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A decomposition is made, in axisymmetric Gauss-Laguerre modes, of the bumpy optical beam shape in a high-grain free electron laser. It is shown that waist position and Rayleigh length can be chosen freely over a wide range of values. A method to optimize the choice is given.

A unified account is given of the normal mode theory of homogeneous unmagnetized plasma .Electron (LANGMUIR). ion sound and electromagnetic waves are treated in stable and (PENXOSE) unstable plasmn with the Van Kampen-Case formalism. using generalized functions . Simplified formulae are derived for second-order Langmuir wavm. taking full account of free-streaming effects .

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