Interaction of electrostatic waves in collisionless plasmast†

The interaction of three electrostatic waves in a collisionless plasma is treated to fourth order neglecting the wave—particle interaction (damping). Using the principles of energy conservation, and invariance under time reversal, conditions on the coupling constants are derived, enabling the solution to be expressed as a function of only two coupling constants. Phase plane diagrams of the solutions are sketched showing that the only singular points are stable equili bria. It is suggested how the theory may be applied to the explanation of the ‘floating spike’ resonance observable when one-half the hybrid frequency is the difference between the plasma and gyro frequencies (Hagg & Muldrew 1968).