Dynamics of electromagnetic field in imploding conducting shell

In this study we derived explicit analytical solutions of two problems. First is a problem of accumulating of magnetic fields in imploding shells with different geometries. The second problem is determining the eigenmodes of a resonator with moving walls. Using the obtained exact solutions we found the regions of validity of an adiabatic approximation when the frequency of the resonator follows the instantaneous values of geometrical parameters, and the amplitude is determined by a conservation of a magnetic flux. The obtained solutions are of interest in design of devices for generation of ultrastrong magnetic fields and powerful electromagnetic radiation.