Status of the AC Dipole Study

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Status of the AC Dipole Study Ryoichi Miyamoto 3/28/2007 LARP Meeting @ Fermilab

description

Status of the AC Dipole Study. Ryoichi Miyamoto 3/28/2007 LARP Meeting @ Fermilab. Basics. δ. ν. @VBPMB18. ν d. 1 - ν d. 0. 1. @VBPMB21. Driven Oscillation ≠ Natural Oscillation. “Relative” β can be measured Need to be scaled to determine the “absolute” function. - PowerPoint PPT Presentation

Transcript of Status of the AC Dipole Study

Page 1: Status of the AC Dipole Study

Status of the AC Dipole Study

Ryoichi Miyamoto

3/28/2007

LARP Meeting @ Fermilab

Page 2: Status of the AC Dipole Study

Basics

@VBPMB18

@VBPMB21

νd

ν

0 11-νd

δ

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• “Relative” β can be measured • Need to be scaled to determine the “absolute” function.

Driven Oscillation ≠ Natural Oscillation

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Courant-Snyder Parameter Measurement@ IP Using CPMs (Sypher’s Scheme)• Gives the scaling to the relative measurement.• β* and waist location are also very important.

BPMU BPMD

@ Tevatron’s IPs

No magnets(except detector’s solenoids) Particles drift x and x’ can be measured

If x and x’ are known…

)2cos( nAxn

2

222

2

1

)2(cos

A

nAxn

,2

1' 22 Ax n 2

2

1' Axx nn

2222

2

1'' Axxxx nnnn

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AC Dipole Version of the Courant-Snyder Parameter Measurement @ IP Using CPMs

))2(sin(

)sin()(

)2sin(

)arctan22)|(2cos(2

1

)arctan22)|(2cos(21

''

'

)2sin(

)arctan2)|(2sin(12

)2)|(2sin(21

)2)|(2cos(21

''

'

)2sin(

)2)|(2cos(2

1

)2)|(2cos(21

''

2

2

222

2

2

2

2

222

2

2

222

2

d

d

nnnn

n

d

dd

nnnn

nn

d

d

nnnn

n

ss

ss

xxxx

x

ss

ssss

xxxx

xx

ss

ss

xxxx

x

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Measured β

ACD DO

βup [m] 29.7 29.6

βdown [m] 34.0 34.0

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Measured α

ACD DO

αup 3.89 3.92

αdown -4.24 -4.22

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Phase Spaces with Different δ (Backup)

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Example of the Pinger’s TBT Data (Backup)

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))(2cos(

)())(2cos(2)()(

)))1(()()1(2cos()(

))()(2cos()()(

ddxdd

)d()d(2)d(2)d(

ddd)d(

ddd)d()d(

sn

ssAAAA

snsA

snsAsxn

)tan(arctan)(

)))1((sin()(4

))(sin()(4

)d()d(

)d()d(xd

d

dd)d(

d

dd)d(

AA

AAs

B

lBA

B

lBA

Analytic Expression of the Driven Oscillation