Use of the Q-cascade in calculation and optimization of multi-isotope separation

The model Q-cascade is a useful tool for fast evaluation of the parameters of a separation cascade in the case of multi-isotope mixtures separation. Earlier the cascade key mass M is used as the optimization variable to search optimum parameters of a Q-cascade. A method is given here to determine the region for the valid values of the M parameter in the case of a Q-cascade with specified concentrations of a target component in its product and waste withdrawals. When a target isotope is contained in more than one component of a separation mixture, the idea for specifying the effective fractions of the target isotope in the withdrawals other than the concentrations of a target component is introduced and applied to the optimization of a Q-cascade. The applicability of the method in the determination of the valid values of the M parameter for specified effective fractions of a target isotope in cascade withdrawals is demonstrated. Examples of enrichment of cadmium and lead isotopes in Q-cascades are given to demonstrate the effectiveness of the suggested method.