An analysis is made of the breakdown and the ionization of the filling gas in toroidal devices. A model is set up to try and reproduce the main features of experimental results, which include upper- and lower-pressure and electric-field thresholds, discharge formation time, particle loss and injection, and initial rates of increase of current and temperature. The model is compared with experiments on devices built at Fontenay-aux-Roses (TA2000 and TFR). Some of the discrepancies between model and experiment may be due to the existence of early run-aways. The absence of an efficient, uniform preionization on TFR could be responsible for the appearance of these run-aways. Finally, it is concluded that impurities from the walls and limiter flow into the TFR plasma right from the start; the rate of influx is estimated for the first few milliseconds. This influx itself is considered indicative of early run-aways.