Ideas on space charge tuneshift compensation using multipoles

Ideas on space charge tune-shift compensation using multi-poles n Analytical expression for space charge tune-shift ¨ 2 D expression by E. Keil, ISR-TH/72 -7 (1972) ¨ 3 D extension by M. Martini, PAC 1993, using series of elliptic integrals ¨ 2 D expression by E. Metral and F. Ruggiero, CERN-AB-2004 -067 (2004) for parabolic distribution ¨ Similar 1 D expression derived for the incoherent beam-beam tune spread using Bessel functions (Y. Papaphilippou and F. Zimmermann, PRSTAB-5, 2002) ¨ Approximate expression derived by expanding the exponential in power series (see A. Hoffman in CAS 1994). 21/12/2006 PS 2 Meeting, Y. Papaphilippou 1

Ideas on space charge tune-shift compensation using multi-poles (cont. ) n Remarks ¨ Influence of octupoles in Landau damping stability diagrams already studied by E. Metral and F. Ruggiero ¨ Octupoles used in SNS mostly for Landau Damping (not strong enough for space charge tune-shift compensation) n Work to be done ¨ Analytical expressions for other distributions and comparison among different analytical formulas ¨Compute the PS octupole strengths needed for compensating the incoherent tune spread (try other multipoles) ¨Simulate the combined effect using ACCSIM, ORBIT at PS injection ¨As octupoles are not placed symmetrically around the PS, resonance may be excited leading to beam loss ¨ Try the compensation in machine experiments in the PS 21/12/2006 PS 2 Meeting, Y. Papaphilippou 2