Hierarchy of time scales and quasitrapping in the N-atom micromaser

We study the dynamics of the reduced density matrix(RDM) of the field in the micromaser. The resonator is pumped by N-atomic clusters of two-level atoms. At each given instant there is only one cluster in the cavity. We find the conditions of the independent evolution of the matrix elements of RDM belonging to a (sub)diagonal of the RDM, i.e. conditions of the diagonal invariance for the case of pumping by N-atomic clusters. We analyze the spectrum of the evolution operator of the RDM and discover the existence of the quasitrapped states of the field mode. These states exist for a wide range of number of atoms in the cluster as well as for a broad range of relaxation rates. We discuss the hierarchy of dynamical processes in the micromaser and find an important property of the field states corresponding to the quasi-equilibrium: these states are close to either Fock states or to a superposition of the Fock states. A possibility to tune the distribution function of photon numbers is discussed