Equilibrium prepinch with trapped magnetic field in a mode of erosion of the liner

At the analysis of conditions of formation powerful radiating Z-pinch the significant attention is directed to mechanism of transformation of a dense solid phase of material in hot plasma with a magnetic field [1-3]. It is represented, that at present time not enough attention is given other important component of all dynamic system, namely, to plasma in the center of the discharge from the moment of its occurrence down to a final stage of compression of the liner. At such approach implosion with a x-ray pulse of radiation it is considered as the natural ending of evolution of prepinch in pinch. Complexity of the description of physical and mathematical property is dictated by representations about a strong cylindrical shock wave, a radiating collapse, turbulent mixing [4]. It is interesting to consider quieter script, at least for the central area, at a stage of the continuous expiration of plasma from periphery of the discharge (erosion of the liner) in the center of system. Here, in addition to speed of plasma production N_L from an internal surface of the liner [2], essential characteristic is rate of submission of a current on a boundary of prepinch. For ideal plasma communication between dissipative boundary layer of the heterogeneous liner and the central area of the discharge is given by integral of freezing-in a magnetic field Ψ = J/nr². In the assumption, that speed of the expiration of plasma is equal to Alfen velocity, value N_L, Ψ are not independent and connected among themselves. There is a question on relative importance of these characteristics - it is known, that definition N_L encounters significant difficulties [1-3]. On the other hand for a center important parameter is dependence Ψ(N) , N - quantity of particles in the cylinder of the current radius. In the present work, for case Ψ = const and Ψ ~ exp(-kN), the degree of heterogeneity of plasma is analyzed. Strong- concentration of plasma on an axis is achieved in the first case and plasma density exponential quickly grows, when `weight´ prep inch N<sub>p</sub> exceeds of threshold value N<sub>p</sub>* = 7.5 π R<sub>o</sub><sup>2</sup> n<sub>o</sub> × zT/m<sub>a</sub>V<sub>0A</sub><sup>2</sup>, V<sub>0A</sub> = H<sub>0</sub>/4π√(m<sub>a</sub>n<sub>0</sub>) where index `0´ concern to a value an internal surface of dissipative boundary layer of the heterogeneous liner and T - is plasma temperature on an axis.