A method capable of producing femtosecond pulses of synchrotron radiat
ion is proposed. It is based on the interaction of femtosecond light p
ulses with electrons in a storage ring. The application of the method
to the generation of ultrashort x-ray pulses at the Advanced Light Sou
rce of Lawrence Berkeley National Laboratory has been considered. The
same method can also be used for extraction of electrons from a storag
e ring in ultrashort series of microbunches spaced by the periodicity
of light wavelength.