Dynamo theory

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History and Definition of Dynamo Theory
– William Gilbert proposed the idea of permanent magnetism as the origin of Earth’s magnetic field in 1600.
André-Marie Ampère suggested internal currents as the cause of Earth’s magnetism in 1822.
– Joseph Larmor proposed the dynamo theory in 1919.
– Patrick Blackett’s experiments found no fundamental relation between angular momentum and magnetic moment.
– Walter M. Elsasser proposed the dynamo theory, explaining Earth’s magnetic field as induced electric currents in the outer core.
Dynamo theory explains the maintenance of a magnetic field in rotating, convecting, and electrically conducting fluids.
– Liquid iron in the outer core acts as the conductive fluid in the geodynamo.
– Ionized gas at the tachocline serves as the conductive fluid in the solar dynamo.
– Three requisites for a dynamo to operate: electrically conductive fluid, planetary rotation providing kinetic energy, and an internal energy source for convective motions.

Tidal Heating and Dynamo
– Tidal forces cause friction and heat up the interiors of celestial bodies.
– Tidal heating helps maintain a liquid state in the interior, necessary for a dynamo.
– Saturn’s Enceladus and Jupiter’s Io have enough tidal heating, but may not conduct electricity to create a dynamo.
– Mercury has a magnetic field due to its conductive liquid core from its iron composition and friction caused by its elliptical orbit.
– The Moon may have had a magnetic field due to tidal heating when it was closer to Earth.

Kinematic Dynamo Theory
– In kinematic dynamo theory, the velocity field is prescribed, without considering the flow response to the magnetic field.
– It can study the variation of magnetic field strength with flow structure and speed.
– Using Maxwell’s equations and Ohm’s law, a linear eigenvalue equation for magnetic fields can be derived.
– The critical magnetic Reynolds number determines if the flow can amplify the imposed magnetic field.
– Kinematic dynamo theory helps test if a velocity field is capable of dynamo action.
– Kinematic dynamo theory can be used to test if a velocity field is capable of dynamo action.
– By applying a velocity field to a small magnetic field, one can observe if the magnetic field grows in response.
– If the magnetic field grows, the system is capable of dynamo action or is a dynamo.
– The membrane paradigm is an analogous method to study black holes using dynamo theory.
– It allows the expression of material near the black hole’s surface in the language of dynamo theory.

Numerical Models and Equations in Dynamo Theory
– Geodynamo models attempt to produce magnetic fields consistent with observed data.
– Magnetohydrodynamic equations are implemented for self-consistency.
Dynamo models are not restricted to geodynamo and can be applied to solar and general dynamos.
– Studying dynamo models has utility in geophysics.
– Glatzmaier model is a visual representation of a dynamo model before dipole reversal.
– Induction equation is used to describe the evolution of magnetic field.
– Transport equation is used to model heat or light element concentration.
– Equations are non-dimensionalized using parameters such as Rayleigh number and Ekman number.
– Magnetic field scaling is often done in Elsasser number units.
– Numerical models are used to simulate fully nonlinear dynamos.

Mechanisms of Magnetic Field Formation and Modern Challenges
– Various mechanisms form magnetic fields in astrophysical bodies like Earth.
– The equations used in numerical models of dynamo are highly complex.
– The progression from linear to nonlinear, three-dimensional models of dynamo was hindered by the search for solutions to magnetohydrodynamic equations.
– Self-consistent dynamo models, determining both fluid motions and magnetic fields, were developed in 1995.
Dynamo models can estimate how magnetic fields vary with time.
– Models can be compared to observed paleomagnetic data to find similarities with the Earth.
– Simplified geodynamo models have shown relationships between the dynamo number and magnetic pole reversals.
– Many models show that magnetic fields have somewhat random magnitudes that average to zero.
Dynamo modelling is limited by the current power of supercomputers.
– Calculating the Ekman and Rayleigh number of the outer core is extremely difficult and requires a vast number of computations.
– Spectral methods have been proposed to simplify computations for complex magnetic field changes.
– Improvements in computing power are necessary for more realistic dynamo models.
– Making methods for computing the model more efficient is important for the advancement of numerical dynamo modelling. Source:  https://en.wikipedia.org/wiki/Dynamo_theory

Dynamo theory (Wikipedia)

In physics, the dynamo theory proposes a mechanism by which a celestial body such as Earth or a star generates a magnetic field. The dynamo theory describes the process through which a rotating, convecting, and electrically conducting fluid can maintain a magnetic field over astronomical time scales. A dynamo is thought to be the source of the Earth's magnetic field and the magnetic fields of Mercury and the Jovian planets.

Illustration of the dynamo mechanism that generates the Earth's magnetic field: convection currents of fluid metal in the Earth's outer core, driven by heat flow from the inner core, organized into rolls by the Coriolis force, generate circulating electric currents, which supports the magnetic field.
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