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TY - CONF AU - Mitchell, C.E. AU - Hwang, K. AU - Ryne, R.D. ED - Liu, Lin ED - Byrd, John M. ED - Neuenschwander, Regis T. ED - Picoreti, Renan ED - Schaa, Volker R. W. TI - Model of Curvature Effects Associated with Space Charge for Long Beams in Dipoles J2 - Proc. of IPAC2021, Campinas, SP, Brazil, 24-28 May 2021 CY - Campinas, SP, Brazil T2 - International Particle Accelerator Conference T3 - 12 LA - english AB - For modeling the dynamics within a dipole of a bunch whose length is much larger than the vacuum pipe radius, it is typical to use a 2D (or 2.5D) Poisson solver, with arc length taken as the independent variable. However, sampled at a fixed time, the beam is curved, space charge is not truly 2D, and the usual cancellation between E and B contributions to the Lorentz force need not exactly hold. The size of these effects is estimated using an idealized model of a uniform torus of charge rotating inside a toroidal conducting pipe. Simple expressions are provided for the correction of the electric and magnetic fields to first order in the reciprocal of the curvature radius. PB - JACoW Publishing CP - Geneva, Switzerland SP - 3217 EP - 3219 KW - space-charge KW - vacuum KW - dipole KW - emittance KW - shielding DA - 2021/08 PY - 2021 SN - 2673-5490 SN - 978-3-95450-214-1 DO - doi:10.18429/JACoW-IPAC2021-WEPAB249 UR - https://jacow.org/ipac2021/papers/wepab249.pdf ER -