Neural-network-based longitudinal electric field prediction in nonlinear plasma wakefield accelerators

Plasma wakefield acceleration holds remarkable promise for future advanced accelerators. The design and optimization of plasma-based accelerators typically require particle-in-cell simulations, which can be computationally intensive and time consuming. In this study, we train a neural network model to obtain the on-axis longitudinal electric field distribution directly without conducting particle-in-cell simulations for designing a two-bunch plasma wakefield acceleration stage. By combining the neural network model with an advanced algorithm for achieving the minimal energy spread, the optimal normalized charge per unit length of a trailing beam leading to the optimal beam-loading can be quickly identified. This approach can reduce computation time from around 7.6 minutes in the case of using particle-in-cell simulations to under 0.1 seconds. Moreover, the longitudinal electric field distribution under the optimal beam-loading can be visually observed. Utilizing this model with the beam current profile also enables the direct extraction of design parameters under the optimal beam-loading, including the maximum decelerating electric field within the drive beam, the average accelerating electric field within the trailing beam and the transformer ratio. This model has the potential to significantly improve the efficiency of designing and optimizing the beam-driven plasma wakefield accelerators.