Transverse envelope analysis for accelerating relativistic electron beams in a linear accelerator as a photon source

Since recent progress of electron guns extends the application of linear accelerators to photon radiation sources, the design and optimization of transverse beam optics over a linear accelerator become important. In this paper, we propose a transverse beam envelope analysis for accelerating beams in a linear accelerator using symplectic matrices based on a normalized emittance. This approach allows a description of the transverse envelope function, which reflects the characteristics of beam optics. Since the envelope function is described in the same phase space as photon radiation, it provides an effective and powerful tool for the design and optimization of the beam optics as a photon source. The emittance based formalism of the beam envelope, which was previously described by Douglas, Kewisch, and York, is first introduced for impulse acceleration, and then extended to a thick accelerator structure. The transverse beam envelope analyses, such as error sensitivity, chromatic aberration, and emittance growth, are presented by applying second-order perturbation treatment to a formulated matrix describing a quasi-periodic lattice in the linear accelerator system.