Fine scale thermal blooming instability: a linear stability analysis

The fine-scale thermal blooming instability of a high power trans-atmospheric laser beam is shown to be affected by the laser pulse length. In this study, we calculate the asymptotic gain of a sinusoidal perturbation as a function of pulse length and perturbation wavenumber. We include the effects of viscosity, diffusion, and wind shear, and we heuristically estimate the effect of turbulence. We find that for short laser pulses, the small wavenumber perturbations are reduced due to acoustic effects. However, large wavenumber perturbations remain large and extend to a higher cutoff in wavenumber than in the long laser pulse limit. At wavenumbers higher than this cutoff, thermal diffusion causes exponential decay of the perturbations. For long laser pulse length wind shear and turbulence limit perturbation growth.