Self-exciting Dynamo Research Articles

Size and Strength of Self-excited Dynamos in Jupiter-like Extrasolar Planets

Abstract The magnetization of solar and extrasolar gas giants is critically dependent on the electronic and mass transport coefficients of their convective fluid interiors. We analyze recent laboratory experimental results on metallic hydrogen to derive a new conductivity profile for the Jovian-like planets. We combine this revised conductivity with a polytropic-based thermodynamic equation of state to study the dynamo action in 100 extrasolar giant planets varying from synchronous hot Jupiters to fast rotators, with masses ranging from 0.3 M J to 15 M J. We find dynamo cores larger than previous estimates, but consistent with the results from Juno, suggesting that the field generation in the more massive planets might be shallow-seated. Our results reveal that most extrasolar giants are expected to possess dipole surface magnetic fields in the range of 0.1–10 Gauss. Assuming radio emission processes similar to our solar giants, the stronger emitters are expected to have maximal cyclotron frequencies between 20 and 40 MHz and for those within few 10 pc, few have flux densities greater than 1 mJy. Our work places new bounds on the observational detectability of extrasolar magnetic fields.

Degenerate Hopf bifurcation in a self-exciting Faraday disc dynamo

In order to further understand a self-exciting Faraday disc dynamo (Hide et al, in Proc. R. Soc. A 452, 1369 1996), showing chaotic attractors with very complicated topological structures, we present codimension one and two (degenerate) Hopf bifurcations and prove the existence of periodic solutions. In addition, numerical simulations are given for confirming the theoretical results.

Synchronization and Electronic Circuit Application of Hidden Hyperchaos in a Four-Dimensional Self-Exciting Homopolar Disc Dynamo without Equilibria

We introduce and investigate a four-dimensional hidden hyperchaotic system without equilibria, which is obtained by augmenting the three-dimensional self-exciting homopolar disc dynamo due to Moffatt with an additional control variable. Synchronization of two such coupled disc dynamo models is investigated by active control and sliding mode control methods. Numerical integrations show that sliding mode control provides a better synchronization in time but causes chattering. The solution is obtained by switching to active control when the synchronization errors become very small. In addition, the electronic circuit of the four-dimensional hyperchaotic system has been realized in ORCAD-PSpice and on the oscilloscope by amplitude values, verifying the results from the numerical experiments.

The Wisconsin Plasma Astrophysics Laboratory

The Wisconsin Plasma Astrophysics Laboratory (WiPAL) is a flexible user facility designed to study a range of astrophysically relevant plasma processes as well as novel geometries that mimic astrophysical systems. A multi-cusp magnetic bucket constructed from strong samarium cobalt permanent magnets now confines a$10~\text{m}^{3}$, fully ionized, magnetic-field-free plasma in a spherical geometry. Plasma parameters of$T_{e}\approx 5$to$20~\text{eV}$and$n_{e}\approx 10^{11}$to$5\times 10^{12}~\text{cm}^{-3}$provide an ideal testbed for a range of astrophysical experiments, including self-exciting dynamos, collisionless magnetic reconnection, jet stability, stellar winds and more. This article describes the capabilities of WiPAL, along with several experiments, in both operating and planning stages, that illustrate the range of possibilities for future users.

Anelastic convection-driven dynamo benchmarks

Benchmark solutions for fully nonlinear anelastic compressible convection and dynamo action in a rotating spherical shell are proposed. Three benchmarks are specified. The first is a purely hydrodynamic case, which is steady in a uniformly drifting frame. The second is a self-excited saturated dynamo solution, also steady in a drifting frame. The third is again a self-excited dynamo but is unsteady in time, and it has a higher Rayleigh number than the steady dynamo benchmark. Four independent codes have been tested against these benchmarks, and very satisfactory agreement has been found. This provides an accurate reference standard against which new anelastic codes can be tested.

Nonlinear feedback and coupling in self-exciting dynamos

Systems of steadily-forced self-exciting Faraday-disk homopolar dynamos that incorporate series motors and the autonomous sets of nonlinear ordinary differential equations (ODEs) governing their behaviour are of intrinsic engineering and mathematical interest. And by providing instructive “low-dimensional” models of self-exciting fluid dynamos in stars and planets they elucidate nonlinear magnetohydrodynamic (MHD) feedback and coupling processes involving the spatial redistribution of kinetic energy by the action of Lorentz ponderomotive forces. The time (t)-dependence of the persistent dynamo current I(t) depends on the control parameters of the system, especially A/B defined by the relationship between I and Lorentz torque, T, that drives the armature of the series motor into rotation relative to the ambient magnetic field, M (amb.), namely T = AI + BI 2 where A and B depend on the design characteristics of the motor [Hide, R., Nonlinear quenching of current fluctuations in a self-exciting homopolar dynamo. Nonlinear Process. Geophys. 1997a, 4, 201–205; Hide, R., The nonlinear equations governing a hierarchy of self-exciting coupled Faraday-disk homopolar dynamos. Phys. Earth Planet. Interiors 1997b, 103, 281–291]. A is non-zero when “external” sources of M (amb.) are present, such as permanent magnets and/or other self-exciting dynamo “sub-units”, whereas B is non-zero when the motor includes a stationary “field winding” through which dynamo current is diverted. Numerical analysis of the governing ODEs using digital and (electronic circuit) analogue computers and guided by Hopf-bifurcation instability theory indicate (i) that when A is non-zero there are regions of multi-dimensional “control-parameter” space where I(t) exhibits large-amplitude chaotic fluctuations reminiscent of polarity reversals and excursions of the main geomagnetic field, and (ii) that such regions shrink in volume as A/B decreases in magnitude and they disappear altogether in the special (but physically realistic) case when A/B = 0, with the sign (direction) of I determined by the initial conditions and its magnitude by the other control parameters. This process whereby nonlinear Lorentz forces attenuate persistent fluctuations or even quench them altogether offers a theoretical basis for interpreting the highly irregular geomagnetic polarity timeseries in the palaeomagnetic record [Hide, R., Generic nonlinear processes in self-exciting dynamos and the long-term behaviour of the geomagnetic field, including polarity superchrons. Phil. Trans. Roy. Soc. Lond. A 2000, 358, 943–955]. In the absence of permanent magnets, the governing ODEs exhibit the same “magnetic symmetry” property characteristic of the governing partial differential equations (PDEs) of unbiased MHD-dynamos, namely that for every solution (u, B) there is a corresponding solution (u, −B) (where u is the instantaneous Eulerian flow velocity and B the magnetic field at a general point P).

Why the first laboratory self-exciting dynamo was at Newcastle

This article describes how a succession of events starting in 1946 led to the world's first laboratory self-exciting simply-connected dynamo in 1963. In Manchester, in l947, an interest in the magnetic deflection of cosmic rays and Babcock's measurement of the magnetic field of a remote star, led Blackett to resurrect the idea of a “fundamental rotation theory” for the production of the Earth's magnetic field. Bullard suggested a geophysical test of the theory – measure the variation of magnetic field with depth inside the Earth. Blackett gave the job of doing this to a newly arrived Junior Lecturer, Runcorn. As the mine work was coming to an end, in 1949 Runcorn took on a Ph.D. student, Lowes, and started him off on a project based on a 1948 suggestion by Bullard that an individual non-dipole field focus could be produced by electromagnetic induction in a rotating eddy in the Earth's conducting fluid core. When Bullard produced his paper, to allow him to get an algebraic solution, he had to assume that his eddy was electrically insulated from the rest of the core. Blackett pointed out that more field might be obtained if the eddies were in electrical contact with the core, and got Lowes to build a laboratory model to simulate and investigate this. The model used a solid-body rotation of a (half) cylindrical “eddy” in a solid “core” having an asymmetrical boundary. A fellow (Theoretical Physics) Ph.D. student Herzenberg became interested, and eventually produced the corresponding theory, for a single rigid-body spherical eddy off-centre in a spherical core. In 1954, Bullard and Gellman produced the first crude numerical “solution” for a kinematic dynamo model in the core; however, there was still great reluctance to accept that there could be self-excitation in a simply-connected homogeneous conductor. Herzenberg then extended his theory to a two-eddy situation in a spherical core, and in 1957 showed rigorously that it could produce a self-exciting dynamo. Now at Newcastle, in 1959, Lowes took on Wilkinson as a Ph.D. student. To test Herzenberg's theory, and look for reversals, Wilkinson built a laboratory dynamo model that eventually achieved self-excitation in 1963; in 1968 another model showed spontaneous reversal.

Unstable periodic orbits in a four-dimensional Faraday disk dynamo

In this article, we return to a four-dimensional model for a self-exciting Faraday disk dynamo, originally investigated by Hide and Moroz [Hide, R. and Moroz, I.M., Effects due to induced azimuthal eddy currents in the self-exciting Faraday disk homopolar dynamo with a nonlinear series motor: I two special cases. Physica D 1999, 134, 387–301]. We extract unstable periodic orbits from long time series of chaotic trajectories by the method of close returns to a Poincaré section. We then employ recently developed topological tools to characterise the underlying chaotic attractor of the dynamo by identifying its branched manifold or template.

Numerical simulation of a spherical dynamo excited by a flow of von Kármán type

In a celebrated recent experiment, Monchaux, et al. (Phys. Rev. Lett. 2007, 98, 044502) created a self-excited dynamo in a cylindrical container of liquid sodium by a turbulent flow created by counter-rotating impellers at the plane ends of the container. A strange feature of the experiment was its failure to generate magnetic field when the impellers were made of stainless steel; success required the impellers to be made of soft iron. The results reported here were generated by numerical simulations of an idealization of the experiment. The container is a sphere and the impellers are replaced by a differential zonal motion of its surface, the northern and southern hemispheres turning about the symmetry axis in opposite senses, the whole system being contained in a thin shell with which it is in perfect electrical contact. This shell has generally a finite electrical conductance and a magnetic permeability that can greatly exceed that of the fluid. The electrodynamic effect of the shell is represented by a thin-wall boundary condition, similar but not identical to that used in MHD duct flow theory. Eleven cases were considered, in four of which the surface shell is an electrical insulator; in the others it is made of a conducting material which, like soft iron, might have a large permeability. In eight cases, a seed field decays away but in three it is amplified and becomes a turbulent self-excited dynamo. Through four cases of the same surface motion and shell permeability, it is inferred that an increase in the shell conductance assists the regeneration of magnetic field. It is also shown that enhancing the shell permeability assists the field creation.

Size and compositional constraints of Ganymede's metallic core for driving an active dynamo

Ganymede has an intrinsic magnetic field which is generally considered to originate from a self-excited dynamo in the metallic core. Driving of the dynamo depends critically on the satellite's thermal state and internal structure. However, the inferred structure based on gravity data alone has a large uncertainty, and this makes the possibility of dynamo activity unclear; variations in core size and composition significantly change the heat capacity and alter the cooling history of the core. The main objectives of this study is to explore the structural conditions for a currently active dynamo in Ganymede using numerical simulations of the thermal history, and to evaluate under which conditions Ganymede can maintain the dynamo activity at present. We have investigated the satellite's thermal history using various core sizes and compositions satisfying the mean density and moment of inertia of Ganymede, and evaluate the temperature and heat flux at the core–mantle boundary (CMB). Based on the following two conditions, we evaluate the possibility of dynamo activity, thereby reducing the uncertainty of the previously inferred interior structure. The first condition is that the temperature at the CMB must exceed the melting point of a metallic core, and the second is that the heat flux through the CMB must exceed the adiabatic temperature gradient. The mantle temperature starts to increase because of the decay of long-lived radiogenic elements in the rocky mantle. After a few Gyr, radiogenic elements are exhausted and temperature starts to decrease. As the rocky mantle cools, the heat flux at the CMB steadily increases. If the temperature and heat flux at the CMB satisfy these conditions simultaneously, we consider the case as capable of driving a dynamo. Finally, we identify the Dynamo Regime, which is the specific range of internal structures capable of driving the dynamo, based on the results of simulations with various structures. If Ganymede's self-sustained magnetic field were maintained by thermal convection, the satellite's metallic core would be relatively large and, in comparison to other terrestrial-type planetary cores, strongly enriched in sulfur. The dynamo activity and the generation of the magnetic field of Ganymede should start from a much later stage, possibly close to the present.

Planar velocity dynamos in a sphere

The Earth's main magnetic field is generally believed to be due to a self-exciting dynamo process in the Earth's fluid outer core. A variety of antidynamo theorems exist that set conditions under which a magnetic field cannot be indefinitely maintained by dynamo action against ohmic decay. One such theorem, the Planar Velocity Antidynamo Theorem , precludes field maintenance when the flow is everywhere parallel to some plane, e.g. the equatorial plane. This paper shows that the proof of the Planar Velocity Theorem fails when the flow is confined to a sphere, due to diffusive coupling at the boundary. Then, the theorem reverts to a conjecture. There is a need to either prove the conjecture, or find a functioning planar velocity dynamo. To the latter end, this paper formulates the toroidal–poloidal spectral form of the magnetic induction equation for planar flows, as a basis for a numerical investigation. We have thereby determined magnetic field growth rates associated with various planar flows in spheres. For most flows, the induced magnetic field decays with time, supporting a planar velocity antidynamo conjecture for a spherical conducting fluid. However, one flow is exceptional, indicating that magnetic field growth can occur. We also re-examine some classical kinematic dynamo models, converting the flows where possible to planar flows. For the flow of Pekeris et al . (Pekeris, C. L., Accad, Y. & Shkoller, B. 1973 Kinematic dynamos and the Earth's magnetic field. Phil. Trans. R. Soc. A 275 , 425–461), this conversion dramatically reduces the critical magnetic Reynolds number.

Clarification of the Hall effect as an energy transfer mechanism in a theory of the Earth’s magnetic field and sunspots

Abstract. Clarification is offered of the energy transfer role played by the Hall effect in a recent paper: de Paor, A., A theory of the Earth's magnetic field and of sunspots, based on a self-excited dynamo incorporating the Hall effect, Nonlinear Processes in Geophysics, 8, 265-279, 2001.

SELF-EXCITING FARADAY DISK HOMOPOLAR DYNAMOS

In this paper we present an overview of recently published work on the Faraday disk self-exciting homopolar dynamos. We also extend the analysis of two such coupled self-exciting disk dynamos with linear series motors [Moroz et al., 1998a; Moroz et al., 1998b] to the situation where one or both dynamo subunits incorporate nonlinear motors. We examine the differences in some of the bifurcation transition sequences between the various cases and consider whether the nonlinear quenching of oscillatory solutions can occur [Hide, 1998].

A theory of the Earth's magnetic field and of sunspots, based on a self-excited dynamo incorporating the Hall effect

Abstract. A new viewpoint on the generation and maintenance of the Earth's magnetic field is put forward, which integrates self-exciting dynamo theory with the possibility of energy coupling along orthogonal axes provided by the Hall effect. A nonlinear third-order system is derived, with a fourth equation serving as an observer of unspecified geophysical processes which could result in field reversal. Lyapunov analysis proves that chaos is not intrinsic to this system. Relative constancy of one of the variables produces pseudo equilibrium in a second order subsystem and allows for self-excitation of the geomagnetic field. Electromagnetic analysis yields expressions for key parameters. Models for secular variations recorded at London, Palermo and at the Cape of Good Hope over the past four hundred years are offered. Offset of the Earth's magnetic axis from the geographic axis is central to time-varying declination, but its causes have not yet been established. Applicability of the model to the explanation of sunspot activity is outlined. A corroborating experiment published by Peter Barlow in 1831 is appended.

EFFECTS DUE TO INDUCED AZIMUTHAL EDDY CURRENTS IN A SELF-EXCITING FARADAY DISK HOMOPOLAR DYNAMO WITH A NONLINEAR SERIES MOTOR II: THE GENERAL CASE

This paper forms the second part of a two-part study into the effects of azimuthal eddy currents in the Faraday disk self-exciting homopolar dynamo, connected in series with the coil when the applied couple driving the disk is steady. The Lorentz couple driving the armature of the motor is a general quadratic function I(1 - ε + εSI) of the current I(t), where 0 ≤ ε ≤ 1. Here we investigate how cases with 0 < ε < 1 relate to the two special cases of ε = 0 and ε = 1, considered in Part I of our study [Hide & Moroz, 1999]. One key difference is that the lack of reflectional symmetry in the general ε problem means that the linear stability curves for the onset of both steady and oscillatory behavior for both the trivial and the nontrivial equilibrium solutions no longer coincide. This results in distinct Takens–Bogdanov double-zero bifurcations for these states, as well as multiple branches to the Hopf bifurcation curves, associated with bifurcations from the nontrivial equilibrium states. Multiple bifurcations involving simultaneous steady and nondegenerate oscillatory solutions are also possible.

A self-excited hydromagnetic dynamo effect can take place in astrobleme impact melts

A self-excited hydromagnetic dynamo effect may take place in the lake of an impact melt with a volume on the order of a hundred cubic kilometers and a temperature of 2000–3000 K formed upon collision of a large meteorite (or asteroid) with a planet. The high temperature results in large electric conductivity and low viscosity of the medium. This circumstance provides explanation for the magnetic anomalies related to the Earth astroblemes.

Generic nonlinear processes in self–exciting dynamos and the long–term behaviour of the main geomagnetic field, including polarity superchrons

When the main geomagnetic field undergoes a reversal in polarity it does so in no more than a few thousand years. Many hundreds of such reversals must have occurred over geological time (the age of...

Relativistic Dynamos in Magnetospheres of Rotating Compact Objects

The kinematic evolution of axisymmetric magnetic fields in rotating magnetospheres of relativistic compact objects is analytically studied, based on relativistic Ohm's law in stationary axisymmetric geometry. By neglecting the poloidal flows of plasma in simplified magnetospheric models, we discuss self-excited dynamos due to the frame-dragging effect (originally pointed out by Khanna & Camenzind), and we propose alternative processes to generate axisymmetric magnetic fields against ohmic dissipation. The first process (which may be called induced excitation) is caused by the help of a background uniform magnetic field in addition to the dragging of inertial frames. It is shown that excited multipolar components of poloidal and azimuthal fields are sustained as stationary modes, and outgoing Poynting flux converges toward the rotation axis. The second one is self-excited dynamo through azimuthal convection current, which is found to be effective if plasma rotation becomes highly relativistic with a sharp gradient in the angular velocity. In this case no frame-dragging effect is needed, and the coupling between charge separation and plasma rotation becomes important. We discuss briefly the results in relation to active phenomena in the relativistic magnetospheres.

A study of two novel self-exciting single-disk homopolar dynamos: theory

A study of two novel self-exciting single-disk homopolar dynamos: theory

Two dynamical models for solar spicules

Solar spicules are luminous jets that erupt up to 10 000 km from the surface of the Sun and have diameters, all along their length, of only about 150–200 km. We first review some recent observations made at the Hα wavelength. According to our models, a solar spicule is a self-channelled proton beam emitted by a magnetic element and surrounded by a cold sheath. The beam originates in a self-excited dynamo that exploits a v × B field and that could be situated either below or above the element, where v is the local plasma velocity and B is the local magnetic flux density. In falling back, the sheath provides a return current of protons that cancels the outgoing current. We discuss the channelling of charged-particle beams of very large cross-section and propose velocity channelling, which is apparently a new concept. We assume a steady state and a hydrogen plasma.