Parametric instabilities in a turbulent inhomogeneous plasma

An absolute parametric instability which occurs in an inhomogeneous plasma with long-wave turbulence is analyzed in detail. The average characteristics of the instability (the growth rates and the average number of unstable modes) and also the distribution functions of these characteristics are derived for a static turbulence. The results are compared with the results of numerical calculations by Nicholson and Kaufman. When the turbulence is time-dependent the problem is solved for two limiting cases, ''fast'' and ''slow'' turbulence. A study is made of the amplification under stable conditions and also in the presence of exponential growth, which occurs when a certain threshold is exceeded. The marked broadening of the spectrum of the amplified wave as this threshold is approached is studied