On the Advantages of Fast Ignition with Ultra-High Intensity Lasers

One of the critical design constraints for fast ignition targets is the need to have a small cross section for the hot spot at the target core while delivering enough power to the hot spot with hot electrons of the proper energy range, $\sim $ 1-3 MeV, to couple to the core. We use two-dimensional Particle-In-Cell simulations of isolated targets to investigate the feasibility of using 1$\mu $m ignition lasers with ultra-high intensities, up to 8x10$^{20}$W/cm$^{2}$, for fast ignition. The self-consistent absorption of energy from an ultra-high intensity laser by overdense plasma and the subsequent energy transport through the collisionless overdense plasma, $\nu _{ei} \quad < \quad \omega _{p}$, of a 50$\mu $m radius isolated target, is explored in detail. At these ultra-high intensities, we find that most of the energy transport is in a hot bulk and not in the super-hot tail of the electron distribution. Electrons in a relatively low energy range, below 3MeV, transport 90{\%} of the heat flux through 50$\mu $m of 100n$_{c}$ plasma to the target core.