Жер және планеталардың магниттік өрісін тудыру механизмі

Mechanism by which a celestial body generates a magnetic field
a proposed theory for the source of a planet's magnetic field

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.

When William Gilbert published de Magnete in 1600, he concluded that the Earth is magnetic and proposed the first hypothesis for the origin of this magnetism: permanent magnetism such as that found in lodestone. In 1822, André Marie Ampère proposed that internal currents are responsible for Earth magnetism In 1919, Joseph Larmor proposed that a dynamo might be generating the field. However, even after he advanced his hypothesis, some prominent scientists advanced alternative explanations. The Nobel Prize winner Patrick Blackett did a series of experiments looking for a fundamental relation between angular momentum and magnetic moment, but found none. Walter M. Elsasser, considered a "father" of the presently accepted dynamo theory as an explanation of the Earth's magnetism, proposed that this magnetic field resulted from electric currents induced in the fluid outer core of the Earth. He revealed the history of the Earth's magnetic field through pioneering the study of the magnetic orientation of minerals in rocks. In order to maintain the magnetic field against ohmic decay (which would occur for the dipole field in 20,000 years), the outer core must be convecting. The convection is likely some combination of thermal and compositional convection. The mantle controls the rate at which heat is extracted from the core. Heat sources include gravitational energy released by the compression of the core, gravitational energy released by the rejection of light elements (probably sulfur, oxygen, or silicon) at the inner core boundary as it grows, latent heat of crystallization at the inner core boundary, and radioactivity of potassium, uranium and thorium. At the dawn of the 21st century, numerical modeling of the Earth's magnetic field has not been successfully demonstrated. Initial models are focused on field generation by convection in the planet's fluid outer core. It was possible to show the generation of a strong, Earth like field when the model assumed a uniform core surface temperature and exceptionally high viscosities for the core fluid. Computations which incorporated more realistic parameter values yielded magnetic fields that were less Earth like, but indicated that model refinements may ultimately lead to an accurate analytic model. Slight variations in the core surface temperature, in the range of a few millikelvins, result in significant increases in convective flow and produce more realistic magnetic fields.

Tidal forces between celestial orbiting bodies cause friction that heats up their interiors. This is known as tidal heating, and it helps keep the interior in a liquid state. A liquid interior that can conduct electricity is required to produce a dynamo. Saturn's Enceladus and Jupiter's Io have enough tidal heating to liquify their inner cores, but they may not create a dynamo because they cannot conduct electricity. Mercury, despite its small size, has a magnetic field, because it has a conductive liquid core created by its iron composition and friction resulting from its highly elliptical orbit. It is theorized that the Moon once had a magnetic field, based on evidence from magnetized lunar rocks, due to its short lived closer distance to Earth creating tidal heating. An orbit and rotation of a planet helps provide a liquid core, and supplements kinetic energy that supports a dynamo action.

In kinematic dynamo theory the velocity field is prescribed, instead of being a dynamic variable: The model makes no provision for the flow distorting in response to the magnetic field. This method cannot provide the time variable behaviour of a fully nonlinear chaotic dynamo, but can be used to study how magnetic field strength varies with the flow structure and speed. Using Maxwell's equations simultaneously with the curl of Ohm's law, one can derive what is basically a 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 the magnetic field dissipates.

The most functional feature of kinematic dynamo theory is that it can be used to test whether a velocity field is or is not capable of dynamo action. By experimentally applying a certain velocity field to a small magnetic field, one can observe whether the magnetic field tends to grow (or not) in response 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 “not a dynamo”. An analogous method called 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.

Kinematic dynamo can be also viewed as the phenomenon of the spontaneous breakdown of the topological supersymmetry of the associated stochastic differential equation related to the flow of the background matter. Within stochastic supersymmetric theory, this supersymmetry is an intrinsic property of all stochastic differential equations, its interpretation is that the model's phase space preserves continuity via continuous time flows. When the continuity of that flow spontaneously breaks down, the system is in the stochastic state of deterministic chaos. In other words, kinematic dynamo arises because of chaotic flow in the underlying background matter.

The scalar product of the above form of Navier Stokes equation with gives the rate of increase of kinetic energy density, , on the left hand side. The last term on the right hand side is then , the local contribution to the kinetic energy due to Lorentz force. The scalar product of the induction equation with gives the rate of increase of the magnetic energy density, , on the left hand side. The last term on the right hand side is then Since the equation is volume integrated, this term is equivalent up to a boundary term (and with the double use of the scalar triple product identity) to (where one of Maxwell's equations was used). This is the local contribution to the magnetic energy due to fluid motion. Thus the term is the rate of transformation of kinetic energy to magnetic energy. This has to be non negative at least in part of the volume, for the dynamo to produce magnetic field. Ω = 2/day = 7.3×10−5/second   and   σ   is approximately   107Ω−1m−1 This gives   2.7×10−4 Tesla. The magnetic field of a magnetic dipole has an inverse cubic dependence in distance, so its order of magnitude at the earth surface can be approximated by multiplying the above result with giving   2.5×10−5 Tesla, not far from the measured value of 3×10−5 Tesla at the equator.

Broadly, models of the geodynamo attempt to produce magnetic fields consistent with observed data given certain conditions and equations as mentioned in the sections above. Implementing the magnetohydrodynamic equations successfully was of particular significance because they pushed dynamo models to self consistency. Though geodynamo models are especially prevalent, dynamo models are not necessarily restricted to the geodynamo; solar and general dynamo models are also of interest. Studying dynamo models has utility in the field of geophysics as doing so can identify how various mechanisms form magnetic fields like those produced by astrophysical bodies like Earth and how they cause magnetic fields to exhibit certain features, such as pole reversals. The equations used in numerical models of dynamo are highly complex. For decades, theorists were confined to two dimensional kinematic dynamo models described above, in which the fluid motion is chosen in advance and the effect on the magnetic field calculated. The progression from linear to nonlinear, three dimensional models of dynamo was largely hindered by the search for solutions to magnetohydrodynamic equations, which eliminate the need for many of the assumptions made in kinematic models and allow self consistency. The first self consistent dynamo models, ones that determine both the fluid motions and the magnetic field, were developed by two groups in 1995, one in Japan and one in the United States. The latter was made as a model with regards to the geodynamo and received significant attention because it successfully reproduced some of the characteristics of the Earth's field. Ultimately, until considerable improvements in computer power are made, the methods for computing realistic dynamo models will have to be made more efficient, so making improvements in methods for computing the model is of high importance for the advancement of numerical dynamo modelling.