a Numerical Study of the Columbia High Beta Device: Torus -

The ionization, heating and subsequent long-time -scale behavior of the helium plasma in the Columbia fusion device, Torus-II, is studied. The purpose of this work is to perform numerical simulations while maintaining a high level of interaction with experimentalists. The device is operated as a toroidal z-pinch to prepare the gas for heating. This ionization of helium is studied using a zero-dimensional, two-fluid code. It is essentially an energy balance calculation that follows the development of the various charge states of the helium and any impurities (primarily silicon and oxygen) that are present. The code is an atomic physics model of Torus -II. In addition to ionization, we include three-body and radiative recombination processes. The plasma is heated by turbulent poloidal skin currents, induced by a fast reversal of the toroidal magnetic field which converts the toroidal z-pinch into a high beta tokamak. The heating dynamics are simulated by solving single-fluid resistive magnetohydrodynamic equations numerically in one- and two-dimensions. Inertia terms are kept to capture the fast-time-scale plasma dynamics. The equations are driven by prescribed boundary conditions for the poloidal flux and current functions. Since the plasma containment vessel is a non-conductor, specification of poloidal flux on the boundary is difficult. Inductance codes are used to describe the flux distribution realistically. Using heating results as initial conditions, a one-dimensional MHD diffusion code, complete with resistivity, thermal conductivity, and radiation losses, is used to simulate the high beta phase. The zero-dimensional code contains more than ionization and recombination modeling. We also include bremsstrahlung and line radiation, ohmic heating of electrons, wave heating of ions, electron-ion energy transfer and other effects. Therefore, the code is useful in linking the above MHD computations. We present results for charge state evolution of all species, as well as, ion and electron temperatures during the z-pinch phase. For the heating phase, profiles of currents, magnetic fields, density, temperature, plasma beta, and safety factor, q, have been obtained. We also identify maximum impurity levels for successful operation as a high beta tokamak. We conclude that Torus-II is an excellent vehicle for high beta research. Some problems associated with the device and how they may be corrected to allow for better operation are discussed.