Main Injector Beam Dynamics

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Main Injector Beam Dynamics

• Jean-François Ostiguy
• Accelerator Division

2
Credits
This presentation is based upon and borrows
liberally from the work of several people

• James MacLachlan Injection schemes studies and
  transition crossing simulations
• Gerald Jackson Injection energy jitter
  control
• King-Yuen Ng Instability thresholds
  calculations
• Nikolai Mokhov Collimation System

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Uncontrolled Loss Budget

• Working assumption acceptable uncontrolled
  averaged power loss (assuming particle energies
  above threshold for activation) 1 W/m
• FMI 3319.4 m Max allowable loss 3.3 kW
• Total beam power at injection energy W 8
  GeV x 1.5 E14 particles /1 .5 s
• 133 kW
• At transition (?t 21.8) W 320 kW
• At top energy W 2 MW

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2-Stage Collimation Concept
One primary and 2 secondary collimators for each
plane. Assumptions 1 collimated at injection
0.5 at top energy
Total power intercepted 11 kW Require steel
shielding 1m x 2.5 m which covers the secondary
collimators and the 1st quad downstream. Sec
Collimator Stainless Steel,
0.5 m long
Size, cost and high power level favors a
localized collimation system.
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Injection
Two scenarios have been explored

• Adiabatic capture from coasting beam (baseline)
• Synchronous injection into waiting buckets

Initial results indicate that losses can be made
negligible for either scenario. Which scenario
is optimal depends on many factors, such as the
effective energy spread of the injected beam and
the availability of a high frequency beam
chopper.
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Adiabatic Capture

• If the energy spread is too low, stability may be
  impaired
• Injected beam needs to be chopped at revolution
  frequency( 90 kHz) (E-deflection possible)
• barrier RF needed to preserve abort gap during
  injection barrier voltage depends on dp/p
• Capture time 30 ms
• A weak modulation (53 Mhz) of the beam is
  necessary to get detectable BPM signal during
  injection

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Synchronous Transfer

• Require 6 ns gaps every 19 ns. This implies
  availability of a high frequency chopper
• As for adiabatic capture, beam must also be
  chopped at 90 kHz to provide abort kicker gap.
• No barrier cavity required to preserve abort gap
• Momentum painting allows matching into bucket at
  higher voltage for better stability
• 2nd Harmonic cavity (50 of fundamental)
  valuable(though not necessary) to match
  rectangular painted space into elliptical
  contours
• Matching operation also requires 30 ms (not
  needed without 2nd harmonic)

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ESME Simulations Synchronous Injection
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ESME Simulation Abort Gap Preservation
(adiabatic capture)
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Transition Crossing Loss Simulations at Intensity
x 5
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?t Jump system
A ?t jump conceptual design was completed in
1997 (PAC 1997 pp 994-996)

• ? ? /- 1 within 0.5 ms d?/dt 4000/s (about
  17 faster than the normal ramp rate)
• 8 pulsed quadrupole triplets
• localized, independent dispersion perturbation

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Energy Spread and Longitudinal Acceptance

• The longitudinal acceptance sets an upper limit
  on the allowable (effective) energy spread in the
  injected linac pulse.
• The measured longitudinal acceptance of the FMI
  is 0.7 eV-s at current intensity (1 E11 ppb).
• Simulations show that with a gamma-t jump system,
  it should be possible to accelerate at least 0.5
  eV-s without loss through transition
• Assuming adiabatic capture, 0.5 eV-s corresponds
  to an energy height of /- 13.5 MeV (0.7eV-s
  corresponds to /-19 MeV)
• The momentum collimation system will limit the
  spread to /- 10 MeV

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MI Beam Stability at Intensity x 5
Tune shifts vertical tune expected to pass
through 3rd order stop-band. Working point will
need to be optimized.
Single bunch Mw Instability longitudinal
transverse below threshold Coupled bunch
Instabilities transverse above threshold
(currently as well), predicted growth time 110
turns (5x faster). Current digital damper system
can be upgraded to suppress both transverse and
longitudinal instabilities. Beam loading With
new cavities, R/Q 25 ohms ( current is 104
ohms) so situation is roughly similar to current
one.
NM Instability (above transition) At 5 times the
intensity, the situation is roughly the same as
now, if the crossing rate is increased by a
factor of 15.8
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Conclusions

• No fundamental obstacle to operating the MI at 5
  times the current intensity has been uncovered.
  This being said, a lot of work remains to be
  done.
• More detailed simulations will be required to
  maximize effective acceptance (transition losses
  below a few tenths of 1) and determine whether
  an inductive insert is necessary.
• Optimization of the injection scenarios will
  continue while adiabatic capture remains the
  baseline design, full understanding of the
  tradeoff with synchronous capture require
  additional studies
• Full scale space-charge 3D simulations will start
  soon.