Theory and simulation of electronic relativistic parametric instabilities for ultraintense laser pulses propagating in hot plasmas

The dispersion relation for electronic parametric instabilities of a circularly polarized laser wave is solved in the case where the distribution function is supposed to be cold in the transverse direction and to be a linear combination of a cold distribution function and of a Maxwellian in momentum in the longitudinal direction. Only densities below the critical density are considered. It is shown that the longitudinal temperature as expected reduces the growth rate, but that the existence of a hot tail is not sufficient to significantly reduce the instability. It is the bulk of the distribution function that must be heated to efficiently stabilize the system. Another important effect of the heating is to reduce the backscattered component of the instability. An example of a one-dimensional particle simulation performed in the exact conditions of validity of the theory is discussed.