Proposed is an enhancement of laser radiative cooling by utilizing laser pulses of small spatial and temporal dimensions, which interact only with a fraction of an electron bunch circulating in a storage ring. The dynamics of such electron bunch when laser photons scatter off the electrons at a collision point placed in a section with nonzero dispersion is studied. In this case of 'asymmetric cooling', the stationary energy spread is much smaller than under conditions of regular scattering where the laser spot size is larger than the electron beam; and the synchrotron oscillations are damped faster. Results of extensive simulations are presented for the performance optimization of Compton gamma-ray sources and damping rings.
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