Parametrization of DT ignition in tight aspect ratio, elongated toroidal plasmas

The plasma geometry plays an important role in the heating and evolution of a tight aspect ratio, magnetically confined plasma. Tight aspect ratio and vertical elongation allow higher magnetic fields and currents, which support higher plasma densities and thus cleaner plasmas, while still permitting deuterium-tritium ignition at relatively low values of the plasma beta. Paramagnetic conditions, in particular a significant poloidal current, a substantial fraction of trapped electrons, and distortion of the plasma current spatial distribution due to the vartical elongation of the magnetic flux surfaces have important effects on the ohmic heating. The existence and size of central sawtooth oscillations depends on the current distribution and, at low beta when the ideal MHD mode is stable, on the exact conditions at the q=1 surface. The ignition process is necessarily transient and difficult to describe with steady state approximations. It turns out to be easy to introduce unrealistic approximations into standard 1 1/2D transport codes, which are sensitive for DT ignition. These are difficult to resolve from available experimental data. The authors therefore, discuss the parametrization of the important 1 1/2D effects and the overall time evolution in terms of analytic expressions and a simple, fast 1D (flux surface variable) transport code that attempts to retain a firm connection to the underlying basic physics and makes it easier to evaluate their relative effects on ignition