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

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.

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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]