The LHC 450 GeV to 7 TeV Synchrotron
Radiation Profile Monitor using a
Superconducting Undulator
R. Jung, P. Komorowski, L. Ponce, D. Tommasini
CERN, CH1211 Geneva 23, Switzerland
Abstract. In LHC it will be important to measure with precision and in a non-destructive way
the proton beam profiles from 450 GeV to 7 TeV. The chosen monitor will make use of a 5 T
superconducting Undulator with two periods coupled to the D3 bending magnet built by BNL.
From the various variants studied, this combination is the only one which could cover the whole
LHC energy range. By locating both magnets in the same cryostat, it will be possible to
minimise the light source length for best precision. The choice of the undulator parameters and
its basic design will be described. The evolution of the synchrotron radiation patterns along the
energy ramp will be given, as well as the performance with respect to sensitivity, depth of field
and diffraction, with a description of the simulation codes used.
INTRODUCTION
There is a strong need in LHC to measure the beam profiles all along a run. The
tight emittance budget asks to measure the emittance at beam injection at 450 GeV to
check that the limit of 5% blow-up between the circular machines is respected. A turnby-turn measurement during the first tens of turns will check that the matching
between the accelerators is done properly (1). A relative accuracy of the order of a few
percent is requested for the measurement of the turn by turn profile oscillations that
are the signature of a mismatch. The beam size evolution has then to be followed
through the acceleration cycle from 450 GeV to 7 TeV where the beam size shrinks
substantially but for which a normalised emittance blow-up of less than 7% is
requested. Finally, the beam profile has to be measured with a relative accuracy better
than a few percent to adjust the aperture controlling collimators. During all these
phases, there is also a demand to measure individual bunches out of the 2808
circulating bunches, at various locations in a 72 bunches batch in order to identify
beam dynamics problems.
An ideal monitor for these tasks is a non-intercepting monitor. One monitor of this
kind is a Synchrotron Radiation (SR) monitor. The main candidate was a monitor
close to a physics Interaction Region (IR), IR1 or IR5, using the light generated in one
of the dogleg bending magnets, D2, bringing the beams back to the nominal LHC
separation after the increased separation in the IR. This monitor was in a favourable
location where the beam size increases at top energy when the beams are brought into
collision optics. Unfortunately, the light production within the spectral range of
CP648, Beam Instrumentation Workshop 2002: Tenth Workshop, edited by G. A. Smith and T. Russo
© 2002 American Institute of Physics 0-7354-0103-9/02/$19.00
220
available detectors, was only sufficient above 2 TeV. From injection energy to 2 TeV,
another solution had to be found. Various solutions were looked at in the RF region
IR4, using room temperature or superconducting undulators to generate enough light
in the neighbourhood of the visible spectrum. These solutions could cover the 450
GeV to 2 TeV region, but were useless above, generating the additional problem of
changing monitors during the delicate process of the energy ramp.
An acceptable solution became possible when the IR4 layout was changed for
economical reasons and a long dogleg was introduced to go from a separation of
420mm in the IR, dictated by the RF cavities, towards the 194mm in the standard LHC
arc dipoles. With this layout, a superconducting Undulator could be introduced in front
of the D3 separating magnet, which deflects the circulating beam from the SR
generated in the Undulator. A mirror can be introduced to collect and deflect out of the
vacuum chamber the SR after a drift of some 10m after D3. Above 2 TeV, the
Undulator radiates again mostly outside the detector range, but this time the edge
radiation of the D3 magnet will be used as SR source. Finally at top energy, the whole
of D3 radiates enough SR, which has this time to be limited to a region close to the
entrance edge for limiting the longitudinal acceptance of the imaging optics.
SR CHARACTERISTICS OF THE UNDULATOR
An Undulator is a periodic magnetic structure that concentrates the SR through
interference in a cone in the forward direction along the beam path (2). It is
characterised by a factor K, with K<1 for an Undulator:
(1)
2nmpc
where Au is the Undulator period and B0 the peak magnetic field on the beam axis.
The coherence condition relates the emitted SR wavelength ?lc to a given direction 0
with respect to the beam axis and the Undulator characteristics by:
(2)
The angular spectral energy density in the deflection plane of the Undulator is given
in equation (3), with the usual notations, k being a constant and Nu the number of
Undulator periods. From this equation, it is clear that the light production will increase
as B02. It can also be seen that the light production decreases when going away from
the beam axis and that the light spectrum narrows around ?lc when the number of
Undulator periods Nu increases:
"
'4.
2
dW
(3)
Based on these considerations, a two period superconducting Undulator, of 28cm
period, and with a peak field of 5T was chosen. The relevant parameters of this
221
Undulator
to ?l
λco
Undulator are:
are: K=
K= 0.07
0.07 and
and λ?tcoco=608nm
=608nm at
at 450
450 GeV
GeV and
and already
already down
down to
=55nm at
at
co=55nm
1.5
1.5 TeV
TeV on
on the
the beam
beam axis.
axis. ItIt isis only
only because
because of
of the
the spectral
spectral width
width due
due to
to the
the small
small
number
–0.5/+1.5mrad, that
number of
of magnetic
magnetic periods
periods and
and to
to the
the angular
angular acceptance
acceptance of
of-0.5/+1.5mrad,
that there
there
will
will be
be aa reasonable
reasonable amount
amountof
ofenergy
energyavailable
availableininthe
thespectral
spectralrange
rangeofofthe
thedetectors.
detectors.
The
The evolution
evolution of
of λ?lcc as
as aa function
function of
of beam
beam energy
energy and
and observation
observation angle
angle is
is given
given in
in
figure
magnet
figure 1.
1. This
This situation
situation isis acceptable
acceptable at
at high
high energy
energy because
because the
the edge
edge of
of the
the D3
D3 magnet
starts
starts to
to produce
produce enough
enoughSR
SRfrom
from 11TeV
TeVonwards.
onwards.
Undulator
Undulator period:
period: 28
28 cm
cm
900
800
MCP
[nm]
600
c
700
500
0.450
0.700
CCD
1.000
7.000
400
300
200
0.0
0.5
1.0
1.5
2.0
2.5
2.5
θ [mrad]
FIGURE
FIGURE 1.
1. Coherence
Coherence wavelength
wavelength versus
versus angle
angle to
to the
the beam
beam direction
direction as
as aa function
function of
of beam
beam energy,
energy,
with
with the
the spectral
spectral sensitivity
sensitivity bands
bands of
of aa back-illuminated
back-illuminated CCD
CCD and
and aa MCP
MCP with
with aa SS25
SS25 photocathode.
photocathode.
SR
SR EMITTED
EMITTED BY
BY THE
THE D3
D3 BENDING
BENDING MAGNET
MAGNET
Starting
Starting at
at 750
750 GeV,
GeV, the
the edge
edge of
of D3
D3 will
will emit
emitlight
lightininthe
therange
rangeof
ofinterest.
interest.
-iT§fr~PH; (mcl)
FIGURE
FIGURE 2.
2. Angular
Angular light
light pattern
pattern resulting
resulting from
from the
the combination
combination of
of the
the SR
SR from
from the
the Undulator
Undulator (ring
(ring
pattern
pattern with
with central
central peak)
peak) and
and of
of the
the D3
D3 bending
bending magnet
magnet input
input edge
edge (at
(at the
the centre
centre of
of the
the Undulator
Undulator
pattern)
pattern) and
and exit
exit edge
edge (peak
(peak at
at the
the left)
left) at
at 11TeV.
TeV.
222
The
as the
the Undulator
Undulator
The light
light is
is emitted
emitted by
by the
the entrance
entrance edge
edge along
along the
the same
same direction
direction as
SR,
and
can
hence
be
extracted
under
the
same
conditions.
This
light
will
interfere
SR, and can hence be extracted under the same conditions. This light will interfere
with
angular light
light pattern
pattern for
for the
the
with the
the light
light produced
produced by the Undulator. A typical angular
intermediate
in figure
figure 2.
2.
intermediate energies is given in
Once
whole core
core of
ofD3
D3will
willproduce
produceSR.
SR.
Once the
the energy
energy increases beyond 2 TeV, the whole
THE LHC SR PROFILE MONITOR
The
of the
the monitor
monitor isis given
given in
in figure
figure 3.3. The
The proton
proton
The principle
principle of implementation
implementation of
beam
right of
of the
the figure,
figure, enters
enters the
the Undulator
Undulator
beam leaving
leaving Interaction
Interaction Point 4 at the top right
before
1.6 mrad
mrad by
by the
theD3
D3magnet
magnettowards
towardsD4.
D4.
before being
being deflected by 1.6
D3
U
IP4
D4
10m
420mm
194mm
Schematic view
view of
of the
the Undulator/D3
Undulator/D3 SR
SR monitor
monitor in
FIGURE 3.
3. Schematic
FIGURE
in IR4
IR4 of
of LHC.
LHC.
The Undulator
Undulator and
and D3
D3 are
are located
located in
the same
The
in the
same cryostat
cryostat to
to minimise
minimise the
the distance
distance
between
them,
in
order
to
reduce
the
extent
of
the
light
source.
The
light
generated
between them, in order to reduce the extent of the light source. The light generated in
in
the Undulator
Undulator and
and at
at the
the edge
edge of
of D3
D3 travels
travels aa distance
distance of
the
of 23m
23m before
before an
an extraction
extraction
mirror can
can be
be inserted
inserted at
at an
an acceptable
acceptable distance
H. The
mirror
distance from
from the
the beam,
beam, typically
typically 15
15 σ<JH.
The
beam
and
the
light
will
travel
in
an
enlarged
vacuum
chamber
with
tapered
transitions
beam and the light will travel in an enlarged vacuum chamber with tapered transitions
at both
both ends
ends in
in order
order to
at
to reduce
reduce the
the perturbation
perturbationtotothe
thebeam.
beam.
The SR
SR monitor's
monitor’s performance
performance and
The
and calibration
calibration will
will be
be checked
checked at
at low
low proton
proton beam
beam
intensity with
with H
H and
and V
V Wire
Wire Scanners
intensity
Scanners located
located atatthe
theexit
exitof
ofD3.
D3.
Undulator Magnet
Undulator
Magnet
The undulator
undulator consists
consists of
of 88 superconducting
superconducting coils
The
coils assembled
assembled around
around ferromagnetic
ferromagnetic
iron
poles
to
produce
two
periods
of
magnetic
field
with
a
sinusoidal
iron poles to produce two periods of magnetic field with a sinusoidalshape:
shape:figure
figure4.4.
To
block
the
conductors
during
magnet
excitation,
the
coils
will
be
clamped
To block the conductors during magnet excitation, the coils will be clamped under
under
pre-stress.
Vertical clamping
clamping will
will be
provided by
pre-stress. Vertical
be provided
by splitting
splitting the
the magnet
magnet into
into aa lower
lower and
and
an upper
upper part,
part, and
and by
by closing
closing the
the structure
structure with
with spacers
an
spacers between
between the
the upper
upper and
and lower
lower
coils outside
outside the
the beam
beam tube.
tube. Horizontal
Horizontal clamping
clamping will
coils
will be
be provided
provided by
by retaining
retaining blocks
blocks
fixed
by
copper/beryllium
tie
bolts.
fixed by copper/beryllium tie bolts.
The main
main parameters
parameters of
The
of the
the Undulator
Undulator are
are listed
listedininTable
Table1.1.
223
TABLE 1. Undulator; main parameters.
Period
length
TABLE
1. Undulator: main parameters.
Number
of periods
Period length
Iron
yoke of
length
Number
periods
Gap
Iron yoke length
Gap tube size
Beam
Beam tubemagnetic
size
Maximum
field in the gap
Maximumfield
magnetic
in ±10
the gap
Maximum
error field
within
mm from axis
Maximum
field error within ± 10 mm from axis
Supply
current
Supply
current
Total
energy
stored at 250 A
Total energy
stored at 250 A
Magnet
inductance
Magnet
Coil
crossinductance
section
Coil cross
Cable
size section
Cable
Overallsize
coil size
Overall coil
size
Operating
temperature
Operating temperature
Margin to quench on load line
Margin to quench on load line
Main field/peak field ratio
Main field/peak field ratio
Hot spot temperature in case of a quench at 5 T
280mm
280 mm 2
710mm
2
71060mm
mm
60ID/OD
mm
50/53 mm
50/53 mm ID/OD
5T
5T
0.25%
0.25%
250 A
250
150AkJ
1504.8
kJ H
4.8mm
H 2
36.5 x 42.5
2
2
36.5
x
42.5
mm
1.25x0.73 mm
2
3
1.25
x
0.73
mm
140 x 223 x 36.5 mm
3
140 x 223 x 36.5 mm
4.2 K
4.2 K
20%
20 %
0.83
0.83
120 K
120 K
Hot spot temperature in case of a quench at 5 T
B[T]
6
B [T] 6
Btotal, y
4
22
-
0
-2
-4
-6
-400
-400 -300
-300 -200
-200 -100
-100 0 0 100
100 200
200 300300 400400
X X[mm]
[ mm ]
Perspective view
view of
of the
coils
FIGURE4.4. Perspective
FIGURE
the 22 period
period Undulator
Undulatorwith
withPole
Polepieces
piecesextending
extendingbeyond
beyondthethe
coils
(totallength
length71cm)
71cm)and
andVertical
Vertical Magnetic
Magnetic Field
(total
Field component
componentalong
alongthe
thebeam
beamaxis.
axis.
Telescope
Telescope
It is intended to re-use the LEP SR telescopes (3) with some modifications. The
It is intended to re-use the LEP SR telescopes (3) with some modifications. The
telescope uses primarily mirrors for folding and focusing. The detectors will be backtelescope uses primarily mirrors for folding and focusing. The detectors will be backilluminated CCDs for highest sensitivity and ordinary CCDs coupled to Multi Channel
illuminated
CCDs for highest sensitivity and ordinary CCDs coupled to Multi Channel
Plate (MCP) intensifiers for single bunch or single batch, down to turn-to-turn,
Plate
(MCP)
for has
single
bunch toorchanging
single batch,
downover
to turn-to-turn,
observations. intensifiers
This telescope
to adapt
conditions
a run. At
observations.
This
telescope
has
to
adapt
to
changing
conditions
over a run. At
injection energy at 450 GeV, the Undulator is used. The beams are large, σ~1.2mm,
injection
at 450
theenergy
Undulator
is used.
large,whilst
a~1.2mm,
and emitenergy
little light.
At GeV,
the top
of 7 TeV,
theThe
D3 beams
magnet are
is used,
the
and
emit
little
light.
At
the
top
energy
of
7
TeV,
the
D3
magnet
is
used,
Undulator emits in the UV at large angles which can reach the detectors.whilst
At thatthe
Undulator emits in the UV at large angles which can reach the detectors. At that
224
energy the beams are also small, a~300|im, and D3 emits a large amount of light. For
that reason, two detector set-ups are foreseen. As there is enough light available at
high energy, a bandpass filter will be used together with a magnifying lens which will
image the beam from the first image plane onto the second detector set. This set-up
can also take into account the longitudinal separation of the Undulator and the D3
edge, which has to be kept below 80cm. Chromatic, linear density and polarisation
filters are installed as well as a slit in the focal plane to restrict the acceptance in D3.
The magnification is determined by the 4m focal length spherical mirror and the
23x23|im2 pixel size. It has been set to G=0.2 in order to have 3 pixels per sigma at 7
TeV, which gives then 13 pixels per sigma at injection. One of the limitations of the
performance is the distance by which the light extraction mirror has to be retracted
from the beam. For the moment, a distance of 15<JH has been asked for. It is hoped that
with operational experience, this distance can be decreased to come closer to the
machine aperture set by the collimators closed to ±7a. In any case, the extraction
mirror will be movable, so that it can follow the 15<JH limit to improve the
performance at high energy.
Due to the long distance to travel and the small opening of the light cone, proper
alignment has to be provided. A set-up using a folding mirror and a laser located close
to the SR telescope will be used: see figure 5. A similar set-up has been used in LEP
and has proven to be extremely useful. The Undulator itself has to be aligned on the
entrance magnetic axis of D3 to a tolerance of the order of ±5mrad.
Uoduiator
folding mirror
aligniitent Laser
FIGURE 5. Monitor layout with alignment set-up of the optical elements of the SR telescope.
PERFORMANCE ANALYSIS
The photon production has been computed with the ray-tracing code Zgoubi (4).
With the optics set-up described there will be a maximum of 200 photons per pixel
(px) at injection and 80 103 photons/px at top energy for a pilot pulse of 5 109 protons
in single turn mode. This will be sufficient to observe the beam behaviour in LHC
before injecting and accelerating a nominal bunch. It should also be sufficient to check
if there are sizeable matching errors. For a nominal bunch of 1.1 1011 protons, there
will be 4 103 photons/px at injection and up to 2 106 photons/px at top energy. This
will permit high precision measurements from a statistical point of view. But the
225
imperfections of the LHC monitor are due, to a large amount, to the source length, the
imperfections of the LHC monitor are due, to a large amount, to the source length, the
interference
between the two sources and the diffraction of the SR light cone due to
interference between the two sources and the diffraction of the SR light cone due to
the
small opening angle at high energy and the limited acceptance of the extraction
the small opening angle at high energy and the limited acceptance of the extraction
mirror. At 450 GeV, the emission pattern is a gaussian like cone with an opening of
mirror. At 450 GeV, the emission pattern is a gaussian like cone with an opening of
~0.8mrad FWHM, within the acceptance of the extraction mirror. At 1 TeV, see figure
~0.8mrad FWHM, within the acceptance of the extraction mirror. At 1 TeV, see figure
2, the light pattern is the superposition of two sources, which will generate a beam
2, the light pattern is the superposition of two sources, which will generate a beam
broadening through interference and diffraction. Finally, at 7 TeV, where mainly D3
broadening through interference and diffraction. Finally, at 7 TeV, where mainly D3
will produce light in the useful spectrum, there is a classical bending magnet SR
will produce light in the useful spectrum, there is a classical bending magnet SR
pattern, with clearly visible edges, cut by the extraction mirror.
pattern, with clearly visible edges, cut by the extraction mirror.
The
the source
source characteristics
characteristics on
on the
the performance
performance was
wasevaluated
evaluatedwith
with
The influence
influence of
of the
the
program
SRW
(5).
SRW
is
a
numerical
code
dedicated
to
the
derivation
of
SR
the program SRW (5). SRW is a numerical code dedicated to the derivation of SR
features
generated
by
an
arbitrary
magnetic
field
pattern
followed
by
a
propagation
features generated by an arbitrary magnetic field pattern followed by a propagation
through
chain producing
producing aa display
display of
ofthe
thePoint
PointSpread
SpreadFunction
Function(PSF).
(PSF).SRW
SRW
through an
an optical
optical chain
provides
the
SR
intensity
distribution
for
a
"filament"
electron
beam,
i.e.
with
zero
provides the SR intensity distribution for a ”filament” electron beam, i.e. with zero
emittance.
The
electric
field
in
the
frequency
domain
is
derived
from
the
Fourier
emittance. The electric field in the frequency domain is derived from the Fourier
Transform
potentials, allowing
allowing to
to perform
perform the
the computing
computingininthe
thefar
far
Transform of
of the
the retarded
retarded potentials,
field,
as
well
as
in
the
near
field
SR
approximations.
The
SR
propagation
from
field, as well as in the near field SR approximations. The SR propagation from aa
transverse
one is
is implemented
implemented using
using the
the Fourier
Fourier optics
optics approach,
approach,
transverse plane
plane to
to another
another one
assuming
angles and
and large
large distances
distances compared
compared to
to the
the wavelengths.
wavelengths.The
Theelectric
electric
assuming small
small angles
field
after an
an optical
optical element
element isis derived
derived by
by applying
applyingan
anoperator
operator
field in
in aa transverse
transverse plane
plane after
describing
The program
program parameters
parameters have
have been
been modified
modified toto take
take
describing the
the optical
optical element.
element. The
into
protons and
and the
the results
resultshave
havebeen
beencross-checked
cross-checkedwith
withZgoubi.
Zgoubi.
into account
account protons
The
will be
be the
the convolution
convolution of
of the
the density
density distribution
distribution
The beam
beam image
image at
at the
the detector
detector will
of
the
beam
and
of
the
PSF
of
the
optical
system.
of the beam and of the PSF of the optical system.
The
beam in
in the
the detector
detector plane,
plane,together
togetherwith
withaacut
cutthrough
through
The images
images of the filament beam
the
horizontal
beam
axis
are
given
in
Fig
6
to
8
for
450
GeV,
1
TeV
and
7
TeV.
The
the horizontal
axis are given in Fig 6 to 8 for 450 GeV, 1 TeV and 7 TeV. The
results
polarisation component
componentofofthe
theSR
SRare
aresummarised
summarisedininTable
Table2.2.
results for the
the horizontal polarisation
TABLE
monitor performance.
performance.
TABLE 2.
2. Undulator SR profile monitor
Beam
PSF
Energy
[\nn\
Beam
PSF
Energy // Sizes [µm]
σ
σaVv
σOH
σaVv
OH
H
H
450
960 1323
1323
141
159 141
450 GeV
159
888
198 120
120
1ITeV
TeV
644
888
198
7 TeV
335
156 194
194
244
335
156
σOH
H
973
973
674
674
290
290
BeamImage
Image
Beam
6aH/a
σaVv δσ
δσ
5aVv/σ
/(7v
H/σHH
V
1330 1.1%
1.1%
0.6%
1330
0.6%
896
4.6%
0.9%
896
4.6%
0.9%
387
18%
15%
387
18%
15%
PSF Horizontal Cut
450 GeV, k = 500 nm
+• PSF
—— Gaussian fit
Horizontal Position
D and
and Horizontal
Horizontal cut
FIGURE 6.
6. 22 D
FIGURE
cut of
of the
the Point
Point Spread
Spread Function
Functionof
ofthe
theSR
SRmonitor
monitoratat450
450GeV.
GeV.
226
Intensity at the Detector
Horizontal Cut
ITeV, ar=5GQnm
-I- PSF
—— gaussian fit
100
Horizontal Position
4QO
200
-200 0
200
400
Horizontal Position
DDand
and
Horizontal
cut
of
the
Point
Spread
Function
of the
the SR
SR monitor
monitor at
at 11 TeV.
TeV.
FIGURE
7.7. 222D
andHorizontal
Horizontalcut
cutof
ofthe
thePoint
PointSpread
SpreadFunction
Function of
FIGURE7.
FIGURE
Intensity at the Detector
Horizontal Cut
7 TeV, X=20Qtim
Slit 3.7mm x 10mm
I PSF
—— gaussian..fit
-200
0
200
Horizontal Position
andHorizontal
Horizontalcut
cutof
ofthe
thePoint
Point Spread
Spread Function
Function of
FIGURE8.
DDand
and
Horizontal
cut
of
the
Point
Spread
Function
of the
the SR
SR monitor
monitor at
at 77 TeV.
TeV.
FIGURE
8.8. 222D
FIGURE
Theimage
image broadening
broadening introduced
introduced by
by the
the PSF
the real
real
The
image
broadening
introduced
the
PSF is
is small
small enough
enough to
to extract
extract the
The
by
beamsize
sizeto
tothe
theexpected
expectedaccuracy
accuracyby
byaaasimple
simplequadratic
quadratic subtraction.
subtraction. The
The broadening
broadening
beam
size
to
the
expected
accuracy
by
simple
beam
willbe
beindependent
independent of
of the
the beam
beam intensity
intensity and
and will
will be
be stable
stable for
for aa given
given light
light pattern,
pattern,
will
be
independent
of
the
beam
intensity
will
and
i.e.
beam
energy.
The
corrections
can
hence
be
calibrated
with
the
Wire
Scanners.
i.e. beam
beam energy.
energy. The
The corrections
corrections can
i.e.
can hence
hence be
be calibrated with the Wire Scanners.
wouldnevertheless
neverthelessbe
beadvantageous
advantageous for
for the
theprecision
precision of
of the
the measurement
measurement that
that the
the
would
nevertheless
be
advantageous
for
ItItItwould
machine
optics
provides
higher
βs.
machine optics
optics provides
provides higher
machine
higher βs.
PS.
ACKNOWLEDGMENTS
ACKNOWLEDGMENTS
ACKNOWLEDGMENTS
It is a pleasure
pleasure to
to acknowledge
acknowledge the
the help
help and
and fruitful
fruitful discussions
discussions with J.
J. Bosser,
ItIt isis aa pleasure
to acknowledge
the help
and fruitful
discussions with
with J. Bosser,
Bosser,
O.Chubar
Chubar (ESRF),
(ESRF), P.
P. Elleaume
Elleaume (ESRF),
(ESRF), A.
A. Hofmann,
Hofmann, F.
F. Méot
Méot (CEA/Saclay),
(CEA/Saclay),
O.
O.Chubar (ESRF), P. Elleaume (ESRF), A. Hofmann, F. Meot (CEA/Saclay),
S.Russenschuck
Russenschuck and
and M.
M. Sassowsky.
Sassowsky.
S.
S.
Russenschuck and
M. Sassowsky.
227
REFERENCES
1.
2.
3.
4.
5.
C.Bovet, R. Jung, EPAC 1996, Sitges, June 1996, pp. 1597-1599
A. Hofmann, CAS, Grenoble, April 1996, CERN 98-04, August 1998, pp. 1-44
G. Burtin et al, CERN SL-99-049 BI, August 1999
F. Meot, S. Valero, CEA-Saclay, DSM/DAPNIA/SEA-97-13, 1997
O. Chubar, P. Elleaume, EPAC 1998, Stockholm, June 1998, pp. 1177-1179
228