Numerical integration of the equations of motion describing the acceleration of plasma particles in Syrovatski\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \)'s model of the dynamic current sheet

The acceleration of solar-wind protons in a current sheet in the Earth's magnetotail, in which the geomagnetic field lines reconnect, is investigated numerically using the dynamic current sheet model proposed by S.I. Syrovatski\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \). The dynamics of current sheets in the Earth's magnetotail is analyzed. In addition to the known solutions, the solution describing a contracting current sheet is derived. The time evolution of the magnetic field structure in Syrovatski\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \)'s model is calculated numerically. The energy spectrum of the protons that are accelerated in the sheet by induction electric fields during rapid changes in the sheet topology is calculated and analyzed. A study is made of proton acceleration up to the time when the current sheet ruptures in the course of its evolution.