Atmosphere-Ionosphere-Coupling and Joule Heating
Authors: Buchert Stephan C. 
Published: March 2024

Loosely following works by Parker (1996) and Vasyli&#363;nas (2012) we present a self-consistent description of an atmospheric dynamo and its power dissipation or Joule heating. Compared to other works and simulations a feedback of the dynamo action on the neutral dynamics is included. It simply consists of adding the Lorentz force jxB to the dynamic equations for the neutral gas or air. In proofing the validity of this (within the assumptions of magnetized electrons and ion-neutral collisions) a generalized Ohm's law of the form E=... (as in plasma physics) is presented for a cold ionosphere with given conductivity tensor. As usual, inserting this generalized Ohm's law into Faraday's equation results in a dynamo equation completing the set of dynamic equations for B and the neutral velocity u complying with Parker's B,u paradigm.
The meanings or semantics of Joule, frictional and Ohmic heating in the ionosphere have been discussed in previous works. In the frame of our description the locally dissipated power can be written as the square of the current density times a Cowling factor, that is as heating by dissipative currents.
Wind fields exist which do not drive any dynamo currents, and a uniform motion of conducting air along a direction of constant B, e.g. magnetically zonal wind in a dipole field, per se, have no electrodynamic effects. Generally, the term uxB with units V/m does not follow Maxwell's equations, Faraday's and Coulomb's laws for electric fields, and this leads to dynamo currents. jxB is forcing winds towards conditions where uxB&#160; complies with Maxwell and the dynamo vanishes, which is perhaps an analogy to Lenz's law. However, jxB competes with other forces like gravity, pressure gradients, Coriolie, etc. In the Earth's ionosphere the atmosphere-ionosphere coupling is weak and a zero-dynamo state is practically unlikely to occur.
The very high conductivity along the direction parallel to the geomagnetic field compared to the perpendicular Pedersen and Hall conductivities short-circuits parallel electric fields. To avoid dynamo currents and their dissipation, uxB needs to be constant along B. The observed solar-quiet (Sq) magnetic variations can be understood as consequencee of that neutral winds where uxB&#160; at magnetically conjugate points don't match. We estimate that the tidal Sq dynamo globally dissipates roughly a power of 2 GW quasi-permanently, and jxB&#160;forcing seems to be partially successful in aligning neutral winds magnetically.
Also atmospheric gravity waves (AGWs) involve variable wind fields where uxB&#160; generally is not constant along B. Thus they should cause electric currents within the dynamo region, dissipation and a damping of AGWs which propagate upward from the lower and middle atmosphere. This electromagnetic damping may exceed the one by the in the thermosphere only small viscosity.
The work should be relevant for answering the question whether dissipation associated with an atmospheric dynamo contributes to heating the thermosphere of Earth and other planets, and how the dynamo affects neutral winds.