Optics matching for LER

Aug. 27, 2021
K. Oide @ SuperKEKB Long-term Planning Meeting
Many thanks to H. Koiso, Y. Suetsugu, and the SuperKEKB/Belle II teams.
Work supported by KEK via K. Furukawa, Y. Suetsugu, M. Tobiyama, S. Yamaguchi, M. Yamauchi,
as well as by FCC-ee via M. Benedikt & F. Zimmermann.

Comparison of beam optics=(60,0.6)
mmfor• Three LER optics are examined at β*x,y352ℒ ≈ 1 × 10 /cm s.
• “Bad OHO”: inherited and squeezed from the given optics, having anirregular optics at OHO, which might have been introduced by KO.
• “perfect”: adjusted phases and βs at SLY to be ideal. Also rectified optics
all around the ring. Skew components in QLCs and QKs, which do not exist,
are introduced.
• “compromised”: Relaxed the conditions for SLC and the IP from “perfect”,
by using only existing magnets. Rest of the ring optics is basically same as“perfect”.
2
Aug. 27, 2021
K. OideComparison of optics
Perfect match

Bad OHO

Compromised

3
Aug. 27, 2021 K. Oide

Dynamic aperture (with beam-beam, CW = 50%)360 sec“perfect”

420 sec“Bad OHO”

optimization not saturated
εx is smaller than others by ∼ 16 % .

430 sec“compromised”

4Aug. 27, 2021 K. OideScaling of Lifetime

Machine Parameters (2)SuperKEKB : June 21, 2020

Unit

Ring

LER

HER

LER

HER

Emittance

4.0

4.6

4.0

4.6

nm

Beam Current

712

607

536

530

mA

978

Number of bunches

978Bunch current

0.728

0.621

0.548

0.542

mA

Lifetime

760

1270

600

1177

sec

Horizontal size σx*

17.9

16.6

15.5

16.6μm

Vertical cap sigma Σy*

0.403

0.317

μm*1

Vertical size σy*

0.285

0.224

μm*2

Betatron tunes νx / νy44.523 / 46.581 45.531 / 43.577 44.525 / 46.581 45.531 / 43.574

βx* / βy*80 / 1.0

60 / 1.0

60 / 0.8

60 / 0.8

Piwinski angle

10.7

12.7

12.3

12.7

Crab waist ratio

80

4080

40

Beam-Beam parameter ξy0.03890.02610.03450.0199mm%

Specific luminosity

5.43 x 1031

6.90 x 1031

cm-2s-1/mA2

Luminosity

2.40 x 1034

2.00 x 1034

cm-2s-1

105

SuperKEKB : July 1, 2020*1) estimated by luminosity with assuming design bunch length*2) divide *1 by √2

Y. Ohnishi @KEKB-ARC 2020

Aug. 27, 2021
K. Oideεy0εyBeam-beam tune survey (BBWS+SAD)

CW = 0%Compromized

CW = 20%

CW = 40%35−2 −1β*=(60,0.6)mm,ℒ=
1×10cmsx,y

CW = 60%

CW = 80%

CW = 100%“perfect match”

6
Aug. 27, 2021
K. Oideεy0εyBeam-beam tune survey (BBWS+SAD)

CW = 0%“Compromized”

CW = 20%

CW = 40%35−2 −1β*=(60,0.6)mm,ℒ=
1×10cmsx,yCW = 60%

CW = 80%

CW = 100%“Bad OHO”

7Aug. 27, 2021
K. Oideεy0εyBeam-beam tune survey (BBWS+SAD)

CW = 0%“Compromized”

CW = 20%

CW = 40%35−2 −1β*=(60,0.6)mm,ℒ=1×10cmsx,y

CW = 60%

CW = 80%

CW = 100%“Bad OHO”

Vertical blowup appears at νy ≳ 0.63 .

7
Aug. 27, 2021
K. OideSummary• Three LER optics are examined: “perfect”, “Bad OHO”, “compromised” with35
2β*x,y = (60,0.6) mm for ℒ ≈ 1 × 10 /cm s.
• The dynamic aperture and the lifetime look insensitive to these optics.
• The luminosity performance is somewhat worse for “Bad OHO”.
• The “compromised” optics using only existing magnets looks OK for the lifetime and theluminosity. This optics can be tried immediately in the next run.
• CW = 50% is also OK up to the HER bunch current ≲ 0.8 mA.
• Above assumes:• chromatic coupling correction by rotating sexts.
• No impedance.
• No lattice errors.

8Aug. 27, 2021
K. Oide