Belle- L 0k W - KEK · 2011. 11. 2. · Belle-lLg0k

BelleWM@NhKw1k

|MwoCHL,[NW;!N+/

$t/:Belle-lLg0k<W

KCG Seminar

Feb. 7, 2002

Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 1/48

Introduction

✏ Motivation

➟ SVD1.0 was killed by the synchrotron radiation (SR) from HER.� �

Limitation for the HER steering magnets� �

Some current values are close to the limits. (

�figure)

➟ Smaller-radius IR beampipe ( �� 2.0 cm

�1.5 cm

�1.0 cm ?)

➟ Larger beam currents for higher luminosities�

more SR

✏ A new idea has been proposed by Hitoshi Yamamoto:

Fitting BPM-measured values�

Real beam orbit�

Wattage distribution in the IR

�Online alarm for SR

➟

� � �� for the HER steering magnets

➟

� � � � �� for detector damages

$t /:�

Belle-lLg0k<W

�KCG Seminar Feb. 7, 2002


-4

-2

0

2

-100 -80 -60 -40 -20 0

In the HER Straight Section

s [m]

Kic

k A

ngle

[m

rad]

QC

SLQ

C1L

EQ

C2L

EZ

HQ

C2L

E

BH

1LE

BH

2LE

ZH

QC

3LE

QC

3LE

BH

3LE

QC

4LE

QC

5LE

BH

4LE

BH

5LE

QA

2LE

QA

3LE

QA

4LE

QA

5LE

QA

6LE

QA

7LE

QC

SLQ

C1L

EQ

C2L

EB

C1L

E

BC

3LE

QC

3LE

ZV

QC

3LE

QC

4LE

ZV

QC

4LE

ZV

QC

5LE

QC

5LE

QA

2LE

QA

3LE

QA

4LE

QA

5LE

QA

6LE

QA

7LE

kick angle on Jan. 28 (2002)

Max. allowed angle

Kick range for 1<r<2cm

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Belle-lLg0k<W



Calculation Method

[I] Orbit Calculation

➟ In the HER straight section (see

�

)

➟ Using a linear approximation

�

transfer matrices

➟ Implemented in my own program

BSWTLE

QA7LEQA6LE

QC2LE

QC1LEQCSL

IP

HER Straight Section

e

(~100m)

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Belle-lLg0k<W



Transfer Matrices

�� "!#$%$%$%$&$(') � � ) * � � + � � + * � � ,-.%.%.%.&.(/

0 � � 1�32 4 567 � 8:9<; = >? �@ !#$%$%$%$&$('A @ A A @ A ,-.%.%.%.&.(/

BC D 0� 8FEG H 9 !#$&$%$%$%$&'6I 2 �J @ JLK M2 �ON � J @

P J2 �ON � J @ 6I 2 � J @ 6I 2 Q �J @ JK M2 �ON Q �J @ J2 �ON Q � J @ 6I 2 Q �J @ ,-.&.%.%.%.&/

RST 0� 8:U�VW 9 ! 8:9<; = >? �@ XY OZ#$($&$%$%$%'A A []\A A [_^ ,-.(.&.%.%.%/ Z

8:9<; = >? �@ XY

`a 7 b BC D 0� 8_c dV e f ! 8; g ? � P hi j OZ 8FEG H 9 Z 8; g ? �Lk h i j

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Belle-lLg0k<W



Check of the Transfer-Matrix Implementation [1]

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

Just after BSWTLE

x [cm]

x’

[mra

d]

α = 1.90, β = 18.8 m, ε = 1.8E-8 m

βx’2 + 2αxx’ + γx2 = ε

-2

-1.5

-1

-0.5

0

0.5

1

-100 -80 -60 -40 -20 0

Beam Orbits (HER)

s [m]

x

[cm

]

QC

SLQ

C1L

EQ

C2L

EZ

HQ

C2L

E

BH

1LE

BH

2LE

ZH

QC

3LE

QC

3LE

BH

3LE

QC

4LE

QC

5LE

BH

4LE

BH

5LE

QA

2LE

QA

3LE

QA

4LE

QA

5LE

QA

6LE

QA

7LE

2√βε (envelope from the design)

0

20

40

60

80

100

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

x (IP) [mm]

37.35 / 32

Constant 70.87 2.861Mean 0.3386E-02 0.3585E-02Sigma 0.1088 0.2685E-02

√βε = 0.106 mm

BSWTLE l P

————————————————————————–> IP

-0.04

-0.02

0

0.02

0.04

-0.02 -0.01 0 0.01 0.02

Just after BSWTLE

y [cm]

y’

[mra

d]

α = -2.61, β = 17.3 m, ε = 3.6E-10 m

βx’2 + 2αxx’ + γx2 = ε

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

-100 -80 -60 -40 -20 0

Beam Orbits (HER)

s [m]

y

[cm

]

QC

SLQ

C1L

EQ

C2L

EB

C1L

E

BC

3LE

QC

3LE

ZV

QC

3LE

QC

4LE

ZV

QC

4LE

ZV

QC

5LE

QC

5LE

QA

2LE

QA

3LE

QA

4LE

QA

5LE

QA

6LE

QA

7LE

2√βε (envelope from the design)

0

10

20

30

40

50

60

70

80

-6 -4 -2 0 2 4 6

y (IP) [µm]

39.54 / 42

Constant 57.92 2.273Mean 0.5096E-01 0.5178E-01Sigma 1.587 0.3508E-01

√βε = 1.587 µm

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Belle-lLg0k<W




Numerical comparison with SAD on QC3LE

In[61]:= TransferMatrix["QC3LE","LX086E.1"]Out[61]:=

{1.0415110062367,1.094542869142296,0,4.440892098501E-16}{.077425177671287,1.0415110062367,3.469446951954E-18,0}{3.382710778155E-17,-3.53883589099E-16,.959055549847622,1.065412001995326}{-2.60208521397E-18,2.775557561563E-17,-.075287731090181,.959055549847622}

monp � m �q rs npt m �q rs np t � uvuwuxuy z {}| ~ y P A i y y

y y y y

y y � � | ~ y P A i � � | ~ y P A h

y y y � � | ~ y P A i�v�w�x�

$t /:�

Belle-lLg0k<W




Numerical comparison with SAD on QKELE

In[62]:= TransferMatrix["QKELE","LC51LAE"]Out[62]:=

{1.000001092692837,.372300042338456,-.00256049953636,-2.68166492929E-4}{1.3572130039052E-5,1.000001092692837,-.013755037460226,-.00256049953636}{-.00256049953636,-2.68166492929E-4,1.000001092692837,.37230004233846}{-.013755037460226,-.00256049953636,1.3572130039019E-5,1.000001092692837}

m np � m �q rs npt m �q rs np t � uvuxuwu� {}| ~ y P A h � � | ~ y P A h � � | ~ y P A h z � | ~ y P A�

� � | ~ y P A A � {}| ~ y P A h y � � | ~ y P A h

� � | ~ y P A h z � | ~ y P A� � { | ~ y P A h � � | ~ y P A h

y � � | ~ y P A h z � | ~ y P A A � {}| ~ y P A h�v�x�w�

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Belle-lLg0k<W



[II] Orbit Fitting

➟ Input parameters:

�� "� �� y y � �� ~�� y ~ � � ��

�� A � � � ¡ ¢�£ � ¤

➟ Floating parameters:

¥§¦©¨ ¦ª¦¨ ¦ ,

¥§«¬ ª«¬➟ ®]¯ °©± ²¬ ³

´¶µ · ²¬ ³ ¸° ¹ µ ·»º¼ ½¾¿ ¸° À ®Á ´¶Â · ²¬ ³ ¸° ¹ Â ·º¼ ½¾¿ ¸° À ® ÃÅÄ ®

➟ Minimization using MINUIT

➟

Æ Ç ÈÉ Ê � Æ ÇÌË k Æ ÇÌÍÈÉ Ê �Î k ÈÉ Ê �Ï � Ð ÇÑËÒÓ Ô � Ë � M ÒÓ Ô � Í � k Ð ÇÑÍÒÓ Ô � Í � M ÒÓ Ô � Ë �M ÒÓ Ô � Ë � k M ÒÓ Ô � Í �

$t /:�

Belle-lLg0k<W



Fitting ExampleÕ BPM resolution: 100 Öm (including offset uncertainties)Õ Data on Nov. 7 (2001)

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-100 -80 -60 -40 -20 0

HORIZONTAL

s [m]

∆x

[cm

]

BPM measurements

QC

SLQ

C1L

EQ

C2L

EZ

HQ

C2L

EBH

1LE

BH

2LE

ZH

QC

3LE

QC

3LE

BH

3LE

QC

4LE

QC

5LE

BH

4LE

BH

5LE

QA

2LE

QA

3LE

QA

4LE

QA

5LE

QA

6LE

QA

7LE

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-100 -80 -60 -40 -20 0

VERTICAL

s [m]

∆y

[cm

]

BPM measurements

QC

SLQ

C1L

EQ

C2L

EB

C1L

EB

C2L

E

BC

3LE

QC

3LE

ZV

QC

3LE

QC

4LE

ZV

QC

4LE

ZV

QC

5LE

QC

5LE

QA

2LE

QA

3LE

QA

4LE

QA

5LE

QA

6LE

QA

7LE

×YÎ ØÚÙ Û Ü �Ý ¤ � ��ßÞ � Ø � � ~ yÞ à ×YáÏ ØÚÙ Û Ü �â ¤ � � � � Þ � Ø � � { yÞ �

Failure withÝ ãä � � �

mm & ×Y ØÚÙ Û Ü å ~

Need Some Offset Corrections!

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Belle-lLg0k<W



Offset Definition

x∆ (BPM)

x∆ (QUAD)

x∆ (QUAD) x∆ (BPM)+

Quadrupole

BPM

Desgin orbit s

Æ Ç ! æèç éê ë æìLí î ç ïðñ cò óõô Î � ïðñ �î÷ö æ k øÎ � fù úû �î k øÎ � ïðñ �î ü P Î � é ê ë æì �î÷ö æ ý Ç

k óþô Ï � ïðñ �î÷ö æ k øÏ � f ù úû �î k øÏ � ïðñ �î ü P Ï � é ê ë æì �î÷ö æ ý Ç

ÿ X � A � �� Ç

$t /:�

Belle-lLg0k<W



Offset DeterminationUsing BETARAW sample: one of the following six sets of steering magnets ON��

� � � ��

m, � ��

m, � � � � �

m, � � � � �

m, � � �� m, � � � � �

m�

An oscillation around the original orbit�

Six different orbits are obtained.

HER BPMs

BPM number from IP

Dev

iati

on f

rom

the

Ori

gina

l Orb

it [

mm

]

-1

-0.5

0

0.5

1

0 100 200 300

Orbit before the kick

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Belle-lLg0k<W



Floating ParametersÕ Starting and ending points of orbits:Ý n æ Òæâ næ Òæ �Ý n��â n��! � ~� �� {� à� �#" � � $ ¢ ¡ � %

Õ Offsets of BPMs and QUADsÕ Scales of bendings:& �' ( ) J n�* J � �+ z-, ¤ | & �. / 0 J n�* JCommon among all the orbits

Global Fit

If we float all,

➟1

100 floating parameters➟ Large offsets (

1

1 cm)➟ Multi-solution➟ Not positive-definite

Hessian matrix

$t /:�

Belle-lLg0k<W


Belle

WM

@N

hK

w1

k|

Mwo

CH

L,[N

W;

!N

+/

13/48

BPM (10) QUAD (11) BEND (5or6)

0 or 1 floated;Others fixed.



Global Fits forAll the Combinations

Criteria

Fitting Parameters

offsets offsets scales

Choose the best χ2 !

Strategy

$t

/:

�Belle

-lL

g0

k<W �

KC

GS

eminar

Feb

.7,

2002


Criteria✏ MINUIT convergence with a positive-definite Hessian matrix

✏

t

BPM offsets

t 2

1 cm

✏

t

QUAD offsets

t 2

1 cm (alignment)

✏

t

BEND rescaling factor

t 2

20% (kick angle)

✏

t Ý ãä t 2 ~

mm

3 t â ãä t 2 ~mm

We find a solution4 With the smallest modification4 Within the scope of the numerical approach

$t /:�

Belle-lLg0k<W



BETARAW sample on Jun. 4, 2001

Horizontalµ � µ � µ � µ �

floating BPM M006QC4LE M006QC4LE M006QC4LE M006QC4LE

floating QUAD QC2LE QC2LE QC2LE QC2LE

floating BEND BH12LE BH45LE ZHQC5LE ®65 Ã87 9 : ; µ <

3.5 3.4 3.4 3.5=

BPM offset

=

[mm]

Á �?> � � @ �?> � � Á �?> � � @ �?> � � Á �?> � � @ �?> � � Á � > � � @ �?> � �

=

QUAD offset

=

[mm]

Á �?> � � @ �?> � � Á �?> � � @ �?> � � Á �?> � � @ �?> � � Á � > � � @ �?> � �

=

BEND scale

=

[%]

Á � > � @ � > � A Á �> � @ � > � A ¹ � > � @ �> B A

IP offset [mm] � ¹ �?> � @ �?> � � ¹ �?> � @ �?> � � ¹ �?> � @ �?> � � ¹ �?> � @ �?> �

M005QC3 offset [mm] ¹ �?> C � @ �?> � � ¹ �?> C C @ �?> � � ¹ �?> C � @ �?> � � ¹ � > C C @ �?> � �

M008QA2 offset [mm] ¹ �?> C � @ �?> � � ¹ �?> C � @ �?> � � ¹ �?> B � @ �?> � � ¹ � > C � @ �?> � �

$t /:�

Belle-lLg0k<W



BETARAW sample on Jun. 4, 2001

VerticalÂ � Â � Â �

floating BPM M002QC1LE M002QC1LE M003QC2LE

floating QUAD QA2LE QA2LE QA2LE

floating BEND ZVQC3LE ZVQC5LE ZVQC5LE ®6D Ã87 9 : ; Â < �?> � �?> � � > �=

BPM offset

=

[mm]

Á �?> � � @ �?> � � Á � > � � @ �?> � � ¹ �?> � � @ �?> � �

=

QUAD offset

=

[mm]

Á �?> C � @ �?> � � Á � > � B @ �?> � � Á �?> � � @ �?> � �

=

BEND scale

=

[%]

Á � � @ � A ¹ � � @ � A ¹ � � @ � A

IP offset [mm] � ¹ � > � � @ �?> � � � � ¹ �?> � � @ �?> � � � ¹ �?> � � @ �?> � � �

M005QC3LE offset [mm] ¹ �?> � B @ �?> � B ¹ � > � � @ �?> � � ¹ � > � C @ �?> � �

M008QA2LE offset [mm] ¹ �?> � � @ �?> � � ¹ � > � � @ �?> � � ¹ �?> � C @ �?> � �

$t /:�

Belle-lLg0k<W



BETARAW sample on Oct. 24, 2001

Horizontalµ � µ � µ � µ �


floating QUAD QC2LE QC2LE QC2LE

floating BEND BH12LE BH45LE ®65 Ã87 9 : ; µ <

3.4 2.8 3.4=

BPM offset

=

[mm]

Á �?> � � @ �?> � � Á �?> � C @ �?> � � Á �?> � B @ �?> � �

=

QUAD offset

=

[mm]

Á �?> � C @ �?> � � Á �?> � � @ �?> � � Á �?> � C @ �?> � �

=

BEND scale

=

[%]

Á � � @ � A ¹ � > � @ � > � A

IP offset [mm] � ¹ �?> C @ �?> � � ¹ �?> � @ �?> � � ¹ �?> C @ �?> �

M005QC3LE offset [mm] ¹ �?> � � @ �?> � � ¹ �?> C � @ �?> � � ¹ �?> �� @ �?> � �

M008QA2LE offset [mm] ¹ � > � � @ �?> � � ¹ �?> C � @ �?> � � ¹ �?> B � @ �?> � �

$t /:�

Belle-lLg0k<W



BETARAW sample on Oct. 24, 2001

VerticalÂ � Â � Â �


floating QUAD QA2LE QA2LE QA3LE

floating BEND ZVQC3LE ZVQC5LE ZVQC5LE ®6D Ã87 9 : D �?> � �?> � �?> �

=

BPM offset

=

[mm]

Á �?> � � @ �?> � � Á � > C � @ �?> � � Á �?> C � @ �?> � �

=

QUAD offset

=

[mm]

Á �?> � � @ �?> � � Á � > � � @ �?> � � ¹ �?> � � @ �?> � �

=

BEND scale

=

[%]

Á � � @ � A ¹ � � @ � A ¹ � B @ � A

IP offset [mm] � ¹ � > � � @ �?> � � � � ¹ �?> � � @ �?> � � � ¹ �?> � � @ �?> � � �

M005QC3LE offset [mm] ¹ �?> � � @ �?> � B ¹ � > � � @ �?> � � ¹ � > � � @ �?> � �

M008QA2LE offset [mm] ¹ �?> � � @ �?> � � ¹ � > � � @ �?> � � ¹ �?> � � @ �?> � �

$t /:�

Belle-lLg0k<W



Results of the Offset Correction(Horizontal case)

W/O the Offset Correction×YÎ ØÚÙ Û Ü �Ý ¤ � ��ßÞ � Ø � � ~ yÞ à-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-100 -80 -60 -40 -20 0

HORIZONTAL

s [m]

∆x

[cm

]

BPM measurements

QC

SLQ

C1L

EQ

C2L

EZ

HQ

C2L

EBH

1LE

BH

2LE

ZH

QC

3LE

QC

3LE

BH

3LE

QC

4LE

QC

5LE

BH

4LE

BH

5LE

QA

2LE

QA

3LE

QA

4LE

QA

5LE

QA

6LE

QA

7LE

W/ the Offset Correction×YÎ ØÚÙ Û Ü �Ý ¤ � � à Þ � Ø ~ y � �ßÞ �

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-100 -80 -60 -40 -20 0

HORIZONTAL

s [m]

∆x

[cm

]

BPM measurements

QC

SLQ

C1L

EQ

C2L

EZ

HQ

C2L

EBH

1LE

BH

2LE

ZH

QC

3LE

QC

3LE

BH

3LE

QC

4LE

QC

5LE

BH

4LE

BH

5LE

QA

2LE

QA

3LE

QA

4LE

QA

5LE

QA

6LE

QA

7LE

$t /:�

Belle-lLg0k<W



Results of the Offset Correction(Vertical case)

W/O the Offset Correction×YÏ ØÚÙ Û Ü �â ¤ � � � � Þ � Ø � � { yÞ �-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-100 -80 -60 -40 -20 0

VERTICAL

s [m]

∆y

[cm

]

BPM measurements

QC

SLQ

C1L

EQ

C2L

EB

C1L

EB

C2L

E

BC

3LE

QC

3LE

ZV

QC

3LE

QC

4LE

ZV

QC

4LE

ZV

QC

5LE

QC

5LE

QA

2LE

QA

3LE

QA

4LE

QA

5LE

QA

6LE

QA

7LE

W/ the Offset Correction×YÏ ØÚÙ Û Ü �â ¤ � à Þ E Ø ~ y � yÞ �

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-100 -80 -60 -40 -20 0

VERTICAL

s [m]

∆y

[cm

]

BPM measurements

QC

SLQ

C1L

EQ

C2L

EB

C1L

EB

C2L

E

BC

3LE

QC

3LE

ZV

QC

3LE

QC

4LE

ZV

QC

4LE

ZV

QC

5LE

QC

5LE

QA

2LE

QA

3LE

QA

4LE

QA

5LE

QA

6LE

QA

7LE

$t /:�

Belle-lLg0k<W



[III] Wattage Calculation

∆φ∆ψ

ψ

∆φ

Using the following analytical formula (Phys. Rev. 75 (1949) 1912) :

F G � �IH �KJ ® LM N ®PO FRQ FS FT �Q

QQVU

®W � Á µ ®X ® Y ®[Z \ ;8] <©Á µ ®� Á µ ® Y ®[^\ ;8] < _Q

`a b!cd ef gih jlkm g cdon p a jd eqr ef m sn t�u ` vn wu xy pp{z

| x} t Ç~ � � Ç

$t /:�

Belle-lLg0k<W



∆s∆φρ�� o�

��

�� K� � � ��

�� I� �K ¡¢

£ ¤ ¡ ¥K¦ ¥K§ ¥¨ ©¦

¦¦Vª

¡« ©¬ ¡® ¡ ¯ ¡±°² ³8´ µ ¬ ¡©¬ ¡ ¯ ¡±¶ ² ³ ´ µ _¦· ³ § µ

¸

3D-integration is performed using BASES. (MC integration)

$t /:¹

Belle-lLg0k<W

ºKCG Seminar Feb. 7, 2002


Projection to a Plane

ψ

tangent

s

orbit

Mapping:

»½¼¿¾ À Á Â

point in the plane

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Belle-lLg0k<W



Check of the Wattage Calculation

by comparing with the SAD calculation

Start with the same lattice model file

(/ldata/KEKB/KCG/HER/herfq270.sad)

For a certain component (e.g. QC3LE)

My Calculation SAD

Wattage distribution in the

ÃÄ

plane at

Å �Æ Ç

cm

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Belle-lLg0k<W



Exact Calculation using SAD

starting with the Feynman-Heaviside formula

ÈÊÉ ³ ÈRËÍÌ Î µ � Ï� ÐÒÑÓ ÈRÔÕ ¡ ¬Õ

Ö¥

¥ ÎÈRÔÕ ¡ ¬ ©

Ö¡¥ ¡

¥ Î ¡ ÈÔ ×

x τ( , )r

q

R

ØÚÙ Û � ØoÜ½Ý Þ � � ßà#á

âäãå æâçã èêé

ë Ø Ù � ØÜ½Ý ì �Íí î ï âð � ì Ý Øòñ Û � Øoó ô ØÙ Û

Poynting vector:

ØÊõ � ØÙ Û ô Ø ñ Û

��

öø÷ù÷

È#ú ³ È Ë Ì Î µ ¥ Îû ÈRü ¥ ýIþ ¢ÿ � � �£

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Belle-lLg0k<W



Example of My Calculation on QC3LEat

� � � �

cm

Y(SR).vs.X(SR)

X [mm]Y [mm]

Wat

tage

[W

/mm

2 ]

-25-20

-15-10

05

1015

200

0.02

0.04

0.06

0.08

Y(SR).vs.X(SR)

X [mm]

Y

[mm

]0

5

10

15

20

-25 -20 -15 -10

� Ã Ý Ä Ý Å �

: Belle coordinate system

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Belle-lLg0k<W



��

4.7 W

(T.Abe)

4.0 W (SAD)

Y = 12 mm AND Z = -80 mm

X [mm]

Wat

tage

[W

/mm

2 ]

T. AbeSAD

0

0.025

0.05

0.075

0.1

-25 -20 -15 -10

X = -17 mm AND Z = -80 mm

Y [mm]

Wat

tage

[W

/mm

2 ]

T. AbeSAD

0

0.025

0.05

0.075

0.1

0 5 10 15 20

��

Y = 12 mm AND Z = -80 mm

X [mm]

Wat

tage

[W

/mm

2 ]

T. AbeSAD

0

0.01

0.02

0.03

-25 -20 -15 -10

X = -17 mm AND Z = -80 mm

Y [mm]

Wat

tage

[W

/mm

2 ]

T. AbeSAD

0

0.01

0.02

0.03

0.04

0 5 10 15 20

0.85 W (T.Abe)

0.75 W (SAD)

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Belle-lLg0k<W



Conclusions on the Wattage Calculation

➟ My geometry calculation is successful.

➟ Good agreements on

Àdistributions

➟ Small differences on

distributions:Â ! "# $

higher than SAD results for

%'& ! "

keV.

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Belle-lLg0k<W



Z = – 8 cm

-20

-10

0

10

20

-20 -10 0 10 20

Y(SR).vs.X(SR)

X [mm]

Y

[mm

]

HE

R m

ask

LE

R m

ask

BC1LEQC1LE

BH12LEZVQC4

ZHQC5

HER SR(2001.11.07.13:00:00)

(*) +, � - Ç.mAÙ& / ß .

keV� 0 1 2 3 ß 4

Magnet Wattage

BC1LE

.65 ß

BH1LE

.65 7 ô ß . î 8

BH2LE

à5 . ô ß . î 8

ZVQC4

95 : ô ß . î ;

ZHQC5

95 : ô ß . î ;

QC1LE

ß5 ß ô ß . î <

QC2LE

ß5 ß ô ß . î =

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Belle-lLg0k<W



Z = + 13.5 cm

-20

-10

0

10

20

-20 -10 0 10 20

Y(SR).vs.X(SR)

X [mm]

Y

[mm

]

HE

R m

ask

LE

R m

ask

BC1LEQC1LE

BH12LEZVQC4

ZHQC5

HER SR(2001.11.07.13:00:00)

(*) +, � - Ç.mAÙ& / ß .

keV� 0 1 2 3 ß 4

Magnet Wattage

BC1LE

.65 ß

BH1LE

.65 7 ô ß . î 8

BH2LE

à5 . ô ß . î 8

ZVQC4

95 : ô ß . î ;

ZHQC5

95 : ô ß . î ;

QC1LE

ß5 ß ô ß . î <

QC2LE

ß5 ß ô ß . î =

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Belle-lLg0k<W



Error Estimation

Errors on the BPM resolutions

>

offset uncertainties are estimated.

➟ Using the data on Nov. 7 (2001) at 1:00PM

➟ If ? @ 2BA � C / ß DE FHGI J KLM 0 NE FHOP Q KLM 0 ô ? @ 2BA � C

so that ? @ �BA í R �2BA � C N ß.

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Belle-lLg0k<W



The values at the asterisks are used.

One-σ Contour

XIP [mm]

Xin

i [

mm

]

0.12

0.14

0.16

0.18

-0.64 -0.635 -0.63 -0.625

One-σ Contour

YIP [mm]Y

ini

[m

m]

-0.68

-0.66

-0.64

-0.62

-0.6

-0.6095 -0.609 -0.6085 -0.608 -0.6075

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Belle-lLg0k<W



Position Errors

for

3 ÃS TU V / NW W Ã X Y[Z F\^] _ KX\ X _ � Ã �Ä

W W X YZ F\^] _ KX\ X _ � Ã �Ä

3 Ä S TU V / NW W Ä X YZ F\^] _ KX\ X _ � Ã �Ä

W W X YZ F\^] _ KX\ X _ � Ã �Ä

$t /:¹

Belle-lLg0k<W



-1

-0.5

0

0.5

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Eγ > 10keV & Wattage > 1E-16W

∆<X

mas

k>

[m

m]

BH

5LE

BH

4LE

ZH

QC

5

ZV

QC

4

BH

3LE

ZV

QC

3

QC

3LE

BH

2LE

BH

1LE

BC

3LE

ZH

QC

2

BC

1LE

QC

2LE

QC

1LE

` � Ã ` �� .65 à

mm

-1

-0.5

0

0.5

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14


∆<Y

mas

k>

[m

m]

BH

5LE

BH

4LE

ZH

QC

5

ZV

QC

4

BH

3LE

ZV

QC

3

QC

3LE

BH

2LE

BH

1LE

BC

3LE

ZH

QC

2

BC

1LE

QC

2LE

QC

1LE

` �Ä ` �� .65 9

mm

$t /:¹

Belle-lLg0k<W


Belle

WM

@N

hK

w1

k|

Mwo

CH

L,[N

W;

!N

+/

35/48

Horizontal Position Systematics (1)

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

∆X

QC1LE+2 mm

– 2mm

QC2LE+2 mm

– 2mm

BC1LE+2 mm

– 2mm

ZHQC2+2 mm

– 2mm

BC3LE+2 mm

– 2mm

BH1LE+2 mm

– 2mm

BH2LE+2 mm

– 2mm

2nd χ 2

3rd χ 2

1st with Q

2nd with QIP constr.

0 1 2 3 4 5

$t

/:

¹Belle

-lL

g0

k<W º

KC

GS

eminar

Feb

.7,

2002

Belle

WM

@N

hK

w1

k|

Mwo

CH

L,[N

W;

!N

+/

36/48

Horizontal Position Systematics (2)

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

∆X

QC3LE+2 mm

– 2mm

ZVQC3+2 mm

– 2mm

BH3LE+2 mm

– 2mm

ZVQC4+2 mm

– 2mm

ZHQC5+2 mm

– 2mm

BH4LE+2 mm

– 2mm

BH5LE+2 mm

– 2mm

2nd χ 2

3rd χ 2

1st with Q


0 1 2 3 4 5

$t

/:

¹Belle

-lL

g0

k<W º

KC

GS

eminar

Feb

.7,

2002

Belle

WM

@N

hK

w1

k|

Mwo

CH

L,[N

W;

!N

+/

37/48

Vertical Position Systematics (1)

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

∆Y

QC1LE+2 mm

– 2mm

QC2LE+2 mm

– 2mm

BC1LE+2 mm

– 2mm

ZHQC2+2 mm

– 2mm

BC3LE+2 mm

– 2mm

BH1LE+2 mm

– 2mm

BH2LE+2 mm

– 2mm

2nd χ 2

3rd χ 2

1st with Q


0 1 2 3 4 5

$t

/:

¹Belle

-lL

g0

k<W º

KC

GS

eminar

Feb

.7,

2002

Belle

WM

@N

hK

w1

k|

Mwo

CH

L,[N

W;

!N

+/

38/48

Vertical Position Systematics (2)

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

∆Y

QC3LE+2 mm

– 2mm

ZVQC3+2 mm

– 2mm

BH3LE+2 mm

– 2mm

ZVQC4+2 mm

– 2mm

ZHQC5+2 mm

– 2mm

BH4LE+2 mm

– 2mm

BH5LE+2 mm

– 2mm

2nd χ 2

3rd χ 2

1st with Q


0 1 2 3 4 5

$t

/:

¹Belle

-lL

g0

k<W º

KC

GS

eminar

Feb

.7,

2002

Belle

WM

@N

hK

w1

k|

Mwo

CH

L,[N

W;

!N

+/

39/48

Wattage Errors on

0

5

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14


∆W/W

BH

5LE

BH

4LE

ZH

QC

5

ZV

QC

4

BH

3LE

ZV

QC

3

QC

3LE

BH

2LE

BH

1LE

BC

3LE

ZH

QC

2

BC

1LE

QC

2LE

QC

1LE

Wat

tage

[W

]

10-14

10-10

10-6

10-210-1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

$t

/:

¹Belle

-lL

g0

k<W º

KC

GS

eminar

Feb

.7,

2002

Belle

WM

@N

hK

w1

k|

Mwo

CH

L,[N

W;

!N

+/

40/48

Wattage Errors on

0

5

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14


∆W/W

BH

5LE

BH

4LE

ZH

QC

5

ZV

QC

4

BH

3LE

ZV

QC

3

QC

3LE

BH

2LE

BH

1LE

BC

3LE

ZH

QC

2

BC

1LE

QC

2LE

QC

1LE

Wat

tage

[W

]

10-14

10-10

10-6

10-210-1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

$t

/:

¹Belle

-lL

g0

k<W º

KC

GS

eminar

Feb

.7,

2002

Belle

WM

@N

hK

w1

k|

Mwo

CH

L,[N

W;

!N

+/

41/48

Wattage Systematics (1)

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

∆W / W

QC1LE+100%

–100%

QC2LE+100%

–100%

BC1LE+100%

–100%

ZHQC2+100%

–100%

BC3LE+100%

–100%

BH1LE+100%

–100%

BH2LE+100%

–100%

2nd χ 2

3rd χ 2

1st with Q


0 1 2 3 4 5

$t

/:

¹Belle

-lL

g0

k<W º

KC

GS

eminar

Feb

.7,

2002

Belle

WM

@N

hK

w1

k|

Mwo

CH

L,[N

W;

!N

+/

42/48

Wattage Systematics (2)

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

∆W / W

QC3LE+100%

–100%

ZVQC3+100%

–100%

BH3LE+100%

–100%

ZVQC4+100%

–100%

ZHQC5+100%

–100%

BH4LE+100%

–100%

BH5LE+100%

–100%

2nd χ 2

3rd χ 2

1st with Q


0 1 2 3 4 5

$t

/:

¹Belle

-lL

g0

k<W º

KC

GS

eminar

Feb

.7,

2002

Belle

WM

@N

hK

w1

k|

Mwo

CH

L,[N

W;

!N

+/

43/48

Wattage Errors on

-0.5

0

0.5

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14


∆W/W

BH

5LE

BH

4LE

ZH

QC

5

ZV

QC

4

BH

3LE

ZV

QC

3

QC

3LE

BH

2LE

BH

1LE

BC

3LE

ZH

QC

2

BC

1LE

QC

2LE

QC

1LE

Wat

tage

[W

]

10-1

1

10

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

$t

/:

¹Belle

-lL

g0

k<W º

KC

GS

eminar

Feb

.7,

2002

Belle

WM

@N

hK

w1

k|

Mwo

CH

L,[N

W;

!N

+/

44/48

Wattage Errors on

-0.5

0

0.5

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14


∆W/W

BH

5LE

BH

4LE

ZH

QC

5

ZV

QC

4

BH

3LE

ZV

QC

3

QC

3LE

BH

2LE

BH

1LE

BC

3LE

ZH

QC

2

BC

1LE

QC

2LE

QC

1LE

Wat

tage

[W

]

10-1

1

10

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

$t

/:

¹Belle

-lL

g0

k<W º

KC

GS

eminar

Feb

.7,

2002

Belle

WM

@N

hK

w1

k|

Mwo

CH

L,[N

W;

!N

+/

45/48

Wattage Systematics (1) ( a b c d keV)

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

∆W / W

QC1LE+100%

–100%

QC2LE+100%

–100%

BC1LE+100%

–100%

ZHQC2+100%

–100%

BC3LE+100%

–100%

BH1LE+100%

–100%

BH2LE+100%

–100%

2nd χ 2

3rd χ 2

1st with Q


0 1 2 3 4 5

$t

/:

¹Belle

-lL

g0

k<W º

KC

GS

eminar

Feb

.7,

2002

Belle

WM

@N

hK

w1

k|

Mwo

CH

L,[N

W;

!N

+/

46/48

Wattage Systematics (2) ( a b c d keV)

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

∆W / W

QC3LE+100%

–100%

ZVQC3+100%

–100%

BH3LE+100%

–100%

ZVQC4+100%

–100%

ZHQC5+100%

–100%

BH4LE+100%

–100%

BH5LE+100%

–100%

2nd χ 2

3rd χ 2

1st with Q


0 1 2 3 4 5

$t

/:

¹Belle

-lL

g0

k<W º

KC

GS

eminar

Feb

.7,

2002


Summary

Methods of the real orbit and wattage calculationshave been established.

Wattage distributions in the IR

✏ My program has been checked comparing with the SAD results

both on the orbit and wattage calculations.

✏ Error estimations have been also done:

➟

ef g [h e Ì e f g ih e j ©

mm

➟

f � k �:

ß . � 9. 4

for

Ù& / ß

keV,à � :

for

Ù& / ß .

keV

$t /:¹

Belle-lLg0k<W



Future Works

✏ For online monitoring

➟ Calculation speed:

9 � l

sec

2

(fit & MC-integrations)

m

OK

➟ Input parameters (BPM,

n

) are already available from the Belle NSM.

✏ Beam size m

to be implemented

✏ Transformation to the corresponding radiation dose m

not yet

➟ Interface to EGS4

✏ Improvement of the offset determination algorithm

➟ Based on the current method➟ To reduce the wattage errors➟ More understanding on the real orbit calculation is needed.

$t /:¹

Belle-lLg0k<W


Documents

Belle- L 0k W - KEK · 2011. 11. 2. · Belle-lLg0k