AC Dipole Based Diagnostics

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AC Dipole Based Diagnostics

• Mei Bai, C-A Department

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Outline

• Introduction of ac dipole
• AC dipole based beam diagnostics
• beam dynamics
• spin manipulation
• RHIC AC dipole system
• Summary

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Abstract
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Introduction of ac dipole

• 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

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Introduction of ac dipole

• Beam emittance gets preserved before and after
  the excitation as long as the ac dipole
  excitation is turned on adiabatically

• 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.

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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
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Ac dipole driven coherent oscillation with
non-zero detuning
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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

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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

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Beam diagnostic applications using AC dipole

• Linear optics measurement

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Beta function and phase advance measurement in
RHIC
Measured phase advance between bpms
Measured beta functions between bpms
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Measure beta function at interaction point
(?R , ?R , ?R)
(?L , ?L , ?L)
S
Dx(R)
Dx(L)
Length
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First test at the end of IP2 Beta Squeeze
experiment
Fulvia, Todd Nikolay, Steve Mei
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First test at the end of IP2 Beta Squeeze
experiment
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Beam diagnostic applications using AC dipole

• Linear coupling measurement

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Beam diagnostic applications using AC dipole

• Local coupling measurement

One turn transfer matrix T
Coupling matrix C changes along the ring and it
can be shown that the determinant of C jumps at
a coupling source.
Courtesy of Rama
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Beam diagnostic applications using AC dipole

• Local coupling measurement

Courtesy of Rama
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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

Courtesy of Rama
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Beam diagnostic applications using AC dipole

• Measure non-linear resonance driving term

• Normal form with free oscillation

R. Bartolini and F. Schmidt, LHC Project Note
132, 1998
?
resonance _at_ (j-k, l-m)
Spectral line _at_ (1-jk, m-l)

• Normal form with driven coherent oscillation

Normal form of particle motion under the
influence of an ac dipole, R. Tomas, Phys.
Review ST-AB, Vol. 5, 054001
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Non-linear driving term measurement in RHIC

• First 3rd order resonance driving term
  measurement in RHIC with ac dipole

Rogelio, Wolfram Rama, Mei,
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Beam diagnostic applications using AC dipole

• 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

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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

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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

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RHIC AC dipole system

• 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

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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.
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RHIC AC dipole circuit
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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

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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.