E ects of Focusing on Radiation Damping and QuantumExcitation in Electron Storage Rings

In this Letter we calculate the eeects of a linearly varying focusing eld on radiation damping and quantum excitation in an electron storage ring using a quantum mechanical perturbation approach. This model correctly predicts the limits of pure bending and pure focusing. We nd that quantum excitation can be exponentially suppressed by the focusing eld when the radiation formation length is comparable to the transverse oscillation wavelength. This new result on quantum excitation may have interesting applications in the generation of ultra-low emittance beams.