Multi-messenger dynamic imaging of laser-driven shocks in water using a plasma wakefield accelerator

Abstract

Understanding dense matter hydrodynamics is critical for predicting plasma behavior in environments relevant to laser-driven inertial confinement fusion. Traditional diagnostic sources face limitations in brightness, spatiotemporal resolution, and in their ability to detect relevant electromagnetic fields. In this work, we present a dual-probe, multi-messenger laser wakefield accelerator platform combining ultrafast X-rays and relativistic electron beams at 1 Hz, to interrogate a free-flowing water target in vacuum, heated by an intense 200 ps laser pulse. This scheme enables high-repetition-rate tracking the evolution of the interaction using both particle types. Betatron X-rays reveal a cylindrically symmetric shock compression morphology assisted by low-density vapor, resembling foam-layer-assisted fusion targets. The synchronized electron beam detects time-evolving electromagnetic fields, uncovering charge separation and ion species differentiation during plasma expansion - phenomena not captured by photons or hydrodynamic simulations. We show that combining both probes provides complementary insights spanning kinetic to hydrodynamic regimes, highlighting the need for hybrid physics models to accurately predict fusion-relevant plasma behavior.

Fig. 1. Setup diagram for multi-messenger imaging of laser-driven hydrodynamic shocks in water.

a The main ultrafast laser pulse is focused on the gas jet driving the plasma wakefield accelerator, generating relativistic electrons and ultrafast X-ray pulses. A secondary long laser pulse is focused on the liquid (water) target creating high-energy-density conditions and driving a hydrodynamic shock. The electron beam profile is recorded with a phosphor scintillating screen, and its spectrum is characterized downstream using a magnetic spectrometer. The betatron X-rays are recorded with an in-vacuum CCD camera, and their spectrum is characterized using a Ross filter wheel. b 529 shots taken continuously measuring the electron beam mean momentum, charge, and FWHM divergence angle. The shaded green bands denote the boundaries of scintillating screens. c Energy spectrum of the betatron X-ray source, recovered by imaging a Ross filter wheel. The uncertainty in the electron and X-ray beam spectra is obtained from the standard deviation of the critical energy across multiple shots.

Fig. 2. Comparison of number-density projection from 3D FLASH simulation with corresponding synthetic phase-contrast X-ray image, including calibration to experimental measurements.

a Illustration of mapping between FLASH projected density distributions to synthetic phase-contrast X-ray images with Fresnel-Kirchhoff algorithm. b Comparison of center lineouts between density simulation, synthetic phase-contrast X-ray image, and experimental data.

Fig. 3. Comparison between betatron X-ray imaging and 3D FLASH hydrodynamic simulations of laser-driven shocks in water.

a Contrast between experimental betatron X-ray images and synthetic phase-contrast X-ray images at different time delays. b and c Lineouts in x direction averaged over 80 pixel rows in the y direction taken at the center of the simulation and experimental images, and stacked together horizontally to obtain a composite picture of the full temporal evolution of the interaction. Cyan dots indicate tracking of shock position.

Fig. 4. Hydrodynamic shock velocity analysis comparing simulation and experiment.

The velocity measurement tracks the point of highest density in FLASH, and the minimum intensity feature in both synthetic and experimental phase-contrast X-ray images. The error bars of  ± 4 μm in the experimental shock position reflect the spatial resolution of the imaging system, and consider the previous edge calibration with simulation density.

Fig. 5. Demonstration of cylindrically symmetric shock compression morphology assisted by low-density vapor.

a Comparison panels with Meijering filter (“Meijering filter”) at Δt ~ 1.0 ns. Panel (1) is an x–y 2D slice from 3D FLASH simulation with no vapor, panel (2) is an x–y 2D slice from 3D FLASH simulation with surrounding vapor profile, panel (3) is a ten-shot-averaged image taken with betatron X-rays, 4) single-shot image taken with betatron X-rays. b z–x 2D slices from 3D FLASH simulation comparing density and pressure maps as a function of time for two cases: in panel (1) water target without surrounding vapor and in panel (2) water target with surrounding vapor profile.

Fig. 6. Electron temperature T_e evolution during laser-water interaction.

2D slices of the x − y and x − z plane are extracted from 3D FLASH simulations of a vapor-enveloped water target heated by a laser at Δt = 0.56 ns.

Fig. 7. Dynamic probing of time-evolving electromagnetic fields in water using the LWFA relativistic electron beam probe.

a Time-series of electron beam profile perturbed by electromagnetic fields around the laser-water interaction region recorded on phosphor screen. b Integrated line profiles for the plasma channel and plasma cloud features for both the difference image (I/I₀ − 1), and recovered electric fields ∫ ∣E∣dl. Error bands in the recovered field magnitude account for chromatic effects and uncertainty in the electron beam probe energy: two limiting cases were considered 1) with E_low = 20 MeV and 2) with E_high = 150 MeV. c Illustration of electric field recovery from electron beam radiographic images (“Field recovery method”). The panel includes the radiographic normalized image I, the difference image (I/I₀ − 1), and recovered field magnitude ∫ ∣E∣dl. Dashed circles highlight two distinct cloud features, an Oxygen plasma (inner circle) and a Hydrogen plasma (outer circle).

Fig. 8. Comparison of vertical and horizontal generated electric fields from laser water interaction.

a Recovered projected electric fields ∫ E_xdl and ∫ E_ydl from experimental data. b Projected electric fields ∫ E_xdl and ∫ E_ydl obtained from 3D simulation. c Slice of electric fields E_y and E_x obtained from 3D simulation. The simulation fields are obtained following the equation E ~ ∇ P/en_e, where P is the pressure field and n_e is the electron number-density field output from the FLASH code.

Fig. 9. Analysis of laser-ablated plasma expansion velocity and comparison with simulation.

For FLASH simulations the measurement tracks the field edge position of the expanding plasma plume. For electron beam radiographic images the measurement tracks annular features expanding in time, where two distinct plasma species components are identified: (1) hydrogen ions plasma and (2) oxygen ions plasma. The uncertainties in the expansion radii are defined as  ± 15 μm for H⁺ feature and  ± 30 μm for O⁺ feature following experimental observations and standard deviation across multiple shots.