1. LHC Momentum in 2008
J. Wenninger
December 2008

2. Injection Test No. 1
SPS momentum set to Pnom,SPS = 450 GeV which corresponds to GeV (calibrated with ions in 2002).
Synchronization test 8-11 August:
Sector 23 offset : -33 units with Pnom,SPS = 450 GeV
Sector 23 offset : -7.3 units with Pnom,SPS = 451 GeV
>> Obtained a difference of 0.26%, expected 0.22%
>> PSPS = Pnom,SPS = 451 GeV
LHC : fRF,LHC = 400'788'790 Hz
SPS : fRF,SPS = fRF,LHC /2 = 200'394'395 Hz
SPS central frequency (2002) fc,SPS = 200'394'215 Hz (+- 70 Hz)
>> fRF,SPS – fc,SPS = 144 Hz >> Delta E = % = -3.9 units
>> ES23 = x (S23 traj) x (central f SPS) = GeV

3. 10th September first turn offsets
LHC fRF,LHC = 400'788‘790 Hz ??
Average offsets b1-b2 differ only by ~ 0.01% = 1 units.
Statistically consistent…

4. 12th September closed orbit
LHC fRF,cap,LHC = 400'788'963 Hz
LHC theoretical fRF,nom-LHC = 400'788‘734 Hz
Average energy offset of CO : % = 9.4 units.
Ft offset consistent with CO within %.
>> Why did it change with respect to 10th ?

5. FT and CO
b1 & b2 FT dp/p offsets on Sept 10th are consistent / show no significant difference.
dp/p = -4 units
fRF,LHC = 400'788'790 Hz (??)
b2 CO dp/p offsets on Sept 12th :
dp/p = -9.4 units
FT seems well centered on CO, i.e. similar shift as CO within 1 unit.
fRF,LHC = 400'788‘963 Hz
>> The RF frequency difference of 173 Hz (wrt 10th) can explain a shift of the FT of -2.2 units due to the energy change in the SPS. Is the remaining shift of -2 to -3 units due to LHC ?
>> A shift of -119 Hz is required to center b2 on the CO:
fRF,LHC = 400'788‘884 Hz
>> The SPS field must be increased by 8 units to re-center FT.
Beam2 data

6. Central orbits – b2
To center the beam2 closed orbit and compensate for the radial offset (-9.4 units):
The b2 central frequency (central = ~ centered in the BPMs) :
LHC fRF,c,b2 = 400'788‘884 Hz
>> 150 Hz higher than design : Ring 2 radius is 1.6 mm smaller than nominal.
>> Note that the SPS radius is 1 cm larger than nominal.
The corresponding SPS extraction frequency is:
SPS fRF,ext = LHC fRF,c,b2 /2 = 200‘394’442 Hz
To be compared with the SPS central frequency (central ~ centered in sextupoles, ):
SPS fRF,c = 200’394’ Hz
>> SPS fRF,ext - fRF,c = Hz
>> Offset of -0.5 permill
>> SPS radial position shifted inwards by -2 mm - OK