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We propose using a radio frequency quadrupole (RFQ) to introduce both the longitudinal spread of betatron frequency and the transverse spread of synchrotron frequency for Landau damping of transverse beam instabilities in accelerators. The existing theory of stability diagrams for Landau damping is applied to the case of a RFQ. As an example, the required quadrupolar strength is calculated for stabilizing the Large Hadron Collider beams at 7 TeV. It is shown that this strength can be provided by a superconducting rf device only a few meters long.