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Resonance compensation in the PS Booster (1 st part)

Resonance compensation in the PS Booster (1 st part). E. Benedetto + M. McAteer (2 nd part) BE/ABP.

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Resonance compensation in the PS Booster (1 st part)

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  1. Resonance compensation in the PS Booster (1st part) E. Benedetto + M. McAteer (2nd part) BE/ABP • Presentation based on: old reports by K. Schindlet al. (available in EDMS), email exchanges between B. Mikulec & M. Chanel, S. Pittet, A. Newborough, PhD thesis of P. Urschutz, material from V. Forte, many discussion & coffees with C. Carli

  2. Outline First part (Elena): • Motivation • A bit of history… • Correctors in the PSB • Example: correcting the half integer line with QNOs Second part (Meghan): • Optics measurements for systematic resonance compensation

  3. Introduction • To reach high brightness and intensity beams, minimizing emittance blow-up and losses • Large space-charge tune footprint at injection • Touches many resonance lines • Not all of them are excited, but if so they need proper compensation • Compensation: • Empirical optimization w.r.t. losses (based on optics considerations) • From optics measurements, minimization of the resonance driving terms P. Urschutz, tune footprint evolution for high intensity beams, “low” working point

  4. A bit of history… • Resonance compensation done already in the late 70ies: • K. Schindl et al., ‘78,-’79 • Working Point was (4.26, 5.55) • Installation of a “new” extra set of multipoles in ’77 to allow simultaneous correction of more then one line (3rd order). • New campaign in 2003-2004 • P. Urschutz, PhD thesis • Measurements of resonance driving terms with turn-by-turn PUs (expert set-up) • Validated choice of moving WP to (4.26, 4.55) to avoid systematic 3Qv=16 • Optimization w.r.t. losses by M. Chanel and OP • Alignments (errors!) change during time, realignment campaign LS1… • Program of measurements (by Meghan) to build up an optics model for the PSB, will lead to a systematic resonance compensation scheme

  5. The situation before LS1 (realignment)

  6. The situation before LS1 (realignment)

  7. Correctors in the PSB • Steerers (dipolar errors, i.e. COD) • QNO, QSK(quadrupolar normal/skew) • XNO, XSK (3rd order normal/skew) • ONO, OSK (4th order, not used) • Harmonic correctors: • ONOHO Landau Damping (not used), • XNOHO chromaticity (used in MDs), • QSKHO Coupling

  8. Correctors in the PSB

  9. Correctors in the PSB

  10. Correctors in the PSB • The same unit combines different correctors (x4 rings) e.g. sitting in 12L1 e.g. sitting in 11L4

  11. Correctors in the PSB • Big improvement w.r.t. last years: • Connected to Acapulco power supplies (except ONOHO and XNOHO) • Controlled by FGC3 • Allow change of polarity in PPM and individual trimming

  12. Resonance compensation For compensating a particular resonance m Qx + n Qy = p, it is sufficient to have 2 lenses of the proper type, provided the betatron phase advance is near: 90o+k*180o(k integer) with respect to the harmonic p considered • E.g. to compensate a dipole error (COD) • 2 steerers located at 90o+k*180ow.r.t. each other provide an orthogonal set • To compensate a field error: • 2 QNOs located at 45o+k*90o • etc… for higher order

  13. Resonance compensation • Quadrupolar error (half integer line, Qy=4.5) • Normal quadrupoles QNOs • QNO4 and QNO8 are located at Dm=Qy/4=1.125 (x 2p = 45o +k90o)  OK! • Actually…QNO412L3, QNO816L3: • Powered in series QNO4-QNO12 and QNO8-16 • Opposite polarities • WHY? • Dm(4-12)=4.5/2=2.25 (x 2p = 90o +k90oi.e. 180o with respect to p=2) • as they have opposite polarity, the effect adds up • Being focusing & defocusing, no changes in the tune • Moreover, considering effect on the integer (Qv=4.0): • Dm(4-12)=4.0/2=2.0 (x 2p = 0o i.e. 360o with respect to p=2) as they have opposite polarity, the effect on the integer line cancel out + QNO8L3 - + QNO4L3 QNO12L3 QNO16L3 -

  14. Summary • Qualitative considerations • Example on how to compensate one single line (2nd order) • Compensation of one line leads to excitation of a second line • More than 2 lenses are needed • More complicated when moving to higher order and to several lines at the same time • More systematics measurements and knowledge of the optics model is needed  Meghan

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