Application of catastrophe theory to a point model for bumpy tori with neoclassical non-resonant electrons

The point model of Hedrick et al. for the toroidal core plasma in the ELMO Bumpy Torus (with neoclassical non-resonant electrons) is examined in the light of catastrophe theory. Even though the point model equations do not constitute a gradient dynamic system, the equilibrium surfaces are similar to those of the canonical cusp catastrophe. The point model is then extended to incorporate ion cyclotron resonance heating. A detailed parametric study of the equilibria is presented. Further, the nonlinear time evolution of these equilibria is studied, and it is observed that the point model obeys the delay convention (and hence hysteresis) and shows catastrophes at the fold edges of the equilibrium surfaces. Although a detailed analysis of the basin boundaries for the simultaneous point attractors is not made, some simple examples are given which illustrate that the final equilibrium state can be drastically affected, not only by the control parameters (neutral density, ambipolar electrostatic potential, electron and ion cyclotron power densities) but also by the initial conditions of the state vector (plasma density, electron and ion temperatures). Tentative applications are made to experimental results.