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Simulation study of a helical cooling channel

Simulation study of a helical cooling channel. It has been presented at Muon Collider Task Force Meeting. K. Yonehara. Contents. Historical background Current issues. Historical background. 2000 : HCC with a wedge absorber Y. Derbenev proposed first HCC design (MuNote0134).

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Simulation study of a helical cooling channel

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  1. Simulation study of a helical cooling channel It has been presented at Muon Collider Task Force Meeting. K. Yonehara MuCool Meeting

  2. Contents • Historical background • Current issues MuCool Meeting

  3. 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/eexchange/workshop/penn.pdf See slide pg.4. • 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)). See slide pg.5. • 2004 ~Present : Further Progress • We have made simulation studies in ICOOL and G4BL (NuFact04, PAC05, COOL05, EPAC06). • HCC design has just received an SBIR phase II grant. • Guggenheim channel was simulated numerically in 2005. MuCool Meeting

  4. HCC with wedge absorber Gregg Penn, 2001 MuCool Meeting

  5. HCC with continuous absorber Y. Derbenev and R. Johnson, 2003 HP GH2 filled high grad cavity + Dispersive device 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 MuCool Meeting

  6. First shot of HCC Front view White: reference particle Blue: off-momentum particle Red: RF cavity Square: 10 cm × 10 cm Magnet conductor is not shown. Side view MuCool Meeting

  7. Historical background (cont’d) • Summer, 2004 @ NuFact04: • First result for HCC with continuous absorber • No stochastic process • Very simple field map (based on linear motion) • obtained cooling factor <1000. • December, 2004 @ Muon Collider Workshop: • Include stochastic process • Bessel type rf field (See slide pg.23) • 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 @ fermilab: • We started discussing with TD people about MANX. • MANX field has been optimized. • Spring, 2006 @ fermilab: • V. Kashikhin et al. have designed a real field map for MANX. MuCool Meeting

  8. Particle motion in HCC Red: Reference orbit Magnet Center Blue: Beam envelope Repulsive force Attractive force Both terms have opposite signs. MuCool Meeting

  9. Chromatic aberration correction • Add sextupole component • It makes bigger acceptance. Transverse e (m rad) Initial e6D (red:correction) = 9,400 mm3 Initial e6D (green:no correction) = 7,500 mm3 at <p> = 150 MeV/c Longitudinal e (m) > 10 % improvement in 6D cooling factor 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) MuCool Meeting z (m)

  10. Is HCC really needed sextupole? R. Palmer, 2006 (I put an underline for my comment.) I do not know how he obtain those numbers. MuCool Meeting

  11. Acceptance study of HCC Effect of higher order field component (w/o absorber, w/o rf field) D+Q+S D+Q+S D+Q D+Q D D Dr [mm] p [GeV/c] • No big difference between D+Q+S and D+Q. • There is a stable region even with only dipoles. MuCool Meeting

  12. 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 MuCool Meeting

  13. R. Palmer, 2006 (I put an underline for my comment.) Dec. 04 100 × 1.41 = 141 m 20 × 33 = 660 m • Other cases in HCC simulation study perform much better. • l=1.0 m, k=1: Merit factor is > 6,000. • Use of ICOOL limits the number of particles to • Investigate channelacceptance. MuCool Meeting

  14. Current issues • High field at conductor • Realistic RF field MuCool Meeting

  15. 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 MuCool Meeting

  16. Definition of analytical field map T. Tominaka et al., NIM A459:398 Above formula well reproduces a field distribution of spin flipping helical dipole magnet. MuCool Meeting

  17. Typical Btotal field distribution in HCC Analytical field calculation Beam position Reference orbit Btotal (T) Beam pipe Contour plot of Btotal in LHe HCC (red: > 5 T, green 3.5 T, blue = 0) MuCool Meeting y (mm) Cross Section of Btotal on y axis

  18. New idea: Helical solenoid • It can make a localized field map. • b (dipole component) and bz are produced. • V. Kashikhin invented this design. • r=0.25 m, length=0.05 m, 18 coils/m in his simulation MuCool Meeting

  19. Bessel type magnetvs Helical solenoid coil V. Kashikhin et al. MCTFM 7/31/06 • Snake type MANX • Consists of 4 layers of helix dipole • Maximum field is ~7 T (coil diameter: 1.0 m) • Field decays very smoothly • Hard to adjust the field configuration • New MANX • Consists of 73 single coils (no tilt). • Maximum field is ~5 T (coil diameter: 0.5 m) • Field decays roughly • Flexible field configuration MuCool Meeting

  20. Quadrupole component in tilted coil Period 1.6 m, G=-0.83 T/m, dG/dz=-0.11 (T/m)/m Helix Solenoid Gradient Period 1.4 m, G=-1.0 T/m K. Yonehara, AD Meeting July 27, 2006 Kappa = 0.8, Helix period = 2 m, G = -0.8 T/m Kappa = 1.0, Helix period = 1.6 m, G=-0.83 T/m Kappa = 1.15, Helix period = 1.4 m, G=-1.0 T/m Specified dG/dz = -0.1 T/m MuCool Meeting

  21. New conceptual design of HCC 200 MHz RF cavity Helical solenoid coil Correction coil layer Conceptual design of HCC (Scale is not correct.) MuCool Meeting

  22. 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 MuCool Meeting

  23. 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 MuCool Meeting

  24. 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 MuCool Meeting

  25. 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-ex:0512005) 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 3~4. • It is not included in g4bl yet but in ICOOL by R. Fernow (MuNote0336). MuCool Meeting

  26. Other R & D Fronts • Matching • Almost done • 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!!! MuCool Meeting

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