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
PEP-X low emittance ring
• 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
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)
Same ring layout as PEP-II in the exist tunnel using existing RF system
Conceptual Layout of PEP-X with photon
beamlines at SLAC
Photon Science
Lab-Office
Building
0
50
100
150
m e te rs
200
R. Hettel et al
EPAC08
PEPX Lattice
DBA
nx=1.523
ny=0.508
nx=0.373
ny=0.124
TME
Injection
Straight
DBA Supercell
4 harmonic sextupoles, 2 families
6 chromatic sextupoles, 4 families
low b ID
high b ID
• Two standard cells are combined into one supercell with a low and high
ID beta: bx,y = 3.00, 6.07 m and bx,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: mx/2p =
1.5+3/128, my = mx/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 3p/4 and p/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 bx = 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
• DBA and TME arcs without wiggler
yield e = 0.38 nm-rad
• 89.3 m wiggler is inserted in one long
straight section yielding e = 0.086 nmrad.
• Wiggler is split in 18 identical sections
to fit FODO cells.
Dispersion in ~5 m wiggler section
• 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).
Optimization of wiggler parameters
Based on analytic formulas:
• Most efficient damping for L < 100 m.
• More damping with a shorter period, higher field and lower bx, 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.
1
0.8
 w = 20 cm, N p = 446
 w = 15 cm, N p = 595
0
e/e0 vs B
Emittance ratio of damping(e/e )
0
Emittance ratio of damping(e/e )
1
 w = 10 cm, N p = 892
 w = 5 cm, N p = 1785
0.6
dot line
<b x> = 5 m
0.4
0.2
0
0
2* DBA + 4*
TME cells
e0= 0.379 nmrad
<b x> = 10.7 m
0.5
1
1.5
2
B field of damping wiggler (Tesla)
2.5
0.8
0.6
2* DBA + 4*
TME cells
e0= 0.379 nmrad
Bw = 1.5T
e/e0 vs L
 w = 20 cm
 w = 15 cm
 w = 10 cm
 w= 5 cm
0.4
0.2
0
0
50
100
Total damping wiggler length (m)
150
Complete ring lattice
TME
DBA
Wiggler
TME
TME
DBA
TME
Symmetric locations of DBA and TME arcs and mirror symmetry
with respect to injection point.
Main parameters of PEP-X
Parameter
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, ex [pm-rad, 0 current]
379
85.7
Tunes, nx/ny/ns
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, a
5.816x10-5
5.812x10-5
Energy spread, sd
0.55x10-3
1.14x10-3
Bunch length, sz [mm]
3
3
Damping times, tx/ty/ts [ms]
101/127/73
20.3/21.2/10.8
bx/by at ID center, [m] (low b)
3.00/6.07
3.00/6.07
bx/by at ID center, [m] (high b)
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
sx
X Aperture in unit of sx at Injection
36.9
36.8
Y Aperture in unit of sy at Injection
100
36.9
90
36.8
sy
150
80
36.7
36.7
70
50
36.4
40
y
60
36.5
100
36.6
n
n
y
36.6
36.5
36.4
50
30
36.3
36.3
20
36.2
36.1
87.1
10
87.2
87.3
2nx+2ny=247
87.4
87.5
nx
87.6
87.7
87.8
0
36.2
36.1
87.1
87.2
2nx+2ny=247
Nominal tune:
nx=86.23 and ny=36.14
87.3
87.4
87.5
nx
87.6
87.7
87.8
nx+2ny=160 2nx+2ny=248
0
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
Tune vs Dp/p
2nd order dispersion
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
Tune spread
Strong chromatic sextupoles generate high
order resonance driving terms
Dynamic aperture
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
• Quad misalignment is ok.
• Sextupole misalignment needs better
orbit correction at sextupoles.
• Horizontal injection aperture is ok.
Multipole + field + all misalignment
Momentum aperture
Momentum Aperture
Non linear longitudinal phase space
0.1
4
0.05
3
0
Acceptance versus Dp/p
d
2
-0.1
-0.15
1
D p/p (%)
-0.05
-0.2
-0.25
0
linear optics
1
2
3optics
4
nonlinear

-1
-2
-3
Obtained in LEGO dynamic
-4 aperture tracking w/o errors
0
500
1000
S (m)
1500
2000
5
6
IBS emittance and Touschek lifetime
1% current stability will require top-off injection every few seconds
PEP-X parameters used for IBS calculations
PEP-X brightness
Emittance Optimization
e x  Cq

2
H
 ex  F

Jx
H    2 e    b  
2
e MEDBA 
C q
2
 , H  F 

 13
3
dba
3
3
Jx
n e tme  2 e dba
2
2
4 15 J x
C q  3 . 83  10
C q
e METME 
C q
2
12 15 J x

3
tme
e com 
m , J x  1,
  8 . 8  10 , n  5 , 48 cells ,  dba  0 . 01441 ,  tme  0 . 0204
3
e MEDBA  5.7  10
 12
mrad ,  dba  98 m
e METME  5 . 4  10
 12
mrad ,  tme  98 m
e com , mim  5 . 48  10
 12
mrad
n2
 tme
 dba
 tme
 dba
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 nx=114.23, ny=43.14
•Energy spread 6.3e-4
•Bunch length 3 mm
•Energy accep. 3.6%
•Natural chromaticity
-141/-121
•MBA
•nx= 2.125
•ny= 0.625
•FODO
•nx= 0.2635
•ny= 0.078975
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
Tune vs Dp/p
2nd order dispersion
Dynamic aperture bare lattice
2.5
D p/p = 0.0
D p/p = 0.5%
D p/p = 1%
D p/p = 1.5%
2
y (mm)
1.5
1
0.5
0
-2
-1
0
1
x (mm)
2
•bx= 11.5 m, sx=1 8 mm
•by= 10.3 m sx=1 .7 mm 1% coupling
3
4
PEP X ERL
e- 150 MeV
•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.
300
e-
200
5 GeV
m
100
0
-100
e- 150-200MeV e- 5 GeV
-300
-300
-200
-100
0
m
100
200
300
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