Basics of Parametric Decay Instability in Magnetized Plasma

Parametric decay instabilities frequently occur in wave interactions. These instabilities typically have thresholds for wave amplitudes. They arise when nonlinearity, such as a spatial pressure inhomogenety, couples different waves. For these instabilities to arise, the waves must satisfy frequency and wavenumber matching conditions, which follow from the laws of energy and momentum conservation. However, parametric instabilities are not limited to wave interactions; the simples form of parametric instability is parametrically coupled oscillators. Magnetized plasma represents a unique wave medium in which numerous waves of various polarizations and spatial-temporal scales are easily excited and weakly damped. The greater the number of wave types, the easier it is to satisfy resonance conditions like the frequency and wavenumber matching conditions, and thus parametrically excite, or "drive" new waves from the initial wave. Therefore, in magnetoactive plasma, all known types of parametric instabilities can arise.