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Resonant decay of a Langmuir wave in the presence of dust grains in a cylindrical plasma

The resonant parametric decay of a Langmuir wave into a backward propagating Langmuir wave and an ion acoustic (IA) wave is studied in a cylindrical dusty plasma. The analysis shows that the frequency of the IA mode decreases with the parameter δc (where δc is the ratio of the ion density to the electron density) for negatively charged dust grains. The growth rate of the resonance decay instability (RDI) and the threshold required for its onset also decrease with δc and are strongly dependent on the electron to ion temperature ratio for both positively and negatively charged dust grains. The results obtained also illustrate the dependence of the threshold of the resonance decay instability (μth) on the plasma cylinder radius.