We report on the realistic scheme of intense X-rays and γ-radiation generation in a laser interaction with thin foils. It is based on the relativistic mirror concept, i.e., a flying thin plasma slab interacts with a counterpropagating laser pulse, reflecting part of it in the form of an intense ultra-short electromagnetic pulse having an up-shifted frequency. A series of relativistic mirrors is generated in the interaction of the intense laser with a thin foil target as the pulse tears off and accelerates thin electron layers. A counterpropagating pulse is reflected by these flying layers in the form of a swarm of ultra-short pulses resulting in a significant energy gain of the reflected radiation due to the momentum transfer from flying layers
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