Topology of steady-state plasma configurations in transverse self-consistent fields: Spatial-periodic structures: II.

This work is the second part of a theoretical study of steady-state plasma configurations with a spatially periodic structure. In part 1 [Nuclear Fusion 3 (1963) 174] two-dimensional solutions were found that describe plasmoids whose particle and current densities, and also magnetic and electric fields, are periodic functions of the coordinates.In this second part the authors analyse the conditions for the existence of those configurations, describing their concrete forms and comparing them with experimental findings. It is shown that, for given parameter values, plasmoids with a smooth and with a periodic (filament) structure can exist, that is a diversity of configuration occurs. States with a spatially periodic structure of order n + 1 represent a system of n + 1 periodically spaced and mutually balanced self-constricted current filaments for which the equilibrium conditions of a linear pinch [3-5, 7, 10, 15-19] are individually satisfied. In the simplest case of a quasineutral electron-ion plasma that assumes axial symmetry and a periodic structure of order n + 1, the number of particles per unit length and the transverse electron and ion currents in the plasmoid are, respectively, The relation between temperature and current is θe + θi = J2/2Nc2(n+l). In the function for the periodic configuration as a whole these quantities are a generalizageneralization from the earlier reported equilibrium conditions of a solitary self-constricted column, and change to the latter for n = 0.The authors discuss the energy advantage of plasma states with a spatially periodic structure over those having a smooth configuration.In strong-current discharges conditions are created that are necessary for the appearance of spatially periodic structures, that is for the formation of a system of local pinches possessing a certain symmetry of distribution. Experiments performed with linear pinches [la, 2, 20] show that for appropriate current values a fairly stable system of E-filaments (oriented along the electric field) does indeed occur in both z pinches and theta pinches. This system is the simplest and corresponds to the theoretical results obtained. A comparison of experiment with calculation shows that they are in satisfactory qualitative agreement.For higher current values, a still more complex system of stable mutually perpendicular filaments appears; this requires a further development of theory for its elucidation.