Wave-field focusings are considered that belong to the class of 3D edge catastrophes and occur when radiation in plasma is simultaneously focused in space and time. Conditions for these types of focusing to be formed at instants of radio-pulse switching are investigated. Space-time reference structures are classified in the case when these structures correspond to simultaneous focusings of various primary (geometrical-optic) and secondary (diffractional) ray sets that yield high-multiplicity and high-modality 3D edge catastrophes. Uniform asymptotic decompositions are obtained that involve special functions of edge and fundamental wave catastrophes and describe electromagnetic fields in 3D focal regions.
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