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Free-electron lasers are devices which use the motion of highly energetic electron beams to produce bright, coherent radiation in the x-ray regime. More specifically, they start with a high-energy electron beam and feed it into an undulator, which is an array of alternating magnetic fields designed to make the electron beam move in a 'zigzag' path with sharp turns on either side, emitting synchrotron radiation during each turn.

The radiation thus produced is added up over successive turns, and it is produced coherently via self-amplified spontaneous emission.

One common question frequently posed of this setup is: is this actually a laser? That is, does it have population inversion, and is the radiation actually emitted via stimulated emission in some suitable understanding of it? People in the know tend to answer in the affirmative, but I've yet to see a nice explanation of why - and definitely not online. So: do FELs actually lase?

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I think you are making a very good point there. The usual theory of FELs is classical or semi-classical, at most. I tried to find a paper with a proper QFT treatment just now and struck out. I do believe to remember that someone had published such a model for channeling, which, I believe, should be similar. If I may wave a giant foam hand... could it be that a full treatment will give rise to an electron-photon quasiparticle state that may have a discrete spectrum with population inversion, after all? – CuriousOne Jan 7 at 3:30
@user1717828: All lasers are tunable to a certain degree by adjusting the resonator. The laser medium is merely an amplifier, albeit a narrow bandwidth one for many types of laser materials, but the actual wavelengths in the beam are set by the resonator (and more often than not it's more than one for spectrally uncontrolled devices). This is no different for free electron lasers and it is not what causes the conceptual problem here. – CuriousOne Jan 7 at 5:51
I understand that the electrons would radiate Bremsstrahlung in any case so that one cannot actually talk of stimulated emission. The interaction between x-rays and electrons seems to achieve x-ray monochromaticity and coherence (by eliminating all but a narrow band of electron speeds and micro bunching) but does not actually stimulate emission. So it's more a LAMER (light amplification by modulated emission of radiation). – Peter A. Schneider Jan 7 at 11:04
Here is an online explanation:… – DarioP Jan 7 at 13:44
+1 for verbing new words. – Federico Poloni Jan 7 at 14:47
up vote 10 down vote accepted

You are missing a crucial aspect of the dynamics of a Free Electron Laser: microbunching. This comes from the fact that although electrons at different energies share basically the same velocity $c$, they have different oscillation amplitudes in the undulator, therefore they shift longitudinally.

Since you mentioned the SASE mechanism let me expand around it: the noise in the initial electron distribution will guarantee you some peaks which will start to radiate coherently (the power going with $N^2$). As the radiation slips through the bunch (remember that photons go straight, while electrons are wiggled) it exchanges energy with it, triggering energy modulations. But, as we saw before, these result in a longitudinal shift therefore we get additional density modulations at the radiation wavelength.

The result is that your initially long bunch slowly splits in a number of very short (micro) bunches, all of them radiating coherently, with a great boost of the radiation intensity gain. Of course the microbunching can not continue endlessly, indeed it comes to saturation, where the dynamics becomes strongly non linear and the gain is stopped.

While microbunching develops, the radiation increases up to saturation.

Therefore for sure you have light amplification by stimulated emission of radiation: the initial radiation stimulates microbunching leading to even more radiation, obviously this is not the standard interpretation of atomic physics, but in common English it fits perfectly. The population inversion might be seen it in the microbunching factor: the initial, more or less uniform, beam is completely "inverted", while, as long as the microbunching develops this is lost up to the saturation.

For some read up (and also source of the nice picture): (use the menu on the left)

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Very good that you point out microbunching as essential part of the FEL process. Note that "stimulated emission" is a fixed technical term describing the preferred emission into highly populated bosonic states and therefore the FEL does not do stimulated emission. – Neuneck Jan 7 at 11:52
@Neuneck It seems pretty natural to me that there cannot be bosonic states within a bunch of free electrons. If you look in this way, the name FEL is itself a contradiction. Instead I think that it is appropriate both for the fact that from few photons in you get a huge number of photons out, and for the properties of the resulting radiation. You just need to stretch a bit the definitions to embrace the different mechanisms. – DarioP Jan 7 at 13:35

FELs produce a coherent, monochromatic, intense light beam that can be collimated with an iris (basically a hole in a large lead block).

An optical cavity can be arranged by putting two mirrors around the undulators, spaced so each pass of the electrons constructively interferes (go here and click Watch a Movie on How HIGS Works to see a movie demonstrating the Duke FEL doing something like this, with an added Compton backscatter).

Is this stimulated emission in the atomic physics sense? No. Does it produce a beam of light so similar to a laser than it can be classified as such? Most physicists I've interacted with say yes.

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I believe that they would not be allowed to be called lasers if the laser experts did not feel comfortable calling them that, but do you have any source to the last paragraph? – Mindwin Jan 7 at 11:53
@Mindwin I'm a physicist. All the physicists and engineers I've worked with (and we've worked with lasers and FELs) have no problem lumping FELs in with lasers. The output is certainly stimulated even tho' it's not stimulated emission :-) . – Carl Witthoft Jan 7 at 15:45
@Mindwin, I only have the same answer as Carl: every physicist I know treats FEL facilities as laser facilities. See page 63 here for an "anecdotal corroboration", but that shouldn't really ease your concerns without actually visiting a laser lab yourself. – user1717828 Jan 7 at 15:50
@CarlWitthoft exactly what I was trying to say. If the laser experts call FEL "laser", who am I to disagree? – Mindwin Jan 7 at 17:11

If you use "population inversion" as an essential part of the definition of what a laser is, then you're right it's not a laser. But that doesn't deny that the properties of light can be just light from any "laser." So, this is a bit of semantics issue, and less about the physics.

Some other "non-laser" coherent light sources: Optical Parametric Oscillator, laser without inversion, etc

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So basically what you're saying is: yes, the light is a laser light but no, the device is not a laser :D – slebetman Jan 7 at 8:43
I can take any light source and convert its light output into a laser-like output. similiarly I can take a laser device and change its light output to appear non-laser like. So what I'm saying is the properties of light aren't necessarily attributable to their sources – JQK Jan 7 at 22:22

Although the initial meaning of laser came from Light Amplification by Stimulated Emission of Radiation, the current "common" meaning of laser comes from coherent light being laser light and therefore, anything that produces coherent light, is a laser. So, do FEL lase? No, are they lasers? Yes.

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Starlight is coherent by the time in reaches earth. Are stars lasers? – JQK Jan 13 at 23:36

A free-electron laser (FEL) is a parametric amplifier, which operates by transferring energy to the output signal (photon pulse) from an oscillator (electron bunch running down a long undulator magnet). An electron bunch is accelerated to relativistic energies and sent through a periodic magnetic structure (undulator) where transverse oscillations and interference produce synchrotron radiation enhanced at specific wavelengths. The intensity of this radiation scales with the number of electrons in the bunch. Photons co-propagate with the relativistic electrons and if the undulator is long enough, induce significant energy modulation in the electron bunch, leading to a periodic density modulation of the electron cloud (microbunching). The resulting microbunches behave like giant charged particles, and emit photons proportional to the square of their total charge at wavelengths longer than the bunch length. So a free-electron laser is not a laser in the usual meaning of the acronym but a parametric amplifier that produces coherent radiation pulses.

Note that because of the need for microbunching for an FEL to operate, there is no FEL that can produce truly continuous photon beams as a function of time today.

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