Evolution
Evolutionofofthe
theSpallation
SpallationNeutron
NeutronSource
SourceRing
RingLattice
Lattice l
1
∗
∗
∗
∗
∗
J.J.Wei
, N.N.Catalan-Lasheras
, A.
, C.J.
, Y.Y.
,
Wei*,
Catalan-Lasheras*,
A.Fedotov
Fedotov*,
CJ.∗Gardner
Gardner*,
Y.Y.†Lee
Lee*,
∗
∗
1
Y.Y.Papaphilippou
, D.D.Raparia
, N.
Papaphilippou*,
Raparia*,
N.Tsoupas
Tsoupas*and
andJ.J.Holmes
Holmes ^
∗
†
Brookhaven
*BrookhavenNational
NationalLaboratory,
Laboratory,Upton,
Upton,NY
NY11973,
11973,USA
USA
Oak
^ OakRidge
RidgeNational
NationalLaboratory,
Laboratory,Oak
OakRidge,
Ridge,TN
TN37831,
37831,USA
USA
Abstract.
Abstract.Requirements
Requirementsofofminimum
minimumbeam
beamloss
lossfor
forhand-on
hand-onmaintenance
maintenanceand
andflexibility
flexibilityfor
forfuture
futureoperations
operationsare
are
essential
essentialforforthe
thelattice
latticedesign
designofofthe
theSpallation
SpallationNeutron
NeutronSource
Source(SNS)
(SNS)accumulator
accumulatorring.
ring.During
Duringthe
thepast
pastseven
seven
years,
the
years,
thelattice
latticehas
hasevolved
evolvedfrom
fromananall-FODO
all-FODOtotoa aFODO/doublet
FODO/doublethybrid,
hybrid,the
thecircumference
circumferencehas
hasbeen
beenincreased
increased
totoaccommodate
accommodateforfora ahigher
higherenergy
energyforeseen
foreseenwith
witha asuper-conducting
super-conductingRF
RFlinac,
linac,and
andthe
thelayout
layouthas
hasevolved
evolved
from
fromananα -a-totoananΩ-Q-geometry.
geometry.Extensive
Extensivestudies
studiesare
areperformed
performedtotodetermine
determineworking
workingpoints
pointsthat
thataccommodate
accommodate
injection
injectionpainting
paintingand
andminimize
minimizebeam
beamlosses
lossesdue
duetotospace
spacecharge
chargeand
andresonances.
resonances.InInthis
thispaper,
paper,we
wereview
reviewthe
the
evolution
of
the
SNS
ring
lattice
and
discuss
the
rationales.
evolution of the SNS ring lattice and discuss the rationales.
movable
movable fixed
fixed
scraper
scraper collimators
collimators
TABLE
1. 1. Major
TABLE
Majorlattice
latticeparameters
parametersofofthetheSNS
SNSring.
ring.
Quantity
Quantity
Value
Value
Unit
Unit
Circumference
Circumference
Kinetic
Kineticenergy
energy
Repetition
Repetitionrate
rate
Number
Numberofofprotons
protonsperperpulse
pulse
Ring
Ringdipole
dipolefield
field
Unnormalized
Unnormalizedfull
fullemittance,
emittance,H+V
H+V
Betatron
Betatronacceptance
acceptance
Momentum
Momentumacceptance
acceptance(full
(fullbeam)
beam)
Number
Numberofofsuper-periods
super-periods
, νyVy
Nominal
Nominaltunes
tunesνxv*,
Transition
Transitionenergy,
energy,γTJT
Maximum
Maximumβxfi, xβ, yPy
, βyjfryininarcarc
Maximum
Maximumβxft,
Maximum
/βminmin(H,
Maximumratio
ratioβmax
Pmax/P
(H,V)V)
Maximum
Maximumdispersion
dispersionDD
x x
) y)
Natural
Naturalchromaticity
chromaticity(ξ(^,
x , ξy%
248.0
248.0
11
6060
1.61.6
0.792
0.792
240
240
480
480
±±2 2
44
6.23,
6.23,6.20
6.20
5.3
5.3
27.9,
27.9,15.7
15.7
12.9,
12.9,13.3
13.3
11.6,
7.5
11.6,7.5
4.0
4.0
−7.9,
-7.9,−6.9
-6.9
mm
GeV
GeV
HzHz
1414
1010
TT
πµ
m
TTjUm
πµ
m
TTjUm
%%
mm
mm
mm
mm
INTRODUCTION
INTRODUCTION
The
TheSNS
SNSproject
projectis isdesigned
designedtotoreach
reachananaverage
averagebeam
beam
powerabove
above1.41.4MW
MWforforpulsed
pulsedneutron
neutronproduction
production
power
Theaccumulator
accumulatorring,
ring,operating
operatingatata afixed
fixedenergy
energy
[1,[1,2].
2]. The
1 GeV,
compressesatat6060HzHzrepetition
repetitionrate
rate1 ms
1 msbeam
beam
ofof1 GeV,
compresses
14 14
pulsescontaining
containing1.6
1.6
protonstoto650
650nsnsbunches
bunches
pulses
× x1010
protons
deliveryonto
ontothe
thetarget.
target.Table
Table1 1lists
listsmajor
majorlattice
lattice
forfordelivery
parametersofofthe
thering.
ring.
parameters
DESIGNEVOLUTION
EVOLUTION
DESIGN
shownininFig.
Fig.1,1,thethering
ringpresently
presentlyhas
hasa afourfourAsAsshown
foldlattice
latticesymmetry
symmetrycontaining
containingfour
fourdispersion-free
dispersion-free
fold
1
1 SNS
SNS
is
is
managed
UT-Battelle,LLC,
LLC,
under
contractDE-AC05DE-AC05managed
byby
UT-Battelle,
under
contract
OOOR22725forfor
U.S.
Department
Energy.
SNSis isa partnership
a partnership
00OR22725
thetheU.S.
Department
ofofEnergy.
SNS
national
laboratories:
Argonne,
Brookhaven,
Jefferson,Lawrence
Lawrence
of of
sixsix
national
laboratories:
Argonne,
Brookhaven,
Jefferson,
Berkeley,
Los
Alamos,
and
Oak
Ridge.
Berkeley,
Los
Alamos,
and
Oak
Ridge.
injection
injectionseptum
septum.!]
&&
bumps
bumps
extraction
extractionkickers
kickers
beam gap kicker
extraction
extractionseptum
septum
beam
RFRF
s
/
instrumentation
instrumentation
FIGURE
FIGURE1.1. Functions
Functionsofofthe
theSNS
SNSaccumulator
accumulatorring.
ring.
straight
straightsections,
sections, each
eachhousing
housinginjection,
injection, collimation,
collimation,
radio-frequency
radio-frequency(RF)
(RF)system,
system,and
andextraction
extraction[3].
[3].
Layout
Layout
pre-constructionstage,
stage,the
thelattice’s
lattice'sfour-fold
four-fold symsymAtAtpre-construction
metry[4]
[4]was
waschosen
chosenagainst
againsta athree-fold
three-foldsymmetry
symmetry[5]
[5]
metry
foritsitsseparate,
separate,dedicated
dedicatedfunction
functionofofeach
eachstraight
straightsecsecfor
tion,reduced
reducedmaximum
maximumdispersion,
dispersion,and
andfewer
fewerstructure
structure
tion,
resonances.Since
Sincethe
thestart
startofofconstruction
constructioninin1999,
1999,sevsevresonances.
eraliterations
iterationshave
havebeen
beenmade
madetotothe
thegeneral
generallayout
layoutofofthe
the
eral
ring.The
Theearly
earlyαa-geometry
(Fig.2)2)was
waslater
laterreplaced
replaced
ring.
-geometry (Fig.
theΩ-geometry
Q-geometrytotoavoid
avoidthe
thecrossing
crossingofofinjection
injectionand
and
bybythe
extractionlines
linesfor
foreasy
easytunnel
tunnelaccess
accessand
andmaintenance.
maintenance.
extraction
Thecircumference
circumferenceofofthe
thering
ringwas
wasalso
alsoincreased
increasedfrom
from
The
221mmtoto248
248mmtotoaccommodate
accommodatethe
thepotential
potentialincrease
increaseofof
221
injectionenergy
energyupuptoto1.3
1.3GeV
GeV(longer
(longerinjection-chicane
injection-chicane
injection
− stripping),
magnetswith
withlower
lowerfield
fieldtotoavoid
avoidHH~
stripping),which
which
magnets
madepossible
possiblebybythe
theadoption
adoptionofofsuperconducting
superconductingRF
RF
isismade
linac,
and
to
reduce
beam
density
and
foil
traversals.
linac, and to reduce beam density and foil traversals.
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
157
25
βx
25
25
25
20
20
20
2025
15
15
15
1520
10
10
10
1015
5
55
510
0
0
005
β β
βxβxx y
ββ
β yy
y
β [m]
[m]
β [m] ββ [m]
β [m]
βx
βy
0
00
0
20
20
20
20
S [m]
S [m]
[m]
S
SS[m]
[m]
40
40
40
[m]
ηηη[m]
[m]η [m]
0
40
Time: Fri Jan 22 13:11:54 1999 Last file modify time: Fri Jan 22 13:11:48 1999
Time: 0
Fri Jan 22 13:11:54 1999 Last file
modify time: Fri Jan 22 13:11:48
1999
20
40
Time: Fri Jan 22 13:11:54 1999 Last file modify time: Fri Jan 22 13:11:48 1999
Time: Fri Jan 22 13:11:54 1999 Last file modify time: Fri Jan 22 13:11:48 1999
η [m]
4.0
4.0
4.0
4.0
3.0
3.0
3.0
3.0
4.0
2.0
2.0
2.0
2.0
3.0
1.0
1.0
1.0
1.0
2.0
0.0
0.0
60
0.0
0.0
60
1.0
60
60
0.0
60
S [m]
Time: Fri Jan 22 13:11:54 1999 Last file modify time: Fri Jan 22 13:11:48 1999
FIGURE
Original
all-FODO
lattice
of SNS
the
SNS
ring.
FIGURE
4.4.Original
Original
all-FODO
lattice
of
the
SNS
ring.
FIGURE
Original
all-FODO
lattice
ofthe
the
SNS
ring.
FIGURE
lattice
of
the
SNS
ring.
FIGURE
4.4.
all-FODO
lattice
of
ring.
FIGURE 4. Original all-FODO lattice of the SNS ring.
FIGURE
Original
α
-layout
of
SNSring.
ring.
FIGURE
Original
-layout
of
theSNS
ring.
FIGURE
2.2. Original
Original
a-layout
the
SNS
ring.
FIGURE
2.2.
Original
-layout
ofof
the
SNS
ring.
FIGURE
2.
ααα
-layout
of
the
FIGURE 2. Original α -layout of the SNS ring.
66
66
βx
β
ββ
x yx
βyβy
β
ηxx
η
η
βxy x
65
5
55
1/2
1/2
β [m ]
1/2 1/2]
1/2 1/2
1/2 β 1/2[m
β [mβ β1/2][m[m1/2] ]
54
4
44
βx
βy
ηx
ηx
4
3
3
33
3
2
2
22
0
00 0
0
20
20 20
20
20
40
40
40
S
[m]
40
S [m]
[m]
40
SS[m]
S
[m]
Time:
Sun
Dec
19 18:38:10
1999
Last
file time:
modify
time:
Fri17
Dec
17 13:56:46
Time:
Sun
Dec
19
18:38:10
1999Last
Last
file
modify
time:
Dec
13:56:46
1999 1999
Time:
Sun
Dec
19
18:38:10
1999
file
modify
FriFri
Dec
17
13:56:46
1999
Time: Sun Dec 19 18:38:10 1999 Last file modify time: Fri Dec 17 13:56:46 1999
60
60 60
60
60
η [m]
4
4
4
43
3
43
3
2
2
3
2
21
1
21
1
0
0
10
0
-1
800-1 -1
-1
80 80
80
-1
80
η [m]
η [m]
η [m]
η [m]
2
1
1
11
1
Time: Sun Dec 19 18:38:10 1999 Last file modify time: Fri Dec 17 13:56:46 1999
FIGURE 5.
5. Present
Present FODO-doublet
FODO-doublet lattice
lattice of
of the
the SNS
SNS ring.
ring.
FIGURE
FIGURE
Present
FODO-doublet
lattice
ofthe
the
SNS
ring.
FIGURE
5.5.
FODO-doublet
lattice
of
ring.
FIGURE
Present
FODO-doublet
lattice
of SNS
the
SNS
FIGURE
5.5.Present
Present
FODO-doublet
lattice
of the
SNS
ring.ring.
(Fig. 7).
7). The
The long
long straight
straight section
section also
also accommodates
accommodates
(Fig.
(Fig.
7).
The
long
straight
section
also
accommodates
(Fig.
7).
The
long
straight
section
also
accommodates
(Fig.
7).
The
long
straight
also
accommodates
(Fig.
7).
The
long
straight
section
also
accommodates
possible
future
arrangement
ofsection
laser-stripping
injection
possible
future
arrangement
of
laser-stripping
injection
possible
future
arrangement
of
laser-stripping
injection
possible
future
arrangement
of
laser-stripping
injection
possible
future
arrangement
of
laser-stripping
injection
possible
arrangement
laser-stripping
injection
[9,
10]. A
Afuture
symmetric
layout of
ofofthe
the
dynamic bump
bump
further
[9,10].
symmetric
layout
dynamic
further
[9,
10].
A
symmetric
layout
of
the
dynamic
bump
further
[9,
10].
A
symmetric
layout
of
the
dynamic
bump
further
[9,
10].
A
symmetric
layout
of
the
dynamic
bump
further
[9, 10]. A symmetric
layout
of the dynamic
bump further
simplifies
the set-up
set-up of
of
transverse
painting [11].
[11].
simplifies
the
transverse
painting
simplifies
the
set-up
of
transverse
painting
[11].
simplifies
the
set-up
of
transverse
painting
[11].
simplifies
the
set-up
of
transverse
painting
[11].
simplifies the set-up of transverse painting [11].
FIGURE3.3. Present
Present Q-layout
Ω-layout of
of the
the SNS
SNSring.
ring.
FIGURE
FIGURE
3.
Ω-layout
of
the
SNS
ring.
FIGURE
3.3. 3.Present
Present
Ω-layout
ofof
the
SNS
ring.
FIGURE
Present
Ω-layout
the
SNS
ring.
FIGURE
Present
Ω-layout
of
the
SNS
Lattice
Lattice
Lattice
Lattice
Lattice
Lattice
Each achromatic
achromatic arc
arc consists
consists of
of 44 FODO
FODO cells
cells with
with
Each
Each
achromatic
arc
consists
of
cells
with
achromatic
arc
consists
of
FODO
cells
with
◦Each
achromatic
arc
consists
of444In
4FODO
FODO
with
Each
achromatic
arc
consists
of
FODO
cells
with
90
horizontal
phase
advance
[6].
1999,
the
origi90°
phase
advance
[6].
InIn1999,
1999,
the
origi◦◦ horizontal
◦horizontal
90
phase
advance
[6].
In
origiphase
advance
[6].
In
1999,
the
origi90horizontal
horizontal
phase
advance
[6].
1999,the
the
origi90
phase
advance
[6].
In
1999,
the
original
all-FODO
structure
(Fig.
4)
was
replaced
a
hybrid
nal
all-FODO
structure
(Fig.
was
replaced
aahybrid
hybrid
nal
all-FODO
(Fig.
4)
was
replaced
structure
(Fig.
4)4)
was
replaced
nal
all-FODO
structure
(Fig.
4)
was
replaced
hybrid
nal
all-FODO
structure
(Fig.
4)
was
replaced
ahybrid
hybrid
structure
withstructure
matched
FODO
arcs
and
doubletaastraights
straights
structure
with
matched
FODO
arcs
and
doublet
structure
with
matched
FODO
arcs
and
doublet
straights
matched
FODO
arcs
and
doublet
straights
structure
with
matched
FODO
arcs
and
doublet
straights
(Fig.
5)
[3].
The
lattice
combines
the
FODO’s
simplicstructure
with
matched
FODO
arcs
and
doublet
straights
(Fig.
5)5)[3].
The
lattice
combines
the
FODO's
simplic(Fig.
5)
The
combines
(Fig.
[3].
The
lattice
combines
theFODO’s
FODO’ssimplicsimplicThe
lattice
combines
the
FODO’s
simplicity
and
ease
oflattice
correction
with the
the
doublet’s
flexibil(Fig.
5) [3].
[3].
The
lattice
combines
the
FODO’s
simplicity
and
ease
of
correction
with
the
doublet's
flexibility
and
ease
of
correction
with
the
doublet’s
flexibility
and
ease
of
correction
with
the
doublet’s
flexibilof
correction
with
the
doublet’s
flexibility
for
injection
and
collimation.
The
12.5
m-long
unity
and
ease
of
correction
with
the
doublet’s
flexibilfor
injection
and
collimation.
The
12.5
m-long
unity
for
injection
and
collimation.
The12.5
12.5
m-long
unityity
for
injection
and
collimation.
The
m-long
uninjection
and
collimation.
The
12.5
m-long
uninterrupted
straight
section
with
a
flexible
phase
advance
ity
for injection
andsection
collimation.
The 12.5
m-long
uninterrupted
straight
with
a
flexible
phase
advance
interrupted
straight
section
with
a flexible
phase
advance
interrupted
straight
section
with
aa flexible
phase
advance
straight
section
with
flexible
phase
advance
further
improves
collimation
efficiency,
and
eliminates
interrupted
straightcollimation
section with
a flexibleand
phase
advance
further
improves
efficiency,
eliminates
further
improves
collimation
efficiency,and
andeliminates
eliminates
further
improves
collimation
efficiency,
improves
collimation
efficiency,
eliminates
magnets
between
secondary
collimators
[7].
Comparing
further
improves
collimation
efficiency,and
andComparing
eliminates
magnets
between
secondary
collimators
[7].
magnets
between
secondary
collimators
[7].
Comparing
magnets
between
secondary
collimators
[7].
Comparing
collimators
[7].
Comparing
with the
thebetween
originalsecondary
lattice, matching
matching
between
the
arcs and
and
magnets
between
secondary
collimators
[7].the
Comparing
with
original
lattice,
between
arcs
with
the
original
lattice,
matching
between
the
arcsand
and
with
the
original
lattice,
matching
between
the
arcs
original
lattice,
matching
between
the
arcs
and
the
straights
increases
the
arc
acceptance
by
50%
with
with
the
original
lattice,
matching
between
the
arcs
and
the
straights
increases
the
arc
acceptance
by
50%
with
the
straights
increases
the
arc
acceptance
by
50%
with
the
straights
increases
the
arc
acceptance
by
50%
with
increases
the arcThe
acceptance
by 50%
thestraights
same magnet
magnet
aperture.
dipoles were
were
alsowith
centhe
same
aperture.
The
dipoles
also
centhe
increases
the
arc
acceptance
by
50%
with
the
same
magnet
aperture.
The
dipoles
werealso
alsocencenthetered
same
magnet
The
dipoles
were
magnet
aperture.
The
dipoles
were
also
ceneach
halfaperture.
cell
tomaximize
maximize
the acceptance.
acceptance.
tered
ininineach
half
cell
to
the
the
same
magnet
aperture.
The dipoles
were also centered
each
half
cell
maximize
the
acceptance.
tered
in each
half
cell
to
maximize
the
acceptance.
half
cell
to to
maximize
the
acceptance.
tered in each half cell toInjection
maximize the acceptance.
Injection
Injection
Injection
Injection
Injection atat aa dispersion-free
dispersion-free
region allows
allows indepenindepenInjectionregion
Injection
Injection
a dispersion-free
region
allows
indepenInjection
at aat
dispersion-free
region
allows
independently
adjustable
painting
in
the
transverse
(with
orbit
a
dispersion-free
region
allows
independently
adjustable
painting
ininthe
transverse
(with
orbit
dently
adjustable
painting
the
transverse
(with
orbit
Injection
at
a
dispersion-free
region
allows
independently
adjustable
painting
in
the
transverse
(with
orbit
bumps
in
the
ring)
and
longitudinal
(with
an
energyadjustable
painting
in
the
transverse
(with
orbit
bumps
ininthe
ring)
and
longitudinal
(with
energybumps
the
ring)
and
longitudinal
(withanan
an
energydently
adjustable
painting
in
the
transverse
(with
orbit
bumps
in
the
ring)
and
longitudinal
(with
energyspreadingphase-modulated
phase-modulated
RF cavity
cavity(with
in the
thean
HEBT)
diring) and longitudinal
energyspreading
RF
in
HEBT)
dispreading
phase-modulated
RF
cavity
inthetheHEBT)
HEBT)
dibumps
in
the
ring)
and
longitudinal
(with
an
energyspreading
phase-modulated
RF
cavity
in
directions
for
a
robust
operation
(Fig.
6)
[8].
With
the
long
spreading
phase-modulated
RF
cavity
in
the
HEBT)
directions
for
a
robust
operation
(Fig.
6)
[8].
With
the
long
rections
for
a
robust
operation
(Fig.
6)
[8].
With
the
long
spreading
phase-modulated
RF
cavity
inlattice,
the HEBT)
directions
aa robust
operation
(Fig.
6)
With
the
long
straightfor
section
provided
bythe
the
doublet
theinjecinjecrections
for
robust
operation
(Fig.
6) [8].
[8].
With
long
straight
section
provided
by
doublet
lattice,
the
straight
section
provided
by the
doublet
lattice,
the
injecrections
for
a
robust
operation
(Fig.
6)
[8].
With
the
long
straight
section
provided
by
the
doublet
lattice,
the
injection
chicane
is
made
independent
from
the
lattice
tuning
straight
sectionisisprovided
by the doublet
the tuning
injection
made
from
the
tionchicane
chicane
madeindependent
independent
fromlattice,
thelattice
lattice
tuning
straight
section
provided
by the doublet
lattice,
injection
chicane
is
independent
from
lattice
tuning
tion
chicane
is made
made
independent
from the
the
latticethe
tuning
tion chicane is made independent from the lattice tuning
Tuning and
and Working
Working Point
Point
Tuning
Tuning
and
Working
Point
Tuning
and
Working
Point
Tuning
Working
Point
Tuning
and
Working
Point
Tune adjustment
adjustment is
is provided
provided by
by five
five families
families of
of
Tune
Tune
isis is
provided
by
five
families
ofof of
Tune
adjustment
provided
byby
fivethe
families
Tune
adjustment
provided
by
five
Tuneadjustment
adjustment
provided
five
families
quadrupole
power supply.
supply.
Horizontally,
phase
adquadrupole
power
Horizontally,
the
phase
adquadrupole
power
supply.
the
phase
adquadrupole
power
supply.
Horizontally,
thethe
phase
ad-adquadrupole
power
Horizontally,
the
quadrupole
power
phase
vance
across
the
arc
issupply.
fixedHorizontally,
toHorizontally,
satisfy achromatic
achromatic
condivance
across
the
arc
is
fixed
to
satisfy
condivance
across
the
arc
is
fixed
to
satisfy
achromatic
condivance
across
the
arc
is
fixed
satisfy
achromatic
condivance
across
the
arc
to
satisfy
achromatic
vance
across
the
arc is
toto
satisfy
condition.
The
tuning
range
is fixed
limited
to
aboutachromatic
one unit
unit (from
(from
tion.
The
tuning
range
limited
about
one
tion.
The
tuning
range
isis
to
one
unit
(from
tion.
The
tuning
range
limited
to
about
one
tion.
The
tuning
range
islimited
limited
toabout
about
one
unitunit
(from
6
to
7)
(Fig.
8).
Vertically,
the
tuning
range
is
about
two
tion.
The
tuning
range
is
limited
to
about
one
(from
to
7)
(Fig.
8).
Vertically,
thetuning
tuning
range
about
two
666units
7)
(Fig.
8).
Vertically,
the
range
isis
two
6to
toto
7)(from
(Fig.
8).
Vertically,
the
tuning
range
to
7)
(Fig.
8).
Vertically,
tuning
range
isabout
about
twotwo
5
to
7)
without
significant
perturbation
from
6
7)
(Fig.
8).
Vertically,
the
tuning
range
is
about
units
(from
to
7)
withoutsignificant
significant perturbation
perturbation from
from
units
(from
to7)
7)7)
significant
perturbation
units
(from
5555to
without
units
(from
to
7)
without
significant
perturbation
from
the
injection
bump
[12].
units
(from
5
to
without
significant
perturbation
from
the
injection
bump
[12].
theinjection
injection
bump
the
bump
[12].
the
injection
bump
[12].
The
nominal
working
point
(
ν
ν
,
)
is
chosen
to
be
x
y
the
injection
bump
[12].
The
nominal
working
point
, v ) is
is chosen
chosen to
to be
be
Thenominal
nominal
working
point
The
point
(((v
The
nominal
working
(νννxxxx,(,,ννννyy,yy)))νis
chosen
to 9).
be be
νischosen
νchosen
(6.23,
6.2)
nearworking
the
coupling
resonance
=
(Fig.
y (Fig.
The
nominal
working
point
is
to
(6.23,
6.2)
near
the
coupling
resonance
=
v
9).
x νvyxx)=
y
ν
(6.23,
6.2)
near
the
coupling
resonance
(Fig.
9).
ννxxx== νyeven
(6.23,
6.2)
near
the
coupling
resonance
(6.23,
6.2)
near
the
coupling
resonance
(Fig.
9).
y
With
full
coupling,
a
round
beam
is
realized
with
νx =
νy with
(6.23,
6.2)
near theaa coupling
resonance
(Fig.
With
full
coupling,
round
beam
is realized
realized
even
with 9).
With
full
coupling,
round
beam
even
With
full
coupling,
aa[8].
round
isis
With
full
coupling,
round
beam
is realized
realized
even
with
correlated
painting
Thebeam
full
tune
spread
is
accomWith
full
coupling,
a
round
beam
is
realized
even
with
correlated
painting
[8].
The
full
tune
spread
is
accomcorrelatedin
painting
[8].
The
full
tune
spread
isis accomcorrelated
painting
[8].
The
full
spread
correlated
painting
[8].
Thewithout
fulltune
tune
spreadlower-order
accommodated
the
tune
space
crossing
correlated
painting
[8].
The
full
tune
spread
is
accommodated
in
the
tune
space
without
crossing
lower-order
modatedin
in
thetune
tunespace
space
without
crossing
modated
the
without
lower-order
modated
in
the
tune
space
without
crossing
lower-order
structure
resonances
(Fig.
9).
Ancrossing
alternative
working
structure
resonances
(Fig.
9).
An
alternative
working
modatedresonances
in the tune(Fig.
space
without
crossing working
lower-order
structure
resonances
(Fig.
9).
An
alternative
working
structure
9).
An
alternative
structure
resonances
(Fig.from
9). the
An structure
alternative
(6.4,
6.3)
is
further
away
lines
2νx =
(6.4,
6.3)
is
further
away
from9).
theAn
structure
linesworking
2v
structure
resonances
alternative
x =
(6.4,
6.3)
isfurther
further
away(Fig.
from
the
structure
lines
==
(6.4,
6.3)
is
away
from
the
structure
lines
222ννworking
νxx x=
(6.4,
6.3)
is
further
away
from
the
structure
lines
12
and
2
=
12,
although
some
thirdand
fourth-order
ν
y
12
and
2v
=
12,
although
some
thirdand
fourth-order
y
(6.4,
6.3)
is
further
away
from
the
structure
lines
2νx =
12
and
2
=
12,
although
some
thirdand
fourth-order
ν
y
12
and
2
=
12,
although
some
thirdand
fourth-order
ν
12 and 2νyy = 12, although some
third- and fourth-order
12 and 2νy = 12, although Hsome
third- and fourth-order
-
HHHH-
H
+
H+
H
+
HH +
+
FIGURE
6.
H
FIGURE
6.
FIGURE
6.
injection
septum
injection
injection
injection
foil
septum
septum
septum
foil
injection
foil
septum foil
D
D
DD
0
-HH
H - H00 H- dump
0H H HHdump
H HH
septum
foil
stripping
stripping
magnet
stripping
magnet
stripping
magnet
magnet
stripping
0
-
dump
0 H H
dump
septum
Hseptum
septum
0
H0 0 dump
HH septum
0
H
D
+
H+
H+
HH +
Q
D
QD
DD Q D
Q
DD
D a FODO
magnet layout with
injection
Q
Q
F
Q
H
F
+QQ
FF
QF
Original
straight.
D
D
Original injection layout with
with aa FODO
FODO
straight.
straight.
FIGURE
FIGURE6.6. Original
Originalinjection
injectionlayout
layoutwith
withaaFODO
FODOstraight.
straight.
FIGURE 6. Original injection layout with a FODO straight.
158
Horizontal
550
Horizontal
Horizontal
290
290
80
80
(2, (2,
(2,−1) −1)
−1
)
(2,
−1
)
3596
3596
12500
1814
12500
2381
2029
3596
400
700
550
12500
(6.23,5.24)
Vertical
Tune
Vertical
Tune
Vertical
Tune
Vertical Tune
(3,−(3,−
(3,−1) 1)
(12 ) (2
(3,− (2,,−2 ,−2
1) −2) )
(2
)
,−
2)
(1,3)
(1
(1,3,3) )
(1,3)
6.5
6.5
6.5 Tune
6.5
Horizontal
Horizontal
Tune
Horizontal
Tune
Horizontal
6.5 Tune
&— — !
X
N
-- \
§teX i
(
)
/^">?
N
^?\d
3)
(0,4)
,−2,−2)
5.7 5.8 (0,4)
(1{
(1,−
(1
^/
\
5.73 (1,35.83
5.93 6.03 6.13
6.33 6.43
6.53
6.63
3) 36.23
)
)
5.7
)
(1,−
5.7
(0,4)
(1,− 6.23
,−2
5.73
5.83
5.93
6.03
6.13
6.33
6.43
16.53
5.73 5.83
5.83 5.93
5.93 6.03
6.03 Horizontal
6.13 6.23
6.23
6.33 6.43
6.43 (6.53
6.53 6.63
6.63
Tune
5.73
6.13
6.33
6.63
)
3
5.7
(1,− Tune
Horizontal
Horizontal
Tune6.33 6.43 6.53
Horizontal
Tune
5.73 5.83 5.93 6.03
6.13 6.23
(0,2)
(6.23,5.24)
(6.23,5.24)
(6.23,5.24)
|l(?--i-4
(1
,3),3
)
/ x (0,2)
(0,2) •"^^
(6.3,5.8)
(6.3,5.8)
(6.3,5.8)
(6.3,5.8)
slf\\>
-r---to#) --- -^
^''>y;
a
' r: lf''V
^ ™//
-^
(0,2) ^^,"v
(0,2)
'^C~~--.
\
^
x
//
^' $<<:\ !/djf-f\
'
(2
(2(,21)
,1,1
(2) )
,1
)
(3,0)
(3,0)
(3,0)(3,0)
(2,0)
(2,0)
(2,0)
(2,0)
5
55 66
6
5
6
**««.
„ ,_^. „ ^ ™ „ „ ™
(6.4,6.3)
(6.4,6.3)
(6.4,6.3)
(6.4,6.3)
(6.23,6.2)
(6.23,6.2)
(6.23,6.2)
(6.23,6.2)
5.5
5.5
5.5
5.5
5.5
'*4
(12 (4,0)
(12 (4,0)
,−
(12 ,−(4,0)
,− 12) 12)
(12 (4,0)12)
,−
12)
((3
2,,−
2−
−((3
11,,−
11
((3
2,,−
−11))) ))
)
((3
2,,−
−11)
)
(1,0)
(2,0)
(4,0)
(3,0)
(1,0)
(2,0)
(4,0)
(3,0)
(1,0)
(2,0)
(4,0)
(3,0)
S- _r^---
\i-j^\:---^
)
,2 )
(2,1
) (3
,2) )
) (22,1
), )
,2 (3
(3
(2,1(3
(2,1
Vertical
Tune
Vertical
Tune
Vertical
Tune
Vertical
Tune
~- -ij.rf-
„ „ „ ^^.^y^^^^
) )) )
,1 ,1,1 ,1
(3 ((33 (3
6
6
6
(0,4)
(0,4)
(0,4)
(0,4)
/' / /
21)
6.5
6.5
6.5
6.5
(0,3)
(0,3)
(0,3)
(1,2)
(1,2)
(1,2)
$" /t^v'^
21,
)(
) ,21)
,21 (21,21
(21 (21
7
7
7
Present injection layout with a doublet straight.
injection
layout
with
doubletstraight.
straight.
Present
aa doublet
Presentinjection
injectionlayout
layoutwith
with
Present
injection
layout
with aa doublet
doubletstraight.
straight.
\ \*^. ,i> ^
^3
6.73
6.73
6.'6.73
6.63
6.73
Horizontal Tune
14 proFIGURE 9. Tune spread of a beam containing 2 × 1014
1414
FIGURE
9.9.
Tune
spread
of
aaabeam
containing
22×
10
proFIGURE
Tune
spread
of
beam
containing
x
10
FIGURE
9.
Tune
spread
of
beam
containing
2
×
10
protons in the SNS ring. The computer-simulation results areproob14 protons
ininthe
SNS
ring.
The
computer-simulation
results
are
obtons
the
SNS
ring.
The
computer-simulation
results
are
obFIGURE
9.
Tune
spread
of
a
beam
containing
2
×
10
the the
SNSUnified-Accelerator-Libraries
ring. The computer-simulation
results
are
obtained with
(UAL)
package
tained
with
the
Unified-Accelerator-Libraries
(UAL)
package
tained
with
the
Unified-Accelerator-Libraries
(UAL)
package
the
Unified-Accelerator-Libraries
(UAL)
package
tons
in
the
SNS
ring.
The
computer-simulation
results
are
ob[13]. Structure resonances are indicated in red.
[13].
Structure
are
[13].
Structure
resonances
are
indicated
red.
Structure
resonances
areindicated
indicatedinininred.
red. (UAL) package
tained
with resonances
the
Unified-Accelerator-Libraries
3 Structure resonances are indicated in red.
[13].
(0,3)
(0,3)
(1,1
(0,3)
((11,1) (2
,1))(2,2) (0,3)
(2,2, )
(0,4) (1,1) 2)
(-^V
(0,4)
2,2
.(0,4)"."(0,4)
)
7
77
(0,4)
(4,0)
(4,0)
(4,0)
(4,0)
FIGURE 7.
FIGURE
7.7.
FIGURE7.
FIGURE
~~^,% >/:{"/ x f
,S--''\ ' \;7^.::::^
1)
3230
2570
6850
−21
)
80
8080
80
40
80
80
80
30
890
2.94 kG
46.2 mr
(21
,
80
40
30
80
40
40
30
100
30
i% K
80
80 80
80 80
80
80
90
150150
150
190
170
100 100
140140
170170
170
80 80
80
40 8040 40
80
55
90 90
150
25
140
80
100 100 100
40
55
25 25
90
55 55
90
90 90
25
70 70
70 70
70 70
70
140
2029
2029
(3,0)
(3,0)
(3,0)
(21 (
,− 21,
−
1
2
(21(3,0)
21
,− ) )
21)
290
190
190
100
90
70
900
1)
(2,
:
3596
890
2.94 kG
890
46.2
mr
2.94
kG
46.2 mr
900
900
1814
914
1814
550
550
1)
(2,
1)
(2, (2,1)
2381
2381
400
400
700
700
)
863
2.75 kG
42.0 mr
(3,1
890
2.94 kG
46.2 mr
990
2.4 kG
42.0 mr
2029
1814
914
914
12500
3230
3230
1530
540
2570
1530428 540
2570
0.04 kG (0.04 kG)
0.25 mr
540
990
2.4 kG
990
42.0 mr
900 2.4 kG
42.0 mr
872
914
3.0 kG
46.2 mr
2381
863
2.75 kG
863
42.0kG
mr
2.75
42.0 mr
550
,1)
(3
)
(3,1(3,1)
21)
700
872
3.0 kG
872
46.2
mr
3.0
kG
46.2 mr
863
2.75 kG
42.0 mr
3230
400
6850
1530
6850
1160
2570
)
500
540
428
428 kG (0.04 kG)
0.04
0.04 mr
kG (0.04 kG)
0.25
0.25 mr
1)
(2,
,1)
1()2 )
(2, (2,1
6850
,
(21
21)
) 21,
,21 ( 21)
(21 (21,
428
0.04 kG (0.04 kG)
0.25 mr
1160
1530
839
0.66
839 kG (0.80 kG)
9.39
0.66mr
kG (0.80 kG)
9.39 mr
839
0.66 kG (0.80 kG)
1650
1160
1650 9.39 mr 1160
1650
(1
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(1,
δp/p=[−0.7%,0.7%] @ 240
π mm
mrad
2)
6.7
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8p/p=[-0.7%,0..7%]@@240
240πJimm
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6.7 (1 (0,3) ,3),3)(1,3) δp/p=[−0.7%,0.7%] @ 240 π mm mrad (1,2()1,2) (1
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6.7 ,2) (0,3)
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6.6 (1,(21,23)()
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6.2
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SNS Working Point (νx,νy)=(6.23,6.20)
SNS
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Point
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,ν
)=(6.23,6.20)
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Working
Point
(ν
,ν(ν
)=(6.23,6.20)
y,ν )=(6.23,6.20)
SNS
Working
Point
SNS
Working
Point
(v
xxx,v
yyx)=(6.23,6.20)
y
δp/p=[−0.7%,0.7%] @ 240 π mm
mrad
center line
-
3000
2.08 kG
110.8
mr
H
H
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1.0 GeV
1.0 GeV
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7
non-structure
non-structureresonances
resonancesmust
mustbe
becrossed.
crossed. A
A split-tune
split-tune
non-structure
resonances
must
be
crossed.
A
split-tune
working
point
(6.23,
5.24)
can
also
be
used
for
decouworking
point
(6.23,
5.24)
can
also
be
used
for
decouworking
point
(6.23,
5.24)
can
also
be
used
for
decouworking
pointresonances
(6.23,Old
5.24)
can also
be used
for
decounon-structure
must
be
crossed.
A
split-tune
pled
operation
[14].
working
points
(5.82,
5.8)
and
pled
operation
[14].
Old
working
points
(5.82,
5.8)
and
pled
operation
[14].
Old
working
points
(5.82,
5.8)
and
pled 5.8)
operation
[14]. Old
working
points
(5.82,
5.8)
and
working
point
(6.23,
5.24)
can
also
be
used
for
decou(6.3,
were
abandoned
due
to
matching
difficulty
and
(6.3,
5.8)
were
abandoned
due
to
matching
difficulty
and
(6.3,5.8)
were
abandoned
due
to
matching
difficulty
and
(6.3, operation
5.8) were
abandoned
due to respectively.
matching
difficulty
proximity
resonance,
pled
[14]. Old
working
points (5.82,
5.8)and
and
proximity
totostructure
structure
resonance,
respectively.
proximityto
structure
resonance,
respectively.
proximity
to
structure
resonance,
respectively.
(6.3, 5.8) were abandoned due to matching difficulty and
and
Perturbations
and
Correction
proximityPerturbations
to structure resonance,
respectively.
Perturbations
andCorrection
Correction
Perturbations
and
Correction
The
injection
chicane
produces
a
perturbation
The
injection
chicane
aCorrection
perturbation
of
about
Theinjection
injection
chicaneproduces
produces
perturbationof
ofabout
about
Perturbations
and
The
chicane
produces
aaperturbation
of
about
β
β
/
,
and
0.1
m
in
D
[12].
Together
with
the
5%
in
∆
y
y
x
βy /βy , and
0.1
mmininDDxx [12].
Together
with
the
5%
inin∆A/Jy/jS^,
5%
and
0.1
[12].
Together
with
the
0.1 m in Dxare
[12].
Together
with
the
5% in ∆βbump,
y /βy , and
dynamic
the
dispersions
perturbed
by
0.25
m
The injection
chicane
produces
aperturbed
perturbation
of
about
dynamic
bump,
the
dispersions
are
by
0.25
mm
dynamic
bump,
the
dispersions
are
perturbed
by
0.25
dynamic
bump,
the dispersions
are perturbed by 0.25 m
(H)
and
0.15
m
(V),
respectively.
5%
in
∆β0.15
, and
0.1
m in Dx [12]. Together with the
(H)
and
(V),
respectively.
(H)
and
0.15
m
(V),
respectively.
y /βym
(H)
and 0.15 m
(V),
respectively.
Correctors
up
to
octupole
are
orbit
Correctors
up
totodispersions
octupole
order
are
used
for
orbit
dynamic
bump,
are perturbed
by
Correctors
upthe
octupole order
order
are used
used for
for0.25
orbitm
Correctors
up
to
octupole
order
are used for orbit
β
-wave
and
vertical-dispersion
correction,
decoupling,
β
-wave
and
vertical-dispersion
correction,
decoupling,
correction,
/3-wave and vertical-dispersion
(H)
and 0.15decoupling,
m (V), respectively.
βcorrection
-wave and(Fig.
vertical-dispersion
correction, and
decoupling,
correction,
17].
correction,
and
resonance
correction
10)
[16,
17].
correction,
andresonance
resonance
correction
(Fig.
10)[16,
[16,
17].
Correctors
to octupole
order(Fig.
are 10)
used
for
orbit
correction,
andupresonance
correction
(Fig.
10)
[16,
17].
β
-wave
and
vertical-dispersion
correction, decoupling,
SUMMARY
SUMMARY
SUMMARY
correction, and resonance
correction (Fig. 10) [16, 17].
SUMMARY
With
With
four-fold
symmetry,
dispersion-free
injection,
colWithfour-fold
four-foldsymmetry,
symmetry,dispersion-free
dispersion-freeinjection,
injection,colcolWith
four-fold
symmetry,
dispersion-free
injection,
collimation,
RF,
and
extraction,
and
a
matched
SUMMARY
limation,
FODOlimation, RF,
RF, and
and extraction,
extraction, and
and aa matched
matched FODOFODOlimation,
RF, and extraction,
and
matched
FODOarc/doublet-straight
optics,
the
lattice
is
arc/doublet-straight
optics,
the
SNS
ring
lattice
is
optiarc/doublet-straight
optics,dispersion-free
theSNS
SNSaring
ring
lattice
isoptioptiWith
four-fold
symmetry,
injection,
colarc/doublet-straight
optics,
the
SNS
ring
lattice
is
optimized
for
maximum
acceptance,
maximized
dispersionmized
for
maximum
acceptance,
maximized
dispersionmized
for
maximum
acceptance,
maximized
dispersionlimation,
RF,
and
extraction,
and
a
matched
FODOmized
for
maximum
acceptance,
maximized
dispersionfree
free
space,
flexible
injection,
high-efficiency
collimation,
freespace,
space,flexible
flexibleinjection,
injection,high-efficiency
high-efficiencycollimation,
collimation,
arc/doublet-straight
optics, the
SNS ring lattice
is optifree
space,
flexible injection,
high-efficiency
collimation,
and
and
easy
corrections.
andeasy
easycorrections.
corrections.
mized
for
maximum
acceptance,
maximized
dispersionand
easy
corrections.
We
We
thank
G.
Rees
and
the
ASAC
committee
for
adWethank
thankG.
G.Rees
Reesand
andthe
theASAC
ASACcommittee
committeefor
foradadfree
space,
flexible
collimation,
We
thank
G.
Rees
and thehigh-efficiency
ASAC
committee
for advice,
and
Y.
Cho,
J.J.J.injection,
Galambos,
N.
S.
Tepikian,
vice,
and
Y.Y.
Cho,
Galambos,
N.
Malitsky,
S.S.
Tepikian,
vice,
and
Cho,
Galambos,
N.Malitsky,
Malitsky,
Tepikian,
and
easy
vice,
andcorrections.
Y. Cho,
J.
Galambos,
Malitsky,
S. Tepikian,
D.
W.
and
Weng
for
D.
Trbojevic,
W.
Wan,
and
W.T.
Weng
for
discussions.
D.Trbojevic,
Trbojevic,
W.Wan,
Wan,
andW.T.
W.T.N.
Weng
fordiscussions.
discussions.
thank G.
for adD.We
Trbojevic,
W.Rees
Wan,and
and the
W.T.ASAC
Weng committee
for discussions.
vice, and Y. Cho, J. Galambos, N. Malitsky, S. Tepikian,
D. Trbojevic, W. Wan, and W.T. Weng for discussions.
[m][m]
∆β∆β∆β
[m]
∆β [m]
Horizontal Tune
FIGURE 8. Nominal (6.23, 6.2) and alternative working
FIGURE
8.8. Nominal
(6.23,
6.2)
and
working
FIGURE
Nominal
(6.23,
6.2)
and alternative
alternative
working
FIGURE
8.
Nominal
(6.23,
6.2)
and
alternative
working
points (6.4, 6.3), (6.23, 5.24)
in the
transverse
tune space.
Sum
points
(6.4,
6.3),
(6.23,
5.24)
in
the
transverse
tune
space.
Sum
points
(6.4,
6.3),
(6.23,
5.24)
in
the
transverse
tune
space.
Sum
points
(6.4,
6.3),
(6.23,
5.24)
in
the
transverse
tune
space.
Sum
structure resonances
up to (6.23,
fourth order
are shown
in red.working
Other
FIGURE
8.
Nominal
6.2)
and
alternative
structure
resonances
up
to
fourth
order
are
shown
in
red.
Other
structure
resonances
up
to
fourth
order
are
shown
in
red.
Other
structure
resonances
up
to fourth
order
areblack.
shown
in space.
red. Other
resonances
up
to third
order
areinshown
in
points
(6.4,
6.3),
(6.23,
5.24)
the
transverse
tune
Sum
resonances
up
resonancesup
upto
thirdorder
orderare
areshown
shownin
inblack.
black.
resonances
totothird
third
are
shown
structure
resonances
uporder
to fourth
orderin
areblack.
shown in red. Other
resonances
up toresonances
third order must
are shown
in black.A split-tune
non-structure
be crossed.
-3
∆βx without sextupoles
∆β
sextupoles
x without
∆β
sextupole
correction
∆β
without
sextupoles
x with
10
10
10
10
0
10
x
correction
——— ∆β
Ap
withsextupole
sextupole
correction
x xwith
∆β
sextupoles
∆β
correction>
y without
x with sextupole
sextupoles
— — - ∆β
Ap
without
sextupoles
y ywithout
∆β
sextupoles
∆β
sextupole
correction
∆β
without
sextupoles
x without
y with
y
correction
_ _ _ _ _ ∆β
^
withsextupole
sextupole
correction
y with
∆β
sextupole
correction
∆β
sextupole
correction
x with
y with
20
30
40 sextupoles
50
60
∆βy without
20
30
40
50
60
20
30
40
50
s [m]
∆β
correction
20
30 with sextupole
40
50
60
ss[m]
[m]y
20
s [m]
30
40
50
60
FIGURE
10. Correction
Correction of
of off-momentum
off-momentum
(∆p/p =
= −0.7%)
−0.7%)
s [m]
FIGURE
10.
(∆p/p
FIGURE
10.
Correction
of
(Ap/p
==-0.7%)
FIGURE
10.
Correction
of off-momentum
off-momentum
(∆p/pcase.
−0.7%)
optics
using
four-family
sextupoles
in
a
mismatched
Data
optics
using
four-family
sextupoles ininaamismatched
case. Data
optics
using
four-family
opticsfrom
using
four-family sextupoles
sextupoles in amismatched
mismatchedcase.
case.Data
Data
taken
[15].
taken
from
[15].
FIGURE
10.
Correction
of
off-momentum
(∆p/p
=
−0.7%)
taken
taken from
from [15].
[15].
optics using four-family sextupoles in a mismatched case. Data
REFERENCES
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