The authors asked whether the Zeeman splitting of visible spectral lines can serve as a non-intrusive way to measure the magnetic field inside a laser-produced plasma. At the LULI2000 laser facility they drove blast waves in 8 mbar air inside a pulsed Helmholtz coil (5–20 T, oriented parallel or perpendicular to the spectrometer line of sight) and recorded time-resolved emission from singly ionized nitrogen (563–574 nm) with a 0.195 nm resolution spectrometer. They measured splitting that depends on field orientation: viewed along the field only the σ components appear and the 567.96 nm line v

A laser blast · a 20-tesla magnet · one colour of nitrogen light

A laser hits a graphite pin inside a magnet 400,000 times stronger than Earth’s field. The blast heats the air to tens of thousands of degrees. Anything you poke into that glow disturbs it — but the nitrogen in it is already reporting the field, in the colour of its light.

20 T · looking along the field → two peaks

Simulation · simplified teaching model of the LULI2000 experiment

Try 0 T , then 20 T . Then flip the spectrometer to look across the field.

Why the field matters

Same blast, three magnets

Magnetic fields steer plasma — gas so hot that its atoms have lost electrons and conduct electricity. In space, fields smooth out the shock waves between stars and can turn the remnant of an exploding star from a sphere into a barrel. In laser-driven fusion experiments, a field can help trap heat in the fuel and reach ignition.

To study this on a tabletop scale, the team fired the LULI2000 laser at a graphite pin in thin air (8 thousandths of an atmosphere), inside a coil whose field they could set to 0, 5, 10, 15 or 20 tesla. These photos are the blast’s own glow, taken 20 and 30 billionths of a second after the laser hit.

The blast wave’s glow, seen from the side

Measured · photographs from the paper

No field: a crisp, round shell that keeps its shape as it grows — a classic blast wave.

Self-emission images (580–850 nm) from Fig. 2 of Triantafyllidis et al., Matter Radiat. Extremes 10, 047603 (2025), CC BY 4.0; split into single panels. The laser comes from the left; the pin sits just outside the frame.

The magnet clearly reshapes the blast. But a photo of the shape can’t tell you how strong the field is inside the glowing gas. The usual tools all have a catch:

B-dot probe — a tiny pick-up coil placed in the plasma. It disturbs the plasma it measures, and electrical noise can fool it.

Faraday rotation — a probe laser’s polarisation twists in a field. It needs roughly 10 T across a millimetre before the twist is measurable.

Proton radiography — shoot protons through and watch them bend. It needs a second powerful laser, and electric fields bend protons too.

So what is the field inside the glow? Did the blast sweep it up and squeeze it — or slip straight through? To find out without touching anything, the team read it from the colour of the light.

Light as a fingerprint

Nitrogen’s barcode

Heat an atom and it glows — but only in particular colours. Each colour comes from an electron dropping between two allowed energy levels, and the size of the drop sets the colour: a bigger drop gives bluer light. Those sharp colours are called spectral lines .

In the blast, nitrogen from the air loses one electron (chemists write it N II ) and glows in a tight cluster of yellow-green lines near 568 nanometres. To see them, the team split the light with two spectrometers: a survey instrument covering 425–675 nm, and a high-resolution one zoomed on a 16 nm window.

Nitrogen’s lines near 568 nm, no magnet

Simulated · line positions from the paper’s Table I

Survey view: the five lines blur into a single lump near 568 nm. Tap a line or switch to high resolution.

What you just sawWith 2 nm of blur the cluster is one lump. The high-resolution spectrometer separates lines only 0.35 nm apart — sharp enough to notice a colour shift of a few tenths of a nanometre.

All six are transitions of singly ionised nitrogen from the 3p to the 3s electron configuration (paper, Table I). The brightest, 567.956 nm, runs from the level labelled ³D₃ to ³P°₂ — it is the line this page follows.

Colour and energy are tied by λ = hc/ΔE: the 567.956 nm photon carries 2.18 electron-volts.

The Zeeman effect

A magnet splits one colour into many

Zoom in on the brightest line, 567.96 nm. Its upper energy level is secretly 7 levels stacked at exactly the same height, and its lower level is 5 . Without a field they are indistinguishable. A magnetic field nudges each one up or down by an amount proportional to the field’s strength — the Zeeman effect , named after Pieter Zeeman, who first saw it in the 1890s.

The electron can now fall along 15 slightly different paths , so one colour becomes 15. Turn up the magnet and watch the ladder fan out.

Energy levels of the 567.96 nm line, and the colours they emit

Simulated · teaching model

0 T: all 15 paths have the same length — one colour, 567.96 nm.

What you just sawThe gaps grow in step with the field. At 20 T the outermost colours move only about half a nanometre — tiny, but larger than the 0.195 nm resolution of the team’s spectrometer.

ΔE = gJ · μB · B · MJ

Each sub-level, labelled by its magnetic number MJ (−J … +J), shifts by ΔE. μB is the Bohr magneton (5.79×10⁻⁵ eV per tesla) and gJ the Landé factor: 4/3 for the upper ³D₃ level and 3/2 for the lower ³P°₂ level. Because the two factors differ, the 15 paths all have slightly different lengths (the “anomalous” Zeeman pattern).

Only jumps that change MJ by 0 (called π) or ±1 (σ) are allowed. At 20 T the energy shifts are around 0.0014 eV, which the paper converts to wavelength shifts of about 0.3 nm or more. Across all six nitrogen lines, the field splits the light into more than 50 components.

Stark broadening

The plasma smears it

But these atoms are not sitting quietly in a vacuum. They float in a sea of free electrons — about a billion billion (10¹⁸) in every cubic centimetre. Each electron that zips past tugs on the atom’s energy levels, so every one of the 15 colours is smeared out. This is Stark broadening : more electrons mean more smear, while hotter, faster electrons smear a little less (the width grows as ne/√Te).

Here is the 20-tesla pattern again, seen from the side. Add electrons.

One ion in the electron sea · the 567.96 nm line at 20 T

Simulated · teaching model

No electrons: the 15 colours stay sharp (only the instrument’s 0.195 nm blur).

What you just sawAt the blast’s density (about 1.6×10¹⁸ cm⁻³ at 5 eV) each colour is smeared by roughly half a nanometre — as wide as the split itself. Seen from the side, the 15 colours melt into one broad hump. Is the magnet’s signature lost?

Which way you look matters

Look down the field

The 15 colours are not all the same kind of light. The five π colours come from charge oscillating along the field, like a tiny radio antenna — and an antenna sends no light out of its own ends. The ten σ colours come from charge circling around the field, which shines in every direction.

Predict first. The spectrometer can look along the field or across it. Which view will show the smeared line split into two peaks?

Pick one, then move the spectrometer below to test it.

Two kinds of light, and a spectrometer you can move

Illustrative emitters · simulated spectrum

90° (across the field): π light fills the middle — one broad hump.

What you just sawLooking along the field, the π light vanishes and leaves a hollow in the middle, so two σ peaks survive the smear. Looking across, π light fills the hollow. Same atoms, same field — different view.

In the real experiment · 20 T

Measured · LULI2000 data from the paper

Each image: wavelength 563.5 → 573 nm left to right, time −16 → 175 ns top to bottom (the same axes as the simulated streak at the top of the page).

Streak images: Fig. 3(d–f); spectra re-plotted from data digitized from Fig. 5 (summed over 50 ns). Triantafyllidis et al., Matter Radiat. Extremes 10, 047603 (2025), CC BY 4.0; cropped.

Measured spectra

Read the magnet

Now do what the researchers did. Each “mystery shot” below is a real spectrum, recorded looking along the field and summed over 50 ns. You don’t know the coil’s setting. Dial a field into the model until its curve lies on the measurement. The computer only adjusts the overall brightness and a straight-line background — as the authors did.

Move the field until the mismatch is as low as you can get it, then lock in.

Measured data (Fig. 5) · simplified teaching model, not the authors’ PPPB code

What you just sawThe mismatch has one clear valley, and it sits at the field the coil was set to. This is how the team read 5, 10, 15 and 20 T from the light: their best fits matched the coil within 2 T. Looking across the field, the valley is wide and shallow — the π light hides the split.

A trap: two different plasmas, one shape

Measured 20 T shot · teaching model

The smear depends on density divided by the square root of temperature. So a thin, cool plasma and a dense, hot one can smear the lines identically (the paper’s Fig. 9). Compare them against the measured 20 T spectrum:

Thin and cool: 1×10¹⁸ electrons per cm³ at 1 eV.

Light alone can’t tell these apart. The team broke the tie with an independent measurement: laser interferometry gave a density of about 1.3–1.8×10¹⁸ cm⁻³ behind the shock, consistent with the spectra, which then point to a temperature of 5 eV (±1 eV) — about 58,000 °C.

The finding

Squeezed or slipped?

Back to the opening question. A blast wave shoves gas outward at kilometres per second. If the plasma conducts electricity well enough, the field is “frozen in”: swept up and squeezed along with the gas, so the field behind the shock becomes stronger than the coil’s. If not, the field slips through and stays close to what the coil made.

Physicists judge this with the magnetic Reynolds number , Rem: roughly, how fast the gas carries the field compared with how fast the field leaks out. Rem of 10 or more means frozen in; around 1 means the field diffuses.

A shock sweeping through field lines

Illustrative 1-D model

Rem ≈ 30: the field is frozen in.

The team estimated Rem ~ 1 behind the shock, with a magnetic diffusion time of 15–100 ns. That predicts almost no squeezing. But the light can check directly: a squeezed field would split the lines wider.

Measured 20 T shot · teaching model

Field inside = coil field (20 T): the model lies on the measurement.

What the team found

In every case they examined — fields of 5 to 20 T, looking along and across — the best match between measured spectra and their Stark–Zeeman simulations came when the simulated field equalled the coil’s field, within 2 T. The field inside the hot gas behind the shock was not compressed. The plasma is in the “resistive” regime, where the field diffuses rather than being swept up, just as Rem ~ 1 predicts.

What this brings closer

A magnetometer made of light

So, how strong is the magnet inside the fireball? In this experiment, just as strong as the coil around it — read from nitrogen’s light to within 2 T, without putting anything into the plasma. The authors see this as a non-intrusive platform for measuring local magnetic fields in laboratory plasmas.

What’s still hidden: the light was faint, so each spectrum had to be summed over tens of nanoseconds — too long to watch the field change as the blast evolves. A coarser grating, longer camera windows, lower magnification and not splitting the light between two spectrometers could together give roughly ten times more signal: a step towards following the field in time.

Reaching weaker fields: the same energy shift becomes a bigger colour gap at longer wavelengths (Δλ = λ²ΔE/hc). Bright infrared lines — or a blast that does squeeze its field — could make weaker fields readable.

How far does a field push a line?

Calculated · same Zeeman physics

—

Magnetic fields shape fusion fuel and exploding stars alike, and measuring them where they act has been one of the hard parts. This work turns a handful of nitrogen lines into a magnetometer for laser-made plasmas — and its measured spectra give other line-shape codes a benchmark to test against.

↑ Back to the shot — try a field yourself

Source

A. Triantafyllidis, J.-R. Marquès, S. Ferri, A. Calisti, Y. Benkadoum, Y. De León, A. Dearling, A. Ciardi, J. Béard, J.-M. Lagarrigue, N. Ozaki, M. Koenig & B. Albertazzi. “Zeeman splitting observations in laser-produced magnetized blast waves.” Matter and Radiation at Extremes 10 , 047603 (2025). doi:10.1063/5.0256859

Figures 1–3 (set-up drawing, self-emission photographs, streak spectra) are reproduced from the article under CC BY 4.0; cropped and split into panels.

Measured spectra in chapters 5–7 are re-plotted from data digitized from Fig. 5 of the article (CC BY 4.0), including the authors’ PPPB fits.

All live spectra on this page come from a simplified Stark–Zeeman teaching model (line positions from the paper’s Table I, Landé factors and line strengths from LS coupling, electron-impact width ∝ ne/√Te, 0.195 nm instrument resolution) — not the authors’ PPPB code. The simulated shot, blast-wave shapes, field-line and emitter animations are illustrations of the experiment.