Statistical method for studying the behavior of an ensemble of charged particles under the influence of their inherent magnetic field

The stationary solutions for the statistical distribution function of the charged particles in a discharge in an ionized gas contracting about its own axis of symmetry under the influence of the inherent magnetic field are given. An isothermal plasma at a very high temperature is considered (completely ionized gas). An exact solution is carried out in the case of cylindrical symmetry. The density distribution depends on an arbitrary constant C which is determined by the experimental conditions. At large r the solution has the asymptotic form\(\frac{1}{{r^4 }}\)