The effect of plasma particle flux recycling at the limiters on the conditions of development of a thermal instability, which is caused by impurity radiation and which limits plasma density, is considered. It is shown that, within certain limits, an increase in the charged particle flux, which can be brought about by increased gas puffing, should raise the maximum plasma density above which current disruption would occur. Some of the results obtained in the Pulsator and D-III experiments are explained within the framework of the model considered.