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6 Longitudinal Space Charge The longitudinal space charge forces on the beam can also affect the beam size at extraction and hence, the extraction efficiency. Given the difficulty of accurately evaluating the effects of the longitudinal space charge force, two different approximations were employed to estimate the induced energy spread and consequently the effect on turn separation at extraction. The first approach was to use a formula by Werner Joho11 that provides an estimate of the total accelerating voltage spread caused by the longitudinal space charge force.
6 B. F. 3", TRI-DN-99-4,January 28, 1999. 7 B. Franzke, Vacuum Requirements for Heavy Ion Synchrotrons, IEEE Trans. on Nuc. Sci. 3, (1981) 2116. 8 N. Bohr and J. Lindhard, Dan. Mat. Fys. Medd. 28, no. 7 (1954). D. Betz and Ch. Schmelzer, UNILAC 1-67 (1967). D. Betz, G. Hortig, E. Leischner, Ch. Schmelzer, B. Stadler, and J. Weihrauch, Phys. Lett. 22 No. 5 (1966)643 11 W. Joho, “High Intensity Problems in Cyclotrons”, 9th Int. Conference on Cyclotrons, p337, Caen, France 1981. M. Gordon, “The longitudinal space charge effect and energy resolution”, 5th Intl.
Three stripper locations will be required to strip all ions to a Q/A ≈ 1/3 though each beam will be stripped only once. The longitudinal dynamics are well matched to the Separated Sector Cyclotron requirements. Separated Sector Cyclotron A high-efficiency system to inject beam from the linac into the Separated Sector Cyclotron has been described. 1% would provide no limitations on the fragment intensities and that this range was achievable for the Separated Sector Cyclotron. A vacuum of ≈10-7 torr was found to provide adequate transmission with the power loss estimated to be only ≈170 W under this condition.