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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.
n beam to
Gran Sasso
SPS
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.
Calibration principle
The speed of the particles c, where c is the speed of light,
can be related to the revolution frequency frev and the
corresponding RF frequency fRF through
The speed pc of the proton beam is related to its momentum P, the
main parameter of interest, and its rest mass mp by
2
P
(  p c)  2
P  (m p c) 2
2
Cf
  Cf rev  RF
h
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.
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 ic of the ions is given by
2
P
( i c)  2
2
P  (mi c / Z )
2
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:
mi

Zmp
p
f
2 1)
RF
P  m pc
(

p
i )
2( f RF
 f RF
(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 !!
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)
Tidal distortions
Central frequency for protons and lead ions (Pb53+)
Hor. tune
The effect of local gravity
changes due to Earth tides
on the circumference is
well known from the LEP
machine.
Hor. tune
Vert. tune
Vert. tune
The change of circumference / central RF frequency is
proportional to the change in gravity, for the SPS :
Df [Hz]  (3.1 0.2) Dg[m / s2 ]
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
Central RF frequency difference Pb53+-p :
Df = 6194.3  1.6 Hz
Df = 6200.4  2.7 Hz
Horizontal chrom. scan
Vertical chrom. scan
Pb53+ was used
instead of Pb82+ to
increase Df
Local gravity change due
to Earth tides between
October 17th and 24th
2002
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 :
p = 449.18  0.16 GeV
(error dominated by H/V difference)
Machine circumference :
C = 6’911.566  0.002 m
C = 6’911.504 m
 R = 1100.0099  0.0004 m
 R = 1100.0000 m
The momentum
is –0.18% lower than the
nominal value of 450
GeV/c.
measured
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