Model of radiation-stimulated growth of coherent structures in a crystalline medium with fast relaxation and slow diffusion

Background. In this research constructed a model for the radiation-stimulated growth of coherent structures based on the nonlinear diffusion of point defects in a crystalline medium. Materials and methods. The main results were obtained with using the method of multiscale expansions and the qualitative theory of differential equations. Results. A model of nonlinear diffusion of point defects with a limited source were formulated. Regimes of growth of coherent structures in a medium with nonlinear diffusion were revealed. Conditions for the formation of a periodic macrostructure and conditions for amplification of the amplitude of the initial periodic distribution of defects were obtained. Conclusions. Accounting for the influence of defects on the process of their generation in the model of irradiation of a crystalline material with a high-energy and high-density particle beam leads to a description of the growth of coherent structures. In this case, there are two modes of growth corresponding to the initial stage of irradiation-relaxation, associated with an increase in the amplitude of the initial distribution of defects, and asymptotic, when the structure is preserved when dynamic equilibrium is established.