Pulse shaping for optimal ion heating in fast ignition

Compared to conventional inertial fusion, fast ignition schemes offer reduced demands on driver energy and capsule symmetry due to their two-stage design. This involves compression of fuel to high density at sub-ignition temperature, followed by rapid heating of a small hotspot region, serving as a 'spark' for the fusion burn. Ignition requires that the hotspot reach sufficient areal density and ion temperature, meaning that efficient coupling of ignitor energy into ions is critical. We investigate pulse shaping to optimize the rate of ion heating. Through tractable analytical models, we present simple bounds on pre-ignition ion heating, applicable to any ignitor that delivers energy primarily to electrons.