The variation with <i>T_e</i> and <i>T_i</i> of the velocity of unstable ionospheric two‐stream waves

Abstract

It is generally accepted that unstable ionospheric plasma waves moving at the ion‐acoustic velocity (“two‐stream” waves) are responsible for the so‐called type 1 VHF radar echoes commonly observed at equatorial and auroral latitudes. These same waves apparently are also the source of type 4 echoes, which have sharply peaked spectra with unusually large Doppler shifts and are seen at auroral latitudes during sufficiently disturbed conditions. But how, exactly, is the observed Doppler shift, or equivalently the ion‐acoustic velocity C s , related to the electron and ion temperatures? The expression usually quoted, with occasional caveats, is the isothermal result C s ² = K ( T e + T i )/ m i . The validity of the isothermal assumption has not been of much concern until recently, when the first simultaneous independent measurements of the temperatures and C s were made in Scandinavia. We argue here that, in fact, the electrons should usually be treated as adiabatic, with three degrees of freedom, while the ions may or may not be adiabatic (with only one degree of freedom), depending upon the temperatures, the altitude, and the radar frequency. In other words, the ion effects generally should be calculated kinetically. The differences between the two models in the computed wave velocity are substantial (∼20–40%). A comparison between European Incoherent Scatter (EISCAT) temperatures and wave velocities measured with the Cornell University Portable Radar Interferometer (CUPRI) shows good agreement with the model given here.