Statistical Theory of the Broadband Two Plasmon Decay Instability

A novel dispersion relation is derived for the two plasmon decay instability using broad-bandwidth laser pulses. The model is derived under the assumption that the light has stationary but otherwise arbitrary statistics. This is done in the framework of the Weyl symbol calculus which has allowed some recent advances in the theory of turbulence. The broadband dispersion relation is then used to study the effects of temporal incoherence on the two plasmon decay growth rate. For a laser pulse modelled by the Kubo-Anderson process with large enough bandwidth, we show that the growth rate follows the well-known scaling law for the TPD instability, but is a factor of seven lower than established theory. Explaining such differences is important as this brings the instability below the collisional damping threshold, thereby allowing higher laser intensities to be safely applied to inertial confinement fusion target designs.