Optics Issues

2015.02.23
11:35 - 12:15

Akio Morita

Contents●Improvements from 19th Review– Lattice Modeling Updates

Solenoid Modeling Updates● Normal Magnet Modeling Parameter Updates●– Estimation of Lifetime Impact by QCS Error field– Dynamic Apeture with Crab Waist●Summary of Past Emittance Study– Vertical emittance with tunnel subsidence– Vertical emittance with random machine error

Belle II Solenoid Deformation (1)●Belle detector solenoid coil geometry isdesigned symmetric, but …
– The center of measured Belle solenoid field isshifted about 440mm toward R-side(Oho side).
●This field center shift corresponds with 30mm coil shift in
2D magnetic field calculation model.

– This issue is figured out by Tsuchiya-san @ IR Tech.

Meeting #96(2013.10.24)– We have to …
●

Re-optimize current density distribution of compensation
solenoid coils for adjusting Bz & ∫Bz distribution– QCS(QC1 & QC2) geometry is already finalized.

Belle II Solenoid Deformation (2)●The effect of the detector solenoid coil shift in
2D solenoid model
Tiny 2D model without compensation solenoid
Belle II solenoid filed looks sensitive
to coil shift compared with Belle.
Belle
Coil Shifted/Belle
Coil Symmetric/Belle

Belle II

Coil Shifted/Belle IIfrom SuperKEKB IR Tech.
Meeting #96(2013.10.24)

Coil Symmetric/Belle IIBelle II Solenoid Defomation (3)●3D solenoid field distribution on HER beam line
before & after Belle II detector solenoid coil shift
V10.4.15(2012.10.05)
before coil shift

R(Oho Side)

L(Nikko Side)

V10.4.17(2014.02.06)
after coil shift

Belle II detector solenoid fieldis shifted by coil deformation.
Normalization condition of detector
solenoid field strength is changedbetween 2 models.

Compensation Solenoid CoilModeling Updates (1)●The compensation solenoid coil modeling for3D magnetic field calculation is updated byusing coil geometry of hardware design.
– It changes field distribution around QC1.
– It changes IR orbit, coupling & dispersion functions.
– We have to …
●

Re-optimize current density distribution of compensation
solenoid coil for adjusting Bz & ∫Bz distribution– QC1/2 geometry is already finalized.

Re-match IR optics.
● Re-optimize dynamic aperture & lifetime.
●Compensation Solenoid CoilModeling Updates (2)Old Coil Model

New Coil Model

Compensation solenoid is constructedby many coil blocks in hardware design.
from SuperKEKB IR Tech. Meeting #110(2014.7.17)

Compensation Solenoid CoilModeling Updates (3)Field distribution before/after L-side compensation solenoid coil modeling update.

QC1LP

New Coil Model
Old Coil Model

QC1LE
L-side solenoid field integral is not adjusted.

∆Bz(New - Old)

In latest IR model(V10.4.25 2014.12.22)● Includes L & R-side new coil modeling● Coil current density is optimized

from SuperKEKB IR Tech. Meeting #110(2014.7.17)

Modeling Parameter Updates
for Normal Conducting Magnets (1)●Magnet group gives us the magnetic fieldmeasurement results of new magnets(dipolesand quadrupoles).
– We have to update lattice modeling parameters fornew magnets(We used temporary values for suchmagnets).
– Effective length(L) and fringe length(F1) paramterschange orbit geometry around dipole magnet, ring
circumference and optical functions.

Modeling Parameter Updates
for Normal Conducting Magnets (2)●Status of model lattice updates– LER model update is completed.
– HER model update is not complated yet.

Table of LER magnet parameter updates
TypeOld Leff (m)New Leff (m) |Δxcenter|(μm)

Displacement of horizontal orbit
at the center of the magnet

B2P

4.189544

4.159654

210

BLC1LP1

1.59

1.603162

40.8

BLC1LP2

2.230292.235386

BLCWRP

2.230292.235386

Δxcenter is acceptable.
6.18 It is negligible small compared with
9.50 good field region.

BLC1RP

2.230292.235386

17.7

BLA1LP

3.989597

3.961671

118

BLX4RP

3.989597

3.961671

BLA6RP

3.989597

3.961671

BC1LP

0.34440.281105

BC1RP0.3444

0.281105

Realigement is not required!

But, we MUST pay attention tothis displacement for comparing
176
magnet alignment with modelgeometry.
5.50
160

2.84

Calculated by H.Sugimoto

Modeling Parameter Updates
for Normal Conducting Magnets (3)●LER circumference is extended about 800μm by dipole
modeling parameter updates.
This displacement is not negligible compared with ±3mm tuning
range of the LER chicane for adjusting circumference.
● Total circumference difference between LER and HER is notconfirmed because HER model updates is not completed yet.
● We have extra circumference adjustment option by using wiggler K .
0●DA optimization is not completed.

DA is reduced by rematching.
DA reoptimization is required.

before updateafter update

Touschek Lifetime with QCS
Non-linear components (1)●QC1LP & QC2LP multipole measurement
results are released from SC group.
– We have to check that the measured error isacceptable or not.
●Both dynamic aperture & Touschek lifetime with multipoleerrors are evaluated by inserting thin multipole element todescribe error field into every QCSs.

Touschek Lifetime with QCS
Non-linear components (2)QCS field measurement results by using harmonic coil
QC1LP with harmonic coil radius 12mm
@ R = 10 mm ,Design4.2K and 1.8 kA@ R= 10 mm
anbn
an
bn

QC2LP with harmonic coil radius 20mm
@ R = 30 mm ,Design4.2K and 1 kA
@ R= 30 mm
an
bn
an
bn

n=12345678910n=12345678910skew

0.0
0.0
0.40
1.57
-0.07
-0.41
0.05
0.19
-0.07
0.00

normal

0.0
10000
3.16
0.75
-0.42
0.06
0.05
0.07
-0.040.03

0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0

0.0
10000
0.0
0.24
0.0
0.54
0.0
0.01
0.0
-0.21

reference

0.0
0.0
1.79
0.00
-0.39
-0.14
0.32
0.14
0.22
0.15

0.0
10000
-0.59
0.45
-0.17
3.54
-0.10
-0.23
0.03
-1.41

Large errors are found in sextupole & octupole mode(n=3,4).
- We CAN re-optimize dynamic aperture by using normal & skew sextupole coiland normal octupole coil in QCS and sextupole families in arc section.

0.0
0.0
0.0
0.0
0.00.0
0.0
0.0
0.0
0.0

0.0
10000
0.0-0.06
0.0
0.28
0.0
0.11
0.0-1.43

from SuperKEKB IR Tech. Meeting #107(2014.6.5)

Touschek Lifetime with QCS
Non-linear components (3)●Touschek lifetime is evaluated by using model
lattice with 4 thin multipole element to describe
multipole errors for QC2R, QC1R, QC1L and QC2L.
– The error field strength is fixed.
– The worst set of the error field sign is selected frompossible combinations.(evaluate worst case)

IPThin multipole inserted for error modelingfrom SuperKEKB Optics Meeting #106(2014.9.17)

Touschek Lifetime with QCS
Non-linear components (4)Model lifetime without error
QC1L & QC1R

QC2L & QC2RError Mode
QC2LP n=6 error strength
QC1LP n=6 error strength
QC1 & QC2

The measured error is not critical,
but it has serious impact to lifetime
under the assumption that QC*RP
have same order error field withthe worst sign configuration.
The lifetime of real machine
depends on QC*RP field quarity.
from SuperKEKB Optics Meeting #106(2014.9.17)

Touschek Lifetime with QCS
Non-linear components (5)Model lifetime without error
QC1L & QC1R

QC2L & QC2RError Mode

QC1 & QC2
10-4 error is acceptable.

from SuperKEKB Optics Meeting #106(2014.9.17)

Dynamic Aperture with Crab Waist (1)●The crab waist optics designs for Higgs factory
collider were reported with enough dynamicaperture.
– In those design, a set of sextupoles is used insteadof single sextupole for compensating the thickness
effect of the sextupole magnet.

QuestionIs those compensation scheme applicable to SuperKEKB?
● What is the difference between SuperKEKB and other collider?
●Dynamic Aperture with Crab Waist (2)●Those compensation scheme WOULD be inapplicable toSuperKEKB.
– Compensation for crab waist sextupoles●The on-momentum aperture of SuperKEKB lattice with crab waist
constructed by thin sextupoles is degraded.

– Compensation for local chromaticity correcoters

The on-momentum aperture of SuperKEKB lattice with crab waist that
does not contain LCC between crab waist sextupoles is degraded.
● In the SuperKEKB design, K β product at the LCC sextupole was2 y
reduced by increasing the horizontal dispersion function ηx in order toavoid the on-momentum aperture degradation by the sexutpole
thickness effect.
●Dynamic Aperture with Crab Waist (3)Comparison of dynamic aperture limit
by the fringe field of final focus quadrupoleRingβy* [μm] K=k1 [m-2] L* [m]Jy/A [μm]SuperKEKB HER

300-3.1

1.220.018

SuperKEKB LER

270-5.1

0.76

0.032

CEPC

1200-0.176

1.50.76

TLEP(BINP design)

1000

-0.16

0.7

1.36

KEKB

5900-1.779

1.762

4.22

●

●〜 1/20

The final focus fringe of SuperKEKB is very strong
compared with other e- - e+ colliders.
This strong fringe effect WOULD be the source ofdynamic aperture difference under crab waist.

< 1/100

Emittance with Tunnel Subsidence
Measured tunnel level
IP

Vertical emittance after orbit & dispersion
correction on tunnel subsidence model(horizontal deformation is not included)
εy with full missalignment

Subsidence rate ~2mm/year

Tsukuba

5pm tolerance

Nikko

3pm

OhoFuji

εy without V-LCC missalignment

Tunnel subsidence model is generated from latest measurement with LPF(λcut〜100m).
Vertical emittance after correction WOULD be improved into acceptable levelby improving both local aligment around V-LCC and correction algorithm.
Already reported in 18th Review(high βy region)
from TUPPC018 @ IPAC '12

Emittance with Machine Error (1)Assumption of Machine Error(Random Error) Simulation
Element TypeΔxrms [μm] Δyrms [μm]Main dipole
Machine Error(ΔK/K)rms

0.1

3.5 x 10 -4

0.17-

Quadrupole

100100

Sextupole100100-1.3 x 10 -3

QC1 & QC2100100--BPM7575Corrector Type# of Correctors-θrms [mrad]1.0x 10 -4-HER LER

Maximum Rating

H-Dipole

218

208

Δθ = 1.0 mrad

V-Dipole

196

215

Δθ = 1.0 mrad

H-Backleg Dipole

3339

Δθ = 0.5 mrad

Quadrupole

292

254

ΔK1/K1 = 5 x 10-3Skew Quadrupole*

64

56

ΔK1 = 5 x 10 -3 m-1 for SD,SL* We have additional skew quadrupole coil on SF type sextupole,
but power supply for skew quadrupole on SF is not ready at T = 0.

Already reported in 19th Review

from SuperKEKB TDR draftEmittance with Machine Error (2)Vertical emittance and dynamic aperture after orbit & optics correction
εy < 1.3pm (90%)

Already reported in 19th Review

εy < 3.7pm (90%)

from SuperKEKB TDR draft

Summary of Past Emittance Study●From orbit & optics correction study fortunnel
subsidence– Vertical emittance WOULD be controled within

acceptable level by taking extra care to V-LCC region.
●

From orbit & optics correction study for randommachine error– Vertical emittance reachs design target.
– The sextupole tuning is required to obtain longerlifetime.

Tasks toward Machine Operation●We have started to develop operation & commissioningsoftwares.
– Optics & Orbit parameter management framework under development– Operation & Tuning Tools

Programable Tune Changer under development● Optics Measurement & Correction Toolset● Chromaticity Tuning Tool
● Continuous Orbit Corrector● Local Orbit Bump Tool
● Luminosity tuning Knobs(Waist, IP coupling, beam size...) under development● Calibration Tools(3-BPM, BBA...)● etc...
●We plan to share framework software between MR and DR.