Shot-noise triggered electron beam micro-bunching in SASE-FELs

In this paper, the evolution of shot-noise micro-bunching in a SASE-FEL is investigated. First, a simple one-dimensional model for phase-space evolution of electrons is presented. Then, for an e-beam with random distribution of electrons (i.e. with shot-noise), the start-up and growth of micro-bunching is calculated. It is shown that shot-noise micro-bunching starts in random positions within the e-beam and grows in amplitude and extent. The final micro-bunching pattern contains distinct regions each with a coherent micro-bunching but with no phase relation with that of the others. Such distinct micro-bunched regions show themselves in the so-called spiky pattern of output radiation.