Numerical study on femtosecond electro-optical spatial decoding of transition radiation from laser wakefield accelerated electron bunches

This numerical study is focused on electro-optic (EO) spatial decoding of transition radiation (TR) produced by a relativistic electron bunch passing through a metal foil. The calculations included the imaging of polychromatic transition radiation from an electron bunch and the process of EO spatial decoding. From an experimental perspective, a careful examination of the calculation approach of the data analysis is essential. Therefore, to thoroughly understand the process of signal generation and examine the possibility of adopting a less time-consuming treatment, comparative studies were conducted on detailed and simplified models of both transition radiation imaging and EO signal generation. All calculations are defined in SI units for the convenience of experimental measurements. For TR imaging, the results suggest that the simplified analytical model is sufficient to perform polychromatic calculations with considerable accuracy. For EO spatial decoding, we discussed the process of EO signal generation using 1D and 2D models. We found that the 1D model was sufficient for rapid data analysis. Furthermore, the temporal energy chirp was demonstrated to have a minimal impact on the shape of the EO signal. Because both the transverse and longitudinal profiles can be calculated with arbitrary distributions, this numerical study can facilitate measurements of 3D electron charge density profiles in both laser wakefield acceleration and conventional accelerator research.