1. E. Benedetto, 29/04/14, OP Shutdown Lecture, Res. Compensation in the PSB Resonance compensation in the PS Booster (1 st part) E. Benedetto + M. McAteer (2 nd part) BE/ABP Presentation based on: old reports by K. Schindl et 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. E. Benedetto, 29/04/14, OP Shutdown Lectures, Res. Compensation in the PSB 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. E. Benedetto, 29/04/14, OP Shutdown Lectures, Res. Compensation in the PSB 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. E. Benedetto, 29/04/14, OP Shutdown Lectures, Res. Compensation in the PSB 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 (3 rd 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 A bit of history…

5. E. Benedetto, 29/04/14, OP Shutdown Lectures, Res. Compensation in the PSB The situation before LS1 (realignment)

6. E. Benedetto, 29/04/14, OP Shutdown Lectures, Res. Compensation in the PSB The situation before LS1 (realignment)

7. E. Benedetto, 29/04/14, OP Shutdown Lectures, Res. Compensation in the PSB Correctors in the PSB Steerers (dipolar errors, i.e. COD) QNO, QSK (quadrupolar normal/skew) XNO, XSK (3 rd order normal/skew) ONO, OSK (4 th order, not used) Harmonic correctors: – ONOHO Landau Damping (not used), – XNOHO chromaticity (used in MDs), – QSKHO Coupling

8. E. Benedetto, 29/04/14, OP Shutdown Lectures, Res. Compensation in the PSB Correctors in the PSB

9. E. Benedetto, 29/04/14, OP Shutdown Lectures, Res. Compensation in the PSB Correctors in the PSB

10. E. Benedetto, 29/04/14, OP Shutdown Lectures, Res. Compensation in the PSB Correctors in the PSB The same unit combines different correctors (x4 rings) e.g. sitting in 11L4 e.g. sitting in 12L1

11. E. Benedetto, 29/04/14, OP Shutdown Lectures, Res. Compensation in the PSB 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. E. Benedetto, 29/04/14, OP Shutdown Lectures, Res. Compensation in the PSB 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: 90 o +k*180 o (k integer) with respect to the harmonic p considered E.g. to compensate a dipole error (COD) – 2 steerers located at 90 o +k*180 o w.r.t. each other provide an orthogonal set To compensate a field error: – 2 QNOs located at 45 o +k*90 o etc… for higher order

13. E. Benedetto, 29/04/14, OP Shutdown Lectures, Res. Compensation in the PSB Resonance compensation Quadrupolar error (half integer line, Qy=4.5) Normal quadrupoles QNOs QNO4 and QNO8 are located at  =Qy/4=1.125 (x 2  = 45 o +k90 o )  OK! QNO4L3 QNO8L3 + + QNO16L3 QNO12L3 - - Actually…QNO412L3, QNO816L3: – Powered in series QNO4-QNO12 and QNO8-16 – Opposite polarities – WHY? –  =4.5/2=2.25 (x 2  = 90 o +k90 o i.e. 180 o 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): –  =4.0/2=2.0 (x 2  = 0 o i.e. 360 o with respect to p=2) as they have opposite polarity, the effect on the integer line cancel out

14. E. Benedetto, 29/04/14, OP Shutdown Lectures, Res. Compensation in the PSB Summary Qualitative considerations Example on how to compensate one single line (2 nd 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