New Methods to Create Hollow Bunches
C. Carli and M. Chanel
CERNPS, CH-1211 Geneve 23, Switzerland
Abstract. New methods to create hollow distributions in longitudinal phase space based on manipulations with
a double harmonic RF system at high energy are presented with application to the PS Booster synchrotron (PSB).
Whereas the first tentative to create hollow bunches at the PSB aimed to improve the performance of the PSB
itself, these new methods are expected to reduce the limitations due to direct space charge forces in the receiving
PS (where no double harmonic RF system is available) after transfer. One method aims to introduce empty phase
space in the centre of the phase space by recombination of the beam in one bucket with another empty bucket.
The second method is based on redistribution of phase space surfaces during the transfer of the beam from one
second harmonic sub-bucket to another. During that process, phase space surfaces are exchanged and low density
from the periphery ends up in the centre, whereas the high density surfaces from the centre are transferred to
the periphery. Both methods have been simulated by particle tracking. The second method has been applied in
practice at the PSB. The set-up turned out to be simple and fast, and to yield hollow distributions with good
reproducibility.
INTRODUCTION
—— T
dt
The performance of accelerators limited by transverse
direct space charge forces, i.e. the "Laslett" tune shift,
may be improved by reducing the peak current inside
a bunch. For given bunch length and intensity, the peak
current is decreased by creating "flat" bunches. One possibility to obtain flat bunches is to create hollow distributions in longitudinal phase space. The scheme used at
the first attempts [1] at the PSB aimed to introduce empty
phase space, before bunching, in the centre of the coasting beam. This was tested and brought close to operation
recently [2].
In this paper, new methods to create hollow bunches in
longitudinal phase space, based on RF gymnastics with a
double harmonic RF system are presented. Those methods are in general not suitable to improve the performance of the machine in which they are applied. But
they are intended to alleviate limitations due to space
charge after transfer into a receiving machine without
other means for bunch flattening.
PRINCIPLE
Both methods presented in this paper have been simulated by particle tracking in longitudinal phase space for
a beam on a high energy flat-top (with increased length).
Therefore, appropriate forms for the RF functions have
been inserted into the equations of motion :
V2(t) sin Un^
-(20! (
V 7o
=
where 1 denotes the time (negative 1 for the "head" of the
bunch) and AE the energy offset of an individual particle
w.r.t. a reference. T ^ r f q and Er are the revolution time,
the momentum slip factor, the charge and the rest mass
of the particle. Vl and V2 are the voltages of the first and
second harmonic RF system. The phase 021 between the
two RF system is a crucial parameter, whereas the phase
0! of the principal RF system is not directly accessible
(influenced by RF loops), but plays only a minor role
and included for completeness only.
Recombination with an Empty Bucket
The method presented in this section has been triggered by tomographic reconstruction of bunch splitting
and is similar to schemes in [3]. The basic idea is to
merge the beam in one bucket with an empty bucket by
appropriate gymnastics with a double harmonic RF system. Adjusting the RF parameters in an appropriate manner, one may insert a lot of empty phase space in the centre leading to a low density there, and insert very little
empty phase space in the periphery.
A simulation of the whole process by particle tracking
is shown in Fig. 1. RF parameters shown in the upper
image are inserted into the equations of motion and
yield phase space portraits below. During the first 14 ms,
starting from a first harmonic bucket (with only a very
small or no voltage of the second harmonic system),
a double bucket structure has to be created such that
the second bucket is outside the area occupied by the
beam. This is achieved by increasing the voltage V2 of
the second harmonic RF system and shifting the phase
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
313
of the
the merged
mergedbunch
bunchand,
and,towards
towardsthe
theend
endmore
moreand
andmore
more
of
empty phase
phase space
space isis mixed
mixed in
in by
by collapsing
collapsing the
the empty
empty
empty
bucket. Care
Care is
is taken
taken that
that the
the buckets
buckets do
do not
notcollapse
collapsetoo
too
bucket.
fast towards
towards the
the end
end of
of the
the merging
mergingprocess,
process,by
bychanging
changing
fast
the RF
RF parameters
parameters slowly.
slowly. At
At time
time 50
50ms
ms the
themerging
mergingisis
the
completed
and
during
the
last
10
ms,
the
RF
system isis
completed and during the last 10 ms, the RF system
brought
back
to
the
initial
state.
brought back to the initial state.
10
2
6
V1
1
4
4
o
0
0
ϕ1
2
−1
V2
0
0
10
10
20
20
30
40
30
40
time (ms)
(ms)
time
50
50
5
5
∆E (MeV)
10
∆E (MeV)
10
0
−5
When applying
applying asymmetric
asymmetric merging
merging of
of aa bunch
bunch with
with
When
an
empty
bucket,
one
has
to
be
careful
to
generate
the
an empty bucket, one has to be careful to generate the
double
bucket
structure
such
that
the
small
bucket
double bucket structure such that the small bucket isis
outside the
the area
area occupied
occupied by
by the
the beam.
beam. For
For instance,
instance, ifif
outside
the
emittance
of
the
beam
would
be
larger,
the small
small
the emittance of the beam would be larger, the
bucket in
in Fig.
Fig. 1 after
after 15
15 ms
ms would
would not
notbe
beempty.
empty.In
Inthe
the
bucket
method outlined
outlinedhere,
here,this
this situation
situationisis created
createdon
onpurpose
purpose
method
(see situation
situation after
after 10 ms
ms in
in Fig.
Fig. 2)
2) and
and isis the
the starting
starting
(see
point of
of the
the redistribution
redistributionprocess.
process.
point
The process
process is
is best
best explained
explained with
with the
the help
help of
of Fig.
Fig. 2.
2.
The
Tracking with
with the
the RF
RF functions
functions shown
shown in
in the
the upper
upper imimTracking
age leads
leads to
to phase
phase space
space distributions
distributionsplotted
plottedbelow.
below.ParParage
ticles
have
different
shades
(or
colours
if
viewed
with
ticles have different shades (or colours if viewed with aa
device rendering
rendering colours)
colours) depending
depending on
on their
their initial
initial disdisdevice
tance from
from the
the bunch
bunch centre
centre in
in order
order to
to distinguish
distinguish parpartance
ticles stemming
stemming from
from different
different initial
initial locations.
locations. During
During
ticles
the first
first 10 ms,
ms, aa double-bucket
double-bucket structure
structure isis created
created with
with
the
the small
small bucket
bucket inside
inside the
the area
area occupied
occupied by
by the
the beam.
beam.
the
Then, the
the RF
RF parameters
parameters are
are adjusted
adjusted such
such that
that the
the iniiniThen,
tially large
large bucket
bucket shrinks
shrinks and
and releases
releases phase
phase space
space sursurtially
faces, which
which start
start to
to surround
surround the
the two
two buckets.
buckets. SimulSimulfaces,
taneously, the
the initially
initially small
small bucket
bucket grows
grows and
and captures
captures
taneously,
phase space
space surfaces
surfaces surrounding
surroundingit.
it. Thus,
Thus, along
alongthe
theproprophase
cess, surfaces
surfaces are
are transferred
transferredfrom
fromone
onebucket
bucketto
tothe
theother
other
cess,
and high
high density
density surfaces
surfaces from
from the
the centre
centre are
are brought
brought to
to
and
theperiphery.
periphery.The
Thetotal
total acceptance
acceptanceof
ofthe
thetwo
twosecond
secondharharthe
monic buckets
buckets together
together isis slightly
slightly larger
larger at
at the
the end
endof
ofthe
the
monic
process in
in order
order to
to mix
mix some
some low
low density
density from
from the
the pepeprocess
riphery with
with the
the dense
dense core.
core.
riphery
− 10
− 0.2 − 0.1 0.
0.
-0.2-0.1
τ (µs)
T(US)
00 ms
ms
0.1 0.2
0.2
0.1
7 ms
7ms
10
5
5
∆E (MeV)
10
∆E (MeV)
Redistribution of
of surfaces
surfaces in
in phase
phase space
space
Redistribution
70
70
0
− 0.2 -0.1
− 0.1 0.
0. 0.1
0.1 0.2
0.2
-0.2
τ (µs)
T(LIS)
0
−5
0
−5
− 10
− 10
− 0.2 -0.1
− 0.1 0.
0.
-0.2
τ (µs)
T(LIS)
− 0.2 − 0.1 0.
0.
-0.2-0.1
0.1 0.2
0.2
0.1
τ (µs)
T(US)
15
ms
15ms
0.1 0.2
0.2
0.1
23 ms
23ms
10
5
5
∆E (MeV)
10
∆E (MeV)
60
60
−5
− 10
0
−5
0
−5
− 10
− 10
− 0.2 -0.1
− 0.1 0.
0.
-0.2
τ (µs)
T(US)
− 0.2 − 0.1 0.
0.
-0.2-0.1
0.1 0.2
0.2
0.1
τ (µs)
T(US)
32 ms
0.1 0.2
0.2
0.1
41 ms
ms
41
10
5
5
∆E (MeV)
10
∆E (MeV)
phases (rad)
8
Voltages (kV)
3
ϕ21
0
−5
0
−5
− 10
− 10
− 0.2 -0.1
− 0.1 0.
0.
-0.2
τ (µs)
T(US)
50 ms
0.1 0.2
0.2
0.1
− 0.2 − 0.1 0.
0.
-0.2-0.1
τ (µs)
T(US)
EXPERIMENTAL RESULTS
RESULTS
EXPERIMENTAL
0.1 0.2
0.2
0.1
60 ms
ms
60
recombination of
of
FIGURE 1. Creation of hollow bunches by recombination
parameters versus
versus time
time
the bunch with an empty bucket. RF parameters
(above) and phase space portraits.
(sufficiently far
far from
from n).
φ02i
π ).Then
Then
21 to an appropriate value (sufficiently
the empty bucket is increased
increased to
to the
the desired
desired size
size while
while
keeping the full
full bucket just
just big enough to contain the
beam. The situation after
after 23 ms is the starting
starting point
point of
of the
the
merging process. RF parameters are adjusted
adjusted such
such that
that
first
first mainly the full
full bucket collapses filling
filling the
the periphery
periphery
314
Redistribution of
of phase
phase space
space surfaces
surfaces necessitates
necessitates relrelRedistribution
ativeley simple
simple RF
RF gymnastics
gymnastics and
and does
does not
not lead
lead to
to aa
ativeley
significant blow-up
blow-up of
of the
the total
total longitudinal
longitudinal emittance.
emittance.
significant
This
This makes
makes itit particularly
particularly interesting
interesting for
for the
the PSB
PSB and,
and,
thus, this
this method
method has
has been
been tested
tested experimentally.
experimentally.After
Afteraa
thus,
short set-up
set-up time,
time, hollow
hollowbunches
buncheshave
havebeen
beencreated
createdwith
with
short
good
good reliability
reliability and
and reproducibility,
reproducibility, even
even with
with the
the highhighest
est intensity
intensity possible
possible in
in the
the PSB.
PSB. Whereas
Whereas the
the simulasimulations
tions had
had only
only been
been done
done for
for aa long
long flat-top,
flat-top,the
themethod
method
has
has been
been tested
tested experimentally
experimentally on
on the
the high
high energy
energy part
part
of
of the
the ramp
ramp as
as well.
well. The
The advantage
advantage isis that
that the
thetotal
totalcycle
cycle
time
time is
is not
not increased
increased and
and the
the process
process may
may take
take longer.
longer.
44
ϕϕ21
21
88
phases (rad)
(rad)
phases
VV11
I. 666
22
W
CD
~ 444
ϕϕ11
20
30
20
30
time
(ms)
time(ms)
40
40
∆E (MeV)
(MeV)
∆E
55
∆E (MeV)
(MeV)
∆E
10
10
00
−−55
ττ(µs)
(µs)
−150
−150 −100
−100 −50
−50
-150
-100
-50
55
ms
ms
5ms
10
10
55
55
∆E(MeV)
(MeV)
∆E
10
10
00
−−55
ττ(µs)
(µs)
10
10ms
10
ms
17
ms
17ms
17
ms
10
10
55
55
∆E(MeV)
(MeV)
∆E
10
10
−−55
00
−−55
−−
0.2
0.1
-0.2
-0.1
0. 0.1
0.1 0.2
0.2
0.2 −−
0.1 0.0.
0.1
0.2
−−10
10
ττT(LIS)
(µs)
(µs)
−-0.2-0.1
0.1 0.2
0.2
−0.2
0.2−−0.1
0.1 0.0. 0.1
0.2
τT(LIS)
τ(µs)
(µs)
25
ms
25ms
25
ms
32
32ms
ms
10
10
55
55
∆E(MeV)
(MeV)
∆E
10
10
00
−−55
ττT(LIS)
(µs)
(µs)
40
40ms
ms
150
150
00
−−10
10
New
New methods
methodsto
tocreate
createhollow
hollowbunches
bunchesby
bygymnastics
gymnastics of
of
of
aa double
doubleharmonic
harmonicRF
RFsystem
system have
havebeen
been presented.
presented.One
One
method
method based
based on
on redistribution
redistribution of
of phase
phase space
space surfaces
surfaces
surfaces
has
has been
been tested
tested successfully
successfully
at the
the PSB.
PSB. The
The
aim isis to
to
successfully at
The aim
to
alleviate
alleviatelimitations
limitationsdue
dueto
to direct
directtransverse
transversespace
spacecharge
charge
forces
forces in
inaareceiving
receivingsynchrotron
synchrotron(in
(inour
ourcase
case the
the PS).
PS).
The
Thenext
nextstep
toverify
verify
thatthe
theperformance
performance
ofspace
space
stepisisto
verifythat
performanceof
charge
chargelimited
limited beams
beamsisisindeed
indeedimproved
improvedwhen
whenthe
the beam
beam
beam
isistransferred
transferred
withhollow
hollowdistribution
distributionin
inthe
thelongitudinal
longitudinal
transferredwith
phase
phase space.
space.
ACKNOWLEDGEMENTS
ACKNOWLEDGEMENTS
−−55
−−
0.2
0.1
-0.2
-0.1
0. 0.1
0.1 0.2
0.2
0.2 −−
0.1 0.0.
0.1
0.2
100
100
−-0.2-0.1
0.1 0.2
0.2
−0.2
0.2−−0.1
0.1 0.0. 0.1
0.2
ττ(µs)
(µs)
00
50
50
50
SUMMARY
SUMMARY AND
AND OUTLOOK
OUTLOOK
OUTLOOK
−−10
10
−−
0.2
0.1
-0.2
-0.1
0. 0.1
0.1 0.2
0.2
0.2 −−
0.1 0.0.
0.1
0.2
00
τx(ns)
τ(ns)
(ns)
FIGURE
FIGURE 3.
3. Tomographic
Tomographic reconstruction
reconstruction of
of
the
phase
after
of the
the phase
phase after
after
redistribution
spacesurfaces.
surfaces.
redistributionof
ofphase
phasespace
surfaces.
00
−−55
−−10
10
00
−6
−6
-6
−-0.2-0.1
−0.2
0.2−−0.1
0.1 0.0. 0.1
0.2
0.1 0.2
0.2
00ms
ms
ms
−2
−2
-2
−4
−4
-4
−−10
10
ττ(µs)
(µs)
∆E(MeV)
(MeV)
∆E
, 000
00
−−
0.2
0.1
0.2 −−
0.1 0.0.
0.1
0.2
-0.2
-0.1
0. 0.1
0.1 0.2
0.2
∆E(MeV)
(MeV)
∆E
60
60
−−55
−−10
10
5.5
5.5
5.5,
44
50
50
22
55
∆E(MeV)
(MeV)
∆E
66
∆E (MeV)
(MeV)
∆E
10
10
10
10
−−10
10
00
00
00
44
22
VV22
00
66
11
22
−−10
10
(A)
II (A)
33
Voltages (kV)
(kV)
Voltages
88
12
Density (10
(1012
p/eVs)
Density
p/eVs)
10
10
10
−-0.2-0.1
0.1 0.2
0.2
−0.2
0.2−−0.1
0.1 0.0. 0.1
0.2
We
We would
would like
like to
to Steve
Hancock for
for stimulating
stimulating
discusSteveHancock
stimulatingdiscusdiscussions
about
the
use
of
the
“Tomoscope”
and many
many
assions about the use of the "Tomoscope"
“Tomoscope” and
many aspects
pects of
of longitudinal
longitudinaldynamics.
dynamics.
τT(LIS)
τ(µs)
(µs)
REFERENCES
REFERENCES
50
50ms
ms
FIGURE
2. Creation
of hollow
hollow bunches
bunches by
by redistribution
redistribution of
of
FIGURE 2.
Creation of
phase
phase space
space surfaces.
surfaces. RF
RF parameters
parameters versus
versus time
time (above)
(above) and
and
phase
phase space
space portraits.
portraits.
A
phase
A tomographic
tomographic reconstruction
reconstruction of
of the
the longitudinal
longitudinal phase
space
after
creation
of
a
hollow
bunch
is
inFig.
Fig.3.
space after creation of a hollow bunch is shown
shownin
3.
On
hollowbunch
bunch(solid
line) isiscomcomOn top,
top,the
the profile
profilewith
withhollow
(solidline)
pared
paredwith
withthe
theprofile
profile of
ofaanormal
normalbunch
bunchwithout
withoutredistriredistribution
bution(dashed
(dashedline).
line).The
Thepeak
peakcurrent
currentisisclearly
clearlyreduced,
reduced,
with
with aa negligible
negligible increase
increase of
of the
the bunch
bunchlength.
length.
1.1. J.P.
J.P.Delahaye,
Delahaye, G.
G.Gelato,
Gelato, L.
L. Magnani,
Magnani,
G.
Nassibian,
Magnani, G.
G.Nassibian,
Nassibian,
F.
F.Pedersen,
K.H.Reich,
Reich,K.
K.Schindl
Schindland
and H.
H.Schönauer,
Schonauer,
Pedersen, K.H.
Schönauer,
Shaping
Shaping
of
Proton Distribution
Distribution for
Raising
the
SpaceShaping of
of Proton
forRaising
Raisingthe
theSpaceSpacecharge
charge of
of the
the PS
PS
Booster,
Proc. 11th
llth Int.
Int. Conf.
Conf.
on
PS Booster,
Booster, Proc.
11th
Conf. on
on
High-Energy
High-Energy Accelerators,
Accelerators,Geneva,
Geneva, 1980,
p299.
1980,p299.
2.
2. A.
A.Blas,
Bias,
S.Hancock,
Hancock,M.
M.Lindroos,
Lindroos,S.
S.Koscielniak,
Koscielniak,Hollow
Hollow
Blas,S.
Hollow
Bunch
Bunch Distributions
Distributions at
at High
High
Intensity
in the
the PS
PS
Booster,
HighIntensity
Intensityin
PSBooster,
Booster,
Proc.
Proc. 7th
7th European
European Particle
Particle Accelerator
Accelerator Conference,
Conference,
Conference,
Vienna,
Vienna, 2000.
2000.
3.
3. S.
S.Hancock,
Hancock, (Unpublished)
(Unpublished)
Simulations using
using
ESME
(Unpublished)Simulations
usingESME
ESME
4.
4. C.
C. Carli,
Carli, Creation
Creation ofof
Hollow
Bunches Using
Using aa Double
Double
ofHollow
HollowBunches
Using
Harmonic
Harmonic
RF
System,
CERN/PS
2001-073 (AE).
(AE).
HarmonicRF
RFSystem,
System,CERN/PS
CERN/PS2001-073
(AE).
315