Nov. 17, 2005Fermi Lab AP Seminar AC Dipole Based Diagnostics Mei Bai, C-A Department.
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Transcript of Nov. 17, 2005Fermi Lab AP Seminar AC Dipole Based Diagnostics Mei Bai, C-A Department.
Nov. 17, 2005 Fermi Lab AP Seminar
AC Dipole Based Diagnostics
Mei Bai, C-A DepartmentMei Bai, C-A Department
Fermi Lab AP SeminarNov. 17, 2005
Outline
Introduction of ac dipole AC dipole based beam diagnostics
beam dynamics spin manipulation
RHIC AC dipole system Summary
Fermi Lab AP SeminarNov. 17, 2005
Abstract
after a short introduction of the system.
In recent years, there has been growing interests in developing non-destructive beam diagnostic tools for high energy accelerators. AC dipole as a tool to adiabatically excite large amplitude coherent betatron oscillations without emittance blowup is very useful in exploring the beam dynamics. This technique was first tested in the Brookhaven AGS with Au beam. It was then used in the AGS polarized proton operation to overcome strong intrinsic spin resonances by inducing a full spin flip. Two AC dipoles were also installed in RHIC for linear optics measurement as well as non-linear resonance driving term measurement. The vertical ac dipole in RHIC can also be resonated close to half of the revolution frequency for spin manipulations. This talk will overview the ac dipole applications
Fermi Lab AP SeminarNov. 17, 2005
Introduction of ac dipole
Beam becomes unstable if m=z
mzm
mcoh βsβ
ννBρ4
LΔBsZ
AC dipole: a dipole magnet with oscillating field
By driving the ac dipole at a frequency at the vicinity of beam betatron frequency, a coherent oscillation can be excited. The size of this excited coherent oscillation is proportional to the strength of the ac dipole. The closer the ac dipole frequency to the beam betatron frequency, the stronger the driven coherent oscillation
By adiabatically ramping up the ac dipole strength, this driven oscillation is well under control and prevent the beam size from being blown up
Fermi Lab AP SeminarNov. 17, 2005
Ac dipole amplitude ramps up in 1000 turns and then kept constant for 1000 turns. The ac dipole amplitude then ramps down to zero in another 1000 turns.
1000 particles in Gaussian before and after the ac dipole excitation. The blue dots are the beam distribution in the rotating frame when the ac dipole amplitude is constant.
-1.5
-1
-0.5
0
0.5
1
1.5
0 50 100 150 200 250 300
Dip
ole
field
D
ipole
field
st
ren
gth
stre
ng
th
Time Time
Introduction of ac dipole Beam emittance gets preserved before and after the excitation as
long as the ac dipole excitation is turned on adiabatically
Fermi Lab AP SeminarNov. 17, 2005
First test results of ac dipole driven oscillation
Ac dipole in the Brookhaven AGS. The ac dipole was first ramped up its maximum amplitude in 1000 turns. The amplitude was then kept constant for another 1000 turns and the ac dipole oscillation amplitude was ramped to zero in the final 1000 turns
Experimental results in the Brookhaven AGS
Before excitation
after excitation
Me
asu
red
rm
s b
ea
m s
ize
[m
m]
Me
asu
red
rm
s b
ea
m s
ize
[m
m]
Fermi Lab AP SeminarNov. 17, 2005
Ac dipole driven coherent oscillation with non-zero detuning
Fermi Lab AP SeminarNov. 17, 2005
Applications of AC dipole
Linear optics measurement Measure beta function and phase advance Measure beta function at interaction point Linear coupling measurement
Local coupling measurement
Non-linear driving term measurement
Dynamic aperture measurement
Spin manipulation
Fermi Lab AP SeminarNov. 17, 2005
Beam diagnostic applications using AC dipole
Linear optics measurement Measure beta functions as well as phase advances
Beta function and phase advance ring wide Beta function at interaction point
22
21 mmm zzz
1
21tanm
m
z
z
)2sin()2cos(
)2sin()(
21 iziz
iziz
mmmm
mm
Fermi Lab AP SeminarNov. 17, 2005
Beam diagnostic applications using AC dipole
Linear optics measurement
'1
1'2
2
z
zM
z
z
12
m12
m1
m2
12m11 sinφ
sinφ
/ββ
/ββββ
131,312
1,311
1121,212
1,211
1 cotφm
mβcotφ
m
mβ
BPM 1 BPM 2 BPM 3
SCSC
SSC
mm
mmM
22
1
21
21
21
21
2111
2
2221
1211
1
Fermi Lab AP SeminarNov. 17, 2005
Measured phase advance between bpms
Measured beta functions between bpms
Beta function and phase advance measurement in RHIC
Fermi Lab AP SeminarNov. 17, 2005
Measure beta function at interaction point
Dx(L) Dx(R)
*
2** )(
)(
sss
(L , L , L) (R , R , R)
RL 11* ***
2
Lengths RL
Length
S*
Fermi Lab AP SeminarNov. 17, 2005
First test at the end of IP2 Beta Squeeze experiment
Fulvia, ToddNikolay, SteveMei
Fermi Lab AP SeminarNov. 17, 2005
IP 2 4 6 8 10 12
Data 1 1.95357 4.858380.8968
21.01364 2.53181 5.85059
Data 2 1.83512 4.862530.8863
50.99743 2.52409 5.862
Data 3 1.86303 4.85470.8734
80.99046 2.51453 5.87384
Data 4 1.88602 4.856480.8740
71.00204 2.53628 6.11184
Average
1.884±0.051
4.858±0.0034
0.883±0.011
1.000±0.0097
2.527±0.0095
5.924±0.125
design 2.0 5.0 0.85 0.85 3.0 5.0
First test at the end of IP2 Beta Squeeze experiment
Fermi Lab AP SeminarNov. 17, 2005
Linear coupling measurement
)]sin()cos(['4
)cos('4
1222
mmx
y
mx
x
QcQcxB
y
QxB
x
Beam diagnostic applications using AC dipole
Skew quadrupole strengthSkew quadrupole strength
yyam
pam
p/x/x
am
pam
pxx
am
pam
p/y/y
am
pam
p
Fermi Lab AP SeminarNov. 17, 2005
Courtesy of Rama
Coupling matrix C changes alongthe ring and it can be shown thatthe determinant of C jumps at acoupling source.
One turn transfer matrix T
Beam diagnostic applications using AC dipole
Local coupling measurement
Fermi Lab AP SeminarNov. 17, 2005 Courtesy of Rama
Beam diagnostic applications using AC dipole Local coupling measurement
Fermi Lab AP SeminarNov. 17, 2005 Courtesy of Rama
Beam diagnostic applications using AC dipole
Local coupling measurement Data taken at injection in Yellow ring The average coupling strength over the ring varied with different local skew quad settings The quality of the data is compromised due to the bpm
problems the continuous linear increase of coupling strength in the middle of arc is against the expectation that the local coupling in RHIC mainly comes from the triplets
Fermi Lab AP SeminarNov. 17, 2005
yyxx
xx
nlmnkjiml
y
kj
xjklm
nixx
eJJjfi
eJnipnx
22122
1
2
222
2
Normal form with free oscillation
Normal form with driven coherent oscillation
Non-linear resonance driving term
xmxnkjikj
xjkx eJjfinipnx 21
2
1'
00 22
Normal form of particle motion under the influence of an ac dipole, R. Tomas, Phys. Review ST-AB, Vol. 5, 054001
R. Bartolini and F. Schmidt, LHC Project Note 132, 1998
Spectral line @ (1-j+k, m-l) resonance @ (j-k, l-m)
Beam diagnostic applications using AC dipole Measure non-linear resonance driving term
Fermi Lab AP SeminarNov. 17, 2005
Non-linear driving term measurement in RHICFirst 3rd order resonance driving term measurement in RHIC with ac dipole
Rogelio, WolframRama, Mei, …
Fermi Lab AP SeminarNov. 17, 2005
Dynamic aperture measurement Limitation of the traditional DA technique is the tune
meter kicker strength at store
With ac dipole, the idea is to drive the beam with a well controlled ramping strength and record the beam oscillation amplitude. In principle, the amplitude of the coherent oscillation saturates when the DA is reached.
One can also extract the frequency spectrum as a function of oscillation amplitude from the million turn bpm data
Beam diagnostic applications using AC dipole
Fermi Lab AP SeminarNov. 17, 2005
Spin manipulation – measure spin tune How to use spin flipper to measure spin tune?
Spin motion nearby a spin depolarization resonance
Induce a coherent spin precession with spin flipper. Measure the turn by turn spin precession. Calculate the precession amplitude of the vertical and radial component.
Currently, we are focusing on analyzing the RHIC pp 2004 spin flipping data
2s
2
sy
K)(νε
KνP
θ)-tan(90εKν Spin tune os
2s
2x
K)(νε
εP
y
x
z
0B
con
beam directionx
B
xP
Fermi Lab AP SeminarNov. 17, 2005
Spin manipulation -- Spin flipping
• spin flipping efficiency in Blue is 66%• yellow got depolarized possibly because yellow spin tune is too close to the spin flipper tune
Fermi Lab AP SeminarNov. 17, 2005
RHIC AC dipole system
(OD)8
71(ID)
8
51(Length)53
''''''
Magnet Air core with Litz wire Ceramic beam pipe with an dimension of
Two aluminum strips outside the beampipe provide a path for image current
Location
Fermi Lab AP SeminarNov. 17, 2005
RHIC AC dipole system
Inductance of the magnet: In parellel: 26.362 uH In series: 104.32 uH
Current achieved In series: 50 Amp ~ 67 Gm In parallel: 160 Amp ~ 106 Gm
This corresponds to a
1.4 coherence at RHIC
store energy The bottom figure shows the vertical 1024 turn by turn beam position data in the middle of the arc. The black solid circles are the measured turn-by-turn beam position data and the red open circles are the fitted turn-by-turn data. The top plot is the phase plot at the same location.
Fermi Lab AP SeminarNov. 17, 2005
RR1, RR3, RR4, RR5, RR6open for series operation
Shorting
RR2 open for parallel operation
C1Bank
C2Bank
C1aBank
C2aBank
"C2" Buss bar
From Power Amp
RR1
RR2
RR3
RR4
RR5
Magnet "2"
Magnet "1"
Magnet "3"
Magnet Current - to scope
Magnet "4"
W1Andrew LDF4RN-50A
1 3
2
Current
T1Current Transformer
W2RG-58
1 3
2
bottom plate
RR7
Rd2
100
Rd1
100
Rd5
100
Rd4
100
Rd3
100
400300 500(60.84KHz ) (36.6KHz )
RR6
L1
L2
Magnet coils
RHIC AC dipole circuit
Fermi Lab AP SeminarNov. 17, 2005
Experience from RHIC AC dipole based beam experiments
Reliable turn by turn data from BPMs are very critical
Sharing magnets between Blue and Yellow makes it very difficult on using ac dipole independently in the two rings
The strength of the spin flipper is kind of marginal, esp. for the spin tune measurement. The current RHIC ac dipole only provides a resonance strength of a few units of 10-4
Fermi Lab AP SeminarNov. 17, 2005
Summary
AC dipole has been demonstrated to be a powerful tool to induce long lasting coherent oscillations. Large coherent oscillations are often needed for measuring the machine optics parameters as well as for studying the non-linear behavior of the beam. This technique has been routinely applied in the Brookhaven RHIC to measure the phase advances as well beta functions. It has also been demonstrated in RHIC to use ac dipole to measure the non-linear resonance driving terms.