By Gawronski W., Shawyer B. L., Trautner R.
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Extra resources for A Banach space version of Okada's theorem on summability of power series
03%) . The particles are tracked from the injection energy to the entrance of the deflector where their position is plotted. 5 Transverse Emittance From Figure 27, a turn separation of approximately 6 mm is achieved with most of the reduction in turn separation attributable to the extreme (± 15o) phase bunches. 8 π mm mrad normalized); this result is given in Figure 28. 28 Figure 28. 8 π mm mrad). From Figure 28, it was determined that after the inclusion of twice the transverse phase space, an rf voltage ripple, and an injection energy spread, there would be 5 mm separation between turns if the beam phase width is limited to ±10o in lieu of ±15 o.
5 mm; a negligible contribution to the turn broadening. 00 100 150 200 250 300 350 400 Figure 30. Radius difference between the particles with vertical (z) displacements and that of a particle that starts on the median plane. 6 π mm mrad were tracked. 8 Extraction Elements The extraction system will consist of the elements specified in Table 8. The SC (Superconducting) elements listed represent an inconsequential cryogenic load and should easily be accommodated by the cryogenic system required for the linac.
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. In this model, the total space charge voltage spread (Vsc) is given by: 2π N 2 VSC = 2800 < I > ∆φ β f Where is the average current, N is the turn number, ∆φ is the total phase width in rf degrees, and β f is the relativistic velocity at the final energy.