Text from the interactive explanation

A Comprehensive Characterization of the Neutron Fields Produced by the Apollon Petawatt Laser

Ronan Lelièvre, W. Yao, Tessa Waltenspiel, Itamar Cohen, Viviange Anthonippillai, P. Antici, Arie Beck, E. Cohen, D. Michaeli, Ishay Pomerantz, Donald Cort Gautier, F. Trompier, Q. Ducasse, P. Koseoglou, P.-A. Söderström, François Mathieu, A. Allaoua, J. Fuchs

Neutrons can look straight through steel and pick out the lithium inside a battery. But they mostly come from nuclear reactors and big accelerators, which are expensive, heavily regulated, and too few to meet demand. Could an intense laser become a compact neutron source?

First, someone has to measure what such a laser actually makes: an invisible burst that is over in less than a millionth of a second. This page follows the team that did it.

01See what X-rays can't

02Pitcher and catcher

03The race against light

04Counting the invisible

05Putting the evidence together

06A dial between two kinds of light

simulatedA slow-motion simulation built from the paper's setup: measured proton spectra (Fig. 2) and Geant4 neutron directions and energies (Figs. 6–7). The camera zooms out from centimetres to the whole room as time speeds up. Neutron colour shows energy: orange is slow, white is fast.

See what X-rays can't

Why anyone wants more neutrons.

X-rays are blocked by electrons , so heavy atoms with lots of electrons, such as iron and lead, cast dark shadows, while light atoms barely show. Neutrons carry no electric charge. They ignore electrons and only bump into atomic nuclei , so they slip through many metals but are stopped by light nuclei, especially hydrogen and lithium .

The two beams therefore see opposite things. Drag the lens across the case: inside it you see the object as neutrons would.

Laser-driven sources could add more. They are compact, and they produce neutrons from below one up to tens of MeV in bursts shorter than a nanosecond. They create no fission products and little activated material. The paper lists uses including radiography of lithium batteries, detecting explosives and narcotics, astrophysics and material analysis.

illustrativeA drawn example of how contrast differs between the two beams. It is not data from this paper.

Pitcher and catcher

How a laser makes neutrons without a nuclear reactor.

Step 1 · Clean the pulse

Apollon's secondary beam fires pulses lasting 24 femtoseconds (24 millionths of a billionth of a second) and carrying about 10.9 joules . Squeezed into a spot about 3 µm across, that reaches roughly 2 × 1021 watts per cm² .

Weaker light leaks out ahead of the main pulse. Compared with the pulse it is faint, but it is enough to heat and tear apart a very thin foil before the main pulse arrives. So without help, the team had to shoot foils about 1–2 µm thick.

The fix is a plasma mirror : a polished glass slab. The weak early light passes straight through it. When the intense main pulse hits, the surface instantly turns into a plasma dense enough to reflect it. Two in a row make a double plasma mirror . The price is energy: only 52% is reflected, leaving about 5.7 J.

illustrativeThe pulse shape and foil response are drawn schematically. The energies are the paper's measured values.

Step 2 · Pitch protons

The laser hurls the foil's electrons out of its back surface. They form a cloud whose electric field pulls protons (hydrogen nuclei) off the rear surface and launches them as a beam. This is called target normal sheath acceleration. Stacks of radiation-sensitive film measured the protons' energies. Fewer and fewer protons are found at higher energies, a steady exponential fall.

With the plasma mirror, the fastest protons went from 25.3 to 35.2 MeV , even with half the laser energy.

Step 3 · Catch them in lithium

A 4 mm slab of lithium fluoride sits 15 mm behind the foil. When a proton with more than 1.88 MeV hits a lithium-7 nucleus, it can swap itself for a neutron: ⁷Li + p → ⁷Be + n. The purple curve shows how likely this is at each energy. The amber area shows which protons actually produce the neutrons. Try your own beam.

illustrativeOur estimate is a simplified "thick target" calculation for lithium only: approximate reaction probability (Fig. 3) and textbook proton stopping in LiF. The paper used full Geant4 Monte-Carlo simulations. Points are read approximately from Fig. 2. The fits use the paper's exact parameters.

The race against light

Timing neutrons over 4.95 metres reveals their energy.

Every neutron leaves the lithium at almost the same instant, but not at the same speed. A neutron's energy fixes its speed , so the arrival time at a distant detector tells you its energy. This is called time of flight.

The starting gun is the X-ray flash . The laser-hit foil emits a burst of X-rays that crosses 4.95 m in 16.5 ns, at the speed of light. Everything after it is a neutron arriving late. Pick an energy and race it.

Run the detector

This is detector #16, a 40 cm plastic scintillator 4.95 m from the target, 19° off the proton axis, behind 15 cm of lead. When a neutron knocks a proton inside the plastic, the plastic gives off a little light, and two photomultipliers turn it into a voltage. Fire a shot and watch the trace. Then drag the cursor to the earliest neutron signal you would trust .

simulatedThe trace is a model built to resemble the paper's Fig. 11. The X-ray flash is sized to the measured flash charge (924.6 pC direct, 378.9 pC with the plasma mirror). The neutron hits are drawn from the simulated spectrum, plus a slow tail of neutrons scattered around the room. The "no lead" option is illustrative. The time-to-energy conversion is exact relativistic kinematics for 4.95 m.

What the real detector recorded

On a direct shot the X-ray flash was so strong that the first trustworthy neutrons appeared 140 ns after it, which means about 5.3 MeV . With the plasma mirror the flash was about 2.5× weaker (924.6 vs 378.9 pC of charge, and 16.1 vs 5.8 µGy per shot on separate X-ray dosimeters). Neutrons showed up from 85 ns , so the detector could see neutrons up to 12.7 MeV .

Why fewer X-rays? Most X-rays are made inside the foil, and the cleaner pulse allows much thinner foils. Between 2.2 and 12.7 MeV, the plasma-mirror shot's signal closely matched the Geant4 prediction.

Counting the invisible

Independent ways to count a burst nobody can see, each checking the others.

The catcher remembers

Every neutron made by ⁷Li + p → ⁷Be + n leaves behind exactly one beryllium-7 atom inside the lithium fluoride. Beryllium-7 is radioactive (its half-life is about 53 days), so the catcher quietly glows with decays long after the shots. Counting those decays counts the neutrons.

One shot leaves only about 5.5 decays per second, which is hard to measure. So the team kept one catcher in place for 40 shots (20 direct, 20 with the plasma mirror) and then measured it with a gamma-ray spectrometer. Load the shots, then measure.

Measured activity: 221.3 ± 12 Bq after 40 shotsdecays per second, from the gamma spectrometer

÷ decay rate of ⁷Be → 1.47 × 10⁹ ⁷Be atoms activity = atoms × ln2 / half-life

÷ 40 shots → 3.67 × 10⁷ neutrons per shot from lithiumone ⁷Be atom per neutron

÷ 0.935 → 3.93 × 10⁷ neutrons per shot the simulation says lithium makes 93.5% of the neutrons; fluorine makes the rest

Simulation predicted 2.70 × 10⁷ (direct) and 2.78 × 10⁷ (plasma mirror) → reality was ≈1.4× higher this measured total is used to normalise the simulated spectra elsewhere on this page

measuredThe chain uses the paper's measured activity and its simulated lithium share. The flashes come at the decay rate this catcher would have; each speck stands for about 108 beryllium-7 atoms.

illustrativeGlow is proportional to each reaction's probability, read approximately from Fig. 9 (EXFOR data).

An energy sieve

Right behind the catcher sat a stack of three metals. Neutrons turn some of their atoms radioactive, and each metal responds to a different range of neutron energies. Copper captures slow neutrons. Indium is knocked into an excited, radioactive state by neutrons of roughly 1–12 MeV, fairly evenly between 2 and 10 MeV. Magnesium only reacts above about 5–6 MeV. Slide the energy to find each layer's window.

Stayed silent, below the detection limit, on both kinds of shot. Few neutrons above 5 MeV, as the simulation predicted.

Close to the prediction: 1.69 × 10⁶ neutrons per steradian per shot between 2 and 10 MeV (1.14 × 10⁶ with the plasma mirror).

38 times too hot! Why?

Make a guess, then reveal.

measuredActivities per shot from Table III, for 20 direct shots. "Per steradian" means per unit of viewing angle; a full sphere is 4π ≈ 12.6 steradians.

Bubbles you can count

A bubble detector is a clear gel holding tiny droplets of liquid kept just above its boiling point. When a neutron hits one, the droplet flashes into a visible bubble. Count the bubbles and you have a dose. These dosimeters sat on the proton axis, 60 cm from the catcher, and respond to neutrons from 0.1 to 20 MeV.

They gave 4.4 × 10⁶ neutrons per steradian per shot on direct shots and 4.7 × 10⁶ with the plasma mirror. That is higher than indium's figure because they count a much wider energy range. They also sat on the forward axis, where emission is strongest, whereas the indium sat close and spread over 2.3 steradians.

One twist: when the team re-checked the detectors against a californium-252 neutron source, the factory calibration had overestimated the response by more than three times for some of them. The corrected values are used.

illustrativeBubble numbers in the animation are illustrative. The fluences quoted are the paper's measured values (±17% direct, ±41% plasma mirror).

Which way do neutrons fly?

The Geant4 simulation counted neutrons in every direction. Emission is almost the same all round , a little stronger forward along the proton beam, with a dip at 90°. The catcher is a disc wider (22 mm) than it is thick (4 mm), so neutrons heading sideways must cross more material and get scattered or absorbed.

Direction also changes energy. Neutrons flying forward carry more of the protons' push, so the fastest ones mostly go forward.

simulatedGeant4 results redrawn approximately from Figs. 6 and 7. Direct and plasma-mirror shots are nearly identical.

Putting the evidence together

One energy spectrum, every instrument.

measured + simulatedRedrawn approximately from Figs. 10 and 13 (forward direction, neutrons per MeV per steradian per shot). Table IV values for the dosimeter and indium points are exact.

Each instrument sees a different slice of the neutron energies. Plotting them together shows where they agree. The simulation (blue) is scaled up by 1.46 so that its total matches the beryllium-7 count. Then tap a finding.

A dial between two kinds of light

Back to the opening question.

Every instrument agreed on one practical result. The plasma mirror cut the laser energy on target by 48% , yet the shots produced similar numbers of neutrons and about 2.5× fewer X-rays . Choosing the mirror and the foil thickness therefore sets the mix of neutrons and X-rays .

The authors suggest using that dial for combined neutron and X-ray radiography : one source whose X-rays outline the heavy materials and whose neutrons reveal the light ones. Here is the case from chapter 1 again.

illustrativeImage blending is a drawn illustration. The neutron and X-ray ratios behind it come from the paper's measurements: 3.93 × 10⁷ neutrons per shot on average with similar emission in both modes, and an X-ray flash of 924.6 vs 378.9 pC.

At a glance

neutrons per shot, from the ⁷Be count (≈1.4× simulation)

fastest protons with the plasma mirror (25.3 MeV direct)

fewer X-rays with the plasma mirror, at similar neutron output

fastest neutrons seen by time of flight (5.3 MeV direct)

Source and credits

Published article: R. Lelièvre, W. Yao, T. Waltenspiel, I. Cohen, V. Anthonippillai, P. Antici, A. Beck, E. Cohen, D. Michaeli, I. Pomerantz, D. C. Gautier, F. Trompier, Q. Ducasse, P. Koseoglou, P.-A. Söderström, F. Mathieu, A. Allaoua, J. Fuchs. "A comprehensive characterization of the neutron fields produced by the Apollon petawatt laser." The European Physical Journal Plus 139, 1035 (2024). doi.org/10.1140/epjp/s13360-024-05679-x

Version used for this page: the submitted manuscript, arXiv:2311.12653v3 (11 December 2023), licensed CC BY 4.0: arxiv.org/abs/2311.12653v3. Its author list does not include V. Anthonippillai and P. Antici, who appear on the published article.

Figures 10, 11 and 13 are reproduced unmodified from the arXiv version under CC BY 4.0. The charts on this page are redrawn approximately from the paper's figures. Exact numbers come from its text and tables.

Simulations and drawings on this page (the slow-motion shot, detector trace, yield estimate, radiographs, bubbles and decays) are illustrative models based on the paper's reported setup and results. The paper's own simulations used Geant4.

The half-life of beryllium-7 (≈53 days) and proton stopping in lithium fluoride are standard nuclear data, not taken from the paper.