  We consider quantum kinetics of an open quantum system in the presence of
periodic fields designed to suppress the internal evolution and shield the
system from generic low-frequency environment (refocusing or dynamical
decoupling in application to multi-qubit systems). Assuming that the refocusing
has order K, that is, for frozen environment the cumulant expansion of the
evolution operator over the period tau begins with the term ~tau^(K+1), we
trace the associated cancellations in the kernel of the quantum kinetic
equation in the Floquet formalism and characterize the remaining decoherence
processes.
