Belle- L 0k W - KEK · 2011. 11. 2. · Belle-lLg0k
Transcript of Belle- L 0k W - KEK · 2011. 11. 2. · Belle-lLg0k
BelleWM@NhKw1k
|MwoCHL,[NW;!N+/
$t/:Belle-lLg0k<W
KCG Seminar
Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 1/48
Introduction
✏ Motivation
➟ SVD1.0 was killed by the synchrotron radiation (SR) from HER.� �
Limitation for the HER steering magnets� �
Some current values are close to the limits. (
�figure)
➟ Smaller-radius IR beampipe ( �� 2.0 cm
�1.5 cm
�1.0 cm ?)
➟ Larger beam currents for higher luminosities�
more SR
✏ A new idea has been proposed by Hitoshi Yamamoto:
Fitting BPM-measured values�
Real beam orbit�
Wattage distribution in the IR
�Online alarm for SR
➟
� � �� � � �� � ��for the HER steering magnets
➟
� � � � �� � �for detector damages
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Belle-lLg0k<W
�KCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 2/48
-4
-2
0
2
-100 -80 -60 -40 -20 0
In the HER Straight Section
s [m]
Kic
k A
ngle
[m
rad]
QC
SLQ
C1L
EQ
C2L
EZ
HQ
C2L
E
BH
1LE
BH
2LE
ZH
QC
3LE
QC
3LE
BH
3LE
QC
4LE
QC
5LE
BH
4LE
BH
5LE
QA
2LE
QA
3LE
QA
4LE
QA
5LE
QA
6LE
QA
7LE
QC
SLQ
C1L
EQ
C2L
EB
C1L
E
BC
3LE
QC
3LE
ZV
QC
3LE
QC
4LE
ZV
QC
4LE
ZV
QC
5LE
QC
5LE
QA
2LE
QA
3LE
QA
4LE
QA
5LE
QA
6LE
QA
7LE
kick angle on Jan. 28 (2002)
Max. allowed angle
Kick range for 1<r<2cm
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�KCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 3/48
Calculation Method
[I] Orbit Calculation
➟ In the HER straight section (see
�
)
➟ Using a linear approximation
�
transfer matrices
➟ Implemented in my own program
BSWTLE
QA7LEQA6LE
QC2LE
QC1LEQCSL
IP
HER Straight Section
e
(~100m)
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Belle-lLg0k<W
�KCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 4/48
Transfer Matrices
��� ����� � ��� "!#$%$%$%$&$(') � � ) * � � + � � + * � � ,-.%.%.%.&.(/
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
$t /:�
Belle-lLg0k<W
�KCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 5/48
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
�KCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 6/48
Check of the Transfer-Matrix Implementation [2]
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
�KCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 7/48
Check of the Transfer-Matrix Implementation [3]
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�
$t /:�
Belle-lLg0k<W
�KCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 8/48
[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  ·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
�KCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 9/48
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!
$t /:�
Belle-lLg0k<W
�KCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 10/48
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
�KCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 11/48
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
$t /:�
Belle-lLg0k<W
�KCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 12/48
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
�KCG Seminar Feb. 7, 2002
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.
0 or 1 floated;Others fixed.
0 or 1 floated;Others fixed.
Global Fits forAll the Combinations
Criteria
Fitting Parameters
offsets offsets scales
Choose the best χ2 !
Strategy
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/:
�Belle
-lL
g0
k<W �
KC
GS
eminar
Feb
.7,
2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 14/48
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
�KCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 15/48
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
�KCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 16/48
BETARAW sample on Jun. 4, 2001
Vertical �  �  �
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
�KCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 17/48
BETARAW sample on Oct. 24, 2001
Horizontalµ � µ � µ � µ �
floating BPM M006QC4LE M006QC4LE M006QC4LE
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
�KCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 18/48
BETARAW sample on Oct. 24, 2001
Vertical �  �  �
floating BPM M002QC1LE M002QC1LE M002QC1LE
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
�KCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 19/48
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
�KCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 20/48
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
�KCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 21/48
[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
�KCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 22/48
∆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
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 23/48
Projection to a Plane
ψ
tangent
s
orbit
Mapping:
»½¼¿¾ À Á Â
point in the plane
$t /:¹
Belle-lLg0k<W
ºKCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 24/48
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
$t /:¹
Belle-lLg0k<W
ºKCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 25/48
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 � � �£
$t /:¹
Belle-lLg0k<W
ºKCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 26/48
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
$t /:¹
Belle-lLg0k<W
ºKCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 27/48
�� � ��� � ��� � � �� ��� � � ��� �
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)
$t /:¹
Belle-lLg0k<W
ºKCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 28/48
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.
$t /:¹
Belle-lLg0k<W
ºKCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 29/48
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 =
$t /:¹
Belle-lLg0k<W
ºKCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 30/48
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 =
$t /:¹
Belle-lLg0k<W
ºKCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 31/48
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.
$t /:¹
Belle-lLg0k<W
ºKCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 32/48
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
$t /:¹
Belle-lLg0k<W
ºKCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 33/48
Position Errors
for
3 ÃS TU V / NW W à X Y[Z F\^] _ KX\ X _ � à �Ä
W W X YZ F\^] _ KX\ X _ � à �Ä
3 Ä S TU V / NW W Ä X YZ F\^] _ KX\ X _ � à �Ä
W W X YZ F\^] _ KX\ X _ � à �Ä
$t /:¹
Belle-lLg0k<W
ºKCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 34/48
-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
` � à ` �� .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
Eγ > 10keV & Wattage > 1E-16W
∆<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
ºKCG Seminar Feb. 7, 2002
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
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
+/
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
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
+/
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
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
+/
39/48
Wattage Errors on
0
5
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Eγ > 10keV & Wattage > 1E-16W
∆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
Eγ > 10keV & Wattage > 1E-16W
∆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
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
+/
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
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
+/
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
Eγ > 1keV & Wattage > 4E-2W
∆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
Eγ > 1keV & Wattage > 4E-2W
∆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
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
+/
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
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@NhKw1k|MwoCHL,[NW;!N+/ 47/48
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
ºKCG Seminar Feb. 7, 2002
Belle WM@NhKw1k|MwoCHL,[NW;!N+/ 48/48
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.
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ºKCG Seminar Feb. 7, 2002