FCC ramp – first stab Mike Lamont

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 FCC ramp From before beam…

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) FCC ramp In fact:.. negligible for all harmonics

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

Snuggly fit the bits together FCC ramp

Snapback FCC ramp Bottura & Sammut – Cham XIV

Ramp parameterization FCC ramp

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

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

Field Model 10 Geometric MDC Saturation Residual

1545 – no corrections(t) FCC ramp Tune modulation up ramp

1580: QPH correction FCC ramp Faster ramp, faster snapback - less well compensated by model

Naked versus correction FCC ramp

Cf. FCC FCC ramp ΔI sb didt end snapback exp alphaLength Ramp [s] design e e-5653 FCC e-4156 alphaTime for 20 [A/s] Design5.9e e-5 FCC1.6e

2012 FCC ramp

FCC – ramp rate 50 A/s to 3.5 TeV FCC ramp

delta current/ramp rate : Current exp max Alpha = para length = Current end para dI/dt at end para amps over by 8.9 seconds dI/dt at 20 A: 4.5 Exponential length 33 Current end exponential deltaLinearCurrent Linear length Length round off 11.8 Total length [s] = 156 Total length [mins] = 2.6 FCC parameters – first stab FCC ramp

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 FCC ramp