THE USE OF INCORRECTLY POSED INVERSE PROBLEMS AND CATASTROPHE THEORY IN ACOUSTOPLASMIC STUDIES
If the discharge current into a plasma contains direct and variable components, the plasma develops wavelike acoustic instabilities and eventually becomes an acoustoplasmа. Such instabilities lead to bistability, multistability, and hysteresis phenomena of the current–voltage characteristics, causing abrupt changes in the state of the plasma medium. These changes can be imagined as phase transitions and described using catastrophe theory. In the present study, the experimental plasma data are approximated by the equations of catastrophes. After reducing the catastrophe equation to canonical form, the points of possible phase transitions are determined. The phase transition coordinates are then converted to coordinates in the experimental system by inverse transformations. In this way, we determine the points of possible phase transitions in a real experiment. Finally, the parameter changes in an acoustoplasma discharge are obtained by solving incorrectly posed inverse problems. The inverse problem of the experimental data is solved at each current time. Within the neighborhoods of singular points, the incorrectly posed inverse problems are solved by the theory of catastrophes. The proposed methods are applicable to various fields of science and technology.
Incorrectly posed inverse problems, theory of catastrophes, phase transitions and jumps