The construction of micro-targets for fusion, based on the concept of shock-free compression was analytically and numerically considered in [1]. Cylindrical layered system [1] can be the basis for such targets. In the present paper, two-stage stratified systems are considered. Laws of energy input into the first and second stages are determined analytically in order to apply shock- free compression to the DT-working area. Their advantage over the single-stage systems is a higher percentage of energy extraction in the cumulation of the DT region and, therefore, a lower value of the required external energy input. Analytical construction of approximate solutions, as well as the results of direct calculations in a complete mathematical formulation are presented in the report.
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