Single Knob Scan
2007/11/30 for KEKB Review
KEKB Naoko.Iida

The optical functions at the IP are adjusted locally in various ways
to optimize the luminosity during physics runs.
In this tuning, the following optical parameters are adjusted.
•Vertical waist•Tilt(xy-coupling) and vertical dispersion•Horizontal dispersion
In KEKB operation panels,
blue and red colors are usually used
as HER and LER.
Because positron means “sun-electron” in Japanese.

•Vertical Waist-The waist of the vertical β-function in each ring is adjusted independently by changing
the fudge factors of the final-focus quadrupoles on both sides of the IP, QCSs andQC1s(only for the HER)
-HER: The vertical waist is changed by QC1{LR}E.
-LER: The vertical waist is changed by QCS{LR} andthat of HER is compensated by QC1{LR}E.

QC1RE

HER
beam

QCSL
QC1LE

QCSR

LER
beam

•Tilts(xy-coupling) and Vertical Dispersion-Tilt(xy-coupling:R1*~R4*), the vertical dispersion function and its slope (ηy * andη’y*) at the IP are adjusted by making vertical bumps at sextupoles.
-16 bumps of sextupoles are used to adjust 12 parameters in each ring.
-The bumps are enough as free parameters.

The definition of xy-coupling parameters anddispersion functions
In the normal coordinate(no xy-coupling space)In the the physical coordinate(real space)" X % " (X %"µ$ ' $'$p('XX$ '+$') = $ 0$ Y ' $ (Y '$ R1$ ' $'$# pY & #('Y &# R3!

0*R4µR2
R4R3µ0

R2 %" x %'$ '*R1 '$ px '0 '$ y ''$ 'µ &# py &µ2+(R1R4-R2R3)=1
δ =Δp/p.
# "X & # µ%( %"'% X(=% 0% "Y ( % R1%( %$"'Y ' $ R30µR2R4)R4R3µ0

R2 &# "x &(% ()R1 (%"' x (0 (% "y ((% (µ '$"' y 'We scan the xy-coulping parameters, R1~R4 and the!
dispersionfunctions, η and η' at the IP(Interaction Point).

How to obtain the bump heights•R1*~R4* at IP
Scan•η*y and η’y * at IP
Scan•R1E~R4E at the exit of knob region0•ηEy and η’y E at the exit of knob region# h1 &% (% h2 (# R1 * &% h3 (%(% (% R2 *(% h4 (% R3 *(% h5 (%(% (% R4 *(% h6 (%" y *(% h7 (%(%h ("'*y%(% 8(C = M% R1 (% h9 (% C(%h (R1% C(% 10 (% R1 (% h11 (%RC (%h (% 1C (% 12 (% "y (% h13 (C%"' (%h ($ y '% 14 (% h15 (% ($ h16 '

Number of parameters

0424212•hn is the bump height at sextupoles.
•M is a 16x12 matrix that is simulated
by SAD computer code in advance.
•16 bump heights are obtained with theSingular Value Decomposition (SVD)
method.

Panel of the LER IP Vertical Dispersion and xy-coupling

IP: Bump Height

The exit ofknob region

16 sextupoles•Horizontal Dispersion-The horizontal dispersion function and its slope (ηx and η’x) at the IP are adjusted bymaking asymmetric horizontal bumps at non-interleaved sextupoles.
-We use 8 sextupole pairs of the closest to the IP in each rings for tuning.
-We can fit 4 parameters using enough free parameters .

IP: Bump Height

The exit ofknob region

8 pairs of sextupolesBumps on non-interleaved sextupoles
Phase advance:-I•Asymmetric bump-dispersion function:leaks around the ring-xy-coupling:
localizes in the sextupole pair
SX.1

SX.2

Phase advance:
-I

SX.1

SX.2

•Symmetric bump-dispersion function:
localizes in the sextupole pair-xy-coupling:leaks around the ringNumber of parameters•η*x and η’x * at IPScan•ηEx and η’x E at the exit of knob region# h1 &% (% h2 (#" x *&% h3 (%(% ("'*% x ( = M %h4 (% "x E (% h5 (% E(% ($"' x '% h6 (% h7 (% ($ h8 '!

022•hn (n=1~8)is the asymmetric bumpheight at non-interleaved sextupoles.
•M is a 8x4 matrix that is simulated
by SAD computer code in advance.
•8 bumps are obtained with theSingular Value Decomposition(SVD) method.

4

Scans in Operation -1•Typical scan (good example)
The position of
luminosity peakcoincides with thatof the minimum
vertical beam size
being scanned.

position of HER
beam size peak

position of
Luminosity peakoriginal value

Data taking

nioctjeInRRELIncjen
it oHEnioct
jeInRHECurrent

Each data are taken at the same current ratio as possible.

LERIenjction

90 sec90 secDatataking

Time
Datataking

Scans in Operation -2•Typical scan (good example)
The position ofluminosity peakcoincides with thatof the minimum
vertical beam size
being scanned.

Slightly different

Scans in Operation -3•Typical scan in bad life time situation
The position ofluminosity peakcoincides with that of
the minimum verticalbeam size being
scanned.
But unfortunately, bothbeam lives areshortened at better
luminosity.
We give up the highest
luminosity and set
tolerable life time.

Scans in Operation -4•Examples with a “cross shape” of beam sizes•The beam sizes are in inverse proportion to each other.
•The shape of the two beam sizes is like a “cross shape”.
•The peak of luminosity is found around the cross point.

Scans in Operation -5•Two peak shape•The luminosity has two peaks with scanning.
•At the position of the minimum beam size in scan, the luminosity is also minimum.

Simulation of Scan in Operation -5by M.Tawada•Two peak shape
HER beam size

Typical example

LER beam sizeLuminosity•In almost cases, the shape is like the typical example.
•The “cross shape” is included in this “two peak” case.

Scans in Operation -6•Bad examples with same shape of the beam size as luminosity•The position of Luminosity peak is the same as the beam size of the other ring.
•In worst case, the shapes of luminosity and that of the beam size in scanning ringare like mountains.

Scans in Operation -7•Situlation sometimes changes.

evening shift（21:00）

day shift（10:00）

Same day•Shift Report Panel•We can check whichknob is effective.

Knob 1

Abort Konb

Knob 3