The model of point vortices located outside a circular domain is considered. The review of stability and instability conditions of a system of identical point vortices located uniformly on a circle is given. Theoretical results are confirmed by numerical calculations.

Abstract. The source of X-ray radiation with the energy of quanta that may vary in the range h = 1÷12 keV was developed for studies in X-ray interaction with matter and modifi cation of solid surfaces. It was based on a vacuum spark discharge with the laser triggering. It was shown in our experiments that there is a possibility to adjust X-ray radiation spectrum by changing the confi guration of the electrode system when the energy stored in the capacitor is varied within the range of 1÷17 J. A comprehensive study of X-ray imaging and quanta energy was carried out. These experiments were carried out for the case of both direct and reverse polarity of the voltage on the electrodes. Additionally, ion composition of plasma created in a laser-triggered vacuum discharge was analyzed. Highly charged ions Zn (+21) , Cu (+20) and Fe (+18) were observed.

No abstract