Self-stabilizing criticality waves

Abstract

An analysis is presented of a recently developed concept, so-called self-stabilizing criticality waves. These waves can be ignited in originally subcritical systems under the condition that the burn up dependent properties of the system satisfy certain requirements, as is shown for an analytically solvable model. The waves have a soliton character, i.e. as a consequence of the non-linear properties of the system they have a self-stabilizing form and a phase velocity that depends on the wave amplitude. For the analytically solvable model (as far as the asymptotic waves are concerned) expressions are given for ignition conditions, wave form, amplitude (i.e. reactor power) and phase velocity. The results are corroborated by computer simulations and the latter are also used for ilustrating a non-analytically solvable case and for studying the pre-ignition phase and the evolution to an asymptotic wave.