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

Abstract

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.

Role of the Hall Current in Magnetohydrodynamic Dynamos

“…We therefore believe that a sustained effort is required to overcome this theoretical deficiency. The present paper is one step in this direction, which adds to previous studies on Hall dynamos (Heintzmann 1983;Galanti et al 1994;Mirnov et al 2002;de Paor 2001;Sano & Stone 2002;Ji 1999;Mininni et al 2002).…”

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

“…In a recent paper on the Earth's magnetic field and sunspots (de Paor, 2001) a key role in deriving equations governing the proposed underlying mechanism was played by the claim that the Hall effect provides "a perfect orthogonal axis energy transfer mechanism." The author has now realised that in his presentation (in Sect.…”

“…(1) and (3) of de Paor (2001), two voltages e z and e x were defined. It was not made clear that these are open-circuit Hall voltages: e z would be measured if i z were zero and e x if i x were zero.…”

On the Earth’s magnetic field and the Hall effect

“…A new theory of the Earth's magnetic field has been put forward recently that depends on the Hall effect (de Paor, 2001). In this theory the Hall effect is called upon as a mechanism for transferring a flow of electrical energy from one direction to another orthogonal to the first.…”