  We report a detailed inelastic neutron scattering study of the collective
magnetic excitations of overdoped superconducting La1.78Sr0.22CuO4 for the
energy range 0-160 meV. Our measurements show that overdoping suppresses the
strong response present for optimally doped La2-xSrxCuO4 which is peaked near
50 meV. The remaining response is peaked at incommensurate wavevectors for all
energies investigated. We observe a strong high-frequency magnetic response for
E >= 80 meV suggesting that significant antiferromagnetic exchange couplings
persist well into the overdoped part of the cuprate phase diagram.
