A statistical theory is constructed to evaluate the multipactor induced breakdown on a dielectric. The calculation employs the integral equation allowing predicting the threshold of multipactor growth. It is found that the action of the rf magnetic field considerably changes the shape of the upper susceptibility curve and, depending on the secondary electron yield, leads either to rising of the slope of the upper boundary or to its complete elimination. The critical value of the secondary yield above which the region of multipactor existence is not restricted from above by any limiting rf electric field strength is estimated. (C) 2011 American Institute of Physics. [doi:10.1063/1.3578397]