Space charge (SC) in a circulating beam in a ring produces both betatron tune shift and betatron tune spread. These effects make some particles move on to a machine resonance and become unstable. Linear elements of beam optics cannot reduce the tune spread induced by SC because of its intrinsic nonlinear nature. We investigate the possibility to mitigate it by a thin McMillan lens providing a nonlinear axially symmetric kick, which is qualitatively opposite to the accumulated kick by SC.

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... entally, the proposed concept can be tested in Fermilab's IOTA ring. A thin McMillan lens can be implemented by a short (70 cm) insertion of an electron beam with specifically chosen density distribution in transverse directions. In this article, to see if McMillan lenses reduce the tune spread induced by SC, we make several simulations with particle tracking code Synergia. We choose such beam and lattice parameters that tune spread is roughly 0.5 and a beam instability due to the half-integer resonance 0.5 is observed. Then, we try to reduce emittance growth by shifting betatron tunes by adjusting quadrupoles and reducing the tune spread by McMillan lenses.