Parametric instabilties of short and ultra-intense laser pulses in a plasma

Parametric instabilities in laser-plasma interactions are investigated in the ultrarelativistic regime, including the leading-order term of the Landau-Lifshitz radiation reaction equation. After a detailed exploration to the theory of parametric instabilities, the effects of the radiation reaction force on the growth rate are discussed by comparing to the results without radiation reaction force. The radiation reaction force leads to merging of the two Raman branches and also excites new modes, e.g. the so-called quasi-modes. Furthermore the radiation reaction force increases the endurance of the short wavelength perturbations. Increased endurence affects the quality of the laser pulse shape, which is important particularly for experiments, which require a precisely-shaped laser pulse