1. Status of PEP-X Lattice Design Study
Yuri Nosochkov
Beam Physics Department
On behalf of BPD Optics Group
ARD Status Meeting
April 7, 2011

2. Motivation
SLAC-PUB-13999, April 2010
2.2 km PEP-II
tunnel

3. Evolution of PEP-X lattice design
Studied lattice configurations
ex0, nm-rad at 4.5 GeV, without / with damping wiggler, no IBS
Year
Minimal PEP-2 HER modification:
6 existing FODO arcs with higher 90 cell phase
4 existing FODO arcs and 2 new DBA arcs
5.0 / 0.41
1.7 / 0.32
2008
Pre-baseline: 4 TME arcs and 2 DBA arcs
0.30 / 0.067
Baseline: 4 TME arcs and 2 DBA supercell arcs with low ID beta
0.38 / 0.086
White Paper
Ultimate: 6 arcs with Multi-Bend Achromat (MBA) cells for lowest emittance
0.029 / ~
under study

4. Baseline design report
Baseline design report SLAC-PUB (2010)
+ 10 conference papers
Lattice
Transverse dynamics
IBS & Touschek lifetime
RF system
Impedance
Collective effects
Partial lasing

5. Baseline ring configuration
The same 2.2 km ring geometry as in PEP-II with six 243 m arcs and six 123 m straights in order to fit into the existing tunnel .
Two new DBA arcs providing 30 straights for ~3.5 m IDs.
Four new TME arcs for low emittance.
90 m damping wiggler with B=1.5T, lp=10cm to lower emittance to 86 pm-rad.
FODO optics in long straights.
PEP-II based injection system.
4.5 GeV beam energy.

6. Schematic of photon beamlines in PEP-X

7. Baseline arc cells: DBA and TME
high b ID
low b ID
DBA
supercell
DBA supercell = two standard DBA cells with a low-b and high-b ID straights: bx,y = 3.00, 6.07 m and 16.04, 6.27 m.
Supercell length = m.
30 dispersion free straights in 2 arcs for Insertion Devices.
Natural emittance = 0.54 nm at 4.5 GeV.
TME
Compact 7.3 m TME cells in 4 arcs for low emittance.
Do not provide ID straights.
Low natural emittance = 0.1 nm.
Combined DBA & TME arcs emittance = 0.38 nm.

8. Baseline parameters with wiggler on and off
Wiggler off
Energy, E0 [GeV]
4.5
Circumference, C [m]
Emittance, ex [pm-rad, 0 current] 86
380
Beam current, I [A]
1.5
Harmonic number, h
3492
Number of bunches, nb
3154
Bunch length, sz [mm]
3.0
Energy spread, sd
1.14 x 10-3
0.55 x 10-3
Momentum compaction, ap
5.81 x 10-5
Tunes, nx/ny/ns
87.23 / /
87.23 / /
Damping times, tx/ty/ts [ms]
20.3 / 21.2 / 10.8
101 / 127 / 73
Energy loss, U0 [MeV/turn]
3.12
0.52
RF voltage, VRF [MV]
8.9
2.0
bx/by at ID center, [m] (low/high b)
[ 3.00 / 6.07 ], [ / 6.27 ]
With IBS at 1.5 A: e = 164 / 8 pm-rad; Touschek lifetime ~30 min.

9. PEP-X baseline brightness
PEP-X, 1.5A, 3.5m ID

10. PEP-X in ERL options
PEP-X baseline ring design is also compatible with the two studied ERL configurations, where:
ERL SC linac is in the SLAC linac tunnel, and the PEP-II injection line and tunnel are reused.
SC linac is inside of the PEP-X ring for potential cost saving.
Simulations of bunches with E=5 GeV, sz=2 ps, Q=77 pC, ge=0.3 mm-rad indicate acceptable (~10%) emittance growth in both options.
Loop
SC Linac
Injection
PEP-X Ring
Extraction
Bypass

11. Toward “ultimate” design
There is a growing interest in the so-called “ultimate” ring design for a synchrotron light source. It aims at achieving a near maximum brightness by reducing the electron emittance in both planes toward and beyond the diffraction limited photon emittance.
where F(l) = photon flux,
Electron & photon size and divergence:
Photon emittance:
(small) e- g x x'
Matched
be- = br
for max B
Matched b for ID length L:
“… To approach diffraction-limited performance: (1) the electron beam emittance, sxysx'y' must be comparable to or less than the intrinsic photon beam emittance, l/4p and (2) the phase space of the electron and photon beam sizes must be matched (i.e., sr/sr' ≈ sx/sx' ≈ sy/sy'). For hard X-ray radiation at l = 0.1 nm, l/4p = 8 pm-rad while for soft X-rays at l = 1 nm the diffraction limit is 80 pm-rad ...”
“The potential of an ultimate storage ring for future light sources.” M. Bei et al., Nucl.Instrum.Meth.A622: ,2010.

12. Scaling for low emittance
where
For N = number of cells in the ring arcs, L = cell length and NL = const:
Need: 1) short cells, 2) low emittance type optics, 3) dipoles with negative gradient for larger Jx.
Consequences:
Smaller b, h and beam size:
Larger ring chromaticity:
Stronger quads and sextupoles:
Smaller dynamic aperture
(affects injection)

13. Multi-bend achromat cell
TME
DBA
½ID
The new cell should provide both the dispersion free ID straights (DBA type) and the low emittance (TME type). This is achieved using multi-bend achromat cell as in MAX-IV below. The latter contains five TME style units in the middle and half-DBA units at each end. For shorter cell, the QD quads in the TME units are removed and replaced by negative gradient in the dipoles.
½DBA
5 × TME
½DBA
MAX-IV

14. PEP-X 7-bend achromat cell
Cell length = 30.4 m, TME unit = 3.1 m, ID straight = 5 m, ID bx,y = 4.9 m / 0.8 m,
5 bends with gradient: LB = 2 m, BB = 1.49 kG, qB = 19.9 mrad, B' = kG/cm,
2 matching bends w/o gradient: LBM = 1.6 m, BBM = 1.48 kG, qBM = 15.7 mrad,
Quad triplets near ID allow more tuning flexibility, Max quad gradient = 4.3 kG/cm,
Natural emittance = 29 pm-rad at 4.5 GeV. Each arc contains 8 cells.
5 TME units

15. Sextupoles in the 7BA cell
TME unit
½ID SF SD
Harmonic sext (or octupoles)
Matching unit
SF and SD sextupoles at dipole and quad locations where dispersion is not zero.
Harmonic sextupoles (or octupoles) at the ID triplets – study in progress.
Presently modeled as thin lenses: SF inside quads, SD at dipole ends.
Max B''L ≈160 kG/cm -- under study.
Realistic design should be based on compact integrated magnet designs – for example, as in MAX-IV where dipole + 2 SD sextupoles are made of one iron block. Similar design is planned for quad + sextupole.
MAX-IV dipole
+ 2 sextupoles in one block

16. Simplified PEP-X ring with 7BA cells
2.2 km ring with 6 identical arcs and 6 identical long straight sections.
Each m arc contains eight 7BA cells for up to 9 ID straights per arc. Injection optics and damping wiggler are to be included later.

17. Lattice parameters without wiggler
Energy, GeV 4.5
Circumference, m
Betatron tune, x/y / 66.14
Synchrotron tune
Beam current, A 0.2
Number of bunches 3154
Natural emittance at 0 A, pm 29 (no IBS)
Emittance at 0.2 A, x/y, pm 47 / 8 (IBS)
RMS bunch length, mm 3.1
RMS momentum spread 7.2e-4
Momentum compaction 5.0e-5
Damping time, x/y/s, ms 75 / 184 / 326
Natural chromaticity, x/y /
Energy loss per turn, MeV 0.36
RF voltage, MV 2.7
Max ID straights per arc 9
Length of ID straight, m 5.0
Beta at ID center, x/y, m 4.9 / 0.8

18. Cell phase advance
Phase advance per cell mx = 21/8 × 2p, my = 11/8 × 2p is chosen based on optimal cell optics properties and maximum dynamic aperture. Each arc (8 cells) has an integer tune advance which provides local cancellation of the sextupole 2nd order geometric and chromatic aberrations in each arc, per K. Brown’s theorem.
Local cancellation of 2nd order dispersion in each arc

19. Cancellation of 3rd and 4th order resonances
LEGO tracking confirms local suppression of the 3rd and most of the 4th order resonance terms in each arc due to the chosen cell phase advance. Due to thin lens sextupole model, the effects of finite sextupole length are not yet included.
3rd order driving terms
4th order driving terms

20. Remaining resonance and tune shift effects
2nx-2ny resonance term is accumulating, and the amplitude dependent tune shifts are quite large. This will affect dynamic aperture. Further optimization may include:
1) sextupoles, 2) minor tuning of cell phase for better 2nx-2ny suppression.
From MAD:
2nx-2ny
dnx/dex
-5.0∙105
dnx/dey
-3.0∙104
dny/dey
3.8∙105
(5 times larger than in baseline)

21. Tune energy dependence
Chromatic and harmonic sextupole families have been optimized for minimal tune dependence on energy for larger tune working area.

22. Dynamic aperture
The simplified ring has reasonably large dynamic aperture – about 170sx × 400sy for 47 / 8 pm-rad emittance. This is helped by the 6-fold periodicity, resonance suppression and thin lens sextupole model. Horizontal aperture corresponds to ~15 mm at injection with bx = 200 m which is sufficient. The injection optics and wiggler will break the periodicity which may reduce the aperture (to be studied).
At ID:
bx = 4.9 m
by = 0.8 m

23. IBS and Touschek lifetime
At I = 0.2 A, the IBS results in ~90% higher horizontal emittance.
Momentum aperture defined by Touschek scattering is from 1.2% (in arcs) to 2.5% (in straights).
Touschek lifetime is ~1 and ~2 hours for diffraction limited and round beam modes.
To maintain stable beam intensity, top-up injection may be used.
coupling
e0 (pm)
eIBS (pm)
sE (10-4)
sz (mm)
T (min)
0.17
24.7 / 8.0
46.8 / 8.0
8.4
3.47 58 1
14.5 / 14.5
27.1 / 27.1
8.0
3.30
109
K. Bane

24. Cell tuning flexibility
The cell includes sufficient number of quadrupole families to provide tuning flexibility. The vertical ID beta function can be varied in the range of ~0.5 m to 5 m without changing the cell phase advance. The horizontal ID beta function and emittance are not significantly changed in this range.
bx (m)
by (m)
ex (pm)

25. Damping wiggler
Preliminary estimate shows a reduction of 29 pm emittance to:
15.7 pm for Lw=89m, B=1.0T, lp=10cm
10 pm for Lw=89m, B=1.5T, lp=5cm
The wiggler also significantly reduces the damping times to msec.
A higher wiggler field increases energy spread and requires smaller wiggler gap which reduces vertical acceptance and increases resistive wall impedance.
e/e0 vs Lw at 1.5T
e/e0 vs B at Lw=89m
sE/sE0 vs B

26. Injection straight section
Injection optics will be included in one of the 6 long straight sections. It will have large bx = 200 m for large acceptance area at septum. This lattice is similar to the PEP-X baseline and should be able to reuse the PEP-II injection components.

27. Summary
The PEP-X baseline ring design was completed and documented in SLAC-PUB Its emittance is 164 / 8 pm at 1.5 A, and the predicted brightness is ~10 times higher than in the NSLS-II. The design is based on existing technology – ready for implementation.
The baseline design is also compatible with the recently studied ERL options at SLAC producing satisfactory beam quality.
“Ultimate” PEP-X lattice for extremely low emittance approaching diffraction limited photon emittance is currently under study.
Simplified 6-fold periodic ring with 29 pm-rad natural emittance (47 / 8 pm at 0.2 A) is designed providing up to nine 5m ID straights per arc.
Dynamic aperture for this ring is sufficiently large due to periodicity, compensated sextupole resonance effects and thin lens sextupole approximation.
Further work will include the injection and wiggler insertions (almost done), more sextupole optimization for maximum aperture, tolerance and correction studies.