The physics of the formation of cryogenic fuel layers with various internal structures has been studied in regard to the development of promising layering techniques for modern inertial confinement fusion (ICF) experiments. The investigations have been made with inertial confinement fusion target (ICF targets) and in a target modeling system (TMS) with the nonisochoric process of cryogenic layer formation. The results indicate that the solidlayer structure in TMS differs essentially from that obtained in ICF targets. The thermal history of a fuel layer at separation into the condensed and vapor phases is found to depend upon whether the initial gas density is more, less, or equal to the critical value for a given fuel material. The issue on the fuel-layer fabrication in the form of a long-living quasiamorphous
layer is considered. A new low-temperature method to homogenize a polycrystalline cryogenic layer has been proposed and examined. The operational temperature was 4.2 K. The time to achieve the complete homogeneity of solid hydrogen was 150 s. No limitation, with respect to the thickness of a cryogenic layer, was found. The critical target is suggested as a new type of an ICF target.