Analytic insights into nonlocal energy transport. I. Krook models

In direct drive laser fusion, nonlocal transport of the more energetic electrons can have at least two potentially important effects. First, the most energetic electrons, furthest out on the tail of the distribution function, can cause preheat of the fuel deep inside the target. Second, nearby the nonlocal deposition of less energetic electrons can spread out the ablation layer, possibly having a stabilizing effect on the Rayleigh Taylor instability. This sequence of two papers treats two different methods of modeling nonlocal transport. For about 20 years, these phenomena have been treated with a Krook model for the electron collisions. However, different versions have given different results, especially as regards preheat. Our first paper attempts to analyze the various reasons for discrepancies and correct errors and derives a variety of simple formulas to evaluate preheat. The second paper offers, for the first time, a steady state, nonlocal method of using the Fokker Planck equation to evaluate the nonlocal transport and deposition of energetic electrons deposited by some mechanism, at some particular point in the plasma. Regarding ablation surface broadening, the two models are not very different; but regarding preheat, the Fokker Planck model gives orders of magnitude less. This is a very optimistic result for a direct drive laser fusion.