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Free Electron Lasers are based on Synchroton coherent radiation when a collimated electron beam suffers trajectory curvature due to a strong bouncing magnetic field inside an undulator.

Free Electron Lasers are currently being built that will produce coherent beams of X-ray laser light.

Since these lasers do not rely on any specific nature-given discrete transition, the question that i have is:

Can a Free Electron Laser be built to create gamma-ray laser light?

if not, why not. If yes, how bigger would have to be the Linear accelerator and the undulator? what are the figures of relevance?

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I am posting this since it is too long for comments and it starts on the way to gamma ray FEL.

It seems that they have managed at SLAC up to X-ray wavelengths.The facility is called LCLS, (Linac Coheren Light Source).

The LCLS uses the final third of SLAC's two-mile linear accelerator to drive electrons to high energy and through an array of "undulator" magnets that steer the electrons rapidly back and forth, generating a brilliant beam of coordinated X-rays. In last week's milestone, LCLS scientists used only 12 of an eventual 33 undulator magnets to generate the facility's first laser light.

On the operations and energies achieved:

At present, the available photon energy range is 480 eV up to about 9.5 keV. The photon energy is set by adjusting the linac electron energy, by switching off or adding klystrons. Such an energy adjustment also requires that the excitation currents in the various bending and focusing magnets be rescaled in order to maintain their electron bending angles and focal lengths.

From a preview while the facility was under construction:

The LCLS pulls its energy from electrons accelerated in the final kilometer of the SLAC linac. The 14 GeV electron beam is so powerful that the LCLS requires less than 0.1% of the linac's energy to create 10 billion watts in X-rays.

We start talking of gammas when the electromagnetic energy goes to MeV, nuclear energies and over. If you read the links it is not a small achievement to have reached these hard X-rays. Particularly the design of the undulators :

The Linac Coherent Light Source (LCLS) undulator line will consist of 33 undulator segments separated bybreaks of various lengths. The undulator segments are 3.4-m-long permanent-magnet planar hybrid arrays with a period of 30 mm and a magnetic gap of 6 mm.The maximumoutside dimension of the vacuumchamber is 5.6 mm.

and the accuracies required of the electron beam

The electron beam trajectory is required to be straight to within a few microns over a distance of ~10 m to achieve adequate overlap of the electron and photon beams

leads me to estimate that raising the energies of the electrons by a factor of 100 to reach an MeV will be a hard exercise. I will also guess that the 30mm periods and the 6mm gaps for the magnet arrays would also scale to smaller scales, presenting a non soluble problem, unless one uses ferromagnetic crystals printed on special boards or something like that.

I was intrigued by your question though I have not answered it really.

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You have mentioned the two key challenges here for building a free electron laser with high photon energy in your answer: Either the energy of the electrons propagating through the undulators must be very high, or the period of the magnetic structure of the undulator must be very short. A gamma-ray FEL is in principle possible, but these two technological challenges are severe... – josteinb May 20 '13 at 12:08

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