Improvement of non-isobaric model for shock ignition

Abstract

In this paper, improved relations of total fuel energy, fuel gain, hot-spot radius and total areal density in a non-isobaric model of fuel assembly have been derived and compared with the numerical results of [J. Schmitt, J.W. Bates, S.P. Obenschain, S.T. Zalesak, D.E. Fyfe, Phys. Plasmas 17, 042701 (2010); S. Atzeni, A. Marocchino, A. Schiavi, G. Schurtz, New J. Phys. 15, 045004 (2013)] and several simulations performed by MULTI-1D radiation hydrodynamic code for shock ignition scenario. Our calculations indicate that the approximations made by [M.D. Rosen, J.D. Lindl, A.R. Thiessen, LLNL Laser Program Annual Report, UCRL-50021-83, pp. 3–5 (1983); J. Schmitt, J.W. Bates, S.P. Obenschain, S.T. Zalesak, D.E. Fyfe, Phys. Plasmas 17, 042701 (2010)] for the calculation of burn-up fraction are not accurate enough to give results consistent with simulations. Therefore, we have introduced more appropriate approximations for the burn-up fraction and total areal density of the fuel that are in more agreement with simulation results of shock ignition. Meanwhile, it is shown that the related formulas of the non-isobaric model for total fuel energy, fuel gain and also hot-spot radius cannot determine the model parameters independently, but improved model choose a better selection and less restrictions on determination of the parameters for the non-isobaric model. Such derivations can be used in theoretical studies of the ignition conditions and burn-up fraction of the fuel in shock ignition scenario.