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


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


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


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


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]


Ac dipole driven coherent oscillation with non-zero detuning


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


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



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


Measured phase advance between bpms

Measured beta functions between bpms

Beta function and phase advance measurement in RHIC


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*


First test at the end of IP2 Beta Squeeze experiment

Fulvia, ToddNikolay, SteveMei


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


Linear coupling measurement

)]sin()cos(['4

)cos('4

1222

mmx

y

mx

x

QcQcxB

y

QxB

x


Skew quadrupole strengthSkew quadrupole strength

yyam

pam

p/x/x

am

pam

pxx

am

pam

p/y/y

am

pam

p


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


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


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


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


Non-linear driving term measurement in RHICFirst 3rd order resonance driving term measurement in RHIC with ac dipole

Rogelio, WolframRama, Mei, …


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



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


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


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


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.


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


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


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.

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.