1. FCC ramp – first stab Mike Lamont

2. I’(t) = 0 to avoid a voltage discontinuity “it has been shown that if I’(t) is kept low at the end of the snapback, the bandwidth of the control system required to dynamically correct this error can be substantially reduced.” Parabolic 25-11-14 FCC ramp From before beam…

3. the magnetic field error produced by inter-strand coupling current (and by other types of eddy currents) is proportional to the ramp rate B’ (t). Therefore, at a constant ramp rate the relative field error i cpl b is highest at low fields. The magnitude of this error can be optimized to be constant if the magnetic field ramp function B(t) is an exponential while ramping in such a way that with Exponential (from PN172) 25-11-14 FCC ramp In fact:.. negligible for all harmonics

4. Linear – dictated by MB maximum ramp rate of 10 A/s Plus parabolic round off Linear & parabolic round-off 25-11-14 FCC ramp

5. Snuggly fit the bits together FCC ramp 25-11-14

6. Snapback FCC ramp 25-11-14 Bottura & Sammut – Cham XIV

7. Ramp parameterization FCC ramp 25-11-14

8. Snap-back snap-back fit:  b 3 [1-(I-I inj )/  I] 3  b3= 3.7units  I = 27A   B = 19 mT snap-back decay 25-11-14 FCC ramp Luca Bottura

9. 25-11-14 FCC ramp Snapback – Q’ Fit snapback: I(t) – MB current at time t I injection – injection value of current  b 3 and  I are fitting constants  b 3 and  I are correlated Sextupole compensation during snap-back in collaboration with FNAL – Luca Bottura

10. 24.01.06 Field Model 10 Geometric MDC Saturation Residual

11. 1545 – no corrections(t) FCC ramp 25-11-14 Tune modulation up ramp

12. 1580: QPH correction 25-11-14 FCC ramp Faster ramp, faster snapback - less well compensated by model

13. Naked versus correction 25-11-14 FCC ramp

14. Cf. FCC FCC ramp 25-11-14 ΔI sb didt end snapback B@end exp alphaLength Ramp [s] design200.635.9e-61095 2012121.21.67.9e-5653 FCC204.51.63.3e-4156 alphaTime for 20 Adidt@20A [A/s] Design5.9e-6 20127.9e-5 FCC1.6e-48.94.5

15. 2012 FCC ramp 25-11-14

16. FCC – ramp rate 50 A/s to 3.5 TeV FCC ramp 25-11-14

17. delta current/ramp rate : 103.022 Current exp max 2740. Alpha = 0.000333059 para length = 54.0444 Current end para 1499.33 dI/dt at end para 27.36 20 amps over by 8.9 seconds dI/dt at 20 A: 4.5 Exponential length 33 Current end exponential 2740. deltaLinearCurrent 2854.31 Linear length 57.0862 Length round off 11.8 Total length [s] = 156 Total length [mins] = 2.6 FCC parameters – first stab 25-11-14 FCC ramp

18. Staying with PELP, can compress snapback in time with a more aggressive start  Example shown has it down to around 9 s  To give a total length of around 160 s  Compare with around 105 s linear (of course not possible) Might worry about:  b3(t) correction with spool pieces  Ability to accurately measure Q’  Bandwidth of tune feedback  Other systems – RF… Given parameters – can actually measure it with beam – would be interesting to see it it scales as expected Conclusions 25-11-14 FCC ramp