concept of an electron temperature runaway. However, because their calculations neglected several important ionospheric cooling mechanisms, their results are not quantitatively accurate and do not predict an electron temperature saturation limit. A computation of electron heating within the SPS microwave beam was described recently by Perkins and Robie (8), including a comprehensive model for the dominant collisional cooling processes. Their results represent the first thorough analysis of the effects of a thermal runaway in the ionosphere, including a steady-state solution for the electron temperature. Additional studies have verified this analysis and extended the results to lower altitudes (9). The electron energy equation in the ionosphere can be expressed as where ne is the electron number density, k is Boltzmann’s constant, dTe/dt is the rate of change of the electron temperature, is the heat source function, and Q describes the volume heat losses. Clearly, whenever the energy input exceeds the cooling losses, the electron temperature must increase. Sufficiently strong ohmic heating can produce a continuously increasing electron temperature, saturating only at some level where the increased ohmic heating is balanced by additional cooling processes. The rate of energy input to the atmospheric free electrons resulting from the absorption of microwave or radio frequency radiation can be attributed entirely to ohmic heating, given by where E is the wave electric field amplitude, fv is the local plasma frequency, f is the electromagnetic wave frequency, and vei, ven are the electron-ion and electronneutral collision frequencies. In the lower ionosphere, the electron-neutral collision frequency dominates and can be approximated by (10) where n(M) is the total molecular number density (cm-3) and Te is the electron temperature (K). As the electrons gain energy from the microwaves or from solar UV radiation, they also lose energy by collisions with atoms and molecules of the background gas. In the collision-dominated lower ionosphere, thermal conduction is not an important cooling mechanism. The most effective kinds of energy transfer collisions are inelastic interactions with O2 and N2, producing rotational and vibrational excitation, and collisions with atomic oxygen, producing excitation of hyperfine levels of the 3P ground state. In the upper atmosphere, thermal conduction is the principal cooling process, rapidly diffusing excess heat along the geomagnetic field lines. The electron temperature is a sensitive balance between heating processes and cooling interactions. As shown in Eqs. 9 and 10, as the electron temperature rises the electron-neutral collision frequency also increases, thereby increasing the ohmic heating. Electron cooling also becomes more efficient as the electron temperature increases above its ambient value. The time it takes a plasma to self-consistently reach an equilibrium between these competing processes is called the heating time scale. After the ionospheric wind has swept this plasma beyond the heating beam, the electron temperature relaxes to its ambient level on a cooling time scale that is
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