The Effect of Modal Interaction in the Xenon Instability Problem

Xenon-135 Induced Instabilities of the Neutron Flux in Nuclear Reactors

“…Returning to equations (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17) it is possible to obtain analytic solutions for those flux levels such that Then equations (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17) With a precise definition of mathematical stability given, the phase plane analysis of equations , , and (2-29) may now be made. Since the model under investigation is spacially independent and thus meant to be informative only, an exhaustive phase plane analysis will not be rendered.…”

“…It will be shown that the material buckling for criticality to exist that results 13 from equation (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17) when high flux levels ($o > 10 ) a r e considered is the same a s equation . Diffusion theory, when the diffusion coefficient and absorption cross section a r e modified to include xenon absorption at high flux, leads to the following for the material buckling.…”

“…Now returning to equation (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)' under the assumption of large flux values 13 (p3 10 , ), the term "Ln(s+l)' will be neglected compared to the "sn term.…”

“…A technique to obtain quasi-solutions for the spacially dependent, perturbed flux a s given by equation (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) can be devolved from a more general mathematical technique called modal analysis. The general application of modal analysis to reactor problems has been discussed by Kaplan (23) and others.…”

“…Since the fundamental mode and the first few harmonics contribute most to the flux distribution the series expansion for the Laplace transformed flux will be truncated a s follows: Now the following inequalities must all be satisfied for stability of the perturbed flux a s given by equation (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24).…”