PEP-X Ultra Low Emittance Storage Ring Design at SLAC
Lattice Design and Optimization
Min-Huey Wang
SLAC National Accelerator Laboratory
With contributions by Yuri Nosochkov, Y. Cai, K. Bane
Mini-workshop on Dynamic Aperture Issues of USR
IUCF, Bloomington, Nov. 11-12, 2010
Outline
• Introduction of PEP-X• Lattice design• Optimization of dynamic aperture• IBS emittance and Touschek lifetime• Future plan
– Emittance optimization• Emittance 30 pm-rad storage design
– PEP X soft x-ray FEL– PEP X ERL
Existing PEP-II rings
• 2.2 km existing rings in PEP tunnel• Six 243 m arcs and six 123 m long straights• 60 or 90 deg FODO lattice• Can reach ~5 nm-rad emittance at 4.5 GeV (w/o wiggler) – too high for a modern light source•No dispersion free straights for IDS
• Design a new low emittance ring in the PEP-II tunnel. – ~0.1 nm-rad emittance at 4.5 GeV for high brightness
– >24 dispersion free straights for insertion devices
– Use existing PEP-II tunnel and utilities
PEP-X low emittance ring
Same ring layout as PEP-II in the exist tunnel using existing RF system
New optics with:• Two DBA arcs yielding 30 ID straights• Four TME arcs for low emittance• ~90 m wiggler to reach ~0.1 nmrad emittance at 4.5 GeV• FODO optics in long straights• PEP-II based injection system(Horizontal injection)
0 50 100 150 200meters
Photon Science Lab-Office
Building
0 50 100 150 200meters
Photon Science Lab-Office
Building
R. Hettel et alEPAC08
Conceptual Layout of PEP-X with photon beamlines at SLAC
PEPX Lattice
DBA
TME Straight
Injectionx=1.523y=0.508
x=0.373y=0.124
DBA Supercell
low b ID high b ID
4 harmonic sextupoles, 2 families6 chromatic sextupoles, 4 families
• Two standard cells are combined into one supercell with a low and high ID beta: x,y = 3.00, 6.07 m and x,y = 16.04, 6.27 m. 8 supercells per arc.
• Phase advance is optimized for compensation of both sextupole and octupole driving terms and maximum dynamic aperture: x/2 = 1.5+3/128, y = x/3.
• Harmonic sextupoles are added for further reduction of the resonance effects and amplitude dependent tune spread.
TME cell
• 7.6 m cell with ~0.1 nm-rad intrinsic emittance.• 32 standard and 2 matching cells per arc.• X and Y phase advance is set near 3/4 and /4 for compensation of
sextupole and octupole effects and maximum dynamic aperture.• Optimized for maximum momentum compaction.
Injection straight section
• Existing PEP-II injection straight with 4 additional quads.• PEP-II vertical injection optics is changed to horizontal to avoid vertical injection oscillations in the IDs.• Large horizontal x = 200 m at septum for larger injection acceptance.• Existing 4 DC bump magnets and 2 fast kickers.
Phase space diagram at injection point
Wiggler straight
Dispersion in ~5 m wiggler section
•DBA and TME arcs without wiggler yield e = 0.38 nm-rad• 89.3 m wiggler is inserted in one long straight section yielding = 0.086 nm-rad.• Wiggler is split in 18 identical sections to fit FODO cells.
•Wiggler parameters optimized for strong damping effect: 10 cm period, 1.5 T field.• The long wiggler can be split in half and placed in two separate straights for better handling of radiated power (4.7 MW at 1.5 A).
0 0.5 1 1.5 2 2.50
0.2
0.4
0.6
0.8
1
B field of damping wiggler (Tesla)
Em
itta
nce
rati
o of
dam
ping
(/
0)
w = 20 cm, N
p = 446
w
= 15 cm, Np = 595
w
= 10 cm, Np = 892
w
= 5 cm, Np = 1785
2* DBA + 4*TME cells
0= 0.379 nmrad
<x> = 10.7 m
dot line <
x> = 5 m
0 50 100 1500
0.2
0.4
0.6
0.8
1
Total damping wiggler length (m)
Em
itta
nce
rati
o of
dam
ping
(/
0)
w = 20 cm
w
= 15 cm
w
= 10 cm
w
= 5 cm
2* DBA + 4*TME cells
0= 0.379 nmrad
Bw
= 1.5T
Optimization of wiggler parameters
vs L
vs B
Based on analytic formulas: • Most efficient damping for L < 100 m.• More damping with a shorter period, higher field and lower x, but the rate of reduction gradually decreases.• High peak field requires a smaller gap which reduces vertical acceptance and increases resistive wall impedance.• Selected parameters: 10 cm period, 1.5 T peak field, 89.3 m total length.
Complete ring lattice
Wiggler
Symmetric locations of DBA and TME arcs and mirror symmetry with respect to injection point.
Main parameters of PEP-XParameter Damping wiggler off Damping wiggler on
Energy, E0 [GeV] 4.5 4.5
Beam current, I [A] 1.5 1.5
Circumference, C [m] 2199.31669 2199.31669
Emittance, x [pm-rad, 0 current] 379 85.7
Tunes, x/y/s 87.23/36.14/0.0037 87.23/36.14/0.0077
RF voltage/frequency, [MV]/ [MHz] 2.0/476 8.9/476
Harmonic number, h 3492 3492
Energy loss, U0 [MeV/turn] 0.52 3.12
Current/charge per bunch [mA/nC] 0.43/3.15 0.43/3.15
Momentum compaction, 5.816x10-5 5.812x10-5
Energy spread, 0.55x10-3 1.14x10-3
Bunch length, z [mm] 3 3
Damping times, x/y/s [ms] 101/127/73 20.3/21.2/10.8
x/y at ID center, [m] (low ) 3.00/6.07 3.00/6.07
x/y at ID center, [m] (high ) 16.04/6.27 16.04/6.27
Optimization of dynamic aperture
• Choose phase advance in a periodic cell which yields a unit (+I) linear transfer matrix in both planes for a section made of these cells (such as DBA or TME arc). In such a system the second-order geometrical (on momentum) aberrations will vanish.
• Fine tune the DBA and TME cell phase advance to minimize the higher order resonance driving terms.
• Optimize sextupole strengths in the DBA and TME cells while keeping the linear chromaticity canceled.
• Optimize the machine betatron tunes in order to minimize the effects of strong resonances and obtain the largest possible dynamic aperture.
• Add geometric (harmonic) sextupoles at non-dispersive locations in order to minimize amplitude dependent tune shifts and high order resonance effects.
Dynamic aperture tune scan
2x+2y=247
87.1 87.2 87.3 87.4 87.5 87.6 87.7 87.836.1
36.2
36.3
36.4
36.5
36.6
36.7
36.8
36.9
X Aperture in unit of x at Injection
x
y
0
10
20
30
40
50
60
70
80
90
100
x
2x+2y=247
87.1 87.2 87.3 87.4 87.5 87.6 87.7 87.836.1
36.2
36.3
36.4
36.5
36.6
36.7
36.8
36.9
Y Aperture in unit of y at Injection
x
y
0
50
100
150
y
x+2y=248x+2y=160
Nominal tune:x=86.23 and y=36.14
Chromatic correction
•DBA and TME sextupole positions and strengths as well as cell and long straight phase advance are optimized for maximum energy dependent aperture.• Optimization of non-linear chromatic terms using MAD HARMON and empiric optimization of momentum dynamic aperture in LEGO tracking simulations
W-functions 2nd order dispersion
Tune vs Dp/p
Tune shift with amplitude
• 2 weak harmonic sextupoles near each ID straight reduce the amplitude dependent tune shift and resonance driving terms generated by chromatic sextupoles and increase dynamic aperture for horizontal injection.• Minor adjustment will be needed to accommodate realistic length harmonic sextupoles.
Frequency map analysis
Strong chromatic sextupoles generate high order resonance driving terms
Dynamic apertureTune spread
Dynamic aperture (1)
Without errors PEP-II multipole field errors only (10 seeds
•Dp/p up to 3%• Effect of multipole errors is small
Dynamic aperture (2)
Multipole + field + quad misalignment Multipole + field + all misalignment
• Quad misalignment is ok.• Sextupole misalignment needs better orbit correction at sextupoles.• Horizontal injection aperture is ok.
Momentum aperture
Acceptance versus p/p
Obtained in LEGO dynamic aperture tracking w/o errors
1 2 3 4 5 6
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
Non linear longitudinal phase space
0 500 1000 1500 2000-4
-3
-2
-1
0
1
2
3
4
S (m)
p/
p (%
)Momentum Aperture
linear opticsnonlinear optics
IBS emittance and Touschek lifetime
PEP-X parameters used for IBS calculations
1% current stability will require top-off injection every few seconds
PEP-X brightness
mradmmradmmrad
cellsn
JmCJ
C
J
CH
FHJ
CF
H
JC
mimcom
tmeMETME
dbaMEDBA
tmedba
xq
tme
x
qMETMEdba
x
qMEDBA
x
qx
xqx
12,
12
12
3
13
32
32
22
3322
1048.598,104.598,105.7
0204.0,01441.0,48,5,108.8
,1,1083.31512154
2
,
Emittance Optimization
dba
tme
dba
tmedbatme
com
n
n
2
2
MBA CELL (on going study)
•Seven bends per cell•8 cells per arc•Total 6 arcs•336 dipoles(240,96)•2.2 km arc length 1.5 km•6 m ID straight• Emittance 27.8 pm-rad •Tune x=114.23, y=43.14•Energy spread 6.3e-4•Bunch length 3 mm•Energy accep. 3.6%•Natural chromaticity
-141/-121
•FODO•x= 0.2635
•y= 0.078975
•MBA•x= 2.125
•y= 0.625
Chromatic correction
•Pair of SD SF for chromaticity correction. • Choose phase advance in a periodic cell which yields a unit (+I) linear transfer matrix in both planes for a section made of these.•K2lSF = 24.68 m^-2, combined with QF•K2lSD = -71.6 m^-2 combined with dipole
W-functions 2nd order dispersion
Tune vs Dp/p
Dynamic aperture bare lattice
-2 -1 0 1 2 3 40
0.5
1
1.5
2
2.5
x (mm)
y (m
m)
p/p = 0.0 p/p = 0.5% p/p = 1% p/p = 1.5%
•x= 11.5 m,x=1 8 m
•y= 10.3 mx=1 .7 m 1% coupling
-300 -200 -100 0 100 200 300
-300
-200
-100
0
100
200
300
m
mPEP X ERL
•Fit into PEPX ring.•Superconducting RF 1.3 GHz, 20MV/m.•370.9 m long Linac accelerate, decelerate of energy range 150 MeV to 5 GeV. •Try to accommodate both PEPX and ERL operation.
e- 5 GeV
e- 5 GeV e- 150 MeV
e- 150 MeV
PEP X soft x-ray FEL
PEP-X ultra-low emittance, high peak current, FEL exponential gain (without saturation) at soft xray wavelengths can occur on a turn-by-turn basis
Equilibrium energy spread (red dashed curve) and FEL power at r= 3.3 nm (blue solid curve) as a function of the undulator length
Z. Huang et al., NIM A 593, 120 (2008)
Conclusion
• The baseline lattice for PEP-X is presented.
• It uses DBA and TME cell optics and ~90 m damping wiggler yielding 30 ID straights and an ultra-low emittance.
• Photon brightness of ~1022 (ph/s/mm2/mrad2/0.1 % BW) can be reached at 1.5 A for 3.5 m IDs at 10 keV.
• Dynamic aperture is adequate to accommodate a conventional off-axis injection system.
• More challenge designs of PEP-X • Horizontal emittance to reach diffraction limit of 10
KeV photon-showing good progress• Storage ring FEL• ERL option
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