Abstract
We present a theory of cavities with longitudinal slits which allow the external Q-factor of modes to be evaluated. We also propose a cavity design with a regular section made of a set of metallic blades separated by slits. 3-D-PIC simulation of a V-band gyrotron operating at the TM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12, 1</sub> mode with an output of about 0.5 GW is carried out.
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