Characterization and automated optimization of laser-driven proton beams from converging liquid sheet jet targets

This paper presents a multi-Hz laser-driven ion acceleration platform using liquid sheet jet targets that achieves an 11% increase in maximum proton energy through real-time, closed-loop Bayesian optimization of the laser wavefront, demonstrating a pathway toward robust, high-repetition-rate ion sources.

The Gist

Imagine trying to hit a tiny, moving bullseye with a super-powerful flashlight beam to create a burst of tiny, fast-moving particles (protons). This is essentially what scientists do when they use high-powered lasers to create particle beams. These beams are promising for things like medical treatments and scientific research, but there's a catch: usually, you can only take one "shot" at a time, and the results can be unpredictable. To make these beams useful for real-world jobs, you need to be able to fire them repeatedly (like a machine gun instead of a single-shot rifle) and make sure they hit the target perfectly every time.

This paper describes a successful experiment that did exactly that: it created a stable, repeatable "machine gun" of protons and taught a computer how to tune the laser to make the beam even better.

Here is a breakdown of what they did, using simple analogies:

1. The Target: A "Water Sheet" instead of a Solid Wall

Usually, scientists shoot lasers at solid metal or plastic sheets. But if you shoot a powerful laser at a solid sheet, it gets damaged, and you have to replace it after every shot. That's slow and messy.

Instead, this team used a liquid water sheet. Imagine a very thin, continuous waterfall flowing down a wall, but only a few hundred nanometers thick (thinner than a human hair).

• Why it's cool: Because the water is constantly flowing, the laser hits a fresh, clean surface every single time. It's like having an endless supply of fresh paper to write on, rather than trying to erase and reuse the same sheet.
• The Result: They proved this "water wall" could survive being hit by the laser 5 times a second (and potentially much faster) without breaking or creating debris that would ruin the equipment.

2. The Experiment: Tuning the "Flashlight"

Once they had a stable target, they needed to figure out how to get the best proton beam out of it. They tested three main things:

• The Angle of the Light (Polarization): Think of the laser light as a wave. They tried shaking the wave side-to-side (s-polarized), up-and-down (p-polarized), or in a circle (circular).
  • The Finding: Shaking the wave up-and-down (p-polarized) was the clear winner. It produced three times more energy and ten times more particles than the other methods. It's like finding that pushing a swing at the exact right moment makes it go much higher than pushing it randomly.
• The Shape of the Pulse: They tweaked the "tempo" of the laser pulse (making it slightly longer or shorter in specific ways).
  • The Finding: The "perfectly compressed" pulse (the standard setting) worked best. Making it too long or too short actually hurt the results.
• The Shape of the Beam (Wavefront): This is like adjusting the focus and shape of a camera lens. If the lens is slightly warped, the image is blurry. They used a special mirror (a deformable mirror) that can bend and twist to fix the shape of the laser beam in real-time.

3. The "Smart" Optimization: Teaching the Computer to Drive

This is the most exciting part. Instead of a human scientist spending days manually tweaking knobs to find the perfect setting, they used Machine Learning (specifically Bayesian Optimization).

• The Analogy: Imagine you are trying to find the highest point in a foggy mountain range, but you can only see a few feet around you.
  • Old Way: You walk in a grid pattern, checking every single spot. It takes forever, and you might miss the peak if the map is too big.
  • New Way (Bayesian Optimization): You have a smart guide. You take a step, look around, and the guide uses what it learned to guess where the peak is likely to be. It takes you there, checks, and updates its map. It learns from every step, even the ones that went downhill.
• The Result: The computer adjusted the shape of the laser mirror automatically. It didn't just find a "good" setting; it found a setting that increased the maximum energy of the protons by 11% compared to what a human had manually optimized beforehand. It also made the laser beam focus tighter, packing more energy into a smaller spot.

4. Watching the "Explosion"

They also used a second, weaker laser to take "photos" of what happened to the water target after the main laser hit it.

• They saw the water turn into plasma (super-hot gas) and expand incredibly fast.
• They watched a "shockwave" form and move outward, similar to the ripples you see when you drop a stone in a pond, but happening in a fraction of a billionth of a second.
• This confirmed that the water target recovers and refreshes itself quickly enough to handle high-speed firing.

Summary

The paper proves that:

1. Liquid water sheets are a fantastic, durable target for making proton beams repeatedly.
2. P-polarized lasers (up-and-down shaking) work best for this setup.
3. AI-driven optimization can automatically tune the laser to get better results than a human can, making these particle sources more reliable and powerful.

This work is a major step toward making laser-driven particle accelerators small, stable, and ready for real-world use, rather than just being one-off scientific experiments.

Technical Summary

Technical Summary: Characterization and Automated Optimization of Laser-Driven Proton Beams from Converging Liquid Sheet Jet Targets

Problem Statement
Laser-driven proton accelerators offer promising capabilities for applications in medicine, materials science, and fundamental physics, characterized by high peak fluxes and low emittance. However, realizing their full potential requires high repetition rate (HRR) operation (Hz to kHz) to generate the sustained average flux necessary for practical applications. A critical bottleneck is the development of robust target systems capable of withstanding harsh radiation environments and maintaining position stability within tight Rayleigh ranges over extended periods. Furthermore, navigating the high-dimensional, nonlinear parameter space of laser and target variables to find experimental optima is inefficient using traditional single-shot or manual scanning methods. There is a need for stable, replenishable target platforms compatible with machine learning techniques for autonomous, real-time optimization of beam properties.

Methodology
The authors utilized a liquid water sheet jet target generated by a tungsten microfluidic nozzle, producing a 600 ± 100 nm thick sheet flowing at ~10 m/s. This target was irradiated by the TA2 laser system at the Central Laser Facility (UK), delivering up to 200 mJ pulses with a duration of 75 ± 5 fs and intensities up to 3 × 10¹⁹ W/cm² at a repetition rate of up to 5 Hz (most data acquired at 1 Hz).

The experimental setup included a comprehensive suite of diagnostics:

• Optical Shadowgraphy: An independent 800 nm probe pulse (40 fs) with variable delay was used to monitor plasma expansion and shock formation up to ~700 ps post-interaction.
• Particle Diagnostics: A magnetic electron spectrometer measured forward-directed hot electrons. A scintillator-based proton beam profiler and a diamond detector time-of-flight (ToF) spectrometer characterized the spatial distribution and energy spectra of accelerated protons.
• Control Systems: The laser wavefront was manipulated using a deformable mirror (DM) controlled via six Zernike mode coefficients. An acousto-optic programmable filter (AOPDF) allowed tuning of group delay dispersion (GDD) and third-order dispersion (TOD).

The study employed two primary analytical approaches:

1. Parametric Scans: Systematic 1D and 2D grid scans over target position and laser pulse parameters (polarization, dispersion) to characterize stability and coupling.
2. Bayesian Optimization (BO): A closed-loop, real-time optimization scheme using Gaussian process regression to maximize the maximum proton energy ($E_{max}$). The optimizer adjusted the laser wavefront (Zernike coefficients) based on feedback from the ToF spectrometer.

Key Contributions and Results

• Target Stability and Dynamics: The liquid sheet jet demonstrated shot-to-shot stability suitable for HRR operation. Optical shadowgraphy revealed that the overdense plasma expanded at ~0.3c initially, followed by the formation of filamentary structures (attributed to Weibel-type instabilities) and a shock front. By ~400 ps, the perturbed region saturated at ~50 µm, suggesting the target recovers sufficiently for kHz repetition rates, though further fluid dynamics studies are needed for scaling.
• Polarization Dependence: The study confirmed a strong dependence of acceleration efficiency on laser polarization. P-polarized pulses yielded proton maximum energies approximately 3 times higher and peak doses nearly two orders of magnitude greater than s-polarized pulses, and an order of magnitude higher than circularly polarized pulses. This is attributed to enhanced vacuum heating mechanisms in p-polarized interactions with the sharp plasma density gradient.
• Pulse Shaping: Scans of GDD and TOD indicated that the best-compression configuration ($\Delta$GDD = 0, $\Delta$TOD = 0) generally yielded the highest electron yields and proton energies. Positive TOD, which can extend the pulse rising edge, did not improve performance in this specific regime.
• Automated Optimization: The Bayesian optimization algorithm successfully tuned the laser wavefront in real-time. Starting from a manually optimized focus, the BO scheme increased the maximum proton energy by 11% (from 5.4 MeV to 6.0 ± 0.1 MeV). This improvement was correlated with a 13% reduction in the radius containing 50% of the pulse energy, indicating enhanced energy concentration in the focal spot. Notably, the integrated proton flux on the ToF detector increased by 60% during optimization, despite flux not being the explicit objective function.
• Parameter Correlations: The BO model inferred correlations between specific Zernike modes (e.g., horizontal coma and vertical astigmatism) regarding their effect on proton energy. However, these correlations did not directly map to changes in the far-field peak laser intensity, suggesting that the optimization leveraged subtle wavefront shaping effects on the plasma interaction rather than simple intensity maximization.

Significance
The paper demonstrates that liquid sheet jet targets provide a stable, debris-minimized platform for high repetition rate laser-driven ion acceleration. The work establishes the viability of using machine learning, specifically Bayesian optimization, to autonomously tune laser wavefronts for improved beam performance in real-time. By achieving an 11% increase in maximum proton energy and significantly higher flux through closed-loop control, the study paves the way for application-ready proton sources. These sources can deliver multi-MeV peak energies with high single-shot doses at multi-Hz repetition rates, actively stabilized and optimized to meet the rigorous demands of future applications in isotope generation and hybrid accelerator development. The authors emphasize that while the current results are promising, further investigation into the complex interplay between laser wavefronts and target plasma is required to fully understand the underlying physics of the observed optimizations.