Analytical Solution Study on Transient Neutron Transport in Homogeneous Bare Reactor Based on Neutron Telegraph Equation

Wang Weiguo; Li Yunzhao; Qin Junwei; Cao Liangzhi

doi:10.13832/j.jnpe.2024.02.0042

Volume 45 Issue 2

Apr. 2024

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Wang Weiguo, Li Yunzhao, Qin Junwei, Cao Liangzhi. Analytical Solution Study on Transient Neutron Transport in Homogeneous Bare Reactor Based on Neutron Telegraph Equation[J]. Nuclear Power Engineering, 2024, 45(2): 42-46. doi: 10.13832/j.jnpe.2024.02.0042

Citation:

Wang Weiguo, Li Yunzhao, Qin Junwei, Cao Liangzhi. Analytical Solution Study on Transient Neutron Transport in Homogeneous Bare Reactor Based on Neutron Telegraph Equation[J]. Nuclear Power Engineering, 2024, 45(2): 42-46. doi: 10.13832/j.jnpe.2024.02.0042

Citation:

Wang Weiguo, Li Yunzhao, Qin Junwei, Cao Liangzhi. Analytical Solution Study on Transient Neutron Transport in Homogeneous Bare Reactor Based on Neutron Telegraph Equation[J]. Nuclear Power Engineering, 2024, 45(2): 42-46. doi: 10.13832/j.jnpe.2024.02.0042

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Analytical Solution Study on Transient Neutron Transport in Homogeneous Bare Reactor Based on Neutron Telegraph Equation

doi: 10.13832/j.jnpe.2024.02.0042

School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an, 710049, China

Received Date: 2023-05-26
Rev Recd Date: 2023-06-16
Publish Date: 2024-04-12

Abstract

Abstract

The Fick's law, as the foundation of the diffusion theory, further neglects the time derivative term of the neutron current density in the P₁ 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.
- Neutron kinetics,
- P₁ approximation,
- Telegraph equation,
- Diffusion equation,
- Analytical solution

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References(12)

References

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