Keywords: fractional divergence, fractional calculus, Laplace Transform, multiplying media, non-multiplying media, neutron flux profile, nuclear reactors, nuclear power, nuclear energy
Fractional divergence for neutron flux profile in nuclear reactors
The concept of fractional divergence is developed for application to the constitutive neutron diffusion equation for describing the neutron flux profile. The analytical solutions for bare reactors in multiplying media and neutron diffusion in non-multiplying media are obtained for fractional-order differential equations. This definition of fractional divergence describes the neutron flux by not considering it as a classical point quantity. Fractional calculus gives a better representation for a distributed system, and takes 'initialisation-function' (instead of a constant of initialisation) in its solution; thereby encompassing the process history. Therefore, this fractional divergence really describes the reactor flux profile, and having a measurement system based on this concept will generate efficient reactor control. The analytical solutions obtained herein may be verified by standard numerical regression methods in a working reactor to evaluate the order of fractional divergence. This paper discusses the practical application of 300 years of fractional calculus theory to describe reactor systems.