Absolute Beam Energy Measurements
in
e
+
e
Storage Rings
M. Placidi
CERN, Geneva, Switzerland
Abstract
The CERN Large Electron Positron collider (LEP) has been dedi-
cated to the measurement of the mass M
Z
and the width
Z
of the
Z
0
resonance during the LEP1 phase terminated in September 1995. The
Storage Ring has b een operated in
Energy Scan
mode during the 1993
and 1995 physics runs bychoosing the b eam energy
E
beam
to correspond
to a CM energy at the IP's
E
peak
CM
1762 MeV. After a short review of
the techniques usually adopted to set and control the b eam energy this
paper describ es in more detail two methods adopted at LEP for precise
beam energy determination, essential to reduce the contribution to the
systematic error on M
Z
and
Z
. The positron beam momentum was ini-
tially determined at the 20 GeV injection energy by measuring the sp eed
of a less relativistic proton beam circulating on the same orbit, taking
advantage from the unique possibility of injecting the two beams into
LEP at short time intervals. The positron energy at the
Z
0
peak was in
this case derived by extrapolation. Once transverse p olarization b ecame
reproducibly available the Resonant Depolarization (
RD
) technique was
implemented at the
Z
0
operating energies providing a
2
10
5
in-
stantaneous accuracy.
RD
Beam Energy Calibration has been adopted
during the LEP Energy Scan campaigns as well as in Accelerator Physics
runs for accurate measurement of machine parameters.
INTRODUCTION
This pap er is intended to giveanoverview of the several techniques which
can provide information on the beam energy in Storage Rings and to account
for the asso ciated precisions.
Accurate knowledge of the beam energy is of relevantinterest in storage
rings dedicated to the measurement of the mass and the width of resonances.
Reducing the uncertainty on the energy scale improves the quality of the de-
termination of the resonance parameters since the energy information level
sets the standard for the systematic contribution to the global error. Besides
this specic issue on the energy scale calibration, the p ossibility of setting,
monitoring and controlling the nominal energy of the accelerator with a high
degree of reliability greatly improves the p erformance of the operation.
After a brief review of standard methods, which provide an energy informa-
tion essentially derived from the measurement of the magnetic eld in reference
magnets or in the ring dip oles, the paper describ es in detail more sophisticated
techniques based on direct measurements of specic properties of beams like
particle
velo city
and
p olarization
.
1
The rst metho d is based on the determination of the velocity of protons
on a sp ecic and repro ducible orbit through a measurement of their revolution
frequency. This provides the momentum p er unit charge associated to that
particular orbit which is the same for protons and leptons.
A second method, (
RD
), by far the most accurate, measures the spin pre-
cession frequency of a vertically polarized beam, directly related to the average
beam energy,by means of a controlled dep olarizing resonance.
Other techniques involving sp ecial detectors or dedicated experiments are
also accounted for to complete the review.
Experimental results from the 1995 LEP b eam energy calibration campaign
with
RD
are shown and eects resp onsible for changes in the CM energy at
the IP's during the physics runs are describ ed.
STANDARD TECHNIQUES FOR ENERGY MONITORING
The Integrating Coil
The usual method adopted to set the energy of a storage ring to some desired
levels consists in measuring the
integrated magnetic eld
R
Bds
in a Reference
Magnet powered in series with the main ring dipoles. The information from a
digital integrator connected to a long rotating coil properly positioned in the
gap provides a continuous measurementof
R
Bds
and is used as a reference for
the current-regulated control of the main power converters. This is particularly
important when the physics runs take place at energies dierent from the
injection one and a magnet-cycling procedure is applied to compensate for
hysteresis eects. The
R
Bds
information is also part of the log-in data set
provided at every ll to the experiments.
The reproducibility and the resolution of of this metho d referred to as
eld
display
(
FD
) (1) are in the range of
(20
30) ppm.
For the eld display to reproduce the situation represented by the dip oles
in the accelerator tunnel the reference magnet should obey two basic rules
i.e.
b eing structurally identical to the ring magnets and undergo the
same environmental history
.Temperature changes aect the nominal
value of
R
Bds
as they mo dify b oth the gap height and the length of the
dipole cores: the
FD
technique provides information on the global eect.
The presence of a long coil in the magnet gap and the associated instru-
mentation together with the need of access for maintenance discourage the
installation of the reference magnet in the tunnel itself, so the
FD
information
requires other calibration techniques to b e used as an absolute energy monitor.
This includes essentially
temperature
changes, although in the case of the LEP dip oles,
where the jokes are made of a mixture of steel laminations and concrete, other parameters
like the
local humidity
are important to be monitored and controlled.
2
The NMR Prob es
Nuclear Magnetic Resonance probes provide a very precise measurementof
the
local magnetic eld
down to a
10
6
accuracy. Their compact volume
allows for direct installation in the gap of the magnets with reduced interfer-
ence with the vacuum chamber which provides on line monitoring of the time
evolution of the dipolar eld.
NMR probes do not provide information on the variations of the magnetic
length with temperature and their use in a reference magnet should be asso-
ciated to adequate temp erature measurements in the accelerator tunnel.
The limitation of this information arises from the small number of sampled
dipoles which requires go od guarantees on the overall homogeneity both of the
magnetic properties of the cores and of their thermal behavior.
The LEP Flux-Lo op System
The LEP reference magnet, made from a stack of standard dip ole lamina-
tions, is installed in a temp erature-controlled environment and series-connected
with the main dip oles. Measurements of the integrated magnetic eld are car-
ried out with a ip coil mounted in the magnet gap along the p osition of the
central orbit.
The LEP dipoles have iron-concrete cores which undergo aging and are sen-
sible to b oth temperature and air humiditychanges. The eld-display infor-
mation from the reference magnet is calibrated perio dically by a direct mea-
surement of the ux variations in an 8-fold lo op consisting of electric wires
mounted in the lower p ole of each of the b ending magnets and connected in
series throughout each LEP o ctant (2) . The induced voltage from the ux
variation in the lo ops when the whole dip ole system undergo es a magnetic
cycle of given excursion is measured by eight digital integrators in the even
underground areas of the machine and provides a direct information on the
R
Bds
along the accelerator from the dip oles in the actual environmental con-
ditions. Polarity reversal permits a measurement of the remanent eld which
is of particular imp ortance for the LEP low eld dip oles.
The attainable accuracy in the determination of the b eam momentum is of
the order of 5
10
4
since the metho d does not account for additional dipolar
bending for orbits o-axis in the quadrupoles.
THE NOMINAL ENERGY
For a given magnetic structure the
nominal energy
E
0
is dened for a
beam circulating on the
central orbit
C
0
going in average through the center
of the quadrup oles so that the b ending strength experienced by the b eam over
a machine revolution comes only from the dip oles:
E
0
ec
=
p
0
e
=
1
2
I
C
0
B
(
s
)
ds
(1)
3
The integration is extended over the central orbit
C
0
dened by the central
revolution frequency
f
0
rev
:
f
0
rev
=
c
C
0
=
c
h
0
RF
(2)
where
0
RF
is the wavelength of the
nominal RF frequency
f
0
RF
and
h
the
harmonic number.
Measuring The Central Orbit
The nominal momentum of a beam o the central orbit in a FODO struc-
ture is mo died by the additional integrated dipolar eld in the quadrup oles
according to Eq.1:
p
=
p
0
c
C
C
0
=
e
2
I
C
G
(
s
)
x
(
s
)
ds
(3)
where
c
is the momentum compaction for the used optics,
G
(
s
) the eld
gradient and
C
=
C
0
+
C
the length of the actual reference orbit. This
eect modies the betatron tunes (chromaticity) and generates closed orbit
distortions induced by angular kicks from the (de)fo cusing strengths, which
are minimum when the beam is centered.
In principle a direct metho d to dene the central orbit would consist in
looking for minimum orbit distortion (orbit dierences) as a function of the
RF frequency for dierent settings in the strength of the arc quadrup oles but
the attainable accuracy is essentially limited by the associated tune shift.
The method commonly adopted in a regular FODO-lattice magnetic struc-
ture exploits the fact that in each magnetic cell the sextupoles are installed on
the same girder as the quadrupoles and precisely aligned with respect to them.
In this assumption a b eam o-axis in the quadrup oles receives additional fo-
cusing from the same misalignment it has in the center of the sextup oles. This
makes the b etatron tunes
Q
x
;
y
depend on the sextupole excitation until the
orbit is
on axis
in the quadrup ole-sextupole complex.
The method then consists in measuring the dependence of the betatron
tunes over the radial p osition of the orbit in the arcs bychanging the RF
frequency for dierent settings of the sextup ole families i.e. for dierentchro-
maticities
Q
0
=
Q=
p=p
.For energy changes small compared to the ac-
ceptance of the machine the chromaticityvaries linearly with the sextup ole
excitation and the lines
Q
x
;
y
(
f
RF
) will cross at one p oint dening the central
RF frequency
f
0
RF
.
If the particle velocity is known, as in the case of ultra-relativistic leptons, the
method provides a measurement of the central orbit length
C
0
(5).
Figure 1 shows an example of the use of positrons (1
e
+
3
10
10
)to
4
determine the length of the LEP
actual circumference
y
from
C
0
=
c
e
+
h
e
+
f
0
RF
;
e
+
(4)
The harmonic number
h
e
+
= 31324 gives
C
LE P
0
=26
:
658873 km. The error in
the circumference measurement is of the order of 0.3 mm corresponding to a
relative error of about 1
10
8
. The accuracy on the frequency measurement
is more than one order of magnitude better.
Figure. 1
.
Positron
chromaticity measurements to determine the central revolution
frequency and the length of the
central orbit
, ref.(5).
THE CENTRAL MOMENTUM
The determination of the momentum on the central orbit requires the use of
non ultra relativistic particles. Protons have b een prop osed (4) as their velocity
c
p
is measurably dierent from the sp eed of light.
After a measurement of the central orbit with positrons, following the metho d
discussed ab ove, protons are injected keeping the
same magnetic settings
and trapp ed by the RF system on a dierent harmonic number
h
p
associated
to the new velocity, determined from the knowledge of the nominal energy
inferred from magnetic measurements.
A measurement of the chromaticity
Q
0
p
for dierent sextup ole settings denes
y
As stated in (3) the concept of
Terra ferma
has to be reconsidered when dealing with
alignment stability in accelerators: the length of the central orbit is time-dep endent due to
seasonal and p eriodic ground motion as discussed in the last chapter.
5
