Scaling Law for Marginal Ignition

LLE Review, Volume 87 153 Introduction In recent years, a considerable effort1–6 has been made to determine the minimum energy required for ignition in inertial confinement fusion (ICF) implosions. Though different conclusions have been reached by different authors, consensus is that the minimum energy required for ignition is a strong function of the shell implosion velocity as well as the shell adiabat. Various approaches to the study of ignition have led to scaling laws in which the shell kinetic energy required for ignition is given as a function of the implosion velocity, shell adiabat (in-flight and at stagnation), and other parameters such as the applied pressure at the end of the acceleration phase. Scientists from Lawrence Livermore National Laboratory (LLNL) have produced a scaling law1,5 for marginal ignition by fitting a large database of LASNEX simulations of implosions with gain approximately equal to unity. The first scaling law by Levedahl and Lindl (LL)1 was obtained by fitting the shell kinetic energy with the in-flight shell adiabat and the shell implosion velocity. The LL scaling law yields