Nonlocal electron transport: direct and Greens function solution and comparison of our model with the SNB model

At least two models, ours [1] and SNB (Schurtz-Nicolai-Busquet) [2], and two methods of solution, direct numerical solution (DS) and Greens function (GF) are being used in multi-dimensional radiation hydrodynamics codes. We present results of a laser target implosion using both methods of solution. Although our model and SNB differ in some physical content, direct comparisons have been non-existent up to now. However a paper by Marocchino \textit{et al.} [3] has recently presented the results of two nanosecond-time-scale test problems, showing that the preheat calculated by the two models are different by about three orders of magnitude. We have rerun these problems and we find much less difference between the two than they do. One can show analytically that the results should be quite similar and are about an order of magnitude less than the maximum, and two orders of magnitude more than the minimum preheating in [3]. We have been able to trace the somewhat different results back to the different physical assumptions made in each model.\\[4pt] [1] W. Manheimer, D. Colombant, and A.J. Schmitt, Phys Plasmas \textbf{19}, 056317 (2012).\\[0pt] [2] G. Schurtz, P. Nicolai, and M. Busquet, ibid, \textbf{7}, 4238 (2000).\\[0pt] [3] A. Marocchino \textit{et al.}, ibid. \textbf{20}, 022702 (2013).