The author reviews fusion science and its extension to astrophysics in the field of theory and computation by picking up five topics. The first is the ablative stabilization of a Rayleigh–Taylor instability at an ablation front and its dispersion relation, the so-called Takabe formula. This formula gives a principal guideline for stable target design and is also applied to studying the turbulent combustion wave in Type Ia supernova explosions. The second is the development of the integrated code ILESTA. The physics of an integrated code, ILESTA (one- and two-dimensional), and analyses and design of laser produced plasmas including the implosion dynamics and stability are reviewed. There are two areas on its applications to implosion analysis: one is an evaluation of mixing layers in one-dimensional implosions by coupling with one- and two-dimensional ILESTA and the other is an extension to include the k–ε type turbulent mixing model, where the details of the formulation are given. The third topic is laboratory astrophysics with intense lasers. This consists of two parts: one is a review of its historical background and the other is on how we relate laser plasmas to wide-ranging astrophysics and the purposes of promoting such research. The fourth topic is on anomalous transport of relativistic electrons in fast ignition laser fusion and its relation to self-organization of magnetic field generation in gamma-ray bursts at cosmological distances. Finally, recent activity related to the application of the author's experience to the development of an integrated code for studying extreme phenomena in astrophysics is briefly explained.
Inertial confinement fusion:The quest for ignition and energy gain using indirect drive