Relativistic effects on the collisionless–collisional transition of the filamentation instability in fast ignition

Relativistic collisional effects on the filamentation instability are analytically and numerically investigated by comparing collisionless and collisional scenarios for a fast ignition (FI) configuration. The theoretical kinetic model, including warm species and space charge effects, predicts the preferential formation of larger filaments and the inhibition/enhancement of the instability when collisions are accounted for. These collisional effects are qualitatively and quantitatively confirmed by 1D and 2D particle-in-cell (PIC) simulations, also providing a physical picture for the inhibition/enhancement regime due to collisions, based on the electron beam slowdown. By plugging typical FI parameters in the dispersion relation, the theoretical model predicts significant growth rates of the instability deep inside the FI target, thus showing the potential role of the filamentation instability as a mechanism for energy deposition into the pellet core.