Transformation method for electromagnetic wave problems with moving boundary conditions

A method for the solution of initial-boundary-value problems of the wave equation with moving boundary conditions is presented, which transforms the wave equation for the region with moving boundary into a form-invariant wave equation for a region with fixed boundary. Two kinds of transformations are found which refer to regions (1) expanding and (2) contracting with (increasing) time. As an application, the compression of microwaves in a one-dimensional cavity 0≦x≦s(t) with fixed liner at x=0 and an inward moving liner at x=s(t) is treated analytically. It is shown that large amounts of microwave energy can be generated in the final compression stage s(t)→0 with the help of a copper liner driven by explosives ( {Mathematical expression}), for times of the order of the electromagnetic diffusion time, τ_D=μσd²∼10^-2s. Such microwave compressions proceed quasi-statically for non-relativistic liner velocities, {Mathematical expression}.