  In this paper, we aim to develop the averaging principle for a slow-fast
system of stochastic reaction-diffusion equations driven by Poisson random
measures. The coefficients of the equation are assumed to be functions of time,
and some of them are periodic or almost periodic. Therefore, the Poisson term
needs to be processed, and a new averaged equation needs to be given. For this
reason, the existence of time-dependent evolution family of measures associated
with the fast equation is studied, and proved that it is almost periodic. Next,
according to the characteristics of almost periodic functions, the averaged
coefficient is defined by the evolution family of measures, and the averaged
equation is given. Finally, the validity of the averaging principle is verified
by using the Khasminskii method.
