Threshold of parametric instability in the ionospheric heating experiments

Many observations in the ionospheric heating experiment, by a powerful high frequency electromagnetic wave with ordinary polarization launched from a ground-based facility, is attributed to parametric instability (PI). In this paper, the general dispersion relation and the threshold of the PI excitation in the heating experiment are derived by considering the inhomogeneous spatial distribution of pump wave field. It is shown that the threshold of PI is influenced by the effective electron and ion collision frequencies and the pump wave frequency. Both collision and Landau damping should be considered in the PI calculation. The derived threshold expression has been used to calculate the required threshold for excitation of PI for several ionospheric conditions during heating experiments conducted employing EISCAT high frequency transmitter in Troms?, Norway, on 2nd October 1998, 8th November 2001, 19th October 2012 and 7th July 2014. The results indicate that the calculated threshold is in good agreement with the experimental observations.