Divergence Angle Consideration in Energy Spread Measurement for High-Quality Relativistic Electron Beam in LWFA

The thorough exploration of the transverse quality represented by divergence angle has been lacking yet in the energy spread measurement of the relativistic electron beam for laser wakefield acceleration (LWFA). In this paper, we address this gap by numerical simulations based on the experimental data. It suggests that in a C-shape magnet magnetic field with the beam focusing effect, considering the divergence angle would result in an increase in the full width at half maxima (FWHM) of the electron density distribution in a uniformly isotropic manner, while the length-to-width ratio decreases. This indicates that the energy spread obtained from the electron deflection distance is smaller than the actual value, regardless of the divergence angle. A promising and efficient way to accurately correct the value is present by considering the divergence angle (for instance, for an electron beam with a length-to-width ratio of 1.12, the energy spread correct from 1.2 to 1.5%), providing a reference for the high-quality electron beam source development.