Origin of the magnetic fields in the giant planets

Recent observations and progress in the understanding of various requirements for the generation of magnetic fields permit much more definite conclusions to be drawn about the fields of the giant planets than was possible until quite recently. The Jovian magnetic field of about 4 gauss could be either of primordial origin or generated by a thermally driven dynamo. The expected Saturnian field of about 1 gauss can be similarly accounted for either by a thermally or by a precessionally driven dynamo. The presence of a field on Uranus of perhaps 0.1 gauss presents a problem because although it could be accounted for by a thermally driven dynamo operating in a highly conductive shell of hydrogen, the so far unobserved thermal flux and convection may be too low. If such a dynamo were to operate then one would expect the field to show seasonal variations. A precessional dynamo driven by Miranda seems to be marginally possible. On Neptune a conductive shell similar to that on Uranus appears to be much thinner, which perhaps explains the absence of an active dynamo driven either thermally or precessionally by Triton. It is, however, very likely that Neptune does have a magnetic field but that it is too weak to lead to observable electromagnetic radiations.     

Solar convection and magnetic fields

Mike Proctor looks at the interplay between convection and magnetism in the Sun's photosphere, using powerful numerical simulations.     

Planar charged-particle trajectories in multipole magnetic fields

This paper provides a complete generalization of the classic result that the radius of curvature () of a charged-particle trajectory confined to the equatorial plane of a magnetic dipole is directly proportional to the cube of the particles equatorial distance () from the dipole (i.e. ³). Comparable results are derived for the radii of curvature of all possible planar chargedparticle trajectories in an individual static magnetic multipole of arbitrary order m and degree n. Such trajectories arise wherever there exists a plane (or planes) such that the multipole magnetic field is locally perpendicular to this plane (or planes), everywhere apart from possibly at a set of magnetic neutral lines. Therefore planar trajectories exist in the equatorial plane of an axisymmetric (m = 0), or zonal, magnetic multipole, provided n is odd: the radius of curvature varies directly as ⁿ⁼². This result reduces to the classic one in the case of a zonal magnetic dipole (n = 1). Planar trajectories exist in 2m meridional planes in the case of the general tesseral (0 < m < n) magnetic multipole. These meridional planes are defined by the 2m roots of the equation cos[m()–_n^m)] = 0, where _n^m = (1/m) arctan (h_n^m/g_n^m); g_n^m and h_n^m denote the spherical harmonic coefficients. Equatorial planar trajectories also exist if (n – m) is odd. The polar axis ( = O,) of a tesseral magnetic multipole is a magnetic neutral line if m > I. A further 2_m(n – m) neutral lines exist at the intersections of the 2_m meridional planes with the (n – m) cones defined by the (n – m) roots of the equation P_n^m(cos ) = 0 in the range 0 < 9 < , where P_n^m(cos ) denotes the associated Legendre function. If (n – m) is odd, one of these cones coincides with the equator and the magnetic field is then perpendicular to the equator everywhere apart from the 2m equatorial neutral lines. The radius of curvature of an equatorial trajectory is directly proportional to ⁿ⁼² and inversely proportional to cos[m(–)]. Since this last expression vanishes at the 2m equatorial neutral ines, the radius of curvature becomes infinitely large as the particle approaches any one of these neutral lines. The radius of curvature of a meridional trajectory is directly proportional to rⁿ⁺², where r denotes radial distance from the multiple, and inversely proportional to P_n^m(cos )/sin . Hence the radius of curvature becomes infinitely large if the particle approaches the polar magnetic neutral ine (m > 1) or any one of the 2m(n – m) neutral ines located at the intersections of the 2m meridional planes with the (n – m) cones. Illustrative particle trajectories, derived by stepwise numerical integration of the exact equations of particle motion, are pressented for low-degree (n 3) magnetic multipoles. These computed particle trajectories clearly demonstrate the non-adiabatic scattering of charged particles at magnetic neutral lines. Brief comments are made on the different regions of phase space defined by regular and irregular trajectories.Also Visiting Reader in Physics, University of Sussex, Falmer, Brighton, BN1 9QH, UK     

Some methods of interpretation of the magnetic fields

Summary The author compares some methods of prospection which are based on the telluric measurements: 1) old method of elliptic representation of the telluric current and constants of conductibility; 2) methods ofKato, Kikuchi, Rikitake, Tikhonov, Cagniard and 3) method proposed by the author in 1952.The theory of «Dreiblätter» developed by the author in 1952 is applied to obtain a simple relation between the telluric values, the magnetic values and the tensor of conductibility. It is shown that in many cases this relation can be a simple algebraic one. The problem of «three» layers is developed with details and the possibility of generatlisation to the case of more than the three layers mentioned.The direct method developed in this paper is not the only possible one. The indirect means values (tensor means) can be also introduced: see our articles C.R. de l'Acad. des Scinces, t. 239, p. 1457, 1954 (Paris) and C.R. de l'Académie des Sciences, t. 239, p. 1766, 1954 (Paris). From the abstract point of view the utilisation of the indirect (tensor) means is simpler, but in order to visualize the pratical applications we have chosen here the direct method of computation.     

The emergence of braided magnetic fields

We study the emergence of braided magnetic fields from the top of the solar interior through to the corona. It is widely believed that emerging regions smaller than active regions are formed in the upper convection zone near the photosphere. Here, bundles of braided, rather than twisted, magnetic field can be formed, which then rise upward to emerge into the atmosphere. To test this theory, we investigate the behaviour of braided magnetic fields as they emerge into the solar atmosphere. We compare and contrast our models to previous studies of twisted flux tube emergence and discuss results that can be tested observationally. Although this is just an initial study, our results suggest that the underlying magnetic field structure of small emerging regions need not be twisted and that braided field, formed in the convection zone, could suffice.     

Observational connection between local high-temperature phenomena within magnetic clouds and the Sun

Magnetic clouds (MCs) frequently show abnormal high-ionization states of heavy ions. The abnormal high-charge distributions are related to the coronal temperature of their source regions. We examined the plasma and magnetic field data of 74 MCs observed by the Advanced Composition Explorer from February 1998 to December 2008. We determined that 14 of the 74 events showed local high-temperature phenomena. We analyzed the correlation between proton temperature and O⁷/O⁶ ratio (or high mean Fe charge state 〈Fe〉) within the local high-temperature regions in the 14 MCs. Results show that proton temperature and O⁷/O⁶ ratio (or high mean Fe charge state) had good correlations in nine MCs, but had no evident correlation in the other five MCs. The local high-temperature phenomena within the nine MCs have resulted from the Sun.     

Terrestrial, planetary and interplanetary magnetic fields

A discussion meeting at Burlington House on 10 March 2000 featured eight speakers and an audience of about 50. Andy Smith reports.     

Global magnetic field of the Sun and long-term variations of galactic cosmic rays

The paper deals with the relation of long-term variations of 10 GV galactic cosmic rays (GCR) to the global solar magnetic field and solar wind parameters. This study continues previous works, where the tilt of the heliospheric current sheet (HCS) and other solar-heliospheric parameters are successfully used to describe long-term variations of cosmic rays in the past two solar cycles. The novelty of the present work is the use of the HCS tilt and other parameters reconstructed from Hα observations of filaments for the period when direct global solar magnetic field observations were unavailable. Thus, we could extend the GCR simulation interval back to 1953. The analysis of data for 1953–1999 revealed a good correlation (the correlation coefficient >0.88) between the solar-heliospheric parameters and GCR in different cycles of solar activity. Moreover, the approach applied makes it possible to describe the behavior of cosmic rays in the epochs of solar maxima, which could not be done before. This indicates both the adequacy of the model and the reliability of the reconstructed global solar magnetic field parameters.     

Response of ionospheric electric fields to variations in the interplanetary magnetic field

The STARE system (Scandinavian Twin Auroral Radar Experiment) provides estimates of electron drift velocities, and hence also of the electric field in the high-latitude E-region ionosphere between 65 and 70 degrees latitude. The occurrence of drift velocities larger than about 400 m/s (equivalent to an electric field of 20 mV/m) have been correlated with the magnitude of the Interplanetary Magnetic Field (IMF) components B_z and B_y at all local times. Observation days have been considered during which both southward (B_z<0) and northward (B_z>0) IMF occurred. The occurrence of electric fields larger than 20 mV/m increases with increases in B_z magnitudes when B_z<0. It is found that the effects of southward IMF continue for some time following the northward turnings of the IMF. In order to eliminate such residual effects for B_z<0, we have, in the second part of the study, considered those days which were characterized by a pure northward IMF. The occurrence is considerably lower during times when B_z>0, than during those when B_z is negative. These results are related to the expansion and contraction of the auroral oval. The different percentage occurrences of large electric field for B_y>0 and B_y<0 components of the IMF during times when B_z>0, clearly display a dawn-dusk asymmetry of plasma flow in the ionosphere. The effects of the time-varying solar-wind speed, density, IMF fluctuations, and magnetospheric substorms on the occurrence of auroral-backscatter observations are also discussed.     

On plane waves in thermo-viscoelastic solids deformed by magnetic fields

Summary In the present paper,Maxwell's electromagnetic equations together with the equation of motion of two types of viscoelastic solids have been used to deal with the propagation of magneto-thermoviscoelastic plane waves.     

The rapid dissipation of magnetic fields in highly conducting fluids

Abstract

This paper treats the dynamical conditions that obtain when long straight parallel twisted flux tubes in a highly conducting fluid are packed together in a broad array. It is shown that there is generally no hydrostatic equilibrium. In place of equilibrium there is a dynamical nonequilibrium, leading to neutral point reconnection and progressive coalescence of neighboring tubes (with the same sense of twisting), forming tubes of larger diameter and reduced twist. The magnetic energy in the twisting of each tube declines toward zero, dissipated into small-scale motions of the fluid and thence into heat.

The physical implications are numerous. For instance, it has been suggested that the subsurface magnetic field of the sun is composed of close-packed twisted flux tubes. Any such structures are short lived, at best.

The footpoints of the filamentary magnetic fields above bipolar magnetic regions on the sun are continually shuffled and rotated by the convection, so that the fields are composed of twisted rubes. The twisting and mutual wrapping is converted directly into fluid motion and heat by the dynamical nonequilibrium, so that the work done by the convection of the footpoints goes directly into heating the corona above. This theoretical result is the final step, then, in understanding the assertion by Rosner, Tucker, and Valana, and others, that the observed structure of the visible corona implies that it is heated principally by direct dissipation of the supporting magnetic field. It is the dynamical nonequilibrium that causes the dissipation, in spite of the high electrical conductivity. It would appear that any bipolar magnetic field extending upward from a dense convective layer into a tenuous atmosphere automatically produces heating, and a corona of some sort, in the sun or any other convective star.     

Predictions of magnetic fields for Uranus and Neptune

Summary The magnetic moments of Uranus and Neptune have been predicted using different scaling laws of planetary magnetism. The predictions for Uranus cover a broad band of values from very weak magnetic fields (tidal relations) to moderate fields (thermal convection hypothesis). Therefore, the direct measurements of this field by Voyager 2 (January 1986) will be very important for testing the individual hapotheses.

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Presented at the Fifth Scientific Assembly of IAGA in Prague 1985.     

A physical approach to computing magnetic fields1

The superposition integral expressing the field due to a magnetic source body is relatively simple to evaluate in the case of a homogeneous magnetization. In practice this generally requires that any remnant component is uniform and the susceptibility of the body is sufficiently low to permit the assumption of a uniform induced magnetization. Under these conditions the anomalous magnetic field due to a polyhedral body can be represented in an intuitive and physically appealing manner. It is demonstrated that the components of the magnetic field H can be expressed as a simple combination of the potentials due to two elementary source distributions. These are, firstly, a uniform double layer (normally directed dipole moment density) located on the planar polygonal faces of the body and, secondly, a uniform line source located along its edges. In practice both of these potentials (and thus the required magnetic field components) are easily computed. The technique is applicable to polyhedra with arbitrarily shaped faces and the relevant expressions for the magnetic field components are suitable for numerical evaluation everywhere except along the edges of the body where they display a logarithmic singularity.     

Modelling magnetic fields due to steel drum accumulations

Modelling the magnetic fields produced by accumulations of steel drums is a problem that is relevant to the detection and evaluation of disposal sites containing materials that are potentially hazardous to the environment. Accurate modelling is possible with existing integral equation techniques but these are numerically intensive due to the need to solve very large systems of linear equations. Use of an approximate iterative technique for the solution of the equations (system iteration) allows the integral equation technique to be extended to modelling the magnetic effect of substantially large accumulations, comprising up to several hundred drums, on very moderate computing facilities. However, even this process remains time‐consuming and suggests the use of more rapid, if less accurate, modifications. Several are available. Surprisingly, quite reasonable results can also be achieved with a very basic approximation that represents each drum by a discrete dipole located at its centroid. The dipole moments are found from the magnetic behaviour of single drums exposed to a uniform inducing field, which can be conveniently defined by a dyadic drum apparent susceptibility. The basic discrete dipole model for drum accumulations can be substantially improved by using a first‐order accommodation of the depolarizing effect produced by the shape of the accumulation. All of the above modelling techniques require details of individual drum locations and orientation. This information is generally unavailable to geophysical practitioners involved in environmental surveys and so prompts the idea of models that represent drum accumulations as a continuous distribution of magnetization. The convenience of neglecting details of drum location and orientation comes at the cost of some loss in accuracy of the modelled responses. However, for accumulations buried sufficiently deep and in which the drums are uniformly distributed, the total field magnetic anomaly is found to be reasonably approximated by the effect of a continuous magnetization, expressible in terms of an effective isotropic susceptibility. Again, the basic model can be improved by the accommodation of demagnetization effects due to the shape of the accumulation.     

Structure of magnetic fields generated by galactic dynamos

Abstract

We investigated global axisymmetric (m = 0) and non-axisymmetric (m = 1) modes of magnetic fields generated by the galactic dynamo including the α²-dynamo. The α²-dynamo is responsible for the field generation in the central region of galaxies where the shear of galactic rotation is weak (e.g. M51). The highest growth rate of m = 1 modes is always smaller than that of m = 0 modes; thus m = 1 modes of the standard galactic dynamo cannot explain the dominance of the bisymmetric fields in spiral galaxies. Radial extent of each m = 1 mode is too narrow to reproduce the observed bisymmetric structure extending over a disk.