Learning a Latent Pulse Shape Interface for Photoinjector Laser Systems

Abstract

Controlling the longitudinal laser pulse shape in photoinjectors of Free-Electron Lasers is a powerful lever for optimizing electron beam quality, but systematic exploration of the vast design space is limited by the cost of brute-force pulse propagation simulations. We present a generative modeling framework based on Wasserstein Autoencoders to learn a differentiable latent interface between pulse shaping and downstream beam dynamics. Our empirical findings show that the learned latent space is continuous and interpretable while maintaining high-fidelity reconstructions. Pulse families such as higher-order Gaussians trace coherent trajectories, while standardizing the temporal pulse lengths shows a latent organization correlated with pulse energy. Analysis via principal components and Gaussian Mixture Models reveals a well behaved latent geometry, enabling smooth transitions between distinct pulse types via linear interpolation. The model generalizes from simulated data to real experimental pulse measurements, accurately reconstructing pulses and embedding them consistently into the learned manifold. Overall, the approach reduces reliance on expensive pulse-propagation simulations and facilitates downstream beam dynamics simulation and analysis.

Figures (11)

• Figure 1: Layout of the modeled photoinjector laser system. Initially in the front-end created pulses undergo nonlinear transformations during propagation to the photoinjector system.
• Figure 2: Representative simulated pulse pair before and after propagation through the fiber system. The input pulse (blue) and the propagated pulse (red) are shown as normalized intensity profiles after centroid and support alignment. Propagation leads to temporal reshaping due to dispersion and nonlinear effects, highlighting the variety of pulse morphologies within the dataset.
• Figure 3: Structure of the convolutional encoder and decoder forming the Wasserstein Autoencoder. Each block consists of one-dimensional convolutions followed by batch normalization and Leaky-ReLU activations. Residual skip connections are included to stabilize training and preserve fine temporal details. Layer output sizes are shown below each block, and kernel sizes are indicated by numbers inside the convolutional layers. The decoder’s final output layer uses a hyperbolic tangent activation to constrain the reconstruction to the normalized signal range.
• Figure 4: Comparison between input pulse profiles from the test dataset (blue) and their corresponding reconstructions (orange) obtained with the trained Wasserstein Autoencoder. The reconstructions capture not only the overall pulse envelope but also higher-frequency oscillatory components, demonstrating the model’s ability to preserve fine temporal structure.
• Figure 5: Visualization of the learned WAE latent space projected onto the first two principal components. Each point represents an encoded pulse, color-coded by normalized pulse energy. The overlaid trajectories correspond to parameterized pulse families shown on the left, whose latent embeddings evolve smoothly along coherent paths across the manifold.