Abstract
We investigate parametric instabilities in a bounded inhomogeneous plasma when the pump wave frequency is close to that of the Gould-Trivelpiece mode. Using a suitable technique, we have obtained a dispersion relation in a radially inhomogeneous plasma column. The growth rates and threshold conditions for purely growing and four-phonon parametric instabilities are calculated. A comparison of these values with those for a homogeneous plasma shows that the plasma inhomogeneity enhances thresholds.
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