Journal of Physical Studies 2(4), 490–495 (1998)
DOI: https://doi.org/10.30970/jps.02.490

THE VORTEX STRUCTURE OF LANGMUIR TURBULENCE IN THE INTERRUPTED MAGNETIC z-PINCH. PART 1

P. Kubes¹, A. K. Prykarpatsky^2,3
¹Dept. of Electrical Engineering, Czech Technical University,
2 Technicna Str., 16627, Praha–6, Czech Republic
²Dept. of Applied Mathem. at the AGH, Krakow 30–059, Poland
³Dept. of Nonlinear Math. Analysis at the Institute for Applied Problems of Mechanics and Mathematics of National Acad. Sci. of Ukraine,
3b Naukova Str., Lviv, UA–290053, Ukraine

The usual state of laboratory plasma is that of turbulence and as a consequence one needs to study its extreme characteristics among which the magnetic z–pinch structure appears to be very important for various technologies, sources of high temperature plasmas and local strong magnetic fields. In a turbulence the energy of the system is shared between very many different modes. If some characteristic time–scales are provided, it then becomes possible to describe the turbulence by kinetic equations governing the transfer of energy between the modes. In this study we shall restrict ourselves to the so called Langmuir turbulence, that is the turbulence dominated by the behaviour of the longitudinal electromagnetic or Langmuir modes, leading to the creation of the vortex structure in the interrupted magnetic z–pinch. This vortex structure is stable enough for a spheroidal plasmoid to exist for a rather long time as it was discovered in recent experiments. Since physical processes giving rise to such a structure are essentially nonlinear, one needs to derive from the very basic principles the corresponding vortex generating equations and to treat them under the conditions at the experiments. As a result we have built the so called paired Hill's vortex solutions compatible with the ambient magnetic field supplying the wanted stability condition of the plasmoid existence at the magnetic z–pinch.