Ignition energy scaling of inertial confinement fusion targets

Scaling of the ignition energy threshold Ei, with the implosion velocity vi , and isentrope parameter ct: of imploding spherical DT shells is investiga ted by performing one dimensional (1-D) hydrodynamic simulations of the imp losion and hot spot formation dynamics. It is found that the a and b expone nts in the power law approximation E-ig proportional to alpha(a)upsilon(im) (-b) depend crucially on the subset of initial configurations chosen to est ablish the scaling law. When the initial states are generated in the same w ay as in the Livermore study (W.K. Levedahl, J.D. Lindl, Nucl. Fusion 37 (1 997) 165), the same scaling, E-ig proportional to alpha(1.7)upsilon(im)(-5. 5), is recovered. If, however, the initial states are generated by rescalin g the parent configuration according to the hydrodynamic similarity laws, a different scaling is obtained, E-ig proportional to alpha(3.0)upsilon(im)( -9.1), which is very close to the alpha(3)upsilon(im)(-10) dependence predi cted by the simple isobaric model for assembled fuel states. The latter is more favourable than the Livermore scaling when rescaling the fusion capsul es to higher implosion velocities, but requires the peak drive pressure to be increased as P proportional to upsilon(im)(5).