The Effect of Temperature on Xenon Instability

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

“…If a xenon free effective multiplication factor i s defined a s However, both stability requirements (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12) and (2-13) a r e extremely restrictive and cannot always be satisfied in general. Thus,one may conclude that the model under investigation i s inherently unstable in the small perturbation sense, and external control is required to maintain stability.…”

“….For the situation in which no external control upon po is imposed then po is given by and combining equations (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) and stability requirement (2)(3)(4)(5)(6)(7)(8)(9)(10)(11) gives…”

“…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.…”

“…Hence, to reconcile equations (3)(4)(5)(6) and (3-41, it is necessary to assume that not only i s the diffusion coefficient space independent, but that the last term in equation It i s interesting to observe that expression (3)(4)(5)(6)(7) vanishes if the gradient of either the flux 'or xenon .concentration is zero.…”

“…where Do (see equation (3)(4)(5)(6)(7)(8)(9) ) is the value -of the diffusion coefficient for the system with no xenon present. Introduction of typical numerical values into equation (3-11) reveals, however, that the difference between "Dn and "Don.…”