Mathematical Modeling of Oxidation and Ignition Processes of Unalloyed Plutonium

The article discusses the problem of oxidation and ignition of plutonium at various temperatures. It is shown that to determine the critical conditions for the ignition of plutonium samples with a characteristic size of up to 2 cm at the stage of the steady-state thickness of the oxide layer, it is sufficient to use the outcomes of the thermal explosion theory formulated by N.N. Semenov. Calculations of the critical ambient temperature above which plutonium ignites are in satisfactory agreement with the experimental results. A model of the oxidation of a spherical plutonium sample in the form of a system of ordinary differential equations is formulated and substantiated. Using this model, it is possible to determine the time before ignition and the amount of oxidized plutonium at any given moment. The model’s operability was tested in an experiment on dynamic heating of a plutonium sample before ignition. As a result, a satisfactory correspondence of the calculated temperature value at the time of ignition to the experimentally recorded value was obtained. Based on the conclusions of the thermal explosion theory, an approach to the determination of the kinetic parameters for the reaction rate of plutonium oxidation is proposed.