Unipolar Induction Research Articles

A model of the heliospheric magnetic field configuration

A three-dimensional model of the magnetic field configuration in the heliosphere is constructed by assuming that the interplanetary magnetic field consists of four components, (i) the solar dipole, (ii) a large number of small spherical dipoles located along an equatorial circle just inside the Sun (representing the magnetic field line arcade), (iii) the field of the poloidal current system generated by the solar unipolar induction and (iv) the field of an extensive current disc around the Sun lying in the ecliptic plane. The magnetic field intensity at a distance of 1 A.U. (about 20 R⊙ above the ecliptic plane) is normalized to fit the observed spiral configuration.

Nonlinear standing Alfvén wave current system at Io: Theory

We present a nonlinear analytical model of the Alfvén current tubes continuing the currents through Io (or rather its ionosphere) generated by the unipolar inductor effect due to Io's motion relative to the magnetospheric plasma. We thereby extend the linear work by Drell et al. (1965) to the fully nonlinear, sub‐Alfvénic situation also including flow which is not perpendicular to the background magnetic field. The following principal results have been obtained: (1) The portion of the currents feeding Io is aligned with the Alfvén characteristics at an angle θA = tan−1 MA to the magnetic field for the special case of perpendicular flow where MA is the Alfvén Mach number. (2) The Alfvén tubes act like an external conductance ΣA = 1/(µ0VA(1 + MA² + 2MA sin θ)1/2) where VA is the Alfvén speed and θ the angular deviation from perpendicular flow towards the direction of Alfvén wave propagation. Hence the Jovian ionospheric conductivity is not necessary for current closure. (3) In addition, the Alfvén tubes may be reflected from either the torus boundary or the Jovian ionosphere. The efficiency of the resulting interaction with these boundaries varies with Io position. The interaction is particularly strong at extreme magnetic latitudes, thereby suggesting a mechanism for the Io control of decametric emissions. (4) The reflected Alfvén waves may heat both the torus plasma and the Jovian ionosphere as well as produce increased diffusion of high‐energy particles in the torus. (5) From the point of view of the electrodynamic interaction, Io is unique among the Jovian satellites for several reasons: these include its ionosphere arising from ionized volcanic gases, a high external Alfvénic conductance ΣA, and a high corotational voltage in addition to the interaction phenomenon with a boundary. (6) We find that Amalthea is probably strongly coupled to Jupiter's ionosphere while the outer Galilean satellites may occasionally experience super‐Alfvénic conditions.

Determination of the electromagnetic field produced by a magnetic oblique-rotator

Approximate solutions for the electromagnetic fields produced by a uniformly magnetized oblique rotator in vacuum are derived systematically in various regions by using general relativistic considerations. The results, which are expressed in compact vector notation, are compared with the component expression of Deutsch (1955) and Backus (1956). In our method, the potentials (ϕ, A) and fields (E, B) due to the rotating magnet are represented in terms of the vector potential for a rest magnet, with the proper correction for rotation. In doing this, the transformation laws for various quantities between the rest and rotating frames play important roles. The meaning of ‘rotating’ magnetic field lines is also considered in connection with the apparent paradox in the gedanken-experiment of a unipolar inductor.

Io's wobbling flux tube and nonuniform surface conductivity: Longitude control of decametric emission and other magnetospheric interactions

A model is proposed relating Io's modulation of Jupiter's decametric radio emission (DAM) and other magnetospheric interactions to periodic changes in flux tube orientation with Io’s surface of nonuniform surface electrical conductivity. Spectral reflectance and albedo data suggest that visually bright surface areas on Io may be highly conducting due to the abundance there of irradiation‐altered salts, while relatively dark areas may be extremely insulating due to the abundance of free sulfur. Geometric correlations show that Io's orbital motion through Jupiter's tilted and offset magnetic field results in a 13‐hour periodic variation in the Io‐graphic surface position of Io's flux tube contact junctions. The resulting variation in effective electrical conductivity of Io results in modulation (switching) of Io's motional emf currents and corresponding flux tube currents. This causes the observed magnetic‐longitude dependence of Io‐dependent DAM, while emission beaming accounts for the observed Io‐phase effect. This switching model suggests that Io is a variable unipolar inductor and that its flux tube varies in electrodynamic character as a function of magnetic longitude; the predicted behavior is consistent with pre‐Voyager observed particle‐injection spikes at Io's L shell, auroral emissions from Jupiter, and may reconcile inconsistencies between theoretical and observed particle sweeping effects of Io. The model predicts a relatively inactive flux tube current system and strong particle sweeping during the Voyager 1 flux tube crossing.

Dynamo action in a thin slab

We consider the dynamo action produced by convection of a partially ionized, electrically conducting gas in a magnetic field. The model consists of two thin, Cartesian unipolar inductors connected in series by the magnetic field. For the case of a uniform magnetic field we compute the total current system generated by an arbitrary gas flow; for the case of a nonuniform field, we compute only the field-aligned coupling current. Application is made to the solar atmosphere.

Reply to ’Comment on ’’Spinning magnetic fields’’ ’

The comment of Viviani and Viviani concerning the old riddle of unipolar induction and the M (moving) and N (nonmoving) hypotheses contains a contradiction.

Primordial metamorphism of asteroids via electrical induction in A T Tauri-like solar wind

Simple evolutionary models of asteroids of various sizes and solar distances have been constructed assuming unipolar electrical induction heating due to passage of the Sun through a T Tauri phase with an increased magnetic field. Typical T Tauri conditions and an elementary solar wind model were used to calculate induced currents in modlels assuming electrical conductivities appropriate for carbonaceous material. Two restrictions with opposite dependence upon radius dominate the results. The electrical insulating tendency of a cold surface favors heating of larger bodies. The current-limiting backpressure of the induced magnetic field favors heating of smaller bodies. Thus it is found that maximum heating, in some cases sufficient for melting, occurs for model asteroids at the inner edge of the belt and with (model-dependent) radii from 25 to 250 km. This effect, if operant, would have produced a primordial distribution of metamorphosed asteroids primarily occurring at small solar distance and intermediate size. The observational evidence for such a distribution is unclear because the primordial distribution has likely been considerably modified by collisions, particularly at smaller sizes. There does seem to be some consistency with the model in the distribution of the largest asteroids, though data are sparse. In particular, this model seems relevant to the well-known dichotomy between Ceres and Vesta.

Some remarks on the classical electrodynamics of moving media

Extension of Maxwell's electrodynamics of media at rest to moving bodies is hampered by a basic difficulty: how to determine the excitation sources and the fields inside a body which is moving relative to the laboratory where the measurements are performed. In this paper various approaches are analyzed and interpreted from a point of view not previously emphasized, i.e., theoretical results are directly related to the Rontgen-Eichenwald experiments and to the phenomenon of unipolar induction. Practical difficulties associated with possible processes of measurement are pointed out.

Sheath-limited unipolar induction in the solar wind

The collection of charged particles by electrodes in plasmas is controlled by the currentvoltage characteristics of the plasma sheath which forms at the electrode surface. This principle is applied to the steady-state electromagnetic interaction of the solar wind with moon-like bodies, or ‘solid-body’ interactions. In some cases the unipolar dynamo response of an electrically conducting body in the solar wind motional electric field can be controlled by sheath effects. This occurs for highly conducting bodies when the body radiusR is less than a critical valueR c , with the result that no induced bow shock wave can form.

The electrical conductivity of Io

If Io has a thin crust of ice [this possibility has recently been suggested by Lewis (1971)] then the electrical resistance of the satellite is determined by an outer layer of thickness ∼8 km and is higher by a factor ∼10 15 than that needed to account for the modulation of Jupiter's decametric radio emission in the unipolar inductor model of Goldreich and Lynden-Bell. The modulation, however, could possibly be accounted for if the surface composition of Io is chondritic or if it has an ionosphere.

Unipolar induction braking of thin metal sheets

The eddy currents due to the motion of a thin conducting strip in the airgap of a d.c.-excited electromagnet are analysed. This permits determination of the braking force exerted on the sheet. A general method for this type of problem is outlined. The current streamlines are shown, and a specific numerical example is given. The results should be of interest in view of the widespread use of electromagnetic braking and damping in measuring instruments, relays etc.

Solar wind torque on the geomagnetic cavity

It is argued that the rotation of the ionospheric plasma drives unipolar induction currents through the solar wind plasma in the boundary layer of the geomagnetic cavity. The consequences of this current include a torque on the earth, Joule heating of the ionospheric plasma, and a magnetic field that is mainly eastward in the northern hemisphere and westward in the southern hemisphere. Assuming that all of the magnetic flux from the regions above the auroral zones threads the solar wind plasma in the boundary layer, the torque on the earth at magnetically quiet times is in the neighborhood of 1020 g cm2/sec2;, corresponding to a decrease in the earth's rotation rate of about one part in 1013 per year. The Joule heating rate is of order 1016 ergs/sec compared with the 1018 ergs/sec presently estimated for the dissipation rate associated with the magnetospheric convection.

Interaction of the solar wind with the moon

During its orbit about the Earth, the Moon is located in the interplanetary medium or the geomagnetosheath-geomagnetotail formed by the solar wind interaction with Earth. In the tail, no evidence is found for a lunar magnetic field limiting the magnetic moment to 10 20 G · cm 3 (< 10 −6 of that of the Earth). In the interplanetary medium, no evidence exists for a bow shock or a trailing shock although a well defined plasma wake region is observed in the anti-solar wind direction. The Moon absorbs the solar wind plasma which strikes its surface and creates a void region or cavity in the flow. Small perturbations of the interplanetary magnetic field magnitude (≲ 30%) and direction (≲ 20°) are observed to be correlated with the location of the solar wind plasma umbra and penumbra. Characteristic perturbations in magnitude are + − + − + as a satellite traverses the wake region. The magnitude of the anomalies is correlated principally with the diamagnetic properties of the solar wind, as measured by β, and less with the direction of the interplanetary magnetic field. The observed lunar Mach cone gives evidence for the anisotropic propagation of waves in the magnetized collisionless warm solar wind plasma. Neither the Gold-Tozer-Wilson mechanism of accretion of field lines or the Sonett-Colburn-Hollweg mechanism of unipolar induction is significant in the interaction. The transmission of microstructural discontinuities in the interplanetary medium past the Moon show little distortion, indicating a low effective electrical conductivity (<10 −4ω −1m −1) which implies a relatively cool interior (≲ 10 3 °K) of the lunar body. Fluctuations of the interplanetary magnetic field upstream from the plasma wake are stimulated by the disturbed conditions in that region. The Moon behaves like a cold, nonmagnetic fully absorbing dielectric sphere in the solar wind flow (see fig. 1).

A Model of the Geomagnetic Cavity

A heuristic model of the geomagnetic cavity is introduced. The model includes a unipolar induction current JU, that is driven by the solar wind. The current is generated by the solar wind plasma flowing in the magnetopause boundary layer. This current closes in the ionosphere. The electromagnetic forces associated with JU drive the magnetospheric convection. Even though the solar wind plasma at the magnetopause is basically collisionless, the plasma penetrates more deeply into the geomagnetic cavity than it would if the magnetopause were an ideal Chapman‐Ferraro sheath because the boundary layer flow is non‐adiabatic in the regions where JU is nonzero. Downstream from the earth the resulting expanded boundary layer forms the plasma sheet and the geomagnetic tail. Since the generation of JU does not depend on the existence of an interplanetary magnetic field, the geomagnetic cavity is closed when the interplanetary field is zero. The tangential drag is developed in the part of the boundary layer that lies forward of the midnight‐meridian intersection of the leading edge of the neutral sheet. The tail is produced by the inflation of the downstream part of the modified cavity that is formed by the superposition of the geomagnetic field and the magnetic field of JU. Transient phenomena produced by changes in JU include substorm expansions and injections of ring current particles which are initiated by decreases in JU. Changes in JU are caused by changes in the solar wind velocity (i.e., by changes in the unipolar emf) and by changes in the effective resistance to the flow of JU. If there is a critical value of |JU| above which the current is unstable, then there is a corresponding critical magnitude of the unipolar emf and therefore of the solar wind velocity. Such an instability in JU would account for the positive correlation between solar wind velocity and Kp. When the interplanetary magnetic field is greater than zero, shear stresses are set up between the solar wind plasma in the magnetopause boundary layer and that in the magnetosheath. The unipolar induction, i.e., the unipolar emf, and the resulting tangential drag then depend on the direction and magnitude of the interplanetary field as well as on the velocity of the solar wind and the electrical (Pedersen) resistivity of the magnetospheric plasma. The many attractive features of the model, especially the simplicity of the tangential drag mechanism, suggest that unipolar induction is a competitive alternative to magnetic field line reconnection and the other mechanisms that have been proposed to account for the tangential drag on the cavity and the various transient cavity phenomena.

Electrodynamical Properties of Empty Space in General Relativity

The general-relativistic formulation of the unipolar induction problem (massive, magnetized, rotating conductor) shows that the external vacuum solution attributes a virtual charge density and a virtual toroidal current to the surrounding empty space. The explanation thereof illuminates a new aspect of the rotational dragging of the inertial frame. If direct consequences of these phenomena could be detected in pulsars or in other astrophysical structures where relativistic gravitation is important, new important verifications of general relativity would be achieved. The main thrust of these considerations lies, however, in their applicability to any rotating metric with a superposed magnetic field.

The melting of asteroidal-sized bodies by unipolar dynamo induction from a primordial T Tauri sun

This paper examines the heating of asteroidal parent bodies by electrical induction during early solar evolution and prior to positioning of the sun onto the main sequence. Under the conditions assumed, which include a high initial solar spin rate, interplanetary electric fields of order 1 V/m would have existed in frames of reference comoving with the planets, leading to electrical heating from joule losses in the asteroidal interiors. The mechanism additionally requires the high plasma efflux characteristic of T Tauri objects and the presence of a circumstellar obscuration of the type commonly associated with early stellar objects. The proper combination of circumstellar obscuration, solar spin, solar wind flow, and starting planetary temperatures is shown to lead to asteroidal heating competitive with that found for a class of fossil radioactive species. The time dependence of the solar spin and plasma flow are shaped so as to be consistent with current views on the evolution to T Tauri objects and of the spin down of stars. Calculations also include cases of joint heating by fossil radionuclides and electrical induction, and show a complicated relationship due to the intrinsic nonlinearity of the electrical heating mechanism. Implications regarding the pre-main sequence dynamics of the sun are contained in the hypothesis of electrical heating if the contribution from radionuclides and gravitational accretion can be shown to be insufficient to account for the heating episode. Finally, some consequences of the mechanism applied to planets in the presence of an intense solar wind are considered.

Unipolar induction in the moon and a lunar limb shock mechanism

Unipolar induction to calculate moon interior electric field profiles, noting magnetic back pressure as limb shock wave and interaction with solar wind

FARADAY UNIPOLAR INDUCTION IN A NONIDEAL TYPE II SUPERCONDUCTOR

A Faraday unipolar inductor using a solid cylinder of a nonideal type II superconductor (unannealed Nb) constitutes a zero internal impedance generator capable of supplying appreciable electrical power and permits continuous study of the behavior of the average internal magnetic field vs the applied field. The various contributions to the observed emf are discussed in terms of the relativistic interpretation of Faraday unipolar induction.

Experimental Study of the Motional Electromotive Force

Experiments are described that develop a pure motional electromotive force detected with a sensitive galvanometer. Old questions are re-examined by an original experimental approach as follows: What are the conditions of relative motion between magnetic field and conductor for developing a motional electromotive force? Unipolar induction is considered when a uniform or symmetrical magnetic field is concerned and special attention is given to the rotation of nonuniform magnetic fields. The results of the latter differ markedly from the former. Concepts of macrostructure and microstructure magnetic fields are considered briefly as applied to the experiments described. References are made to theoretical treatments to clarify the issues, but discussions are kept to the experimental approach with a qualitative rather than quantitative treatment.

LXXXII. On the outer unipolar rotation and the outer unipolar induction

LXXXII. On the outer unipolar rotation and the outer unipolar induction