4.6.4 Neutron flux distribution

Evaluation of the non-leakage probability factor re­quires knowledge of the rate of diffusion and the distribution of neutrons throughout the reactor core. The neutrons tend to diffuse from regions of high flux to regions of lower flux. Thus a stable distribution is established such that the production, absorption and diffusion of neutrons into and out of each region of the reactor is in balance. Since neutrons can only escape completely from the reactor at its boundaries this leads to a lower neutron flux at the edge of the reactor rather than at the centre.

The neutron diffusion theory is similar to that developed for other diffusion controlled phenomena: temperature in a heated body, dye in a liquid solution, smoke particles in air. The mathematics of the diffu­sion theory, the derivation of the diffusion equation and application of its solution to various core geo­metries may be readily found in reactor physics text­books. Here the solution of the thermal neutron flux distribution is presented for a cylindrical core height L and radius R:

ф — Фо cos (тг L/L’) Jo (2.405 R/R’)

where L’ and R’ are the extrapolated height and ra­dius of the reactor, see Fig 1.15, and Jo is a Bessel function. The equation gives the relative flux variation; the absolute magnitude is determined by the arbitrary constant 0o-

It may be seen that the neutron flux ф does not fall to zero at the physical boundaries of the core. If this were so no neutrons would leak from the reactor as there would be no neutrons at the core boundary. The flux level at the edge of the core is such that it appears to be falling to zero at points outside the core. These points form the extrapolated boundary of the reactor.

Thus the neutron flux distribution in a cylindrical reactor, Fig 1.15, is given by:

•

Axial flux shape — cosine.

• Radial flux shape — Jo Bessel function.