Effect of an angular trajectory kick in a high-gain free-electron laser

In a free-electron laser, a transverse momentum offset (or ``kick'') results in an oscillation of the centroid of the electron beam about the undulator axis. Studying the influence of this effect on the free-electron laser (FEL) interaction is important both from a tolerance point of view and for its potential diagnostic applications. In this paper, we present a self-consistent theoretical analysis of a high-gain FEL driven by such a ``kicked'' beam. In particular, we derive a solution to the three-dimensional, linearized initial value problem of the FEL through an orthogonal expansion technique and also describe a variational method for calculating the average FEL growth rate. Our results are benchmarked with genesis simulations and provide a robust theoretical background for a comparison with previous analytical results.