Radiation Physics and Engineering
A peer-reviewed journal published by K. N. Toosi University of Technology

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

Document Type : Research Article

Authors

Mohammad Mahdi Shadman 1
Fatemeh Mansourzadeh 1
Valiyollah Ghazanfary 2
Younes Amini 1

1 Nuclear Fuel Cycle Research School‎, ‎Nuclear Science and Technology Research Institute‎, ‎P.O‎. ‎Box 11365-8486‎, ‎Tehran‎, ‎Iran

2 Reactor and Nuclear Safety Research School, Nuclear Science and Technology Research Institute, ‎Tehran‎, Iran

https://doi.org/10.22034/rpe.2024.467634.1210
Abstract
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 (∑Lε02)/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.

Highlights

  • The study applies the Q-cascade model, a novel approach, to optimize parameters for cadmium isotope separation.
  • The research determines the optimal value of the M∗parameter to enhance the separation process.
  • Researchers developed a combined Newton-Raphson and direct substitution algorithm.
  • This is an innovative computational approach to solve the nonlinear equations in the cascade design

Keywords

Isotope separation
Newton-Raphson solver
Q-cascade model
Optimization
Direct Substitution Method
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Radiation Physics and Engineering
Volume 5, Issue 3
Summer 2024
Pages 49-55

  • Receive Date 13 July 2024
  • Revise Date 04 August 2024
  • Accept Date 11 August 2024

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