Tetra Cooling Ring

1
Tetra Cooling Ring

• Steve Kahn
• For
• V. Balbekov, R. Fernow, S. Kahn, R. Raja,
• Z. Usubov

2
Tetra Ring Parameters
Parameter Value
Circumference 36.954754 m
Kinetic Energy at Bends 0.250 GeV
Dipole Bending Field 1.453 T
Normalized Gradient Index 0.5
Maximum Long Solenoid Field 5.155 T
RF Frequency 205.69 MHz
Accelerating Gradient 15 MeV/m
LH2 Absorber Length 1.2 m
LiH Wedge Absorber 14 cm
3
Tetra Ring Simulations

• Original concept for this ring comes from V.
  Balbekov.
• Originally simulated in Valeris program.
• Documented
• V. Balbekov et al., Muon Ring Cooler for the
  Mucool Experiment, Proc PAC 2001 Conf., p. 3867.
• Updated in MUCnote 249 (2002).
• GEANT simulation of Tetra Ring.
• Worked on by Z. Usubov, R. Raja, and myself.
• ICOOL simulation of the Balbekov Ring.
• MUCnote 258.

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Hardedge Model

• Wedge Dipole
• Combined function
• Index 1/2
• ?52 cm defines reference
• radius
• Step function s dependence.
• No dependence inside
• Zero outside
• Solenoids
• Effect of fringe field is approximated by
  transverse impulse proportional to radial
  position.

5
Coil configuration to represent mirror plate
boundary condition in ICOOL
Long Solenoid Arrangement
Boundary Condition Coils
Actual Hardedge Coils
Boundary Condition Coils
Short Solenoid Arrangement
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Actual Hardedge Coils
Boundary Condition Coils
Boundary Condition Coils
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ICOOL Hardedge Emittances
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Tracking in GEANT

• This figure shows a sample of 500 events tracked
  in GEANT.
• The beam is smallest in the LH2 absorber where
  the field is largest.
• The beam is the largest in the field flip short
  solenoid.
• Muons are most likely to be lost in the vicinity
  of the bend magnets.

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Emittances from GEANT
6D Emittance
Transmission
4D Emittance
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Toward a Realistic Muon Cooling Ring

• The hardedge field description of this cooling
  ring violates Maxwells equations.
• It is likely that smoothing out a step function
  to a tanh or Enge function would solve this, but
  this has to be demonstrated.
• There is no free space in the lattice.
• This space would be necessary for flux returns
  for the solenoids and field clamps for the dipole
  magnet.
• Flux returns and field clamps are necessary to
  separate the function of the different lattice
  elements.
• Difficult engineering issues like how to inject
  (eject) beam into (out of) this ring.
• These kind of issues will be ignored at this
  point.

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Saturation in Dipole Magnet

• Figure shows the permeability for the vertical
  midplane of the magnet.
• ?lt10 on inner edge of the aperture.

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By Off Vertical Symmetry Plane
Index Calculated on Difference Planes
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Dipole Field along Reference Path
Figure 4 Field components for a path displaced
10 cm vertically from the reference path
Figure 3 By along central reference path.
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Field and Geometry of the Long Solenoid
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Field and Geometry of the Short Solenoid

• Figure at left shows Bs for cases
• Mirror plate boundary condition
• Partial mirror plate with 18 cm aperture
• No mirror plate. Full 29 cm aperture

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Comparison of Realistic to Hardedge Field
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Inserting a Gap into the Lattice

• Part of the difficulty with the Tetra ring is
  that there is no extra space in the lattice for
  flux return, field clamps, etc.
• We have studied what is necessary to add a gap
  between the end of the solenoids and the dipole
  magnet

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Inserting a Gap

• The extra focusing coils are placed symmetrically
  at the ends of the solenoids into the lattice to
  compensate and to match into the bending dipoles.
• The requirements on the focusing coils are
• They retain the focusing of the solenoid, ie
  is unchanged.
• The value of Bs at the absorber remain unchanged.
• These requirements uniquely specifies the
  focusing and other solenoid currents.
• The RF frequency must be changed to account for
  the additional length.
• The harmonic number is not changed.
• The wedge angle in the field flip solenoid should
  be adjusted for the focusing coil and other
  solenoid current changes.

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Field Flip Solenoid Field with Extra Focusing Coil
Original Coil Configuration
Adjusted with extra focusing coil

• Difference of 5º phase between these two
  configurations. This is not corrected for.

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Effect of Placing a Gap Between the Dipole Magnet
and the Solenoids

• Curves show transmission, ?tr, ?L vs. extra
  focusing coil current.
• Cases shown are for 5cm, 10 cm, and 15 cm gaps.
• PL is held constant and no decays in this
  comparison.

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Effect of Placing a Gap Using the Whole Momentum
Range

• Gaussian distribution for PL with ?P18 MeV/c.
• Plots show T, ?tr, ?L vs. focusing coil current.
• Transmission drops with increasing gap

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A More Realistic Description of the Solenoids in
ICOOL

• As a step toward a more Maxwellian description to
  the solenoid fields was tried
• Mirror plate boundary conditions are removed in
  solenoid regions.
• Fringe fields from solenoid sheets are
  superimposed on the dipole region.
• The solenoid fringe field along the reference
  path is the axial field. This, of course, is not
  correct.
• The solenoid end kicks used to describe the
  fringe fields are removed.
• The wedge bend magnet is still the hardedge
  model.
• The following transparency shows the emittance
  calculated in ICOOL for this scenario.

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ICOOL Emittances with Real Solenoids