**Oleg A. Sinkevich**
*Science Technological Center of Associated Institute for High Temperature, Russian Academy of Science and Moscow Power Engineering Institute (Technical University), Russia*

**S. E. Chikunov**
*Science Technological Center of Associated Institute for High Temperature, Russian Academy of Science and Moscow Power Engineering Institute (Technical University)*

**Vasilii V. Glazkov**
*Moscow Power Engineering Institute (Technical University), Russia*

**E. Kh. Isakaev**
*Science and Engineering Center for Energy-Efficient Processes and Equipment of Joint, Institute for High Temperatures of Russian Academy of Sciences Izhorskaya 13/19, Moscow, 127412, Russia*

**A. G. Khachaturova**
*Science Technological Center of Associated Institute for High Temperature, Russian Academy of Science and Moscow Power Engineering Institute (Technical university)*

Within the framework of a program devoted to complex research on electric arcs and near-electrode processes, a simplified 2-dimensional mathematical model of electric
arc with self-settled length in a cylindrical cooled channel with axial injection of working gas was developed. To find electric arc length in the channel it was supposed that the arc moves downwards on a flow and makes casual wandering on cross section of the channel under action of whirlwinds, which each bent site of an arc generates in a flow behind itself. Within these assumptions the equation for mean arc length was obtained. Created model of an electric
arc complemented by a condition of short circuit quite satisfactorily describe known experimental data.