Resonance Compensation Raymond WASEF S.Gilardoni, A.Huschauer, D.Schoerling Acknowledgments M.Delrieux, J.C.Dumont, H.Genoud, C.Hernalsteens and all PS operators 19/03/131PS-LIU

Current situation A. Huschauer Operation area 19/03/132 To overcome space charge limitations there are two possibilities:  Reduce the tune-spread of the beam (large dispersion optics, flat bunches…etc.)  Increase the available space in the tune diagram (resonance compensation) PS-LIU

19/03/133 2D calculation including Gaussian distribution of the position of the coils and the shape of the iron with up to 22 DOFs per magnet (OPERA) 1000 models per magnet type and current level have to be calculated Performed for momentum of 2.14 GeV/c, 2.78 GeV/c, 14 GeV/c, 26 GeV/c Coils can be displaced, no rotation: Main coils (2 x 4 DOFs),  = 3 mm F8 (2 x 4 DOFs),  = 1 mm PFW (2 x 2 DOFs),  = 0.7 mm Iron is displaced in y-direction,  = 0.02/3 mm Daniel Schoerling Statistical analysis (Opera) PS-LIU

Including magnetic error 19/03/134 In MAD the main magnets are divided in 4 elements 2D & 2F  400 elements Magnetic errors have been implemented in the lattice up to the octupolar terms (normal & skew). They have been introduced as a Gaussian distribution, each element has been given a random number (400 numbers per multipolar field error) Using these distributions, one can estimate the driving terms of the different resonances with PTC. F F F F D D D D PS-LIU

Previous compensation scheme 19/03/135 In 80’s there were several compensation schemes using normal and skew sextupoles in the PS (sections 2, 52, 14, 64). The air-cooled sextupole magnets have been installed in the winter shutdown in sections 2, 52, 14, 72 (instead of 64) Using the new locations and the error distribution, a compensation scheme for each of the resonances 2Qx+Qy=19 and 3Qy=19 PS-LIU

6 Scan direction Compensation of 2Qx+Qy=19 A. Huschauer 19/03/13PS-LIU

7 Scan direction Compensation of 3Qy=19 A. Huschauer 19/03/13PS-LIU

Transverse profile for 3Qy compensation 19/03/138 Horizontal profileVertical profile Measurements done after a ramp over Qy[6.3=>6.38] and Qx=6.2. The vertical profile develops heavy tails without correction. Both profiles are close to a Gaussian with the correction PS-LIU

Conclusion & future steps 19/03/139 The compensation of 2 different betatronic resonances has been successful The 4Qy=19 is excited (by space charge) A study of the effects of the distribution on the compensation has to be done The magnetic error estimation has to be optimized since the phase- space deformation due to these errors is not enough to create losses PS-LIU