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For the limit , the magnetic diffusion equation = is just a vector-valued form of the heat equation. For a localized initial magnetic field (e.g. Gaussian distribution) within a conducting material, the maxima and minima will asymptotically decay to a value consistent with Laplace's equation for the given boundary conditions.
In the height region between about 85 and 200 km altitude on Earth, the ionospheric plasma is electrically conducting. Atmospheric tidal winds due to differential solar heating or due to gravitational lunar forcing move the ionospheric plasma against the geomagnetic field lines thus generating electric fields and currents just like a dynamo coil moving against magnetic field lines.
A transport equation, usually of heat (sometimes of light element concentration): = + where T is temperature, = / is the thermal diffusivity with k thermal conductivity, heat capacity, and density, and is an optional heat source. Often the pressure is the dynamic pressure, with the hydrostatic pressure and centripetal potential removed.
It is often useful to give the gyrofrequency a sign with the definition = or express it in units of hertz with =. For electrons, this frequency can be reduced to , = (/).. In cgs-units the gyroradius = | | and the corresponding gyrofrequency = | | include a factor , that is the velocity of light, because the magnetic field is expressed in units [] = / /.
[1]: 117 The formula above is known as the Langevin paramagnetic equation. Pierre Curie found an approximation to this law that applies to the relatively high temperatures and low magnetic fields used in his experiments. As temperature increases and magnetic field decreases, the argument of the hyperbolic tangent decreases.
The impact of the solar wind onto the magnetosphere generates an electric field within the inner magnetosphere (r < 10 a; with a the Earth's radius) - the convection field. [1] Its general direction is from dawn to dusk. The co-rotating thermal plasma within the inner magnetosphere drifts orthogonal to that field and to the geomagnetic field B o.
The magnetic field in the Sun's corona is often approximated as a force-free field.. In plasma physics, a force-free magnetic field is a magnetic field in which the Lorentz force is equal to zero and the magnetic pressure greatly exceeds the plasma pressure such that non-magnetic forces can be neglected.
Magnetic reconnection is a breakdown of "ideal-magnetohydrodynamics" and so of "Alfvén's theorem" (also called the "frozen-in flux theorem") which applies to large-scale regions of a highly-conducting magnetoplasma, for which the Magnetic Reynolds Number is very large: this makes the convective term in the induction equation dominate in such regions.