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

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tmeMETME

dbaMEDBA

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12,

12

12

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32

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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