What quenches the helium shell flashes

An analysis is conducted of a typical stellar helium shell flash cycle. A sequence of 12 flashes for a population I star is considered. The changes taking place at a constant mass layer in the helium-burning shell are studied as the flash develops. A highly simplified mathematical description is presented, taking into account the three necessary conditions for the occurrence of the flash and the pressure-density and temperature-density relationships. Quantities which are helpful in explaining what triggers the flash are found to be useful in explaining what quenches the flash.