Optimized Q-cascade approach for stable cadmium isotope purification using Newton-Raphson and direct substitution methods.

In this study, the objective was to separate cadmium isotopes using the Q-cascade approach. The optimal value of the parameter M* was determined by minimizing the function (∑Lε²₀)/2P within the Q-cascade. To overcome computational challenges, the Newton-Raphson solver and direct substitution algorithm were employed to solve the system of nonlinear equations. The direct substitution method was used to provide a suitable initial guess for the Newton-Raphson method. Validation of the developed algorithms using stable cadmium isotopes showed that the value of M* undergoes slight changes with variations in the target isotope concentration in the product and waste streams. For enriching Cd-106 in the product, M* was approximately 108.5, corresponding to the average molar mass of Cd-106 and Cd-111. As the target isotope concentration in the product increases, the number of enrichment stages increases more steeply compared to the number of stripping stages. Similarly, increasing the Cd-116 enrichment in the waste leads to a larger increase in the number of stripping stages compared to enrichment stages. [ABSTRACT FROM AUTHOR]