status of the ac dipole study

Status of the AC Dipole Study

Ryoichi Miyamoto

3/28/2007

LARP Meeting @ Fermilab

Basics

@VBPMB18

@VBPMB21

νd

ν

0 11-νd

δ

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

Driven Oscillation ≠ Natural Oscillation

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

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

Measured β

ACD DO

βup [m] 29.7 29.6

βdown [m] 34.0 34.0

Measured α

ACD DO

αup 3.89 3.92

αdown -4.24 -4.22

Phase Spaces with Different δ (Backup)

Example of the Pinger’s TBT Data (Backup)

))(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