Evolution of a warm bunched beam in a free drift region

The state of the art of FELs development at present is "Table-Top X Ray Free Electron Lasers". Many such schemes involves a pre-bunched electron beam [1]. In this paper we will analyze the evolution and "survivability" of bunching introduced into the beam in the free drift region prior to the wiggler [2-6]. We examined analytically the first order degradation in beam bunching due to space charge effect. It will be shown that there is a limited interaction region, characterized by an exponential decay of the bunching factor, having a length inversely proportional to the square of the electron beam normalized temperature, followed by a stable bunch region. We will present examples of the effect for several schemes of X Ray and Tera Hertz FELs considered or being constructed presently.