  We propose a theory for photon-assisted macroscopic quantum tunneling (MQT)
in a stack of capacitively-coupled intrinsic Josephson junctions in which the
longitudinal Josephson plasma, i.e., longitudinal collective phase oscillation
modes, is excited. The scheme of energy-level quantization in the collective
oscillatory states is clarified in the $N$-junction system. When the MQT occurs
from the single-plasmon states excited by microwave irradiation in the
multi-photon process to the uniform voltage state, our theory predicts that the
escape rate is proportional to $N^2$. This result is consistent with the recent
observation in Bi-2212 intrinsic Josephson junctions.
