The FEL SASE operation, bunch compression and the beam heater

We discuss the conditions required for an optimal SASE FEL operation when bunch compression techniques are exploited to enhance the bunch peak current. We discuss the case of velocity bunching and magnetic bunch compression. With the reference to the latter technique we provide a quantitative estimate of the amount of laser heater power necessary to suppress the micro-bunching instability without creating any problem to the SASE dynamics