STABILITY/INSTABILITY MAPS OF THE NEUTRON POINT KINETIC MODEL WITH CONFORMABLE AND CAPUTO DERIVATIVES

F. A. Godã Nez, G. Fernã Ndez-Anaya, S. Quezada-Garcã A, L. A. Quezada-Tã‰llez and M. A. Polo-Labarrios
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F. A. Godã Nez: Instituto de Ingeniería, Coordinación de Sistemas Mecánicos, Energéticos y de Transporte, Universidad Nacional Autónoma de México, Av. Universidad 3000, Ciudad Universitaria, Coyoacán 04510, Ciudad de México, México†Unidad de Investigación y Tecnología Aplicadas, Universidad Nacional Autónoma de México, Vía de la Innovación No. 410, Autopista Monterrey-Aeropuerto, km. 10 PIIT, Apodaca 66629, Nuevo León, México
G. Fernã Ndez-Anaya: ��Departamento de Física y Matemáticas, Universidad Iberoamericana Ciudad de México, Prolongación Paseo de Reforma 880, Lomas de Santa Fe 01219, Ciudad de México, México
S. Quezada-Garcã A: �Departamento de Sistemas Energéticos, Facultad de Ingeniería, Universidad Nacional Autónoma de México, Av. Universidad 3000, Ciudad Universitaria, Coyoacán 04510, Ciudad de México, México
L. A. Quezada-Tã‰llez: �Escuela Superior de Apan, UAEH, Carretera Apan-Calpulalpan km. 8, Colonia Chimalpa Tlalayote, Apan, Hidalgo, C. P. 43900, México
M. A. Polo-Labarrios: �Departamento de Sistemas Energéticos, Facultad de Ingeniería, Universidad Nacional Autónoma de México, Av. Universidad 3000, Ciudad Universitaria, Coyoacán 04510, Ciudad de México, México∥à rea de Ingeniería en Recursos Energéticos, Universidad Autónoma Metropolitana-Iztapalapa, Cd. Mexico 09340, Mexico

FRACTALS (fractals), 2023, vol. 31, issue 03, 1-17

Abstract: Behavior analysis of the neutron point kinetic model with Caputo and conformable derivatives (Khalil and Almeida operators) was performed. Hence, boundary thresholds that delimit the stability/instability zones within the anomalous diffusion exponent-reactivity parameter space were found. Stability criteria are established to limit the region of the values of the anomalous diffusion coefficient and reactivity parameters with which the oscillatory behavior of the neutron density does not exceed a value greater than 30% with respect to the value of the classical model. The parameter space map corresponding to the model with Caputo derivative shows a larger stability behavior zone than that obtained with the Khalil derivative defined in terms of a linear kernel. In a more general sense, the Almeida operator allows one to freely define the kernel function. A kernel of exponential type produces instabilities of different nature (significant increase in neutron density followed by a series of decreasing oscillations few moments after the start-up, or a rapid growth in neutron density resembling a Gaussian pulse appearing seconds after the start-up), as well as stability/instability zones of different shapes and sizes as the parameters in the kernel vary. Interestingly, it was possible to reduce the instability behavior zone with the exponential kernel and approximate its size with that of the zone predicted with the Caputo derivative.

Keywords: Reactor Dynamics; Fractional Neutron Point Kinetic Model; Anomalous Diffusion Exponent; Conformable Derivative; Caputo Fractional Derivative; Laplace Transform Method (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23500305

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