Acceleration of charged particles turbular model of a z-pinch

The linear theory of axial-symmetric instability in relativistic electromagnetogasdynamics for hallow distribution of the initial equilibrium current density is considered. In this case the analytical problem solution is turned out to be possible if restricts oneself by a case of incompressible motions in the region of a sufficiently thin tube with the uniform current density. The simplest model of electric field generation and electron and ion acceleration inside a fixed infinite thin hollow tube, where electric current changing in time runs, is considered. The problem of finding the electromagnetic field at the given current is reduced to the solution of the Maxwell electrodynamic equations with the correspondent boundary conditions. When estimating the accelerated particle energy, the characteristic time of current change is adopted as coinciding in the value order with the reverse increment of axial-symmetric instability development