---
title: "How a free-electron laser gathers electrons into a brighter beam"
description: "Light changes electron energies, then electrons gather into tiny groups that amplify the light. Delayed X-ray pulses can follow a sample as it changes."
canonical_url: "https://sandboxphysics.com/stories/instruments/xray-free-electron-laser/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/instruments/xray-free-electron-laser/"
last_modified: "2026-11-13"
---

[How physics instruments measure](https://sandboxphysics.com/stories/instruments/)

# How a free-electron laser gathers electrons into a brighter beam

Send fast electrons through alternating magnetic poles and they wiggle gently as they emit X-rays. If the light can also rearrange the electrons, later electrons can strengthen the wave already passing through them. This interaction drives a free-electron laser.

Sandbox Physics · 2026-11-13

## A wave changes how electrons advance

The magnets make each electron follow a shallow wavy path. Light travels forward and gradually overtakes it. A suitable combination of magnet spacing, electron energy and wavelength lets the electron meet a similar part of the wave at successive magnetic periods. This is resonance.

The electric field gives energy to some electrons and takes energy from others, according to where they meet the wave. An initially almost uniform electron distribution develops a repeating energy variation. The static magnetic field bends trajectories; the light field exchanges energy with the electrons.

Slightly different energies produce slightly different rates of forward advance. Some electrons catch their neighbours and others fall behind. Energy variations turn into alternating dense and sparse regions, spaced roughly one light wavelength apart. This is microbunching. Each tiny group is much smaller than the whole electron bunch supplied by the accelerator.

Sources: [1] [2]

## The groups give energy to the light

Radiation from randomly arranged electrons partly cancels. Once the tiny groups form, more electrons can reinforce the same wave. Stronger light changes their energies and positions further, so amplification continues along the magnets.

The added radiation energy comes from electron kinetic energy. Eventually the energy loss changes the resonant condition. Electrons move back and forth relative to the wave, and growth slows toward saturation.

Sources: [1] [2]

## The first light can come from a seed or from noise

A weak X-ray seed at a suitable wavelength can enter with the electron bunch. The beam then amplifies that supplied wave. A visible or infrared pump pulse used later at the sample follows a separate path and has a different job.

Amplification can also start from spontaneous radiation. A finite number of electrons has small fluctuations in its arrangement. Some of the resulting light grows through self-amplified spontaneous emission, or SASE. Its starting fluctuations differ between pulses. A smooth average intensity curve can hide the temporal structure of an individual pulse.

Sources: [1] [2]

## Delay one pulse to watch a sample change

In a pump–probe experiment, one pulse excites a sample and an X-ray pulse measures what happens afterwards, for example through a change in transmission. Repeating the measurement at different arrival intervals builds a picture of the evolving sample.

A moving mirror lengthens the optical pump path. In a double-pass delay stage, moving the carriage by one distance adds twice that distance to the route. The pump arrives later. An X-ray pulse that previously crossed an excited sample can then cross before excitation.

Relative arrival times also fluctuate between shots. A timing diagnostic splits off a little of each beam and compares them at a film. X-rays change its optical transmission, leaving a bright-to-dark transition in the optical image. Tilted geometry assigns different positions to different relative times. Known delays calibrate that mapping before an individual exposure is read.

Sources: [3]

## Read the sample response together with the pulse

Each transmission reading combines the finite pump pulse, the X-ray pulse and the sample response. A broad transition might reflect slow recovery, a broad illuminating pulse or both. Photon number and detector gain affect the reading too. Reference exposures before and after the unknown help distinguish these contributions.

Timing-pixel spacing sets a sampling interval. Film response, optical blur and electronic noise determine how much fine structure survives. A known fast-response reference tests the complete measurement chain. The data must distinguish a recovery time before that time can be assigned to an unknown sample.

Sources: [3]

## [Follow microbunching into a pump–probe measurement](https://sandboxphysics.com/labs/xray-free-electron-laser/)

Compare short, long and detuned seeded gain, then move the delay stage and inspect per-shot timing and transmission.

A finite one-dimensional seeded source and a calibrated weak-absorber model, with a separate short unseeded startup comparison.

## Sources and further reading

1. [Huang & Kim · Review of x-ray free-electron laser theory (2007)](https://doi.org/10.1103/PhysRevSTAB.10.034801)

   Read the review and SLAC-PUB-12262 author manuscript, Section II on resonance and microbunching and Section III on one-dimensional gain. Model documentation states the phase and field normalization separately.

2. [European XFEL · How it works](https://www.xfel.eu/facility/overview/how_it_works/index_eng.html)

   Read the descriptions of electron bunches, alternating magnets, microbunching and SASE; facility performance figures are not inputs to the teaching model.

3. [SLAC LCLS · MEC laser characteristics and timing diagnostics](https://lcls.slac.stanford.edu/instruments/mec/laser-characteristics)

   Read the per-shot diagnostics, X-ray-induced window shadow, tilted timing window and target-plane timing checks. The teaching film response and pixel pitch are separately supplied and calibrated. Checked 13 November 2026.

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atomic spacing](https://sandboxphysics.com/stories/instruments/powder-xray-diffractometer/) [How Small-Angle X-ray Scattering Reads a Particle Halo](https://sandboxphysics.com/stories/instruments/small-angle-xray-scattering/) [Why X-ray fluorescence depends on sample thickness](https://sandboxphysics.com/stories/instruments/xray-fluorescence-spectrometer/) [Why an AFM makes a bump look wider](https://sandboxphysics.com/stories/instruments/atomic-force-microscope/) [How a small indentation separates hardness from elasticity](https://sandboxphysics.com/stories/instruments/nanoindenter/) [How Differential Scanning Calorimetry Reads a Melting Peak](https://sandboxphysics.com/stories/instruments/differential-scanning-calorimeter/) [How thermogravimetry separates mass loss from the gas around it](https://sandboxphysics.com/stories/instruments/thermogravimetric-analyzer/) [How a diamond anvil cell reads pressure in ruby 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## Keep reading

How physics instruments measure · Reading path

### How physics instruments measure

1. [Article **How a vernier reads between millimetres**](https://sandboxphysics.com/stories/instruments/length-metrology/)
2. [Article **Air helps hold up the object on a balance**](https://sandboxphysics.com/stories/instruments/precision-balance/)
3. [Article **How Cavendish Measured the Attraction Between Spheres**](https://sandboxphysics.com/stories/instruments/cavendish-balance/)
4. [Article **Which pressure does a liquid column measure?**](https://sandboxphysics.com/stories/instruments/manometer/)
5. [Article **The cup absorbs heat too**](https://sandboxphysics.com/stories/instruments/calorimeter/)
6. [Article **Rotational rheometers need both torque and speed**](https://sandboxphysics.com/stories/instruments/rotational-rheometer/)
7. [Article **Why the air beyond a pipe changes its resonance**](https://sandboxphysics.com/stories/instruments/resonance-tube/)
8. [Article **How a seismometer reads the ground through motion inside its case**](https://sandboxphysics.com/stories/instruments/seismometer/)
9. [Article **Why does a meter change the circuit?**](https://sandboxphysics.com/stories/instruments/electrical-meters/)
10. [Article **How a null detector reveals a resistance**](https://sandboxphysics.com/stories/instruments/resistance-bridges/)
11. [Article **Why a capacitor can behave like an inductor**](https://sandboxphysics.com/stories/instruments/lcr-impedance/)
12. [Article **Where does the slow wave on an oscilloscope come from?**](https://sandboxphysics.com/stories/instruments/digital-oscilloscope/)
13. [Article **How a lock-in amplifier finds a signal buried in noise**](https://sandboxphysics.com/stories/instruments/lock-in-amplifier/)
14. [Article **Where a small peak in a spectrum can come from**](https://sandboxphysics.com/stories/instruments/spectrum-analyzer/)
15. [Article **How a network analyzer separates the cable from the device**](https://sandboxphysics.com/stories/instruments/vector-network-analyzer/)
16. [Article **When a slower quartz crystal can measure added mass**](https://sandboxphysics.com/stories/instruments/quartz-microbalance/)
17. [Article **How an echelle spectrograph gives overlapping colors a second direction**](https://sandboxphysics.com/stories/instruments/echelle-spectrograph/)
18. [Article **How total brightness reveals many infrared colors**](https://sandboxphysics.com/stories/instruments/ftir-spectrometer/)
19. [Article **Measuring a Solution’s Concentration with Light**](https://sandboxphysics.com/stories/instruments/uv-vis-spectrophotometer/)
20. [Article **How an ellipsometer reads thin-film thickness from reflected light**](https://sandboxphysics.com/stories/instruments/spectroscopic-ellipsometer/)
21. [Article **How a polarimeter reveals mixed polarization**](https://sandboxphysics.com/stories/instruments/mueller-polarimeter/)
22. [Article **How individual photons reveal a fluorescence lifetime**](https://sandboxphysics.com/stories/instruments/tcspc-fluorescence-lifetime/)
23. [Article **Brillouin Microscopy Listens to Sound with Light**](https://sandboxphysics.com/stories/instruments/brillouin-microscope/)
24. [Article **How a white sphere compares a lamp’s total output**](https://sandboxphysics.com/stories/instruments/integrating-sphere-radiometer/)
25. [Article **How powder rings reveal atomic spacing**](https://sandboxphysics.com/stories/instruments/powder-xray-diffractometer/)
26. [Article **How Small-Angle X-ray Scattering Reads a Particle Halo**](https://sandboxphysics.com/stories/instruments/small-angle-xray-scattering/)
27. [Article **Why X-ray fluorescence depends on sample thickness**](https://sandboxphysics.com/stories/instruments/xray-fluorescence-spectrometer/)
28. [Article **Why an AFM makes a bump look wider**](https://sandboxphysics.com/stories/instruments/atomic-force-microscope/)
29. [Article **How a small indentation separates hardness from elasticity**](https://sandboxphysics.com/stories/instruments/nanoindenter/)
30. [Article **How Differential Scanning Calorimetry Reads a Melting Peak**](https://sandboxphysics.com/stories/instruments/differential-scanning-calorimeter/)
31. [Article **How thermogravimetry separates mass loss from the gas around it**](https://sandboxphysics.com/stories/instruments/thermogravimetric-analyzer/)
32. [Article **How a diamond anvil cell reads pressure in ruby light**](https://sandboxphysics.com/stories/instruments/diamond-anvil-cell/)
33. [Article **How diamond fluorescence reveals a magnetic-field direction**](https://sandboxphysics.com/stories/instruments/nv-center-magnetometer/)
34. [Article **Reading a magnetic field in the rhythm of atoms**](https://sandboxphysics.com/stories/instruments/optically-pumped-magnetometer/)
35. [Article **Keeping a laser in time with atoms**](https://sandboxphysics.com/stories/instruments/optical-lattice-clock/)
36. [Article **Why a Kibble balance needs two experiments**](https://sandboxphysics.com/stories/instruments/kibble-balance/)
37. [Article **How a dilution refrigerator keeps carrying heat away**](https://sandboxphysics.com/stories/instruments/dilution-refrigerator/)
38. [Article **Why a bigger vacuum pump may barely help the sample**](https://sandboxphysics.com/stories/instruments/ultra-high-vacuum-system/)
39. [Article **How microwaves read a superconducting qubit**](https://sandboxphysics.com/stories/instruments/superconducting-qubit-readout/)
40. [Article **How current leaves a voltage across a thin sheet**](https://sandboxphysics.com/stories/instruments/four-probe-hall/)
41. [Article **How an ion flight becomes a mass spectrum**](https://sandboxphysics.com/stories/instruments/time-of-flight-mass-spectrometer/)
42. [Article **How four straight rods select ion mass**](https://sandboxphysics.com/stories/instruments/quadrupole-mass-filter/)
43. [Article **How a rapidly reversing field can hold ions**](https://sandboxphysics.com/stories/instruments/paul-ion-trap-mass-spectrometer/)
44. [Article **How a cyclotron keeps a proton on the accelerating beat**](https://sandboxphysics.com/stories/instruments/cyclotron-synchrocyclotron/)
45. [Article **Why the drift tubes in an RF linac get longer**](https://sandboxphysics.com/stories/instruments/radio-frequency-linac/)
46. [Article **The directions hidden inside a small beam spot**](https://sandboxphysics.com/stories/instruments/beam-diagnostics/)
47. [Article **How defocusing magnets help a beam stay in a ring**](https://sandboxphysics.com/stories/instruments/synchrotron-storage-ring/)
48. [Article **Why a collider cannot keep every collision**](https://sandboxphysics.com/stories/instruments/collider-trigger-daq/)
49. [Article **Getting synchrotron light onto a sample**](https://sandboxphysics.com/stories/instruments/synchrotron-beamline/)
50. [You are here **How a free-electron laser gathers electrons into a brighter beam**](https://sandboxphysics.com/stories/instruments/xray-free-electron-laser/)
51. [Article **Following energy exchange with neutron flight times**](https://sandboxphysics.com/stories/instruments/pulsed-neutron-time-of-flight/)