Abstract
An umber of theoretical and experimental investigations have suggested that the Free Electron Laser operating with Storage Rings produce effects which inhibit various type of beam instabilities. We exploit simple arguments, based on well-known heuristic criteria, to derive the critical intracavity power necessary to switch off longitudinal instabilities of the microwave and saw-tooth type. The dynamics of the instability is described by exploiting a couple of equations which account for the evolution of the instability growth rate and for the consequent e-beam energy spread enhancement. These equations, implicitly containing the Boussard criterion, are combined to the Free electron laser rate equations model, to study the dynamical interplay between the laser growth and the mechanisms which lead to the instability suppression and to precise the conditions under which this effect occurs.
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