Estimation of the FST-Layering Time for Shock Ignition ICF Targets

Abstract

The challenge in the field of inertial confinement fusion (ICF) research is related to the study of alternative schemes for fuel ignition on laser systems of medium and megajoule scales. At the moment, it is considered promising to use the method of shock ignition of fuel in a pre-compressed cryogenic target using a focused shock wave (shock- or self-ignition (SI) mode). To confirm the applicability of this scheme to ICF, it is necessary to develop technologies for mass-fabrication of the corresponding targets with a spherically symmetric cryogenic layer (hereinafter referred to as SI-targets). These targets have a low initial aspect ratio Acl (Acl = 3 and Acl = 5) because they are expected to be more hydrodynamically stable during implosion. The paper discusses the preparation of SI-targets for laser experiments using the free-standing target (FST) layering method developed at the Lebedev Physical Institute (LPI). It is shown that, based on FST, it is possible to build a prototype layering module for in-line production of free-standing SI-targets, and the layering time, τform, does not exceed 30 s both for deuterium and deuterium-tritium fuel. Very short values of τform make it possible to obtain layers with a stable isotropic fuel structure to meet the requirements of implosion physics.

Ulam Stability of Fractional Hybrid Sequential Integro-Differential Equations with Existence and Uniqueness Theory

“…In a variety of scientific and engineering fields such as the electrodynamics of complex media, statistics, chemistry, biology, heat transfer analysis, hydro and thermo dynamics, several waves phenomena, fractal theory, physics, control theory, economics, image signals and processing, and bio-physics, various phenomena are modeled mathematically in the form of linear/nonlinear fractional ordinary differential equations/fractional partial differential equations (FODEs/FPDEs) [1,2]. Similarly, the concept of symmetry is a novel phenomenon in fractional calculus applied to investigate real-world problems, as well as used to study the correlation between applied and mathematical sciences [3][4][5][6], for example physics, fluid mechanics, dynamical systems, biology, control theory, entropy theory, and many areas of engineering [7][8][9]. Fractional differential equations can be used to more accurately describe some real-world issues in physics, mechanics, and other disciplines.…”