| In the ionospheric modification experiments, parametric instability is directly and indirectly utilized to explain the experimental observations, such as the HF-enhanced plasma lines (HFPLs) and HF-enhanced ion lines (HFILs), the enhanced airglow, the excitation of the plasma wave, the formation of the small scale field-aligned irregularities (FAIs), the anomalous absorption of the radio wave, stimulated electromagnetic emissions (SEEs), etc. The ionosphere is a nonlinear medium with high frequency and low frequency plasma oscillation modes which are parametric coupling together. When a high power high-frequency radio wave injects into the ionospheric plasma, the radio wave as a pump wave simultaneously excites a high frequency and a low frequency plasma waves via the parametric coupling effect.In the past five decades, parametric instability is one of the most interesting topics in the researches on the ionospheric heating experiments. Lots of new phenomena are observed during the ionospheric heating experiments since several powerful ground-based heating facilities have been operating. Parametric instability is also employed to explain these new observations. The present theory of parametric instability neglects the direct interaction of the pump and the electrons and also cannot explain the excitation of parametric instability during X-mode heating experiments at Tromsa, Norway, run by European Incoherent Scatter Scientific Association (EISCAT). Thus, this paper focuses on the theoretical and experimental research on the parametric instability. The conclusions in this paper can be mainly outlined as following:1. The dispersion relations of parametric instability and thermal parametric instability are derived from the plasma magneto-hydrodynamics equations. Both the pondermotive force and the pump wave are contributed to the excitation of the parametric instability; whereas the thermal parametric instability excitation attributes to the force directly from the pump wave, the non-oscillating beating current driven by the pump wave, the nonlinear Lorentz force, which is the pondermotive force in the unmagnetized plasma, and the differential Ohmic heating force caused by the electron energy dissipation in the high-frequency wave field. In the heating experiments, the differential Ohmic heating force overcomes the nonlinear Lorentz force in the excitation process of the thermal parametric instability.2. The threshold field and growth rate of the parametric instability are derived from the dispersion relation. The threshold filed increases with the effective electron collision frequency, the pump wave frequency and the ion acoustic speed. The threshold field also depends on the propagation direction of the excited Langmuir wave, i.e. the threshold reached the minimum value when a parallel or anti-parallel propagating Langmuir wave is excited. For the parametric decay instability (PDI), the threshold filed not only depends on the effective electron collision frequency, but increases with the product of the effective electron and ion collision frequencies. The threshold field of PDI decreases with the increase of the wave number of the excited Langmuir wave. The growth rate of the parametric instability is proportional to the effective radiated power (ERP). The growth rate of the oscillation two-stream instability (OTSI) goes up with the increase of the effective electron collision frequency, while the growth rate of PDI depends on the products of the effective electron and ion collision frequencies. The calculation results employed with the expression of the threshold and growth rate in this paper is good agreement with the experimental observations.3. The threshold and growth rate of the thermal parametric instability are obtained from the dispersion relation. For the thermal parametric instability, the frequency of the excited upper hybrid wave determines the threshold field. The threshold field also depends on the effective electron and ion collision frequencies, electron temperature and the wave number of the excited upper hybrid waves. The maximum transverse scale of the small scale FAIs caused by thermal parametric decay instability depends on the ERP of the pump wave and the minimum transverse scale is limited by the electron Landau damping on the lower hybrid wave. The growth rate of the thermal parametric decay instability increase with the ERP of the pump wave and the effective electron and ion collision frequencies. For the thermal oscillation two-stream instability, the threshold depends on the pump wav frequency, the ion acoustic speed, the effective electron collision frequency, the electron temperature, the wave number of the excited upper hybrid wave (or the transverse scale of the small scale FAIs). The threshold is proportional to the wave number of the excited upper hybrid wave, leading to a fact that the generations of smaller scale FAIs requires higher pump wave power. During the excitation of the thermal oscillation two-stream instability, the minimum transverse scale of FAIs depends on the pump wave power and the maximum scale is determined by the growth rate. The calculation results in this paper are agreement with the experimental observations at Troms(?), Norway.4. This paper theoretically studies the parametric instability by the X-mode heating wave. Firstly, the experimental observations under the X-mode heating wave are presented. The spectrum of the observed HFPLs and HFILs suggests the excitation of the parametric instability. Moreover, the height of the observed HFPLs and HFILs indicates that the X-mode heating wave is responsible to the HFPLs and HFILs. Secondly, the dispersion relation of the parametric instability by the X-mode heating wave is obtained. The dispersion relation demonstrates that the pondermotive force and the pump wave are attributing to the excitation of parametric instability. Thirdly, the threshold field and growth rate of the parametric instability by the X-mode heating wave is shown. A parallel electric field of the X-mode heating wave is required to excite the Langmuir wave propagating along the magnetic field. The threshold of PDI increases with the heating wave frequency, ion acoustic speed, the products of the effective electron and ion collision frequencies and the reciprocal of the wave number of the excited Langmuir wave. The growth rate increase with the heating wave ERP. The threshold of OTSI is in direct proportion to the heating wave frequency, the effective electron collision frequency and the ion acoustic speed. The growth rate depends on the effective electron collision frequency.5. This paper analyses the excitation condition of the parametric instability under X-mode heating wave. Firstly, according to the experimental observation, the frequency matching condition can satisfy near the X-mode reflection height. It is suggested that the full dispersion relation of Langmuir wave is employed to satisfy the frequency matching condition. Secondly, the inhomogeneous structures in the ionosphere significantly affect the electric field of the X-mode heating wave near its reflection height. A full-wave Finite Difference Time Domain (FDTD) simulation has been performed to demonstrate that a small parallel component of pump wave electric field can be achieved during X-mode heating in the presence of inhomogeneous plasma. The presence of medium-scale (-1 km) field-aligned density irregularities around the X-mode reflection altitude significantly enhances the parallel component of the pump electric field within the irregularities. This provides a mechanism by which the high threshold for the OTSI could be exceeded by an X-mode wave. |
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