Abstract
An arbitrary radiation field inside a free electron laser cavity can be expanded into Gauss-Laguerre modes. During the amplification stage, several transverse resonator modes can be excited simultaneously inside the undulator. The number of modes and their relative power depend on the electron beam properties and on the cavity geometry. In this paper the authors investigate the mode content for several currents and transverse dimensions of the electron beam as well as for different resonator geometries. It is shown that the mode content can be changed drastically by changing the radius of curvature of the mirrors. In all cases studied, the fundamental Gaussian mode is the dominant mode. The numerical results are compared with analytical relations obtained in the low-gain regime. Some general conclusions are drawn concerning the resonator geometry giving optimum mode quality.
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