We discuss the explosive instability caused by the nonlinear interaction of two positive energy waves and one negative energy wave and its stabilization by higher-order nonlinear effects.

The interaction of three monochromatic waves (two positive energy longitudinal waves and one negative energy wave) is investigated. When only the first-order nonlinear interactions are considered, an explosive instability occurs. However, this instability is stabilized by the higher order nonlinear interactions. The matrix elements of the three-wave and the four-wave interactions in a magnetized plasma are calculated.

A possible mechanism is discussed for the hard-x-ray emission observed in vacuum spark plasmas. The mechanism is based on the hypothesis that in the process of a sausage instability in a plasma pinch the plasma can have very high resistivity due to the constriction and strong turbulence, so that the conduction current is virtually cut off. In such a case strong electric fields should appear which could accelerate the electrons and ions to produce hard x rays as energetic as 20 times the discharge potential. The kinetic energies of ions and electrons are calculated.

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