A wave spectrum peaked in angle and broadened in wave number is found from a non-linear saturation theory for the decay-type parametric instability in the case of nearly equal electron and ion temperatures. The dominant saturation mechanism is nonlinear damping of Langmuir waves by induced scattering from ions. The nonlinear resistivity for transverse waves, including the pump, is obtained from the related mechanism of conversion of transverse into longitudinal waves due to interaction with ions.
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DuBois et al. (1972) studied this question.
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