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The multi-energy group kinetics system configuration is the most widely used in the modern-day reactor for the analysis, operation, control, and design. The present work aims to develop and analyze the system of the multi-energy group point telegraph model in the presence of I groups of delayed neutrons. The spatial and time-dependent stiff coupled partial differential equations for a multi-energy group of telegraph model with multi-group of delayed neutrons are analytically derived. Moreover, an analytical solution of the two-energy group point telegraph model is presented based on Magnus expansion with an exponential representation of the matrix exponential function using eigenvalues and eigenvectors. The developed model of the point kinetics model (PKM) and point telegraph model (PTM) is applied to different benchmarks in the time domain using successive approximations of Magnus expansion in case of a step, ramp, and sinusoidal reactivity. The effect of the fast and thermal relaxation times for the kinetics two-energy group point telegraph model is obtained and analyzed for time-varying reactivity. The results indicate that the relaxation times increase, the solution response is relaxed behind that of the diffusion model, while as the same parameters tend to zero, the response of the neutron density tends to that of the diffusion case. |
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