Abstract

The purpose of this paper is to show that a Free Electron Laser (FEL) can be operated in x-ray region (2-3 Ångstroms) provided that suitable machine parameters can be realized. The main problem appears to be in the optics of the system. Are there mirrors that can reflect x-rays with reflectivities greater than 90%? We have investigated the reflectivity properties of silicon perfect crystals Bragg diffracting x-rays at θ = 90°, using dynamical theory of x-ray diffraction. Our analyses show that, for example, the (422) reflection has a reflectivity greater than 91% at 90°, over an angular range of 5.0 minutes of arc, at λ = 2.217 Å. The mirrors can be bent into spherical shapes without loss of reflectivity. For a FEL oscillator to work in the 2 - 3 Å region, the undulator should have a period of 2 cm., a magnetic field of 0.2 T, an electron energy between 3.0 and 3.5 GeV, with a spread ΔE/E less than 10⁻³, for an undulator 6 m long, with 300 periods. The emittance ε should be kept below 2 × 10⁻⁹ m-rad. A gain g_o = 0.215 can be obtained^1-2 at λ = 2.5 Å with a current I_O = 0.5 Å in one bunch, and an accelerating voltage of 4 MV, with a harmonic number equal to 1000. The power available from such x-ray FEL should be 250 watts,² on average, with a peak value of 4 × 10⁶ watts. Alternate schemes based on ring geometry will also be discussed.

© 1983 Optical Society of America