McMillan electron lens in a system with space charge

Abstract

Space charge (SC) forces of a circulating beam in a ring have both linear (defocusing) and nonlinear components, due to a nonuniform beam distribution. The linear component of SC forces produces a betatron tune shift, which is the largest for a zero-amplitude particle, while the nonlinear component produces an amplitude-dependent betatron tune spread. These SC effects are responsible for several undesirable phenomena in accelerators: emittance growth, particle losses, beam halo, etc. In this paper, we investigate the possibility to mitigate the distributed SC forces by a thin McMillan lens, providing an axially-symmetric kick, which is qualitatively opposite to the accumulated effect of beam's own SC. Experimentally, the proposed concept can be tested in Fermilab's IOTA ring. A thin McMillan lens can be implemented by a short (70) insertion of an electron beam with a specifically chosen density distribution in transverse directions. In this article, to test if McMillan lenses can reduce the tune spread induced by SC, we make several simulations with a 6-D particle tracking code, Synergia. We choose such beam and lattice parameters that the SC tune spread is roughly 0.5 and the emittance growth due to the half-integer resonance is clearly observed without the SC compensation. Then, we focus on reducing the emittance growth by adjusting the bare betatron tunes using the ring quadrupoles, and reducing the tune spread by the McMillan lenses. The results of reducing a large tune spread (≈ 0.5), reported here, are not perfect, but substantial. There is still room for further investigation. The simulations performed so far indicate that McMillan lenses can cope with an SC tune spread of ≈ 0.1 per lens.