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Electromagnetic field transformations due to the time changes of the plasma frequency inside a bounded region are investigated in this paper. A half-restricted plasma with a plane boundary and a completely restricted plasma in a cylinder are considered. It is shown that the interaction of the electromagnetic field with the time-varying plasma changes drastically in the presence of the boundaries compared to the unbounded time-varying plasma. The plasma plane boundary makes an image of a point source in the transformed waves. It is also shown that the field transformation depends on the size of the region occupied by the nonstationary plasma and the shape of the plasma boundary.