Three models have been created to visualize and characterize the voltage response of a standing wave accelerating cavity system. These models are generalized to fit any cavity with known values of the quality factor, coupling factor, and resonant frequency but were applied to the Arizona State Universities Compact X-ray Free Electron Laser. To model these systems efficiently, baseband I and Q measurements were used to eliminate the modeling of high frequencies. The three models discussed in this paper include a single standing wave cavity, two cavities coupled through a 3dB quadrature hybrid, and a pulse compression system. The second model on two coupled cavities will demonstrate how detuning will impact two cavities with the same RF source split through a hybrid. The pulse compression model will be used to demonstrate the impact of feeding pulse compression into a standing wave cavity. The pulse compressor will demonstrate more than a 50\% increase of the voltage inside the cavity.
For this thesis, the energy of the CXLS electron beam was measured and the beam’s energy jitter was calculated. It is essential to characterize the beam’s en- ergy and energy jitter in order to ensure that the powerful x-rays produced by CXLS will be of a consistent and desirable energy. The energy of the electrons within the electron beam can be calculated through utilizing basic physics prin- ciples and the geometry of the beamline. The energy of the beam for the data collected was found to be 3.426 MeV at POP module 1 and 12.3 MeV at POP module 9. The energy jitter of the beam was determined for four different angle settings of the VPSPD for linac 1 and found to be lowest when the linac 1 VPSPD was set to an angle of 97°. The energy jitter of the beam was 1.50e-03 MeV when the VPSPD for linac 1 was set to 97°.