Frequency response to an electron energy shift

Abstract

In a free electron laser (FEL) oscillator, the optical pulse evolves through mode competition as a result of mirror losses, desynchronism, and amplification by the electron beam. The finite time for this evolution determines the optical response to an electron beam energy change. The ability of the FEL operating frequency to follow modulations in electron energy has been demonstrated experimentally [l-3] and theoretically [4]. Using a self-consistent FEL theory with dimensionless parameters [5], a longitudinal multimode simulation follows the evolution of the optical pulse over many passes of a FEL oscillator. The optical frequency response to an electron energy shift is summarized in Fig. 1. The characteristic response time II, measures the number of passes for the optical frequency centroid to reach l/e of its new steady-state position after an electron energy shift is imposed at steady-state saturation. The parameters in the simulation are chosen so that the optical pulse reaches steady-state saturation fields without the trapped-particle instability and the growth of optical sidebands. The current density j can be related to the weak-field, single-mode gain, G = 0.135 j, and the energy loss at each pass is given by l/Q. The pulse length, cr:, and desynchonism, d. are measured in terms of the slippage distance, NA. For small Q and low desynchronism d, the optical pulse resides predominantly in the region of the electron pulse. Within the bulk of the optical pulse, strong-field saturation limits changes in the optical fields and the frequency remains unchanged. In the back of the optical pulse where the fields are weak and the interaction with the energy-shifted electron beam changes the optical frequency. Desynchronism d transfers these changes toward the front of the pulse at each pass. The centroid of the optical power spectrum shifts linearly with the number of passes during the middle of the response. In Fig. 1, for a given Q and oz = 2 the response time n, falls off as l/d. For large Q and small uz, the bulk of the optical pulse resides in an exponentially decaying profile outside the interaction region. in the short interaction region, changes