Emittance Dilution
Dilution In
Emittance
In HERA-p:
HERA-p: Lessons
Lessons and
and Overview
Overview
R.
R. Wanzenberg
Wanzenberg
DESY, Notkestr. 85, 22603 Hamburg, Germany
DESY, Notkestr. 85, 22603 Hamburg, Germany
Abstract. Protons of an energy of 920 GeV collide with positrons or electrons (energy 27.5 GeV) in the HERA
Abstract.
of anToenergy
920 luminosity
GeV collideanywith
positrons
or electrons
27.5Different
GeV) in sources
the HERA
acceleratorsProtons
at DESY.
obtain of
a high
emittance
dilution
must be(energy
minimized.
of
accelerators
at DESY.
To are
obtain
a high Effects
luminosity
anyfrom
emittance
dilution
mustoscillation
be minimized.
Differentofsources
potential emittance
growth
discussed.
arising
a coherent
injection
or a mismatch
the beta-of
potential
growth
are discussed.
Effects
arisingdilution
from a coherent
oscillation
or a mismatch
of the
betafunctionsemittance
are the main
sources
of transverse
emittance
at HERA.injection
In addition
a longitudinal
emittance
growth
functions
are
the
main
sources
of
transverse
emittance
dilution
at
HERA.
In
addition
a
longitudinal
emittance
growth
during the acceleration of the protons has been observed in HERA. Finally the emittance growth due to intra-beam
during
the isacceleration
of the protons has been observed in HERA. Finally the emittance growth due to intra-beam
scattering
briefly discussed.
scattering is briefly discussed.
oscillation, aamismatch
mismatchofofthe
thelinear
linearbeam
beamoptics
optics(beta(betaoscillation,
function
or
dispersion),
nonlinear
fields
or
coherent
function or dispersion), nonlinear fields or coherent
beam instabilities.
instabilities. The
The different
different effects
effects are
areestimated
estimated
beam
in
the
following
sections
for
the
HERA-p
ring
based
in the following sections for the HERA-p ring based
on
the
data
and
formulas
from
Ref.
[2].
on the data and formulas from Ref. [2].
TABLE1.1.HERA
HERAparameters
parameters(pre
(preupgrade).
upgrade).
TABLE
Parameter
HERA-p
HERA-e
Parameter
HERA-p
HERA-e
920
27.5
EE/GeV
/ GeV
920
27.5
I/mA
100
50
I / mA
100
50
bunches
180
189
##bunches
180
189
10
7.3
3.5
NN/10
/ 1010
7.3
3.5
41
5.0
8
/nm
x
5.0
41
εx / nm
0.1
11
0.1
εy/εx
1.1
19
19
1.1
σoz z//cm
cm
Scattering
of
particles,
such
as
residual
gas
Scattering of particles, such as residual gas
scattering
or
intra-beam
beam
scattering
also
results
scattering or intra-beam beam scattering also results inin
an emittance
emittance growth.
growth. Intra-beam
Intra-beamscattering
scattering(IBS)
(IBS)isisa a
an
multiple Coulomb
Coulombscattering
scatteringprocess
processofofthe
theparticles
particlesinin
multiple
the bunch,
bunch, which
which cause
cause an
an emittance
emittance growth
growth ofofthe
the
the
beam inin all
all three
three beam
beam dimensions.
dimensions. The
Thelongitudinal
longitudinal
beam
emittance growth
growth due
due toto IBS
IBS isisaagood
good candidate
candidatefor
for
emittance
the observed
observed generation
generation ofofcoasting
coastingbeam,
beam,which
whichmay
may
the
resultinto
intobackground
backgroundproblems
problemsfor
forHERA-B
HERA-B[3].
[3].
result
INTRODUCTION
INTRODUCTION
HERA,
circumference of
of about
about 6.3
6.3 km,
km, isis
HERA, with
with aa circumference
the
largest
accelerator
facility
at
DESY
in
Hamburg.
A
the largest accelerator facility at DESY in Hamburg. A
920
GeV
proton
beam
and
a
27.5
GeV
polarized
920 GeV proton beam and a 27.5 GeV polarized
positron
electron beam
beam are
are provided
provided for
for four
four high
high
positron or
or electron
energy
physics
experiments.
HI
and
ZEUS
are
e/p
energy physics experiments. H1 and ZEUS are e/p
collider
while two
two fixed
fixed target
target
collider experiments,
experiments, while
experiments
use of
of the
the polarized
polarized ee++ (or
(or ee")-beam
experiments make
make use
)-beam
(HERMES)
or
the
halo
of
the
p-beam
(HERA-B).
The
(HERMES) or the halo of the p-beam (HERA-B). The
two
accelerator
rings
for
the
p
and
e-beam
are
shown
two accelerator rings for the p and e-beam are shown
in
1. The
beam parameters
parameters which
which were
were used
used
in Fig.
Fig. 1.
The basic
basic beam
until
the
year
2000
are
listed
in
Table
1.
During
until the year 2000 are listed in Table31 1. During
aa
-2 -11 and a
typical
luminosity of
of 1.8
1.8 10
1031 cm
cm'V
typical run,
run, aa peak
peak luminosity
s
and
a
30
2
-2 -1
specific
of 0.8
0.8 10
1030
cm^s^mA"
have been
been
specific luminosity
luminosity of
cm
s mA-2 have
achieved
6). In
In 2001
2001 the
the interaction
interaction regions
regions
achieved (see
(see Fig.
Fig. 6).
were upgraded for an increase in the
the specific
specific
luminosity by a factor
factor of 2.76. Ref.
Ref. [1]
[1] presents
presents
further
HERA parameters and
and future
future
further details on these HERA
plans.
8y/8X
TRANSVERSEEMITTANCE
EMITTANCE
TRANSVERSE
DILUTION
DILUTION
The
The emittance
emittance dilution
dilution ininthe
thetransverse
transverseplanes
planesisis
mainly
mainly caused
caused from
from injection
injection errors
errors atat HERA.
HERA.After
After
each
each magnet
magnet cycle
cycle aa careful
careful adjustment
adjustmentofofthe
thetunes,
tunes,
energy
energy and
and injection
injection trajectory
trajectoryisis necessary
necessarysince
sincethe
the
magnetic
magnetic fields
fields inin the
thesuperconducting
superconductingmagnets
magnetsdiffer
differ
from
from cycle-to-cycle
cycle-to-cycle due
due toto the
the induced
induced persistent
persistent
currents.
currents. The
The reproducibility
reproducibility ofof the
the injection
injection
trajectory,
trajectory, the
the precision
precision ofofthe
thebeam
beamposition
positionmonitors
monitors
(BPMs)
(BPMs) of
of about
about0.5
0.5mm
mm(resolution
(resolution0.1
0.1mm)
mm)and
andthe
the
kicker
kicker ripple
ripple of
of about
about11%%results
resultsinto
intoa atotal
totalinjection
injection
trajectory
trajectory error
error ofofabout
about11mm.
mm. This
Thisisisachieved
achievedafter
after
pilot
injection
of
a
few
proton
bunches
which
pilot injection of a few proton bunches whichare
areused
used
to
to adjust
adjust the
the trajectory
trajectory ofof the
the injected
injected beam
beam toto the
the
closed
closed orbit.
orbit. The
The maximum
maximum beta-function
beta-function atat the
the
FIGURE 1. Photograph of
of the
the HERA
HERA tunnel.
tunnel. The
The
superconducting magnets of the proton ring
ring are
are installed
installed
above the (normal conducting) magnets of
of the
the electron/
electron/
positron ring.
SOURCES OF EMITTANCE
EMITTANCE DILUTION
DILUTION
An emittance dilution is caused by filamentation
filamentation of
of
a
coherent
oscillation.
Possible
sources
a coherent oscillation. Possible sources are
are an
an injection
injection
CP642, High Intensity and High Brightness Hadron Beams: 20th ICFA Advanced Beam Dynamics Workshop on
High Intensity and High Brightness Hadron Beams, edited by W. Chou, Y. Mori, D. Neuffer, and J.-F. Ostiguy
© 2002 American Institute of Physics 0-7354-0097-0/02/$ 19.00
65
injection amounts to about 10 % - 15 % (Ref [2]).
LONGITUDINAL
LONGITUDINALEMITTANCE
EMITTANCE
LONGITUDINAL
EMITTANCE
DILUTION
DILUTION
DILUTION
2.6
2.6
_u_u
29.03.2000 100 mA
29.03.2000100mA
29.03.2000
10091
mA
01.03.2000
mA
01.03.200091
mA
01.03.2000
91 93
mAmA
28.03.2000
28.03.2000
93 mA
28.03.2000 93 mA
average of bunch length
average
of bunch
(FWHM)
in ns length
(FWHM) in ns
2.4
2.4
factor of 6 during the ramp, which is shown in Fig. 3.
400
400
400
300
300
200
200
Two
Tworf-systems
rf-systems with
with frequencies
frequencies ofof 5252 MHz
MHz
Two
rf-systems
frequencies
of 52
(harmonic
number
h h= =1100)
and
(h(h==MHz
4400)
(harmonic
numberwith
1100)
and208
208MHz
MHz
4400)
(harmonic
number
hHERA-p
=HERA-p
1100) ring.
and
208
MHz
(h =bunch
4400)isis
are
ininthethe
The
proton
areinstalled
installed
ring.
The
proton
bunch
are
installed
in
the
HERA-p
ring.
The
proton
bunch
isrfessentially
essentiallyinjected
injectedinto
intoa abucket
bucketofofthe
the5252MHz
MHzrfessentially
injected
into
a
bucket
of
the
52
MHz
rfsystems
systems(total
(totalvoltage
voltage140
140kV)
kV)with
with anan additional
additional
systems
(totaldeformation
voltage
140from
kV) towith
additional
small
208
MHz
smallbucket
bucket
deformation
from
tothe
thean
208
MHzrfrfsmall
bucket
deformation
from tototo
the
208 MHz
rfsystem
(about
1010kV)
increase
Landau
system
(about
kV)included
included
increase
Landau
system
(about
10the
kV)
included
to40GeV
increase
Landau
damping.
During
from
damping.
During
theramp
ramp
from40
GeVtoto920
920GeV
GeV
damping.
During
the
ramp
from
40
GeV
to
920
GeV
thethe
voltage
(to
voltageofofthe
the208
208MHz
MHzrf-systems
rf-systemsisisincreased
increased
(to
the voltage
of the
208
MHz rf-systems
islongitudinally.
increased (to
about
compress
the
about600
600kV)
kV)toto
compress
thebunch
bunch
longitudinally.
aboutbunch
600 kV) to compress
the bunch
longitudinally.
The
The bunchlength
lengthand
andthe
theenergy
energyofofa aproton
protonbunch
bunch
The
bunch
length
and
the
energy
of
a
proton bunch
during
duringthetheramp
rampofofthe
theHERA-p
HERA-pring
ringisisshown
shownininFig.
Fig.
during the ramp of the HERA-p ring is shown in Fig.
2.2.
2.
.
.
The
Thebunch
bunchlength
lengthisisobserved
observed to
to decreased
decreased from
from about
about
2.4
ns
to
1.6
ns
(FWHM).
These
measurements
The
is observed
decreased
from aboutare
2.4bunch
ns tolength
1.6 ns
(FWHM).toThese
measurements
are
based
on
signals
from
gap
One
2.4
ns to
ns (FWHM).
These
measurements
based
on1.6
signals
from aa resistive
resistive
gap monitor.
monitor.are
One
would
even
smaller
length
ifif the
based
onexpect
signalsan
from
a resistive
gap
monitor.
would
expect
an
even
smaller bunch
bunch
lengthOne
the
longitudinal
emittance
would
be
not
diluted
during
would
expect
an
even
smaller
bunch
length
if
thethe
longitudinal emittance would be not diluted during
the
ramp.
longitudinal
emittance
isis increased
by
longitudinal
would
be not diluted
during the
ramp. The
Theemittance
longitudinal
emittance
increased
by aa
factor
of
6
during
the
ramp,
which
is
shown
in
Fig.
ramp.
emittance
by a3.
factorThe
of 6longitudinal
during the ramp,
whichisisincreased
shown in Fig.
3.
average of bunch emittance
(FWHM) in meVs
average of bunch emittance
(FWHM) in meVs
injection
injectionenergy
energyofof4040GeV
GeVisisabout
about9090m,
m,while
whilethe
the
emittance
of
the
injected
proton
beam
is
0.12
jim.
The
injection
energy
40 GeVproton
is about
90ism,0.12
while
emittance
of theofinjected
beam
µm.the
The
emittance
due
injection
errors
isisabout
emittance
ofdilution
the injected
beam
is 0.12
µm. 8The
emittancedilution
duetotoproton
injection
errors
about
8%.
%.
emittance
dilution
due
to
injection dilution
errors is about
8 %.
Other
sources
of
emittance
are
of
less
Other sources of emittance dilution are of less
significance.
The
dilution
due
a amismatch
Other sources
of
emittance
dilution
are
of less
significance.
Theemittance
emittance
dilution
duetoto
mismatch
of
the
beta
function
is
about
3
%
assuming
significance.
The emittance
dilution
due to a amismatch
of the beta function
is about
3 % assuming
abeta-beat
beta-beat
of
A/?//?
dilution
due
ofofthe
beta
isThe
about
3 % assuming
a beta-beat
Theemittance
emittance
dilution
dueaadisdis∆β
/ β=function
=1010%.%.
ofpersion
The
emittance
dilution
due
a
dis∆β / mismatch,
βmismatch,
= 10 %.coupling
persion
in
the
transfer
line
and
coupling in the transfer line and
nonlinear
fields
isisnot
than
persion
mismatch,
coupling
in line
the
line and
nonlinear
fieldsininthe
thetransfer
transfer
linetransfer
notlarger
larger
than
about
%.%. The
total
emittance
nonlinear
in
transfer
line is dilution
not
largerduring
than
about 1 1 fields
Thethe
total
emittance
dilution
during
injection
about
1010%%-15
about
1 amounts
%.
Thetotototal
dilution
during
injection
amounts
aboutemittance
- 15%
%(Ref
(Ref[2]).
[2]).
29.03.2000100mA
29.03.2000 100 mA
01.03.2000
01.03.2000
91mA
mA
29.03.2000
100 91
mA
28.03.2000
93
28.03.2000
93mA
mA
01.03.2000
91 mA
28.03.2000 93 mA
100
100
0
0
0
0
20
20
10
10
20
30
30
30
40
time
timeininmin
min
40
40
50
50
60
60
time in min
FIGURE
FIGURE 3.3. Longitudinal
Longitudinal emittance
emittance of
of aa proton
proton bunch
bunch
FIGURE
3.ramp
Longitudinal
emittance
of a proton
bunch
during
ofofthe
ring
from
duringthe
the
ramp
theHERAp
HERAp
ring(Adapted
(Adapted
from [4].)
[4].)
during the ramp of the HERAp ring (Adapted from [4].)
An
Ananalysis
analysisofofmulti-bunch
multi-bunchphase
phase oscillation
oscillation of
of the
the
An analysis of (see
multi-bunch
phase oscillation
of the
proton
protonbunches
bunches (seeRef.
Ref. [4])
[4]) indicates
indicates that
that aa possible
possible
proton bunches (see Ref. [4]) indicates that a possible
cause
cause ofof the
the emittance
emittance dilution
dilution isis aa coupled
coupled bunch
bunch
cause of the emittance dilution is a coupled bunch
instability.
instability.The
Themodal
modalspectrum
spectrum of
of multi-bunch
multi-bunch phase
phase
instability. The modal spectrum of multi-bunch phase
oscillationsisisshown
shownininFig.
Fig.44 ..The
Themodes
modes 1=1,
l=1, which
which
oscillations
oscillations is shown in Fig. 4 . The modes l=1, which
has aaphase
phase shift
shift ofof 2n
2π along
along the
the bunch
bunch train,
train, and
and
has
has a phase shift of 2π along the bunch train, and
l=163(phase
(phaseshift
shiftabout
about3;c/4)
3π/4)are
arethe
thedominant
dominantmodes
modes
1=163
l=163 (phase shift about 3π/4) are the dominant modes
inthe
thespectrum.
spectrum.
ininthe
spectrum.
2.2
2.2
2.0
2.0
1.8
1.8
1.6
1.6
1.4
1.4
1.4
0
0
10
10
2020
20
3030
30
4040
40
5050
50
6060
60
time
in
min
time
min
time
inin min
energy in GeV
energy in GeV
1000
1000
800
800
800-
>
?
?
o>
—h?T—¥-\—
/r
i
/——
600
600
600
400
400
400
~
200
200
2000 -0
0
/
!
! V
INTRA-BEAM
SCATTERING
INTRA-BEAM
SCATTERING
INTRA-BEAM
SCATTERING
——|——[__.....
1
00
!
FIGURE
Modal
spectrum
of
the
multi-bunch
phase
FIGURE
4.4.4.Modal
spectrum
of of
thethe
multi-bunch
phase
FIGURE
Modal
spectrum
multi-bunch
phase
oscillations
(Adapted
from
[4].)
oscillations
(Adapted
from
[4].)
oscillations
(Adapted
from
[4].)
0
1
10
10
10
l
20
20
20
I
'
30 40 40
30
30
40
50
50
50
60
60
60
time in min
time
time inin min
min
FIGURE2.
Bunchlength
lengthand
andenergy
energy
aproton
proton
bunch
FIGURE
2.2. Bunch
Bunch
of
aa proton
bunch
FIGURE
length
and
energy
ofof
bunch
during
the
ramp
of
the
HERA-p
ring
(Adapted
from
[4].)
during
the
ramp
of
the
HERA-p
ring
(Adapted
from
[4].)
.
during the ramp of the HERA-p ring (Adapted from [4].). .
66
Intra-beam scattering
scattering was
was first
first analyzed
analyzed
Intra-beam
Intra-beam
scattering
was
first
analyzed
theoreticallyinininRef.
Ref.[5].
[5].
The
transverse
emittance
theoretically
The
transverse
emittance
theoretically
Ref.
[5].
The
transverse
emittance
growth
caused
a decrease
decrease
of
thespecific
specific
luminosity
growth
caused
a adecrease
of of
thethe
luminosity
growth
caused
specific
luminosity
during
a
long
(say
10
h)
run.
Data
from
the
HERA
during
a
long
(say
10
h)
run.
Data
from
the
HERA
during a long (say 10 h) run. Data from the
HERA
to the
the HERA
HERA lattice
lattice predicted
predicted an
an initial
initial growth
growth of
ofthe
the
to
to the length
HERA of
lattice
predicted
an initial growth
of of
thethe
bunch
1.8
%.
An
alternative
analysis
bunch
%. An
An alternative
alternativeanalysis
analysis ofthethe
bunch length
length of
of 1.8
1.8which
%.
bunch
length
data,
is based
based on
on rf-noise,
rf-noise,ofcan
can be
bunch
length
data,
which
is
bunch length data, which is based on rf-noise, can bebe
found
in Ref.
Ref. [8].
[8].
found
in
archive
archive are
are shown
shown in
in Fig.
Fig. 6.
6. The
The average
average specific
specific
archivedecrease
are shown
in Fig.
6.
The
average
specific
luminosity
during
that
run
was
about
10
%.
luminosity
decrease
during
that
run
was
about
10
luminosity
decrease
during
that
run
was
about
10%.%.
The
archive
data
show
also
the
influence
of
orbit
drifts
The archive
datadata
show
alsoalso
thethe
influence
of of
orbit
drifts
The archive
show
influence
orbit
drifts
on
specific luminosity,
which
could
be
on the
the
luminosity,
which
could
beberemedied
remedied
on specific
the specific
luminosity,
which
could
remedied
by
of
in
interaction
region.
by resteering
resteering
of the
the
beam
in the
the
interaction
region.
by resteering
of beam
the
beam
in the
interaction
region.
During
the
same
luminosity
run
the
bunch
length
During
the same
luminosity
runrun
thethe
bunch
ofof
During
the same
luminosity
bunchlength
lengthof
proton
bunch
number
144
was
recorded.
The
increase
proton
bunch
number
The
increase
proton bunch number 144 was recorded. The increase
of
width
half
maximum
of the
the
full full
width
halfhalf
maximum
of full
the
width
maximum(FWHM)
(FWHM)ofofthe
the
longitudinal
proton
bunch
profile
from
longitudinal
proton
bunch
profile
frominitially
initiallyofof
longitudinal
proton
bunch
profile
from
about
2.25
ns
2.5
ns
thethe
runrun
is is
show
to about
ns during
showinin
aboutabout
2.252.25
ns to
tonsabout
about
2.5 2.5
ns during
5 also
(see
A to
fit recorded
to recorded
data
shows
Fig.
(see
Ref.
[6]).[6]).
A
data
Fig. 55Fig.
(see
alsoalso
Ref.Ref.
A fit
fit
shows
that
the
initial
increase
in
bunch
length
is
2
%
per
that
the
initial
increase
in
bunch
length
is
2
%
per
that the initial increase in bunch
in
agreementwith
withintra-beam
intra-beam
hour.
This
in
agreement
hour.hour.
ThisThis
in good
goodgood
scattering
theory
of Ref.
applicationofofthe
the
scattering
theory
of
[7].[7].
AnAn
application
scattering
theory
of Ref.
Ref.
formula:
formula:
formula:
1
τs
1
= A
σh
σp
found in Ref. [8].
initiaHncrease: 2 % / h
(fit to data)
time/h
f (a, b, q)
=τ s A σσ hp f (a, b, q)
FIGURE 5. Bunch length (FWHM) of bunch number 144
FIGURE
5. Bunch
Bunch length
length
(FWHM)
ofbunch
bunchnumber
number144
144
FIGURE
of
during the5.luminosity
run on(FWHM)
July 27, 2000.
during the
the luminosity
luminosity run
run on
on July
July 27,
27, 2000.
2000.
during
( the function f and the parameters a, b and q are
( the function
function /f and
and the
the parameters
and qq are
(the
parameters a,
a,bband
are
defined in Ref. [7])
defined in
in Ref.
Ref. [7])
[7])
defined
FIGURE 6. The proton current (93 mA, black line), the positon current (initially 50 mA, red line), the luminosity (initially 1.8
ili 1030 cm-2s-1mA-2, blue line) are shown versus time during a
10 cm s , brown line) and the specific luminosity (aboutlll0.8
FIGURE
6. The
The
proton
current
(93
mA,
black
line),
the
positon
current
(initially
50
luminosity
run
at
July
27,
2000.
FIGURE
6.
proton
current
(93
mA,
black
line),
the
positon
current
(initially
50 mA,
mA, red
redline),
line),the
theluminosity
luminosity(initially
(initially1.8
1.8
31
-2 -1
30
-2 -1
-2
3103:00:21
-2 -1 2000
Ju 127
1031 cm'Y
cm s1,, brown
brown line)
line) and
and the
the specific
specific luminosity
s mA 2,, blue
10
luminosity (about
(about 0.8
0.8 10
1030 cm
cm'Y^A"
blue line)
line) are
areshown
shown versus
versustime
timeduring
duringaa
3. HERA-B Target Group, Ehret, K. et al., Nucl. Instrum.
luminosity
run
at
July
27,
2000.
luminosity run at July 27, 2000.
Meth. A 456 , 206-216 (2001).
3.
HERA-B
Target Group,
K.
Nucl.
Instrum.
3.
HERA-B
Group, Ehret,
Ehret,
K.etetal.,
al.,for
Nucl.
Instrum.
ACKNOWLEDGMENTS
4. Vogel, E.,Target
Fast Longitudinal
Diagnostics
the HERA
Meth.
A
456
, ,206-216
(2001).
Mem.
A
456
206-216
(2001).
Proton Ring, Thesis, University of Hamburg, Hamburg,
I would like to thank G. Hoffstaetter, E. Vogel and F.
2002, DESY-THESIS-2002-010.
ACKNOWLEDGMENTS
4.
Vogel,
E.,
4.
Vogel,
E., Fast
Fast Longitudinal
Longitudinal Diagnostics
Diagnosticsfor
for the
theHERA
HERA
ACKNOWLEDGMENTS
Willeke, for helpful discussions.
thUniversity of Hamburg, Hamburg,
Proton
Ring,
Thesis,
Proton
Ring,
Thesis,
University
of
Hamburg,
Hamburg,
5.
Piwinski,
A,
Proc.
9
Int.
Conf.
on
High
Energy
Acc.,
would like
like to
to thank
thank G.
G. Hoffstaetter,
Hoffstaetter, E.
II would
E. Vogel
Vogel and
and F.
F.
2002,
DESY-THESIS-2002-010.
SLAC,
Stanford, 1974, p. 405.
2002,
DESY-THESIS-2002-010.
Willeke, for
for helpful
helpful discussions.
discussions.
Willeke,
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67