional circulation first to high latitudes and then down below to the tachocline. Dynamo models based on these ideas match different aspects of observational data reasonably well.     

A dynamo theory of solar flares

It is proposed that the solar flare phenomenon can be understood as a manifestation of the electrodynamic coupling process of the photosphere-chromosphere-corona system as a whole. The system is coupled by electric currents, flowing along (both upward and downward) and across the magnetic field lines, powered by the dynamo process driven by the neutral wind in the photosphere and the lower chromosphere. A self-consistent formulation of the proposed coupling system is given. It is shown in particular that the coupling system can generate and dissipate the power of 10²⁹ erg s^#X2212;1 and the total energy of 10³² erg during a typical life time (10³ s) of solar flares. The energy consumptions include Joule heat production, acceleration of current-carrying particles along field lines, magnetic energy storage and kinetic energy of plasma convection. The particle acceleration arises from the development of field-aligned potential drops of 10–150 kV due to the loss-cone constriction effect along the upward field-aligned currents, causing optical, X-ray and radio emissions. The total number of precipitating electrons during a flare is shown to be of order 10³⁷–10³⁸.     

New characteristics of the solar cycle and dynamo theory

Based on an analysis of the observational data for solar cycles 12–23 (Royal Greenwich Observatory-USAF/NOAA Sunspot Data), we have studied various parameters of the “Maunder butterflies.” Based on the observational data for cycles 16–23, we have found that BT/Land S depend linearly on each other, where B is the mean magnetic field of the cycle, T is the cycle duration, S is the cycle strength, and L is the mean sunspot latitude in the cycle (the arithmetic mean of the absolute values of the mean latitudes in the north and south). The connection of the observed quantities with the α-ω-dynamo theory is discussed.     

Solar dynamo theory and the models of Babcock and Leighton

The dynamo theory of the solar cycle as developed by Parker and others, and the observational models of Babcock and Leighton have been examined, with the conclusion that the dynamo theory is not applicable to the Sun and that the models fail.An essential part of the theory is an adequate effective diffusion coefficient. Fields are continuously sheared and amplified and, in this theory, these may not be allowed to accumulate; all subsurface fields of an old cycle must be eliminated. Ohmic diffusion is negligible and turbulent diffusion is invoked. However, this requires that all solar fields are tangled to a small scale, which is contrary to observation; for Hale's polarity laws are strictly observed, and large-scale surface features are common at the end of an 11-yr cycle in the same general area where new fields are appearing.The erupted (sunspot) fields lie generally above the unerupted, toroidal fields so that, even if they are merged as required, the centroid of the new system would be above that of the old. The result is not a steady-state oscillator, as required, but the complete loss of the solar field.It is concluded that for these and other reasons a shallow, reversing field is unacceptable, and that a deeply penetrating field is required. Reference is made to an alternative theory of the solar cycle based on a deep magnetic field.     

Comparisons and connections between mean field dynamo theory and accretion disc theory

The origin of large scale magnetic fields in astrophysical rotators, and the conversion of gravitational energy into radiation near stars and compact objects via accretion have been subjects of active research for a half century. Magnetohydrodynamic turbulence makes both problems highly nonlinear, so both subjects have benefitted from numerical simulations.However, understanding the key principles and practical modeling of observations warrants testable semi‐analytic mean field theories that distill the essential physics. Mean field dynamo (MFD) theory and alpha‐viscosity accretion disc theory exemplify this pursuit. That the latter is a mean field theory is not always made explicit but the combination of turbulence and global symmetry imply such. The more commonly explicit presentation of assumptions in 20th century textbook MFDT has exposed it to arguably more widespread criticism than incurred by 20th century alpha‐accretion theory despite complementary weaknesses. In the 21st century however, MFDT has experienced a breakthrough with a dynamical saturation theory that consistently agrees with simulations. Such has not yet occurred in accretion disc theory, though progress is emerging. Ironically however, for accretion engines, MFDT and accretion theory are presently two artificially uncoupled pieces of what should be a single coupled theory. Large scale fields and accretion flows are dynamically intertwined because large scale fields likely play a key role in angular momentum transport. I discuss and synthesize aspects of recent progress in MFDT and accretion disc theory to suggest why the two likely conspire in a unified theory (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The quasi-biennial cycle of solar activity and dynamo theory

We have investigated the behavior of dynamo waves within the framework of a nonlinear αω-dynamo by taking into account the thickness of the convective zone, turbulent diffusivity, and meridional circulation. We show that there exists a regime in the model where short and longer patterns are simultaneously observed in the butterfly diagrams for the magnetic field. This regime is similar to the mixed cycle of the Sun, when fast quasi-biennial oscillations are observed against the background of the 22-year cycle.     

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.     

Outline of a theory of solar wind interaction with the magnetosphere

Some new ideas on the interaction of the solar wind with the magnetosphere are brought forward. The mechanism of reflection of charged particles at the magnetopause is examined. It is shown that in general the reflection is not specular but that a component of momentum of the particle parallel to the magnetopause changes. A critical angle is derived such that particles whose trajectories make an angle less than it with the magnetopause enter the magnetosphere freely, so transferring their forward momentum to it. Spatially or temporally non-uniform entry of charged particles into the magnetosphere causes electric fields parallel to the magnetopause which either allow the free passage of solar wind across it or vacuum reconnection to the interplanetary magnetic field depending on the direction of the latter. These electric fields can be discharged in the ionosphere and so account qualitatively for the dayside agitation of the geomagnetic field observed on the polar caps. The solar wind wind plasma which enters the magnetosphere creates (1) a dawn-dusk electric field across the tail (2) enough force to account for the geomagnetic tail and (3) enough current during disturbed times to account for the auroral electrojets. The entry of solar wind plasma across the magnetosphere and connection of the geomagnetic to interplanetary field can be assisted by wind generated electric field in the ionosphere transferred by the good conductivity along the geomagnetic field to the magnetopause. This may account for some of the observed correlations between phenomena in the lower atmosphere and a component of magnetic disturbance.     

Power transmission from the solar wind-magnetosphere dynamo to the magnetosphere and to the ionosphere: Analysis of the IMS Alaska meridian chain data

It is shown that the power ε generated by the solar wind-magnetosphere dynamo is transmitted to the convective motion of magnetospheric plasma. This convective motion generates what we may call the “Pedersen counterpart currents” in the magnetosphere and drives a large part of the “region 1 and 2” field-aligned currents which are closed by the Pedersen currents in the ionosphere. These results are based on a self-consistent set of the ionospheric current and potential distribution patterns obtained from a study of the International Magnetosphere Study Alaska meridian chain data.     

Vorticity in the magnetosphere

It is shown that Birkeland current and vorticity in the magnetosphere are intimately related, suggesting the importance of taking explicit account of vorticity, particularly velocity shear, when considering magnetospheric motions. An equation of motion for the magnetosphere coupled to the ionosphere is derived. It is suggested that experience with MHD fluids generally might fruitfully be brought to bear on certain problems in the magnetosphere to answer the question, not ‘why a sheet of Birkeland current,’ but rather ‘why a localised velocity shear.’     

Sodium in the Jovian magnetosphere

Observations of sodium D-line emission from Io and the magnetosphere of Jupiter are reported. A disk-shaped cloud of sodium is found to exist in the Jovian magnetosphere with an inner edge at about 4R and an outer edge at about 10R . The gravitational scale height above the equatorial plane is a few Jovian radii. The data are interpreted in terms of a sputtering model, in which the sodium required to maintain the cloud is sputtered off the surface of Io by trapped energetic radiation-belt protons. Conditions on the atmospheric density are obtained. The Keplerian orbits attainable by such escaping sputtered atoms can provide the observed spatial distribution. The required 500-keV proton flux required to provide the 1–10 keV protons which will sputter the sodium at the surface of Io is consistent with the limiting trapped flux determined by ion-cyclotron turbulence.Publication No. 1410, Institute of Geophysics and Planetary Physics, University of California, Los Angeles 90024, Cal., U.S.A.     

VLF waves in the magnetosphere

The study of VLF waves at ground based stations is an important source of information on particles trapped in the magnetosphere. By various techniques it is also possible to measure plasma densities, electric fields and monitor energetic particle injection. By studying the propagation of waves beneath the ionosphere it is possible to study particle precipitation from the magnetosphere. In this paper we summarise some of the techniques and results obtained from the study of VLF waves at the South African research station in Antarctica.     

Three dimensional periodic orbits in three dipole problem

In the three dipole problem where enormous electromagnetic forces obstruct the three dimensional movement of the charged particle we determined for the first time families of three dimensional asymmetric periodic orbits. We study how these families appear, branching from the planar motion and we develop the procedures we have followed to determine them numerically. Also we give their characteristics and the conical projections and plottings of some orbits.     

Birkeland currents in the Earth's magnetosphere

As a result of his polar expeditions at the beginning of this century, Kristian Birkeland determined that intense ionospheric currents were associated with the aurora. Birkeland suggested that these currents originated far from the Earth and that they flowed ointo and away from the polar atmosphere along the geomagnetic field lines. The existence of such field-aligned or Birkeland currents was disputed because it was not possible to unambiguously identify current systems that are field-aligned (as suggested by Alfvén, 1939, 1940) and those which are completely contained in the ionosphere (as developed by Vestine and Chapman, 1938) with surface magnetic field observations. The presence of Birkeland currents has been absolutely confirmed with satellite-borne particle and magnetic field experiments conducted over the past two decades. These satellite observations have determined the large-scale patterns, flow directions, and intensities of Birkeland currents in the auroral and polar regions, and their relationship to the orientation and magnitude of the interplanetary magnetic field. The Birkeland currents are directly associated with visible and UV auroral forms observed with satellites. The results obtained from a variety of recently launched satellites are discussed here. These include Sweden's first satellite, VIKING, which has provided evidence for resonant Alfvén waves on the same geomagnetic field lines that guide stationary Birkeland currents. These observations demonstrate the important role that these currents play in the coupling of energy between the interplanetary medium and the lower ionosphere and atmosphere.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.