Ignition energy scaling of inertial confinement fusion targets

Scaling of the ignition energy threshold Eig with the implosion velocity vim and isentrope parameter α of imploding spherical DT shells is investigated by performing one dimensional (1-D) hydrodynamic simulations of the implosion and hot spot formation dynamics. It is found that the a and b exponents in the power law approximation Eig ∝ αavim-b depend crucially on the subset of initial configurations chosen to establish the scaling law. When the initial states are generated in the same way as in the Livermore study (W.K. Levedahl, J.D. Lindl, Nucl. Fusion 37 (1997) 165), the same scaling, Eig ∝ α1.7 vim-5.5, is recovered. If, however, the initial states are generated by rescaling the parent configuration according to the hydrodynamic similarity laws, a different scaling is obtained, Eig ∝ α3.0 vim-9.1, which is very close to the α3vim-10 dependence predicted by the simple isobaric model for assembled fuel states. The latter is more favourable than the Livermore scaling when rescaling the fusion capsules to higher implosion velocities, but requires the peak drive pressure to be increased as P ∝ vim5.