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Corrections - b3

As long as we don't go correcting for other effects with the b3 spool pieces the change during decay is approx. the SB amplitude

SB

delta b3 ~ 1.8 units gives around 2.7 deltaQ'/second - whichh if we mop up 80% with the model leaves 0.55 units/s

1.7 units gives +71 Q'H and - 64 Q'V

 

 

 

Pre-series dipoles: decay ~+1.7 units    +71/-64 Q'h/Q'v

Luca's offering 0.6 total with linear model   0.41 from power cycle variations   -   24%

 

 

b3 and chromaticity

Use MCS - sextupole spool pieces correctors in MBA and MBB

Nominal field 0.471 T at 17 mm, magnetic length 0.11 m, I nominal = 550 A,

Inductance per magnet 0.8 mH, Inductance of 154 magnet circuit 132.2 mH

Maximum family size 154 magnets per string, in fact 154 magnets per arc per aperture

Nominal field .471 T at 17 mm, therefore nominal gradient 3259.5 T/m^2

Remember not designed to correct chromaticity, rather chromaticity split arising from b3 error. b3 of -3.3 gives -138 Q'H, +127Q'V)

Excel - courtesy Freddy Bordry

Sextupole spool pieces

RCS

16 circuits

beam 1 and beam 2 ; one per arc => 16 circuits

Each circuit: 154 magnets in series

Converter

600

Imax (A) �

10

Umax (Volt)

Lcircuit

0.123

H

Rcircuit

0.0083

Ohm

Ucollision

4.98

V

Note : Rcircuit = 4.2 mOhm for 2 circuits in UA43 ; not a big change

Time_constant

14.82

s

f open_loop_B

0.0107

Hz

10.7

mHz

Large signal

dI/dtmax

41

A/s

Umax/Ucollision

2.0

= f closed_loop_B/ f open_loop_B

Sext

f closed_loop_B

0.022

Hz

21.6

mHz

tr

16

s

Small signal

f closed_loop_B

1

Hz

Uavailable/Ucollision

93

Uavailable

5.02

V

(= Ummax - Ucollision)

Ustat

0.054

V

54

mV

DI

6.5

A

1.1

% of Imax