Introduction

Any change in the state of a medium, for example, a change of

its material properties or a movement of its boundaries, affects

the characteristics of an electromagnetic field existing in this

medium. This influence is very strong, even in the simplest non-

dispersive electromagnetic structures. As there are two temporal

processes in this case, medium change and field change, the points

of their origin acquire principal importance, and the corresponding

mathematical problems become initial boundary value ones. It is

evident that a dispersive structure adds new special features to the

change of the electromagnetic field state and can greatly influence

transient electromagnetic processes. In practice, waveguides and

resonators, where the electromagnetic field interacts with matter

in bound areas of space constrained by waveguide or resonator

walls, are very important dispersive structures with the presence

of the walls bringing a dispersive character to electromagnetic

wave propagation in the region considered. The field interaction

with a non-stationary medium acquires new features under these

conditions. In addition, because of the difference between the phase

and the group velocities of the waves conditioned by the dispersion,

the importance of taking into account some initial time of the

interaction process arises. This importance increases in the case

where a medium or its borders moves, when the relationship

between all three velocities, the phase and the group velocities of

the waves and the motion velocity, begin to play a significant role.

Investigations of transients in waveguides have a long history, but

they concern the degradation of pulses in stationary waveguides

and, principally, metallic waveguides.