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Published online by Cambridge University Press: 09 March 2009
Starting from two-wave coupled plasma equations the parametric decay instabilities appearing in homogeneous plasmas are discussed as a first step. If damping is present, the instabilities may appear, and when the damping is so small that it can be neglected, there exists only spatial gain. The analytic solution for inhomogeneous plasma, as a second step, with density varying almost linearly is obtained and the conditions for the instabilities to occur are discussed.