The Fick's law,as the foundation of the diffusion theory,further neglects the time derivative term of the neutron current density in the P,approximation equation(telegraph equation)of the neutron transport equation.Therefore,it is difficult to accurately describe the actual neutron kinetic behavior in the transient process.In this paper,based on the monoenergetic neutron telegraph equation,an analytical solution is derived for the one-dimensional infinite slab bare reactor neutron kinetics problem using the method of separation of variables,and it is compared and analyzed with the analytical solution of the neutron diffusion equation.The study reveals that during transient changes,the spatial term of the telegraph equation still maintains the form of a cosine function compared to the diffusion equation's solution,but the variation of the temporal term is more complex.Firstly,the combination form of the temporal term's orders is influenced by the geometry and materials of the problem.Secondly,higher-order harmonics exhibit oscillatory changes with time.These research findings can provide references and foundations for subsequent numerical theoretical studies based on the neutron telegraph equation.
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