Frictional/Joule heating

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Introduction

Electric field is a potential heat source for ionospheric particles (Rees, 1989). It is due to the fact that, under the action of an electric field, charged particles drift relative to one another and relative to neutral particles. Collisions between species limit the drift velocities and convert some of the drift energy into thermal energy. This is called frictional heating. The resulting steep gradient between the region of heating (about 200-400 km) and the topside ionosphere leads to upward diffusion with velocities of hundreds of m/s. This mechanism is behind the formation of some ionospheric troughs.

The convection electric field is the main ionospheric source of strong enough electric fields. There are some indications that the whole convection pattern in the midnight sector can vary from minute to minute (Williams et. al., 1990), producing the spiky structure of high time resolution ion temperature. Frictional heating is also very typical near auroral arcs that are related to electric field structures of their own.

Neutrals and electrons

Although the heating rates for neutrals and ions are very comparable, any increase in Tn should be far smaller than the corresponding increase in Ti due to the greater heat capacity of the neutral gas. However, the effect of frictional/Joule heating of neutrals in the auroral electrojet region can lead to upward neutral wind in a region of high electron densities and strong electric fields (Winser et. al., 1986). Also, for a given magnitude of electric field, electron heating is substantially smaller than ion heating in the F - and E - regions of the ionosphere, and becomes comparable only in the D - region. It has been estimated (see, e.g., Schlegel and St.-Maurice, 1981) that the frictional electron heating rate due to 70 mV/m electric field at 110 km would amount to temperature enhancement of only a few degrees or tens of degrees.

Ions

We will concentrate here on ion heating. If we assume the the force per unit mass on the ions due to collisions with neutrals is proportional to the velocity difference between the two species, the rate of frictional heating is

Q = (eE)^2 n/Mv

where n is the ion density, M is the reduced mass, and v is the collision frequency. Taking into account Earth's magnetic field this can be written as

Q = (eE)^2 Sum( (n/M) v/(w^2 + v^2) )

where the summation over i and n apply if several ion and neutral species are present. The new term, w, ion gyrofrequency, comes from the fact that ions gyrate about the magnetic lines of force when not traveling parallel to B. The other way to describe the frictional heating is Joule heating due to the Pedersen current (e.g., Rees et. al., 1983). The last equation can be written as Q = pE^2, where p is the Pedersen conductivity.

Frictional heating rate can be so large at high latitudes, that the ion temperature exceed the electron temperature (usually we had Te > Ti >Tn). In the work by McCrae et. al. (1991) all enhancements in ion temperatures measured parallel to B larger than 100 K were identified as frictional heating events. They concluded that a velocity difference of order 1 km/s provides sufficient heat input to double the ion temperature (at about 300 km, when unperturbed Ti was about 900 K). This heating is important both in F - and upper E - region (e.g., Schlegel and St.-Maurice, 1981), i.e., above about 130 km. This is due to the increasing magnetization of the ions with altitude and the consequently higher relative velocities between ions and neutrals (Robinson and Honary, 1990).

It is also possible that the collisions between the drifting ions and neutrals set the neutral gas in motion, leading to an equalization of the ion and neutral velocities in a steady state (Kelley, 1989, p. 331). In this case there would be almost no frictional heating although the ion gas can be moving quite rapidly. It has been shown (Baron and Wand, 1983) that the neutral wind speed approaches that of the ions with a time constant t which is inversely proportional to the ion density n,

t = n(neutral)/(nv).

This is the reason for, e.g., the ion temperature structure in the high latitude nightside trough. We can conclude that the best way to measure the effects of frictional heating is to measure directly both the ion drift (using incoherent scatter radars) and neutral wind velocity (using Fabry-Perot interferometers), as is done, e.g., by Hagan and Sipler (1991).

Different kind of frictional heating (and anisotropic ion temperatures) can be produced due to ion-ion collisions as the minor ion species with mass less than the mean ion mass are accelerated through the ion gas (Kelley, 1989, p.316). For example, at high latitudes, both H+ and He++ can be accelerated along field lines through O+ gas and be subjected to this heating process.

Frictional ion heating can also lead ionospheric thermal ion outflow events.

References

Baron, M. J., and R. H. Wand, F region ion temperature enhancements resulting from Joule heating, J. Geophys. Res., 88, 4114-4118, 1983.
Hagan, M. E., and D. P. Sipler, Combined incoherent scatter radar and Fabry-Perot interferometer measurements of frictional heating effects over Millstone Hill during March 7-10, 1989, J. Geophys. Res., 96, 289-296, 1991.
Kelley, M. C., The Earth's ionosphere: Plasma physics and electrodynamics, Academic Press, 1989.
Rees, M. H., Physics and chemistry of the upper atmosphere, Cambridge University Press, 1989.
Rees, M. H., B. A. Emery, R. G. Roble, K. Stamnes, Neutral and ion gas heating by auroral electron precipitation, J. Geophys. Res., 88, 6289-6300, 1983.
Robinson, T. R., and F. Honary, A resonance broadening kinetic theory of the modified two-stream instability: Implications for radar auroral backscatter experiments, J. Geophys. Res., 95, 1073-1085, 1990.
Schlegel, K., and J. P. St.-Maurice, Anomalous heating of the polar E region by unstable plasma waves 1. Observations, J. Geophys. Res., 86, 1447-1452, 1981.
Williams, P. J. S., G. O. L. Jones, B. Jones, H. Opgenoorth, and I. Häggström, High-resolution measurements of magnetospheric electric fields, J. atmos. terr. Phys., 52, 439-448, 1990.
Winser, K. J., G. O. L. Jones, and P. J. S. Williams, A quantitative study of the high latitude ionospheric trough using EISCAT's common programmes, J. atmos. terr. Phys., 48, 893-904, 1986.