Dynamo theory

The Dynamo theory proposes a mechanism by which a celestial body such as the Earth generates a magnetic field.

History of theory

In 1905, shortly after composing his Special relativity paper, Albert Einstein described the origin of the Earth's magnetic field as being one of the great unsolved problems facing modern physicists. In 1919, Joseph Lamor suggested that the magnetic field of the Sun arises from dynamo action^[1]. Following on that idea, in 1939 Walter M. Elsasser proposed that the Earth’s magnetic field arises as a consequence of a self-exciting dynamo-like action in the Earth’s fluid core^[2]. Since then, there have been many studies of the geodynamo problem based on historical measurements of the earth’s field and these works often descend into the domain of the theoretical mathematician, all of which have assumed that the iron-alloy Earth’s is the electrically conducting operant fluid. In 2007, J. Marvin Herndon suggested instead that the electrically conducting operant fluid, and thus region of dynamo action, may be contained within the geocentric nuclear fission reactor, called the georeactor, in its fluid sub-shell, rather than the in Earth’s iron-alloy core^[3]^[4].

Formal definition

Dynamo theory, as used to explain planetary and stellar magnetic fields, is an application of magnetohydrodynamic. Generally, a magnetic field arises from the movement of electrical charges. Dynamo theory describes the process through which motion of a conductive body in the presence of a magnetic field acts to regenerate that magnetic field.

Geomagnetic dynamo theory

The application of the theories of Carl Friedrich Gauss to magnetic observations proved that Earth's magnetic field has an internal, rather than external, origin. In 1939 Walter M. Elsasser proposed that the Earth’s magnetic field arises as a consequence of a self-exciting dynamo-like action in the Earth’s fluid core as a consequence of convection^[5]. At the time there was no reason to suspect that there might be another fluid conducting body within the deep interior of Earth. Generally, in the case of the Earth, the magnetic field is believed to be caused by the convection within the electrically conducting operant fluid interacting with a Coriolis effect caused by the overall planetary rotation that tends to organize currents in rolls aligned along the north-south polar axis. When an electrically conducting operant fluid flows across an existing magnetic field, electric currents are induced, which in turn creates another magnetic field. When this magnetic field reinforces the original magnetic field, a dynamo is created which sustains itself. Despite numerous polarity reversals, the geomagnetic field has existed continuously for more than 3 billion years which necessitates circumstances favoring very stable convection in the operant electrically conducting fluid. Thermally induced convection arises as a consequence of heating a fluid from beneath and maintaining an adverse temperature gradient^[6]. J. Marvin Herndon has pointed out the following reasons why long-term stable convection would not be favorable within the Earth’s fluid core^[7]^[8]: Maintaining stable convection would require maintaining an adverse temperature gradient, which would require efficient removal of heat brought to the top of the core by convection , but the Earth’s core is insulated by a 2900 km thick blanket of silicate rock, the mantle, which has a much lower thermal conductivity, lower heat capacity, and higher viscosity than the core; all impediments to efficient removal of heat brought to the top of the core by convection. Herndon pointed out that these impediments would not be the case for convection within the georeactor sub-shell, which surrounds the actinide, heat producing sub-core, and which itself is surrounded by the inner core, acting as a heat sink, surrounded by another heat sink, the core, both of which are reasonably good conductors of heat. Moreover, radioactive decay of neutron-rich fission products in the georeactor sub-shell assures a continuous supply of charged particles for establishing a seed-field for dynamo initiation.

Planetary magnetic fields

In 2007, based upon the commonality of matter in the Solar System and common operating environments, J. Marvin Herndon suggested that planetary and satellite magnetic fields arise from the same georeactor-type assemblage which he suggested powers and provides the operant fluid for generating by dynamo action the Earth’s magnetic field.^[9]^[10]

Kinematic dynamo theory

Dynamo theory is a very complex concept to study. Often, college courses and research focuses mainly on kinematic dynamo theory, which is a more simplistic version of the former. It involves the vector velocity field, V, which is prescribed, instead of also varying according to the forces exerted upon the fluid. To examine this sector of the theory, an assumption that must be made is that the magnetic field has to be sufficiently small so that it cannot affect the velocity field. Because of this, the approach cannot divulge anything about the long-term behavior of a dynamo system. This analysis begins with the magnetohydrodynamic theory version of Ohm's law once it has been modified to include resistivity (resistivity is the reciprocal of conductivity σ, J is the current density), which is often assumed to be a constant in order to further simplify the investigation. Using Maxwell's equations simultaneously with the curl of the aforementioned equation, one can derive what is basically the linear eigenvalue equation for magnetic fields (B) which can be done when assuming that the magnetic field is independent from the velocity field. One arrives at a critical magnetic Reynolds number above which the flow strength is sufficient to amplify the imposed magnetic field, and below which it decays. The most functional feature of kinematic dynamo theory is that it can be used to determine what fields or systems are or are not dynamos. By applying a certain velocity field to a small magnetic field, it can be determined through observation whether the magnetic field tends to grow or not in reaction to the applied flow. If the magnetic field does grow, then the system is either capable of dynamo action or is a dynamo, but if the magnetic field does not grow, then it is simply referred to as non-dynamo. The membrane paradigm is a way of looking at black holes that allows for the material near their surfaces to be expressed in the language of dynamo theory.

Nonlinear dynamo theory

The kinematic approximation becomes invalid when the magnetic field becomes strong enough to affect the fluid motions. In that case the velocity field becomes affected by the Lorentz force, and so the induction equation is no longer linear in the magnetic field. In most cases this leads to a quenching of the amplitude of the dynamo. Such dynamos are sometimes also referred to as hydromagnetic dynamos. Virtually all dynamos in astrophysics and geophysics are hydromagnetic dynamos.