In this study, we analyzed a toroidal discharge formation, and determined the breakdown condition of JFT-2M by 2-dimensional computer simulations based on a collisional ionization model. Though the toroidal discharge consists of three processes; (1)breakdown process, (2)plasma formation process, (3)plasma current ramping up process, we restrict our interests to (1) and (2). In these processe, casual electrons are accelerated by the electric field and avalanching by the collisional ionization, while some electrons vanish by clashes into a vacuum vessel. The breeding rates are estimated from the cross sections of elementary processes which strongly depend on the energy of electrons. The density and energy of electrons are determined by conservation laws. Since the orbits of electrons are chiefly determined by the magnetic field, the poloidal magnetic field significantly affects the breakdown condition. Thus, the current distribution in the vacuum vessel is obtained by coupling poloidal field coils and the vacuum vessel. This current distribution and its time derivative enable us to compute the poloidal magnetic field and the electric field in the in-vessel region. By use of our code, we have a qualitative agreement of simulations and experiments by JFT-2M without the use of a center solenoid for the breakdown condition of pressure and electric field.
 K. Tsuzuki, et al., Nucl. Fusion 43 (2003) 1288.