Fully Ionized Pinch Collapse

Abstract

A fully ionized plasma is assumed. To this plasma cylindrically-symmetric magnetic fields are applied, thus causing a pinch collapse. The plasma is treated in hydromagnetic approximation, including electric and thermal conductivity. Separate temperatures are assigned to the electrons and ions. Two schemes are developed for solving numerically the resulting system of six partial differential equations: the explicit scheme for rather fast pinches, where a numerical stability requirement causes the timestep to be bounded by the characteristics given by the ALFVÉN speed, and an implicit scheme, which consists essentially in converting the momentum equation into a second order difference equation with coefficients determined by iteration; here there is no such restriction on the timestep. These schemes were made to work on the U.K.A.E.A. IBM 704 and IBM 709. A run is described in which the initial state was one with uniform density, temperature and Bz field. The boundary temperatures were assumed to remain constant, while the magnetic fields at the boundary were determined by the circuits for the jz and jΘ currents. The results of the computations are in good agreement with experimental results obtained at the Technische Hochschule München by one of the authors (KÖPPENDÖRFER). The whole program is a joint effort between A.E.R.E. Harwell and the Max-Planck-Institut, intended to discover by comparison with experiments how good the hydromagnetic approximations are. If the agreement is satisfactory (eventually using a generalised program which includes neutral gas) it should be possible to design experiments so that specified field configurations are set up.