Free-Electron X-ray Lasers

Peak Brightness, a Billion Times Over

The flashes of an X-ray free-electron laser reach about a billion times the peak brightness of the best conventional X-ray sources, the synchrotrons; in average brightness the European XFEL is about 10,000 times ahead. Each flash lasts a few to about 100 femtoseconds, at a peak power of 10⁠–⁠100 gigawatts, with wavelengths down to about 0.05 nm.

It is not a laser in the usual sense: no mirrors and no laser crystal. What shines is a beam of electrons wiggling between magnets, and the light is amplified by many orders of magnitude in a single pass. The model follows the European XFEL’s layout: injector, superconducting linac, undulator and experiment hutch, with the kilometres of tunnel between them left out.

peak brightness about 10⁹ × the best synchrotrons · a few to about 100 fs

The Machines

The first hard X-ray free-electron laser was SLAC’s LCLS: on 10 April 2009, using the last third of SLAC’s two-mile copper linac to drive electrons to 13.6 GeV, it lased at 1.5 Å, 120 pulses a second. Its superconducting upgrade, LCLS-II (4 GeV), made its first X-rays in 2023 and reached about 93,000 pulses a second in December 2025.

Japan’s SACLA (first lasing June 2011) and Switzerland’s SwissFEL (inaugurated December 2016) took another route: shorter undulator periods (18 and 15 mm) and C-band copper accelerating structures, in facilities about 700 m and 740 m long, at 8 and 5.8 GeV. The European XFEL spends 3.4 km on a superconducting linac: up to 17.5 GeV and up to 27,000 pulses a second.

3.4 km · 17.5 GeV (European XFEL) · about 700 m · 8 GeV (SACLA) · 740 m · 5.8 GeV (SwissFEL)

Light Knocks Out Electrons

It all starts at a small cathode. The European XFEL’s gun is a copper resonator of one and a half cells with a caesium telluride cathode in its back wall. A laser (1047 nm, converted to ultraviolet in two stages) strikes the cathode and frees a bunch of electrons, and the cavity’s 1.3 GHz field pushes them away at once. A coil round the gun, the solenoid, holds the bunch together with its magnetic field.

The charge of a bunch can be set from 20 to 1000 pC. The LCLS cathode is copper; SACLA uses no laser at all but a thermionic gun.

caesium telluride cathode · ultraviolet laser · 20⁠–⁠1000 pC a bunch

Superconducting Cavities

The European XFEL’s accelerator lies in a tunnel about 2 km long (1.7 km of it accelerates): 96 modules hang from the tunnel ceiling, each holding eight nine-cell niobium cavities, 768 in all. The cavities sit in superfluid helium at 2 K (−271 °C), where niobium is superconducting and the microwaves lose very little in its walls. Microwaves at 1.3 GHz ring in them, and as an electron crosses each cell, that cell’s field is pushing it forward.

The cavities’ design gradient is 23.6 MV per metre. The electrons reach up to 17.5 GeV (user runs mostly use 14 GeV); then γ is about 34,000 and they are slower than light by only 4.3 × 10⁻¹⁰, 13 cm a second. On the floor under the modules stand the klystrons, pulse transformers and racks: one 10 MW klystron feeds four modules, 32 cavities.

96 modules · 768 niobium cavities · 2 K · up to 17.5 GeV

Squeezing the Bunch

Before compression a bunch is long and thin: at LCLS its peak current is only 33 A. The fix is a bunch compressor: four bending magnets send the electrons sideways and back, round a detour. The linac leaves the bunch’s tail a little higher in energy than its head; higher-energy electrons bend less and take the shorter path, so the tail catches up, the bunch gets shorter and the current higher.

LCLS used two stages in 2009: 33 A to 250 A, then to 3,000 A, a compression of about 90. The European XFEL has three, which split its linac into L1, L2 and L3: peak currents of 3⁠–⁠5 kA and bunches 3 to 150 fs long after compression.

33 A → 250 A → 3,000 A (LCLS, 2009) · 3⁠–⁠5 kA (European XFEL)

Magnets Make Them Wiggle

An undulator is two rows of permanent magnets, one above the beam and one below, their poles alternating. The electrons are pushed from side to side and follow a tiny slalom, sending a little light forward at every bend. The European XFEL’s SASE1 and SASE2 each have 35 undulator segments 5 m long with a 40 mm period; the 1.1 m between segments hold quadrupoles, phase shifters and beam position monitors.

The wavelength follows the undulator equation: λ = λu / 2γ² · (1 + K² / 2), where λu is the magnets’ period and K is set by the field (K = 0.934 · B[T] · λu[cm]). The period is centimetres, but γ² is around a billion, so out come X-rays of a fraction of a nanometre: 0.147 nm at 17.5 GeV and K = 3.9.

λ = λu/2γ² · (1 + K²/2) · 40 mm period · 35 × 5 m

Electrons Line Up

At first the electrons are scattered at random in the bunch, their light out of step and weak. The light is faster than the electrons and gains one wavelength on them every magnet period; on the way it speeds some electrons up and slows others down. The electrons gather into thin slices one wavelength apart; the electrons in a slice shine in step, the light grows, and the slices sharpen further.

This is self-amplified spontaneous emission, SASE: it starts from the electrons’ own shot noise, the power grows exponentially with distance and saturates after about 20 gain lengths. At LCLS the gain length is about 3.5 m and saturation comes at about 60 m; at the European XFEL, at 9.3 keV, about 100 m. Hence undulators more than 100 m long.

shot noise → exponential growth → saturation after about 20 gain lengths

A Few Femtoseconds

Each flash lasts a few to about 100 fs, at 10⁠–⁠100 GW peak; at the European XFEL a flash carries up to about 2 mJ (7⁠–⁠14 keV). The price of starting from noise is that no two flashes are alike: each is a cluster of spikes in time and in spectrum, and its energy varies from flash to flash.

The European XFEL’s superconducting linac can accelerate up to 2,700 bunches, 222 ns apart, in one 600 µs radio-frequency pulse; ten times a second, that is up to 27,000 pulses a second. A distribution system sends bunches to different undulator lines, so several experiments run at once.

10 trains a second × up to 2,700 · 222 ns apart

Cut Open: the Module

A module cut open: innermost, eight nine-cell niobium cavities, each about 1 m (1.038 m active), with 70 mm irises, each in its own helium tank full of superfluid helium. The wide pipe above is the helium gas return pipe; outside it, the insulation; outermost, the vacuum vessel. At the end sit a superconducting quadrupole and a beam position monitor.

Why 2 K: niobium’s losses fall exponentially with temperature, and only at 1.8⁠–⁠2 K do high gradients and very high quality factors come together; superfluid helium also conducts heat superbly. Each cavity has its own power coupler to a waveguide; twelve modules, cooled as one string, are the linac’s unit of installation.

8 cavities + quadrupole + beam position monitor · superfluid helium at 2 K

The Gap Sets the Wavelength

The undulator’s two rows of magnets sit on two girders that four spindles move apart or together. The European XFEL’s 40 mm undulators work at gaps of 10⁠–⁠20 mm, measured to about ±1 µm. A wider gap means a weaker field, a smaller K and a shorter wavelength: K = 3.9 at 10 mm, 1.65 at 20 mm.

So, without touching the electron energy, the gap alone changes the wavelength: at 17.5 GeV, from 0.147 nm down to 0.040 nm. The magnets are permanent and need no current: the European XFEL’s are planar hybrid (magnets and poles), LCLS’s neodymium-iron-boron magnets with vanadium permendur poles.

10 mm → K 3.9 · 20 mm → K 1.65 · 0.147⁠–⁠0.040 nm (17.5 GeV)

Diffract Before Destroy

In the experiment hutch the X-rays are focused onto a thin liquid jet carrying tiny protein crystals. Every flash destroys the sample it hits, but if the flash is short enough, the diffraction pattern is recorded before the sample is visibly damaged. Computer simulations proposed the idea in 2000.

In 2011 LCLS collected more than 3 million diffraction patterns from nanocrystals of photosystem I (about 200 nm to 2 µm), with pulses of 10, 70 and 200 fs, at doses of up to 700 MGy a flash, where conventional experiments tolerate about 30 MGy. In 2018 the European XFEL did the same at a 1.1 MHz pace: a jet 1.8 µm across, moving at 50⁠–⁠100 m/s, blown apart and back in less than 1 µs, in time for the next pulse.

over 3,000,000 patterns (2011) · 1.8 µm jet · 1.1 MHz (2018)

Molecular Movies

An ordinary laser pulse starts a reaction, and an X-ray flash arrives a precise time later: pump and probe. Change the delay, put the snapshots in order, and you have a movie of molecules moving. In photoactive yellow protein the chromophore turns from trans to cis between 100 fs and 3 ps after the light (LCLS, 2016); in myoglobin, once the iron–carbon-monoxide bond breaks, the whole protein moves within 500 fs (2015).

Timing is the hard part: in the 2016 experiment the jitter between laser and X-rays was about 280 fs, longer than the process itself, so a timing tool measured every pulse and the patterns were sorted after. In 2018 every stable intermediate of photosystem II’s water-splitting cycle was resolved at 2.04⁠–⁠2.08 Å.

pump → wait Δt → X-rays · 100 fs–3 ps (photoactive yellow protein)

Costs and Limits

Big and costly: the European XFEL’s tunnels lie 6⁠–⁠38 m underground, it cost about €1.22 billion (2005 prices) and runs on about €140 million a year; LCLS cost about $420 million, LCLS-II about $1.1 billion, SwissFEL about CHF 275 million. Superconducting does not mean free of power: it needs a 2 K helium plant and klystrons of 10 MW peak each.

Noisy and scarce: SASE starts from noise, so every flash differs in time, spectrum and energy; self-seeding, shown at LCLS in 2012, narrows the bandwidth 40⁠–⁠50 times. The electrons’ arrival time jitters by about 20⁠–⁠30 fs. A machine has only a few stations: the European XFEL’s first call drew 63 proposals and granted 14. Damage has not gone away: by the end of a 100 fs pulse every atom in a crystal has, on average, been ionized once.

about €1.22 billion (2005 prices) · 2 K cryogenics · 20⁠–⁠30 fs jitter · 14 of 63 proposals

Taken Apart

The gun, the drive laser, the bunch compressor, the module’s vessel and its cavity string, the RF station, the undulator, the intersection, the bending magnet and dump, the focusing tank, the sample chamber, the detector and the pump laser’s table, one by one.

Rest the pointer on a part (tap it on a phone) and it lifts out alone, named, while the rest fades.