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Figure 2
Why are the emitted wavelengths in the X-ray range? Relativity provides the answer. (a) The relativistic electron approaches the periodic B-field of the undulator. (b) In the electron reference frame the undulator period L is Lorentz-contracted to L/γ and the B-field is accompanied by a transverse E-field perpendicular to it: the two fields resemble an electromagnetic wave. (c) This wave stimulates the electron to oscillate and emit waves of equal wavelength. (d) The (relativistic) Doppler effect further reduces the wavelength in the laboratory frame, bringing it to the X-ray range.

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