Titlebook: Space Charge Physics for Particle Accelerators; Ingo Hofmann Book 2017 The Author(s) 2017 Space charge models.Vlasov-Poisson equations.Wea

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Matched Beams,defined initial “matched beam” solution. In constant focusing this could be a wide class of time-independent distribution functions of the Hamiltonian, which has to include the self-consistent space charge potential with its shielding properties. In periodic focusing a matched beam is ideally a solu

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Beam Mismatch and Halo,tors. However, discontinuities in focusing geometry, rf frequency or phase etc. are often inevitable sources of mismatch, which result in emittance growth, beam halo and loss. This chapter discusses some basic aspects of the role of rms mismatch with regards to beam halo. Interpreting mismatch and h

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Vlasov and Envelope Analysis,alled distribution by Kapchinskij and Vladimirskij. This chapter introduces the required linearization – with emphasis on 2D beams. The role of rms envelope models as second order approximations, often sufficient for layout and first order design of accelerator lattices, but insufficient in the presence of nonlinear forces, is also discussed.