Ignition energy scaling of inertial confinement fusion targets

Scaling of the ignition energy threshold E sub(ig) with the implosion velocity v sub(im) and isentrope parameter alpha 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 powerSlaw approximation E sub(ig) proportional to alpha super(a)v super(-) sub(i) super(b) sub(m) 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, the same scaling, E sub(ig) proportional to alpha super(1.7)v super(-) sub(i) super(5) sub(m) super(.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, E sub(ig) proportional to alpha super(3.0)v super(-) sub(i) super(9) sub(m) super(.1) which is very close to the alpha super(3)v super(-) sub(i) super(1) sub(m) super(0) 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 proportional to V super(5) sub(i) sub(m).