Abstract
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 atx=0 and an inward moving liner atx=s(t) is treated analytically. It is shown that large amounts of microwave energy can be generated in the final compression stages(t)→0 with the help of a copper liner driven by explosives (\(\left| {(\dot s(t)} \right| > 10^3 m/s\)), 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,\(\left| {\dot s(t)} \right| \ll c\).
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