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Ultrafast proton radiography of the magnetic fields generated by a laser-driven coil current

Using ultrafast proton radiography, researchers successfully measured magnetic fields of approximately 40–50 Tesla generated by a laser-driven current in a U-shaped copper coil, providing critical insights for future high-energy-density science applications.

Original authors: Lan Gao, Hantao Ji, Gennady Fiksel, William Fox, Michelle Evans, Noel Alfonso

Published 2026-07-09

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Lan Gao, Hantao Ji, Gennady Fiksel, William Fox, Michelle Evans, Noel Alfonso

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you want to see the invisible wind swirling around a spinning fan, but you can't see the air itself. To solve this, you throw a handful of tiny, super-fast ping-pong balls at the fan. If the wind is strong, it will push the balls aside, creating a clear, empty circle in the middle of where they land. By looking at that empty circle, you can figure out how strong the wind is.

This is essentially what the scientists in this paper did, but instead of wind and ping-pong balls, they used magnetic fields and protons (tiny particles found in atoms).

Here is the story of their experiment, broken down simply:

The Goal: Making a "Magnet Bomb"

The researchers wanted to create a very strong magnetic field using a laser. They didn't use a giant electromagnet plugged into a wall; instead, they built a tiny, microscopic circuit out of copper.

The Setup: They took two small, flat copper sheets (like tiny coins) and connected them with a U-shaped copper wire, looking a bit like a tiny horseshoe.
The Trigger: They fired two powerful laser beams through holes in the front copper sheet and hit the back sheet.

How It Works: The "Hot Electron" Battery

When the intense laser hit the back copper sheet, it acted like a super-heated stove. It boiled off tiny, super-fast electrons (think of them as tiny, charged marbles) from the metal.

These hot electrons flew off the back sheet, leaving it positively charged (like a balloon rubbed on your hair).
Some of these electrons got caught by the front sheet, making it negatively charged.
This created a massive electrical "pressure" (voltage) between the two sheets.
Because the U-shaped wire connected the two sheets, the electricity rushed through the wire to balance things out. This rush of electricity is called a current.

Just like electricity flowing through a wire creates a magnetic field (the principle behind your fridge magnet), this massive rush of current created a powerful, invisible magnetic field around the U-shaped wire.

The Detective Work: Proton Radiography

Now, how do you measure a magnetic field that is too small and too fast for normal tools? The scientists used a clever trick called ultrafast proton radiography.

The Probe: They fired a beam of protons (tiny, fast-moving particles) at the target.
The Interaction: As these protons flew past the U-shaped wire, the magnetic field acted like an invisible hand, pushing the protons away.
The Result: The protons didn't hit the detector in a straight line. Instead, they were pushed aside, leaving a perfectly empty oval-shaped hole (a "void") in the middle of the image where no protons landed.

Think of it like shining a flashlight through a foggy window. If there's a strong wind blowing the fog away in a specific spot, you see a clear patch. The size and shape of that clear patch told the scientists exactly how strong the magnetic field was.

What They Found

By measuring the size of that empty hole, the scientists calculated:

The Current: The laser created a massive electrical surge of about 18,000 to 22,000 amps (that's enough to power thousands of homes, but it only lasted for a few billionths of a second).
The Magnetic Field: This current created a magnetic field so strong it reached 200 to 250 Tesla right on the surface of the wire. To put that in perspective, a standard MRI machine is about 3 Tesla. This was nearly 100 times stronger.
The Decay: As you moved away from the wire to the center of the "U," the field got weaker, dropping to about 40 to 50 Tesla.

The "Plasma Rain" Problem

The images weren't perfectly clean. The scientists also saw dark, stringy lines in the pictures. They explained that the laser didn't just heat the electrons; it also created a cloud of hot gas (plasma) that expanded outward. This plasma acted like a messy rainstorm, pushing the protons around in weird ways and making the edges of the empty hole a bit fuzzy.

The Conclusion

The paper concludes that they successfully used a laser to turn a tiny piece of copper wire into a super-powerful, short-lived magnet. They measured the magnetic field directly using the proton "shadows."

They also tested a setup with two of these U-shaped wires (like a double horseshoe). They found that the copper sheets acted more like a voltage source (a battery) than a current source, meaning the design of the circuit matters a lot for how much magnetic energy you can store.

In short: They used a laser to boil electrons, created a massive electrical surge, and used a beam of protons to "see" the resulting magnetic field, proving they could generate incredibly strong magnets in a tiny space for a split second.

Technical Summary: Ultrafast Proton Radiography of Magnetic Fields Generated by a Laser-Driven Coil

Problem and Motivation
While magnetic fields can be spontaneously generated in laser-driven high-energy-density (HED) systems, the ability to create a controlled, strong external magnetic field source offers new opportunities for basic and applied HED science. Potential applications include creating laboratory magnetic reconnection geometries, magnetizing HED plasmas for fusion yield enhancement, guiding hot electrons in fast ignition, and collimating positrons and electrons. A primary technique for generating such fields involves irradiating a metallic coil target with a high-energy laser. However, previous measurements of these fields have relied on magnetic pickup probes or optical polarimetry. These diagnostics are limited by electrostatic pickup contamination and the critical density constraints of optical beams, often restricting measurements to distances of approximately millimeters from the coil center. Consequently, field strengths closer to the coil have been inferred using vacuum models, which may lead to an overestimation of the total magnetic energy stored. This paper addresses the need for direct, spatially resolved measurements of magnetic fields near the coil source.

Methodology
The experiments were conducted on the OMEGA EP Laser System at the Laboratory for Laser Energetics. The target consisted of two parallel copper (Cu) foils (50 µm thick, 1.5 mm × 1.5 mm) separated by 600 µm and connected by a U-shaped Cu coil with a wire cross-section of 50 µm × 50 µm. A plastic spacer maintained the foil planarity.

Two long-pulse laser beams (each ~1.25 kJ, 1 ns duration, 351 nm wavelength) were focused onto the back foil through entrance holes in the front foil, achieving an intensity of ~3 × 10¹⁶ W/cm². This interaction generated hot electrons that escaped the back foil, creating a potential difference that drove a large current through the connecting U-shaped coil.

To diagnose the resulting magnetic fields, the team employed ultrafast proton radiography. A short-pulse backlighter beam (0.3 kJ, 1 ps) irradiated a separate Cu foil to generate a beam of protons (up to 55 MeV) via the target normal sheath acceleration mechanism. This proton beam probed the main target in a face-on geometry. The protons were detected using a filtered stack of radiochromic film, providing two-dimensional images with a spatial resolution of 5–10 µm and a temporal resolution of a few picoseconds.

To interpret the data, the authors developed a 3-D particle ray-tracing model to simulate proton trajectories through prescribed electromagnetic fields generated by the coil current. They also derived an analytical estimate based on paraxial mapping to characterize the formation of proton voids and caustic boundaries.

Key Contributions and Results
The study successfully demonstrated the direct measurement of magnetic fields generated by a laser-driven current using proton radiography. The key findings include:

Magnetic Field Structure: The proton radiographs revealed a distinct "proton void" around the apex of the U-shaped coil, characterized by a sharp caustic boundary. This void results from the path-integrated deflection of protons by the poloidal magnetic fields generated by the current in the half-circular wire.
Current and Field Amplitudes: By matching the size of the observed proton voids ( $R$ ) with simulation results, the authors inferred the coil current. At approximately 3–4 ns after laser irradiation, the current amplitude was measured to be ~18–22 kA. This current generated magnetic fields of ~200–250 T at the surface of the wire, which spatially decayed to ~40–50 T at the center of the coil.
Temporal Evolution: The data indicated that the current was relatively static over a 21 ps interval but decayed from ~22 kA at $t \approx t_0 + 3.1$ ns to ~18 kA at $t \approx t_0 + 4.1$ ns.
Energy Conversion: The magnetic energy stored in the U-shaped coil was estimated at ~0.26–0.4 J, corresponding to a laser-to-magnetic energy conversion efficiency of ~0.01–0.02%.
Plasma Effects: The images also showed dark filamentary structures, attributed to coronal plasma expansion and self-generated electromagnetic fields associated with plasma instabilities. These filaments complicated the identification of the lower foil-side boundary of the void but were distinct from the magnetic field-induced void.
Voltage Source Characterization: Experiments with two U-shaped coils in a Helmholtz-like configuration demonstrated that the target acts as a voltage source rather than a current source. In this configuration, the conversion efficiency increased to ~0.02%, suggesting that stored magnetic energy could be increased by adding extra coils.

Significance
The paper claims that these experiments provide significant insight for future target designs aimed at developing powerful external magnetic field sources for high-energy-density science. By utilizing ultrafast proton radiography, the authors overcame the limitations of previous diagnostics, allowing for direct measurement of field generation closer to the coil than previously possible. The results validate the use of laser-driven coils as a method for generating multi-tesla magnetic fields and establish a framework for understanding the underlying physics of field dynamics in these systems. The authors note that future work will focus on developing lumped circuit models to better control field dynamics and designing targets with longer straight coil sections or shielding to mitigate plasma interference.