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There is a large interest in the production of high power, ultra-short, one femtoseconds or less, coherent X-ray pulses, for atomic physics and other applications. However the present design of X-ray SASE FELs leads to an X-ray pulse about 100 times longer. Several methods to reduce the bunch length to the 10-1 fs region have been proposed. These methods are based on electron bunch manipulation to cut the lasing part of the bunch to a fraction of the total length, thus reducing the X-ray pulse length. We are considering here a different method, using ultra-short, very low charge electron bunches, with a length of the order or shorter than the FEL cooperation length. In this case the X-ray pulse length after amplification in the undulator is a few times the electron bunch length. Our simulations show that in an LCLS-like case we can obtain coherent, Fourier transform limited, X-ray pulses, consisting of a single spike, with a FWHM of about 0.1 um, corresponding to about 300 as, a peak power of about 5 GW, and an intensity of about 10 uJ.
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