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It is shown that the Lorentz forces of a low-energy, magnetically stabilized electron beam, or “electron lens”, can introduce transverse nonlinear focusing sufficient for Landau damping of transverse beam instabilities in accelerators. Unlike other nonlinear elements, the electron lens can provide the frequency spread mainly at the desirable range of particle amplitudes, thus permitting to avoid the beam lifetime degradation.

On Landau damping restoration with electron lenses in space-charge dominated beams