On the Self Similar Energy Gain Scaling in Isobaric Approach of ICF Targets

In this paper we start with Meyer-Ter-Vehn isobaric fusion model and try to reconstruct all equations by introducing a dimensionless variable ?i=ri/Rm. Then we investigate the proper sets of spark confinement parameter and temperature {Hs,Ts} which satisfy ignition conditions of spark ignition in deuterium-tritium (DT) equimolar mixture in terms of isentrope parameter, ?, implosion velocity, Uim. Finally, limiting fuel energy gain curve (Gf*) as function of ignition energy (Eign) for different implosion velocities is calculated. By this simple modification of our original formulation, we obtain fuel energy scaling as Ef??3 Uim?10 for desirable range of ignition parameters. Since in our formulation HsTs product has appeared, it enabled us to insert a scaling relation for ignition condition in fuel energy, Ef which this in turn decreases implosion velocity exponent in our scaling relation to 7.0.