Application of the catastrophe theory to acoustoplasma research

Abstract

In the paper the possibility of applying the mathematical theory of catastrophes to the processes occurring during the interaction of acoustic fields with plasma is considering. In particular, it is proposed to apply the theory to find out possible jumps in parameters and phase transitions in an acoustoplasmic medium. Based on the experimentally obtained database (in this case, for acoustoplasmic processes), a mathematical model of the process under study was constructed. And then, applying the theory of catastrophes, it is determined whether there are sudden changes in the values of control parameters in the area under consideration, critical points of unstable equilibrium and phase transitions, i.e. catastrophic parameter jumps. The choice of the equation describing the process is made based on the number of control parameters for this process. It is also proposed to use the methodology in various fields of science and technology, where similar conditions may arise.