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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
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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