SPACECHARGE EXPERIMENTS

1
SPACE-CHARGE EXPERIMENTS AT THE CERN PROTON
SYNCHROTRON
M. Giovannozzi, M. Martini, R. Steerenberg
(CERN), G. Franchetti, I. Hofmann (GSI), J.
Qiang, R.D. Ryne (LBL)
E. Métral
and

• Introduction
• Several space-charge studies
• Crossing of the integer or half-integer stop band
  ? S. Cousineau
• Space-charge and octupole driven resonance
  trapping ? G. Franchetti
• Intensity-dependent emittance transfer between
  the transverse planes
• Montague-Baconnier first (single-particle)
  approach
• 2D theory for emittance transfer based on the KV
  envelope equations
• Measurements made in the CERN PS vs. 2D theory
  and simulations
• Conclusion

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INTRODUCTION
CNGS beam (CERN Neutrino beam to Gran Sasso) ?
Ultimate goal 4.8 1013 p/p
Acceleration
Transition
Detailed study of all the bottlenecks
1010
61012 p/b
Time ms
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MONTAGUE-BACONNIER FIRST APPROACH (1/2)

• Montague showed in 1968 that the space-charge
  potential could excite a 4th order coupling
  resonance
• ? Beating in amplitude between x and y for the
  single-particle motion, resulting in an apparent
  increase in emittance in the plane of smaller
  emittance ? Growth in few ( 1-5) turns for
  synchrotron at the space-charge limit
• Montague said that this effect should be taken
  into account in the choice of parameters for
  future high-intensity synchrotrons
• Baconnier knew in 1987 that The Montague stop
  band was certainly one of the most effective in
  losing particles at injection in the CERN PS

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MONTAGUE-BACONNIER FIRST APPROACH (2/2)

• Baconnier applied Montagues theory
• Using Keils computation for the incoherent
  space-charge tune shift (instead of deducing it
  from the potential limited to 4th order)
• Giving a procedure, which works only if the
  stop-band is attacked from above (i.e. Qy gt Qx)
  when the beam is larger in the X than Y plane

Maximum amplitudes reached

• Example

Initial boundary at 2s of the beam
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2D THEORY FROM THE KV ENVELOPE EQUATIONS (1/4)
cf. CERN-AB-2003-001 (ABP)
KAPCHINSKIJ AND VLADIMIRSKIJ (KV) ENVELOPE
EQUATIONS
These KV envelope equations have been solved for
small perturbations on top of equilibrium beam
sizes
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2D THEORY FROM THE KV ENVELOPE EQUATIONS (2/4)
? Transverse emittances in the presence of space
charge when the coupling resonance is crossed
Equilibrium (in the presence of space charge but
far from the resonance) beam sizes
Incoherent small-amplitude space-charge tune
shift
Symmetrical stop-band and complete exchange
predicted
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2D THEORY FROM THE KV ENVELOPE EQUATIONS (3/4)
Average over 1 period of the oscillating
term
Time scale
G 10
G 5
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2D THEORY FROM THE KV ENVELOPE EQUATIONS (4/4)
? These formulae have the same form as the ones
already derived for emittance exchange by linear
betatron coupling. Example of a resonance
crossing in 100 ms with skew quads
Physical emittances at 2s µm
HTheoExp
VTheoExp
Time ms
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MEASUREMENTS MADE IN THE CERN PS (1/7)
STATIC CASE in 2002 (constant tunes from
injection to the measurement point)
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MEASUREMENTS MADE IN THE CERN PS (2/7)
STATIC CASE in 2003(constant tunes from
injection to the measurement point)
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MEASUREMENTS MADE IN THE CERN PS (3/7)
DYNAMIC CASE in 2003 (the horizontal tune was
changed linearly from 6.15 to 6.25 in 100 ms)
? 44 000 turns
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MEASUREMENTS MADE IN THE CERN PS (4/7)
STATIC CASE in 2003 with RF OFF(constant tunes
from injection to the measurement point)
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MEASUREMENTS MADE IN THE CERN PS (5/7)
DYNAMIC CASE in 2003 with RF OFF (the
horizontal tune was changed linearly from 6.15 to
6.25 in 100 ms)
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MEASUREMENTS MADE IN THE CERN PS (6/7)
DYNAMIC CASE in 2004 (the horizontal tune was
changed linearly from 6.15 to 6.25 in 100 ms)
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MEASUREMENTS MADE IN THE CERN PS (7/7)
DYNAMIC CASE in 2004 (the horizontal tune was
changed linearly from 6.25 to 6.15 in 100 ms)
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MEASUREMENTS vs. SIMULATIONS
STATIC CASE in 2003 (constant tunes from
injection to the measurement point)
Asymmetrical stop-band predicted by
simulations
Fully 3D PIC code IMPACT
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NEW RESULTS FROM SIMULATIONS (1/2)
? See paper Dynamical Effects in Crossing of the
Montague Resonance, by I. Hofmann et al.,
EPAC2004
Simulations were made until now in the static case
This is what was predicted analytically by the
2D analytical model
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NEW RESULTS FROM SIMULATIONS (2/2)
? The crossing speed has to be slow compared to
the time scale during which the coupling occurs?
Full exchange, as predicted by the 2D analytical
model
? The crossing speed has to be fast compared to
the synchrotron motion ? Not taken into account
in the present analytical model
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2D THEORY vs. SIMULATIONS
DYNAMIC CASE in 2003 (the horizontal tune was
changed linearly from 6.15 to 6.25 in 100 ms)
Scaled simulation (4800 turns)
Without synchrotron motion ? 2D
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MEASUREMENTS vs. 2D THEORY AND 3D SIMULATIONS
DYNAMIC CASE in 2003 (the horizontal tune was
changed linearly from 6.15 to 6.25 in 100 ms)
Scaled simulation (4800 turns)
Mixing due to longitudinal motion
? IBS is suspected (by I. Hofmann) to play a role
(additional mixing) after the resonance crossing
and will be investigated in detail
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CONCLUSION (1/2)

• An analytical formula is available to explain the
  intensity dependent emittance exchange when the
  coupling resonance is crossed much faster than
  the synchrotron period (? 2D model)

? Very good agreement with simulations in 2D !
Without synchrotron motion
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CONCLUSION (2/2)

• When the crossing speed is not much faster than
  the synchrotron period (usual case in practice),
  a mixing effect due to the longitudinal motion is
  predicted by simulations (after crossing)
• ? Longitudinal motion not yet included in the
  analytical model, but the formulae give at least
  the evolution of the emittances until the
  resonance crossing
• An additional mixing effect due to IBS is
  anticipated
• Next year the CERN PS machine will be in shutdown
  ? No possibility to make new measurements before
  at least 2006
• However, the CERN PSBooster will be in operation
  and had changed its working point since the
  beginning of 2004 (same tune integer in both
  planes!)

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ACKNOWLEDGEMENTS
Many thanks to G. Franchetti and I. Hofmann for
this very interesting collaboration started in
2002 !