Gain of a compressed DT fuel statistically ignited by a multispark assembly

Abstract

Most of the current inertial confinement fusion (ICF) schemes are based on the ignition of a high-density DT fuel by a single, high-temperature spherical hot spot (the spark). The spark is self-generated by the implosion process, which is used to bring the fuel to high density. To start ignition the spark has to be dimensioned in such a way that the ion temperature would be greater than 5–7 keV, and that the spark radius would be greater than the α-particle range. A spark with these features is indicated as supercritical. In the scheme based on self-generated spark, ignition can fail to occur when the produced spark strongly deviates from spherical shape, which can make all the surface losses highly relevant. High deformation, or even spark splitting, can occur due to the amplification of initial deviations from spherical shape by hydrodynamic instabilities (or by secular growth) during the implosion process. In principle, ignition can be recovered if the implosion is designed in such a way as to make supercritical at least one of the portions of hot fuel which are produced in this way near stagnation. As a general trend, more compressed final assemblies are required. In this paper we present fuel gain calculations (Gain = Thermonuclear energy/Energy in the compressed fuel) for DT assemblies ignited at the end of an implosion process by a supercritical spark statistically created within a cluster of many subcritical sparks. It is assigned the total number of sparks and the probability of having at least one of them supercritical. As a function of these quantities we calculate, in the framework of an isobaric model, the average thermal energy associated with the spark assembly. The same model is also used to evaluate, by statistical arguments, the areal mass, the burn fraction, and the system’s total fuel gain. It is found that the energy distribution function of the sparks is influenced only by a single global parameter, in which the assigned ignition probability and the number of sparks are also represented. Compared to the single central-spark approach, being the final states with allowed inner turbulence, the multispark scheme is characterized by relaxed initial symmetry requirements. For multispark systems we can realistically consider the achievement of fuel gains comparable or greater than those typical of the single-spark approach, when evaluated for currently accepted spark convergence ratios. With regard to the single spark case, higher cold fuel densities are needed, as expected (typically 2×–3×, for the same gain, depending on the energy distribution function).