1. Energy Calibration of the SPS with Proton and Lead Ion Beams
  J. Wenninger, G. Arduini, C. Arimatea, T. Bohl, P. Collier, K. Cornelis (CERN, Geneva)
Introduction
Since the shutdown of LEP at the end of 2000, the SPS machine is
modified and adapted to its role as injector for the LHC collider.
As LHC injector, the SPS must deliver very bright beams with high
efficiency and without emittance degradation to both LHC rings.
The machine model is re-measured in details and as part of this
effort, the beam momentum at the extraction energy of 450 GeV/c
was calibrated in order to obtain the best possible initial energy
setting when the LHC will be commissioned.
n target
n beam to
Gran Sasso
SPS
Calibration principle
The speed bpc of the proton beam is related to its momentum P, the main parameter of interest, and its rest mass mp by
The speed of the particles bc, where c is the speed of light, can be related to the revolution frequency frev and the corresponding RF frequency fRF through
An ion beam of charge Z, injected into the same magnetic machine
and on the same orbit than the proton beam has a momentum
Pi= Z P. We define the proton equivalent momentum of
the ion as P = Pi/Z. The speed bic of the ions is given by
where h is the harmonic number of the RF system, h = 4620 for the SPS. C is the machine circumference. To determine the speed b and therefore the momentum, both C and frev must be known.
To determine momentum and machine circumference at the same time, frev is measured for two particles with different masses (or charge over mass ratio) that are injected into exactly the same magnetic machine and on the same orbits. In our case the measurements are performed for a proton and an lead ion beam.
The two equations can be solved for the proton beam momentum P:
(p = proton, i = ion)
Central RF frequency measurement technique
Horizontal chromaticity scans
The goal of the energy calibration is the determination of the beam momentum on the central orbit, where the beam is centered on
average in the machine quadrupoles. On this orbit the momentum is
entirely determined by the dipole field and the measurement of the
beam momentum under such conditions provides a calibration of the
integrated field of the main dipoles.
In practice the central RF frequency is determined by centering the beams in the machine sextupoles. For that RF frequency value, the transverse tune no longer depends on the setting of the chromaticity. For a sufficiently large number of sextupoles and a correct alignment of the sextupoles with respect to the quadrupoles, the beam should be centered in the sextupoles and quadrupoles at the same time. Systematic alignment effects can be probed by performing the measurement for the horizontal plane and for the vertical plane independently.
Hor. tune
Vertical
chromaticity scans
Ver. tune
In this example the central frequencies obtained by changing the horizontal and vertical chromaticity differ !!

2. Energy Calibration of the SPS with Proton and Lead Ion Beams
  J. Wenninger, G. Arduini, C. Arimatea, T. Bohl, P. Collier, K. Cornelis (CERN, Geneva)
Central frequency for protons and lead ions (Pb53+)
Tidal distortions
The effect of local gravity changes due to Earth tides on the circumference is well known from the LEP machine.
Hor. tune
Hor. tune
The change of circumference / central RF frequency is proportional to the change in gravity, for the SPS :
Vert. tune
Vert. tune
Horizontal and vertical chromaticity scans for proton and lead ion beams
Tidal corrections must be applied because the measurements were spread over a 48 hours period
Measurements
Gravity change
Pb53+ was used instead of Pb82+ to increase Df
Local gravity change due to Earth tides between October 17th and 24th 2002
Central RF frequency difference Pb53+-p :
Df =  1.6 Hz Horizontal chrom. scan
Df =  2.7 Hz Vertical chrom. scan
The difference between
H and V scans is 6.1  3.1 Hz
(corrected for tidal effects)
October 2002
Proton beam momentum
Momentum for proton beam :
The momentum
is –0.18% lower than the nominal value of 450 GeV/c.
p =  0.16 GeV (error dominated by H/V difference)
Machine circumference :
C = 6’  m  R =  m measured
C = 6’ m  R = m model
Systematic studies
The difference in central frequency between H and V corresponds to a difference in radial position between the two SPS sextupole families of:
DR = 0.8 mm at 450 GeV/c !!
This unexpected difference was studied, and was found to depend on the momentum, vanishing at injection energy.
A mechanical movement has been excluded, a possible source may be shifts of the magnetic center of the sextupole magnets.
Corresponds to a radial offset of 0.8 mm between sextupole families