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
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.