Ionization instabilities of an electromagnetic wave propagating in a tenuous gas

A theory is developed to study the scattering instability that occurs when a laser pulse propagates through and ionizes a gas. The instability is due to the intensity dependence of the ionization rate, which leads to a transversely structured free electron density. The instability is convective in the frame of the laser pulse, but can have a relatively short growth length scaling as Lg∼k0/kp2, where k0 is the laser wave number, kp2=ωp2/c2 and ωp is the plasma frequency. The most unstable perturbations correspond to a scattering angle for which the transverse wave number is around the plasma wave number, kp. The scattered light is frequency upshifted. The comparison between simple analytic theory and numerical simulation shows good agreement.