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Free-electron laser : ウィキペディア英語版
Free-electron laser

A free-electron laser (FEL), is a type of laser that uses very-high-speed electrons that move freely through a magnetic structure, hence the term ''free electron'' as the lasing medium.〔(【引用サイトリンク】 url=https://www.jlab.org/free-electron-laser )〕 The free-electron laser has the widest frequency range of any laser type, and can be widely tunable,〔F. J. Duarte (Ed.), ''Tunable Lasers Handbook'' (Academic, New York, 1995) Chapter 9.〕 currently ranging in wavelength from microwaves, through terahertz radiation and infrared, to the visible spectrum, ultraviolet, and X-ray.
The term free-electron lasers was coined by John Madey in 1976 at Stanford University.〔Hans Motz, W. Thon, R.N. Whitehurst, Experiments on radiation by fast electron beams, ''Journal of Applied Physics'', 24(7):826-833, 1953.〕 The work emanates from research done by Hans Motz and his coworkers, who built an undulator at Stanford in 1953, using the wiggler magnetic configuration which is the heart of a free electron laser. Madey used a 43-MeV electron beam and 5 m long wiggler to amplify a signal.
== Beam creation ==

To create an FEL, a beam of electrons is accelerated to almost the speed of light. The beam passes through an undulator, a side to side magnetic field produced by a periodic arrangement of magnets with alternating poles across the beam path. The direction of the beam is called the longitudinal direction, while the direction across the beam path is called transverse. This array of magnets is called an undulator or a wiggler, because it forces the electrons in the beam to wiggle transversely along a sinusoidal path about the axis of the undulator.
The transverse acceleration of the electrons across this path results in the release of photons (synchrotron radiation), which are monochromatic but still incoherent,
because the electromagnetic waves from randomly distributed electrons interfere constructively and destructively in time, and the resulting radiation power scales linearly with the number of electrons. If an external laser is provided or if the synchrotron radiation becomes sufficiently strong, the transverse electric field of the radiation beam interacts with the transverse electron current created by the sinusoidal wiggling motion, causing some electrons to gain and others to lose energy to the optical field via the ponderomotive force.
This energy modulation evolves into electron density (current) modulations with a period of one optical wavelength. The electrons are thus clumped, called ''microbunches'', separated by one optical wavelength along the axis. Whereas conventional undulators would cause the electrons to radiate independently, the radiation emitted by the bunched electrons are in phase, and the fields add together coherently.
The FEL radiation intensity grows, causing additional microbunching of the electrons, which continue to radiate in phase with each other. This process continues until the electrons are completely microbunched and the radiation reaches a saturated power several orders of magnitude higher than that of the undulator radiation.
The wavelength of the radiation emitted can be readily tuned by adjusting the energy of the electron beam or the magnetic-field strength of the undulators.
FELs are relativistic machines. The wavelength of the emitted radiation, \lambda_r, is given by
: \lambda_r = \frac(1+K^2) ,
or when the wiggler strength parameter K, discussed below, is small
: \lambda_r \propto \frac ,
where \lambda_u is the undulator wavelength (the spatial period of the magnetic field), \gamma is the relativistic Lorentz factor and the proportionality constant depends on the undulator geometry and is of the order of 1.
This formula can be understood as a combination of two relativistic effects. Imagine you are sitting on an electron passing through the undulator. Due to Lorentz contraction the undulator is shortened by a \gamma factor and the electron experiences much shorter undulator wavelength \lambda_u/\gamma. However, the radiation emitted at this wavelength is observed in the laboratory frame of reference and the relativistic Doppler effect brings the second \gamma factor to the above formula. Rigorous derivation from Maxwell's equations gives the divisor of 2 and the proportionality constant. In an x-ray FEL the typical undulator wavelength of 1 cm is transformed to x-ray wavelengths on the order of 1 nm by \gamma ≈ 2000, i.e. the electrons have to travel with the speed of 0.9999998''c''.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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