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Summary form only given. Simulations of the time evolution of the discharge for the small and large versions of IGNITEX are presented. Fusion ignition requires that the ignition factor, defined as the alpha heating rate divided by the power loss, be larger than one. The ignition factor depends on density and temperature. The plasma should have enough excess power to be able to evolve from the low-temperature region at discharge start-up to the ignited region within the constraint of limited time imposed by the heating of the toroidal field magnet. This time is estimated as ≅6 s for the small version and ≅20 s for the large version. The time evolution of the ion, electron, and thermalized alpha densities and the ion and electron temperatures are described by a system of ordinary differential equations which is integrated over the plasma volume. Electrons are heated by the ohmic power and later in the discharge by the alpha particle energy deposition (considered instantaneous). Ions are heated by collisional interaction with electrons at the beginning of the discharge and directly from alpha particles later in the discharge. Energy losses include those by transport and radiation. The effect of the energy confinement scaling on the plasma conditions at the flat top of the discharge is studied. For neoalcator-type scaling laws, the thermal runaway is controlled by cyclotron radiation emission [ABSTRACT FROM PUBLISHER]