The Copper Foil That Timed An X-Ray Flash

There is a particular kind of claim that sits uncomfortably in accelerator physics: the machine is doing something, the simulations say what, and no instrument on the premises can check. Attosecond hard X-ray pulses have been in that position for several years. The recipe for making them was understood, the electron-beam diagnostics were consistent with it, and the users who wanted to do attosecond science at 9 kiloelectronvolts were told, in effect, that the pulses were probably short enough. On 20 October a team led from the Linac Coherent Light Source at SLAC published in Nature Photonics the measurement that closes the gap: hard X-ray pulses of 100 to 400 attoseconds, timed not by an electron diagnostic but by the response of a copper foil placed in the beam.

LCLS first produced attosecond pulses in 2019, in the soft X-ray range below about 5 keV, and the reason that regime came first is almost entirely about measurement rather than generation.

A soft X-ray pulse can be timed by angular streaking. Overlap the X-ray pulse with a circularly polarised infrared field, let the X-rays ionise a gas, and the infrared field kicks each escaping photoelectron in a direction that depends on the instant it was born — the field's rotating vector acts as the hand of a clock, and the angular distribution of photoelectrons maps directly onto the temporal profile of the pulse. It is an elegant technique and it has a floor: it needs a healthy photoionisation cross-section, and it needs the photoelectron to be slow enough that the infrared field can meaningfully deflect it.

At 9 keV neither condition holds comfortably. Photoionisation cross-sections fall steeply with photon energy, so there are few electrons to work with, and the ones that appear leave with kinetic energies so large that an infrared field barely bends their trajectories. The clock hand is too weak to move the electron. Every other standard approach has an equivalent problem; cross-correlation against an optical pulse requires a material response faster than the thing being measured, and at a few hundred attoseconds there is almost nothing in condensed matter that qualifies.

So the hard X-ray attosecond programme ran for several years on inference. The electron beam was configured to produce a very short, very bright current spike; simulations said that spike would radiate for a few hundred attoseconds; the X-ray spectra were broad in a way consistent with a short pulse. All true, and none of it a measurement of duration.

The generation recipe is worth setting out, because the measurement only makes sense against it.

A free-electron laser radiates when a relativistic electron bunch is sent through a periodic magnetic undulator. The electrons bunch at the optical wavelength, radiate coherently, and the duration of the X-ray pulse follows the length of the slice of beam that is lasing. To make a few-hundred-attosecond pulse you therefore need a slice of beam a few hundred attoseconds long carrying enough current to reach saturation inside the undulator — in this experiment, a current spike of roughly 10 kiloamps as measured, estimated at 10 to 20 kA and simulated at 20 kA, riding on a 10.263 GeV beam.

Compressing a bunch that hard has a side effect. The same manipulation that creates the spike leaves a steep energy chirp along it: the electrons at the head and the tail of the spike differ in energy by a substantial amount, here corresponding to around 75 MeV per femtosecond. An energy chirp is poison for FEL gain, because the resonant wavelength of an undulator depends on electron energy, and a slice whose energy is sliding has no single resonance to amplify.

The fix is to make the undulator slide too. The LCLS undulator line was linearly tapered — the undulator parameter K stepped down by 0.0014 from one segment to the next — so that the resonance condition tracks the energy chirp along the spike as it propagates. Undulator segments outside the lasing set were detuned so they could not contribute. The result is an X-ray pulse carrying about 1 microjoule on average, with the best shots reaching about 3 microjoules, and a spectrum roughly 20 electronvolts wide at full width half maximum.

That bandwidth is the first quiet hint about duration. A transform-limited Gaussian pulse has a time-bandwidth product of about 1.8 femtosecond-electronvolts, whatever the photon energy, so 100 attoseconds requires about 18 eV of bandwidth; the pulses analysed here, with bandwidths between 15 and 35 eV, are broad enough to support durations of roughly 50 to 120 attoseconds. It is a necessary condition, not a sufficient one — a pulse can be broad in spectrum and long in time if it is chirped — but it says the pulses are not obviously much longer than the bandwidth allows.

The measurement itself turns on a piece of atomic physics with a convenient timescale.

Drive a copper foil hard enough with 9 keV photons and you strip 1s electrons out of a large fraction of the atoms in the illuminated volume. That creates a population inversion between the 2p and 1s levels — more vacancies below than above — and a medium with an inversion will amplify any spontaneous photon that happens to travel along the gain path. The copper Kα₁ line at 8048 electronvolts — and, far more weakly, Kα₂ at 8028 — stops being ordinary isotropic fluorescence and becomes amplified spontaneous emission: a bright, directional, strongly nonlinear burst along the beam axis. In ordinary fluorescence the two lines come out in a 2:1 ratio; in the amplified regime Kα₁ dominates, which is itself one of the paper's observations.

The useful part is that the inversion is not stable. A 1s core hole in copper fills in roughly 400 attoseconds, somewhat more often than not by Auger decay — copper's K-shell fluorescence yield is about 0.44, so a little over half of all core holes close non-radiatively — and every hole that fills is a hole that no longer contributes gain. So the inversion is being created by the pump and destroyed by Auger decay at the same time, and whether it ever reaches the density needed for appreciable amplification depends on which process wins.

This is a leaky bucket. The pump pours and the Auger channel drains, and the level only rises if you pour faster than it drains. For a fixed amount of water — a fixed pulse energy — a short pulse pours fast and fills the bucket; a long pulse delivers the same energy slowly and never gets the level up. The yield of amplified Kα photons therefore depends steeply on pulse duration at constant pulse energy, which is exactly the lever a duration measurement needs.

The experiment reads that lever shot by shot. Part of the beam goes to an intensity monitor that measures pulse energy without disturbing the beam; the rest is focused onto a 20-micrometre copper foil by advanced Kirkpatrick-Baez mirrors to a spot about 150 nanometres across, giving an on-target intensity on the order of 10¹⁹ watts per square centimetre. The Kα₁ photons emitted along the beam are selected by a silicon (220) analyser crystal and counted on a two-dimensional detector. Every shot thus produces a pair of numbers — energy in, amplified photons out — and the population of those pairs is compared against three-dimensional Maxwell-Bloch simulations run for Gaussian pump pulses of 100 attoseconds, 400 attoseconds and 1 femtosecond.

Two results come out. A simple threshold argument — combining the threshold pulse energy for ASE measured here, about 1.5 microjoules, with copper's previously measured ASE threshold intensity of about 2 × 10¹⁹ watts per square centimetre — gives a duration of roughly 300 attoseconds. The full comparison with the simulations gives a range: shot-to-shot durations between about 100 and 400 attoseconds, with the shortest shots at the 100-attosecond end of the simulated set.

It is worth being precise about the limits of this, because the paper is.

The measurement is indirect and model-dependent. It does not record a temporal profile; it records a photon yield and infers a duration by comparing that yield against simulated pulses of assumed Gaussian shape. A pulse with substructure — a few spikes rather than one smooth envelope — could in principle produce a similar yield, and the method would report an effective duration rather than describing the spikes.

Photon statistics bite at the interesting end. Below about 2 microjoules of pulse energy the amplified signal is only a few photons per shot, so the confidence intervals widen just where the pulses are most likely to be short, and the data in that regime are consistent with durations as long as 1 femtosecond for some shots. And the copper core-hole lifetime, the very thing that makes the technique work, also sets its floor: a clock whose tick is 400 attoseconds cannot resolve an event much shorter than about 50 attoseconds, and below that the method returns an upper bound rather than a value.

None of this undermines the result. The claim being made is that hard X-ray pulses at this facility are a few hundred attoseconds long, and the data support it. The claim being carefully not made is that any individual shot has been characterised.

The scientific motivation is the one attosecond science has always had, moved into a photon energy range where it can reach the electrons that matter.

Hard X-rays penetrate. They reach core levels of heavier elements, they diffract from crystal lattices, and they pass through sample environments — pressure cells, liquid jets, dense plasmas — that are opaque to soft X-rays. Doing attosecond physics at 9 keV means doing it on core-level dynamics in real materials rather than on valence electrons in dilute gases.

The second motivation is damage, and it is the one most likely to change how experiments are designed. An intense X-ray pulse destroys what it measures: it ionises the sample, the ions begin to move, and the structure recorded in the scattered signal is the structure of something already coming apart. Making the pulse shorter than the damage process is the standard answer, and at a few hundred attoseconds the pulse is shorter than almost anything the sample can do in response — including the Auger cascade that starts the destruction.

For plasma physics the appeal is similar. Hot dense plasmas are a mess of overlapping, rapidly evolving states, and conventional probes average over the evolution.

One number in this experiment deserves more attention from optical engineers than it usually gets: 150 nanometres.

An attosecond pulse carrying a microjoule is not, by itself, enough to drive copper into population inversion. The intensity has to be of order 10¹⁹ W/cm², and the only way to get there from a microjoule is to put the energy into a very small spot. At 9 keV that means grazing-incidence reflective optics — the refractive index of every material differs from unity by only about one part in a hundred thousand, so a single refractive surface has almost no power, and even the stacked compound refractive lenses used elsewhere on hard X-ray beamlines cannot combine this numerical aperture with acceptable transmission — and the mirrors that do it are among the most demanding optical surfaces made anywhere: elliptical in figure, held to height errors of a couple of nanometres and slope errors of a few tens of nanoradians, because at grazing incidence the beam's footprint is stretched by the reciprocal of the grazing angle, so that accuracy has to be maintained over a mirror hundreds of millimetres long.

Advanced Kirkpatrick-Baez configurations, which use four mirrors rather than two, exist precisely to beat the aberrations that limit the simpler arrangement at high numerical aperture. The headline here is an accelerator result and an atomic-physics measurement, but neither works without an X-ray mirror system delivering a sub-200-nanometre focus with enough stability to sit on the same spot of foil for thousands of shots. The attosecond pulse was made by the undulator. The intensity was made by the optics.

Before 20 October, hard X-ray attosecond pulses were a capability the facility believed it had. Now they are a capability it can demonstrate, with a number and an error bar and a method that any FEL with a nanofocusing beamline and a metal foil can repeat. That matters more than it sounds, because beam time is allocated on proposals, and a proposal that depends on a pulse duration nobody has measured is a weaker proposal than one that depends on a published measurement.

It also hands the field a working diagnostic rather than a one-off result. The copper foil is not a special apparatus; it is a target, an analyser crystal and a detector, and the physics it exploits — a core-hole lifetime comparable to the pulse duration — is available in any 3d transition metal, with the lifetime tuning the sensitive range. The honest limitation is that the diagnostic is destructive of the measurement's own simplicity: it needs the nanofocus, it needs good photon statistics, and it returns an inferred duration rather than a profile. A single-shot, non-invasive hard X-ray attosecond diagnostic is still missing.

What has arrived is the proof that the pulses are real, and with it a specific target for the people who build X-ray optics: shorter is now established, and the next constraint on what these pulses can do is how tightly, and how reproducibly, anyone can focus them.