Simulation study of a helical cooling channel

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Simulation study of a helical cooling channel

• K. Yonehara

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Contents

• Historical background
• Current issues

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Historical background

• 2000 HCC with a wedge absorber
• Y. Derbenev proposed first HCC design
  (MuNote0134).
• V. Balbekov made first simulation effort
  (MuNote0146).
• G. Penn made simulation studies in ICOOL
  http//www.fnal.gov/projects/muon_collider/eexchan
  ge/workshop/penn.pdf
• 2001
• Simulation of a HCC Using GEANT4 V.D.Elvira,
  P.Lebrun, P.Spentzouris (MuNote0193)
• 2003 HCC with a continuous absorber
• HP RF cavity has been proposed and approved
  SBIR/STTR phase II grant.
• Y. Derbenev and R. Johnson proposed a new HCC
  design by using HP GH2 continuous absorber
  (MuNote0284, PRSTAB 8, 041002 (2005)).
• 2004 Present Further Progress
• We have made simulation studies in ICOOL and G4BL
  (NuFact04, PAC05, COOL05, EPAC06).
• HCC design has received SBIR phase II grant.
• Guggenheim channel has been simulated numerically
  in 2005.

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HCC with wedge absorber
Gregg Penn, 2001
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HCC with continuous absorber
Y. Derbenev and R. Johnson, 2003
HP GH2 filled high grad cavity Dispersive
devise for emittance exchange
HP GH2 filled 800 MHz rf cavity
Helical cooling channel with continuous absorber

• Continuous Gaseous H2 works
• Suppression of rf breakdown
• Ionization cooling material

Dispersive beam element for emittance exchange
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Historical background (contd)

• Summer, 2004 _at_ NuFact04
• First result for HCC with continuous absorber
• no stochastic process
• very simple field map (based on linear motion)
• December, 2004 _at_ Muon Collider Workshop
• Include stochastic process
• Bessel type rf field
• Stopped using ICOOL since it cannot put a
  displacement for RF cavities.
• R. Palmer pointed out that the HCC helical dipole
  component requires a very large field at the
  conductors at large R to enclose 200 MHz RF
  cavities.
• February, 2005
• We designed a new HCC (MANX) which does not have
  any rf.
• HCC cooling performance has been improved by
  taking into account the non-linear effect which
  is caused by the ionization energy loss process.
• October, 2005 _at_ fermilab
• We started discussing with TD people about MANX.
• MANX field has been optimized.
• Spring, 2006 _at_ fermilab
• Vladimir Kashikhin et al. have designed a real
  field map for MANX.

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Particle motion in HCC
Red Reference orbit
Magnet Center
Blue Beam envelope
Repulsive force
Attractive force
Both terms should be opposite sign.
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Chromatic aberration correction

• Add sextupole component

• It makes bigger acceptance.

Transverse e (m rad)
Initial e6D (redcorrection) 9,400 mm3 Initial
e6D (greenno correction) 7,500 mm3 at ltpgt
150 MeV/c
gt 10 improvement in 6D cooling factor
Longitudinal e (m)
But b is not needed at the beginning of the HCC
where Palmer assumed large R and large field at
the conductor
6-Dimensional e (m3)
z (m)
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Acceptance study of HCC
Effect of higher order field component (w/o
absorber, w/o rf field)
DQS
DQS
DQ
DQ
D
D
Dr mm
p GeV/c

• No big difference between DQS and DQ.
• There is a stable region even D only channel.

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Field strength study
l 0.8 m
Guggenheim (Path length 660 m)
Eye guide
l 1.0 m
l 1.5 m
l 2.0 m

• p 0.25 GeV/c
• GH2 pressure 400 atm
• k 1.0

• Cooling factor Initial e6d/Final e6d
• b is the total b field on the reference orbit.
• Total path length 212 m

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R. Palmer, 2006 (I put an underline for my
comment.)
Dec. 04
20 33 660 m
100 1.41 141 m

• This is not the best shot in HCC simulation
  study.
• l1.0 m, k1 Merit factor is gt 6,000.
• Use of ICOOL limits the number of particles to
• Investigate channel acceptance.

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Current issues

• High field at conductor
• Realistic RF field

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High Field

• Analytical solution of Maxwell equation
• Bessel type field
• Quite useful for study of the HCC.
• Numerical solution of Maxwell equation
• Localized field distribution by using tilted coil
• Practical design

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Definition of analytical field map
T. Tominaka et al., NIM A459398
Above formula well reproduces a field
distribution of spin flipping helical dipole
magnet.
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Typical Btotal field distribution in HCC
Analytical field calculation
Reference orbit
Beam position
Btotal (T)
Beam pipe
Contour plot of Btotal in LHe HCC (red gt 5 T,
green 3.5 T, blue 0)
y (mm)
Cross Section of Btotal on y axis
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Using tilted coil

• It can make a localized field map.
• b (dipole component) and bz are produced.
• V. Kashikhin has parameters of tilted coil.
• r0.25 m, length0.05 m, 18 coils/m in his
  simulation

b
bz
(Scale is not correct.)
Tilted coil
Particle track
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Analytical field calculation vs Field map by
using tilted coil
Analytical field calculation
Field map by using tilted coil
Same numbers of grid in x-y plane
Maximum b lt5 T
Maximum b 6.2 T
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Quadrupole component in tilted coil
Field gradient in tilted coil is
ex). Required b -0.7 T/m _at_ bz 3.5 T b1.0
T Numerical result in tilted coil b-0.8
T/m. Need small correction field.
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New design of HCC
RF cavity
Tilted coil
Correction coil layer
Conceptual design of HCC (Scale is not correct.)
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Realistic RF field in simulation

• Does longitudinal rf field work in Helical
  Cooling Channel?

E
r (Transverse)
z (longitudinal)

• Is there any difference between uniform Ez and
  Bessel type Ez?

RF cavity
RF cavity
Uniform r distribution
Bessel type r distribution
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Gaseous p 400 atm Bessel type rf
Gaseous p 400 atm Uniform rf
Lab frame
Time of Flight in HCC
Helix frame
6D emittance evolution
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HCC field solutions under investigation

• Magnets alternating with RF
• locate rf cavities between tilted coils
  (Kashikhin)
• Alternate longer HCC segments (MANX) with RF
  segments
• lower average momentum may improve effective
  focusing
• Continuous RF inside magnet coils
• Most efficient since maximum RF, dE/dx, but
  requires HPRF
• Precooling allows smaller, higher frequency RF
  cavities, smaller R coils at the beginning of the
  HCC
• As cooling shrinks the beam, fRF increases, coil
  R shrinks and B increases

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Emittance in series of HCC

• 6D cooling factor in the series of HCC is
  50,000.
• Muon collider is required the cooling factor 106.
• Recent muon scattering experiment in low Z
  material (MUSCAT, hep-ex0512005) shows the
  conventional multiple scattering angle is
  overestimated.
• This is predicted by U. Fano (PR93,117,1954) and
  A. Tollestrup (MuNote0176).
• The new scattering model will improve the cooling
  factor 34.
• It is not included in g4bl yet but ICOOL by R.
  Fernow (MuNote0336).

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Other R D Fronts

• Matching
• (backup slides, if time)
• Frontend
• More muons, reduce beam size before HCC
• new grant with Dave Neuffer
• Design demo experiment (6DMANX)
• Magnets, spectrometers, PID,
• Extra cooling (for LEMC)
• Parametric Ionization Cooling
• Reverse Emittance Exchange
• 50 T solenoid
• Find new cooling schemes (more innovations)

Your contributions are welcome!!!
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Backup slide

• Matching
• MANX

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Matching

• V. Balbekovs ideas
• Adiabatic method
• Flip solenoid field direction
• From recent study
• Perturbative method
• Use helical channel at front end

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Adiabatic matching
b b0/2 (tanh ((z-8.0)/3.5 1))
Matching

• Adiabatically turn on bd
• It needs 15 meters

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Perturbative matching
Red particle orbit
Green Inner of magnet
Upstream
Matching LHe HCC

• The matching section starts from z1 and
• it is ended at z4 m.
• 4 m LHeHCC is following.
• Only 3 meters are needed for matching

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Flipped field matching

• V. Balbekov suggested this idea.
• This method can be very effective for downstream
  of HCC.
• No simulation study yet.

Cancel out angular momentum (pj) by flipped bz.
Bz
Bz
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HCC at frontend

• No matching problem at all

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Emittance evolutions in 6DMANXby using a flat
beam

• Tran/longi cooling factors are 1.5,
  respectively.
• 6D cooling factor is 3.8.
• Average transmission efficiency is 50 by
• using a flat beam.

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t vs Ptotal Z0 m
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t vs Ptotal Z1 m
Dptotal 0.937 /m
Dt 1.001 /m
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t vs Ptotal Z2 m
Dptotal 0.829 /2m
Dt 1.002 /2m
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t vs Ptotal Z3 m
Dptotal 0.762 /3m
Dt 1.003 /3m
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t vs Ptotal Z4 m
Dptotal 0.735 /4m
Dt 1.005 /4m