A conservative scaling analysis of Z-pinch dynamic Hohlraums for inertial confinement fusion

Abstract

In this paper, physical issues of Z-pinch dynamic Hohlraums aimed at ignition are numerically investigated. Three-wave propagation, including the thermal wave, the ablation shock driven by radiation emitted by the nested tungsten wire-array plasma, and the main shock, is found to determine the Hohlraum formation at high currents. Based on requirements of high temperature radiation, three-wave isolation, and a suitable Hohlraum-capsule size ratio, a converter with an initial radius of 5 mm is suggested. As the rise time of the drive current is varied, two kinds of Hohlraum designs are examined. One is to fix the wire-array mass and vary the wire-array radius; the other is to fix the wire-array radius and vary the wire-array mass. In situations of long rise times, the first kind of Hohlraum design should be adopted. Preliminary simulations show that a radiation source with a peak temperature over 308 eV and large enough energy with longer pulse duration is critical for a volume capsule design. Based on the considerations of (1) not underestimating the magneto-Rayleigh–Taylor effect, (2) avoiding the direct shock thermalization on the axis, (3) using of a suitable converter radius, and (4) iteration of dynamic Hohlraum and capsule calculations, a conservative Hohlraum design is proposed. In this Hohlraum design, a radiation pulse with a peak temperature of 312 eV and an efficient time duration of ∼9 ns, which is cut before the main shock arrives at the axis, is produced to drive a two-shell capsule to generate over 10 MJ fusion yield in the case of 50 MA and 100 ns.