Theory of high gain harmonic generation: an analytical estimate

We discuss the theory of the High Gain Harmonic Generation (HGHG). First, we describe an analytical estimate using the HGHG parameters in the DUVFEL project at BNL as an example. We show that the effective energy spread in a chicane dispersion section is found to be very small, and the effect of finite emittance can be neglected during the calculation of coherent harmonic generation. Then we discuss some issues such as the intensity stability, and how to use HGHG to obtain information about local energy spread. We compare these issues with recent experimental results in the infrared. We discuss some of the key issues in the cascading HGHG scheme and its possible limitations.