1 / 16

Status of Low-  FOFO Snake for Final Stage of 6D Ionization Cooling

Status of Low-  FOFO Snake for Final Stage of 6D Ionization Cooling. Y. Alexahin (FNAL APC). Neutrino Factory & Muon Collider Collaboration Meeting, Oxford MS January 13-16, 2010. Goals. 2. +. –. +. –. “cell”.

kipp
Download Presentation

Status of Low-  FOFO Snake for Final Stage of 6D Ionization Cooling

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Status of Low- FOFO Snake for Final Stage of 6D Ionization Cooling Y. Alexahin (FNAL APC) Neutrino Factory & Muon Collider Collaboration Meeting, Oxford MS January 13-16, 2010

  2. Goals 2 + – + – “cell” FOFO “snake” to achieve T < 0.5mm, L < 1mm requires:  Small -function at absorbers (at the solenoid center if the phase advance >180/cell  Transverse B-field to generate dispersion, can be created by tilting / displacing the solenoids or by additional dipole coils Nomenclature:  HFOFO = Helical FOFO channel of alternating solenoids (ASOL)  FOFO-xyz = FOFO with xyz resonance phase advance per focusing cell consisting of one solenoid + all other stuff (RF cavities etc.) Low- HFOFO Status - Y. Alexahin NFMCC Meeting Oxford, MS, January 14 2010

  3. FOFO snake for final 6D cooling - original idea 3 + – Bz (T) 10*By (from Dec.2008 MCDW @ Jlab) Q1, Q2 p/100 z orbit lengthening x,y [cm] p/100 - no 2nd order chromaticity, - momentum compaction too small and of the wrong sign! z Low- HFOFO Status - Y. Alexahin NFMCC Meeting Oxford, MS, January 14 2010

  4. Helical snake for final 6D cooling - the puzzle 4 By increasing B-field strength it is possible to get phase advance >180/cell and small -function at the solenoid center  much smaller emittance. Tune / period > odd_integer for resonant orbit excitation Puzzle: 2-cell period (planar snake), Q>1 6-cell period, Q>3 4-cell period, Q>3 6-cell period, Q>5 p < 0 significant over-focusing required p > 0 Naiive 1-dimensional considerations do not work for coupled motion: besides 180 phase advance of the normal mode there is also 180 rotation of the normal mode  the transverse field phase should change by either 360 or 0 / cell ! Low- HFOFO Status - Y. Alexahin NFMCC Meeting Oxford, MS, January 14 2010

  5. Return to FOFO-180° 5 (from Dec.2009 MCDW @ BNL) Since there is no clear gain in going to 270° (just problems), more effort was applied to find solution for 180°. A superposed dipole field generated by additional coils can do the job. Such a field can not be obtained by displacing solenoids: Bz / BLS y x By / BLS Dy Dx Actually constant By works just as well! Low- HFOFO Status - Y. Alexahin NFMCC Meeting Oxford, MS, January 14 2010

  6. FOFO-180° Momentum Acceptance 6 Q1 - 1 Q2 - 1 p/p0 p/p0 – 1 _min [cm] This design is not finished yet Search for a helical configuration is underway Emittances well below 0.5mm can be expected Attempts to equalize cooling rates of the transverse modes were unsuccessful so far p/p0 Low- HFOFO Status - Y. Alexahin NFMCC Meeting Oxford, MS, January 14 2010

  7. Next Stop - HFOFO-240° 7 4/3 per cell  4  2 per 6-cell period: the resonance By harmonic is 4, but actually the 1rd harmonic is the most efficient! No big problem with the transverse mode cooling rate equalization: With solenoid pitch 1.4 mrad, constant quadrupole field of gradient 0.75T/m, 6mm LiH absorbers mode I II III tune 0.286+0.0024i 4.384+0.0049i 4.388+0.0048i _eq (mm) 0.74 0.38 0.40 But the momentum acceptance is too small: Q3 Q2 p/p0 Another difficulty: too high synchrotron tune with 6-cell period: Q1 ~ 0.3 Low- HFOFO Status - Y. Alexahin NFMCC Meeting Oxford, MS, January 14 2010

  8. HFOFO-270° 8 Bz / Bz0 2.6 ! 1 2 4 3 r / Rin 3/2 per cell  3  2 per 4-cell period: the fundamental By harmonic is 1, the 3rd harmonic is working Original HFOFO-270° channel parameters (4-cell period): 800 MHz pillbox RF 2  8cm, Emax=32MV/m Solenoids: L=8cm, Rin=16cm, Rout=26cm, Inclination: 3mrad v+ h+ v- h- Absorbers: LiH, width (on-axis) 1.5cm, no wedge angle Total length of 4-cell period 1.12m Problems: Bzmax=18.5 T (on-axis) for p0=100MeV/c Limited dynamic momentum acceptance Large ratio Bz_coil/Bz_axis=2.6 ! B (V.Balbekov’s formulas used) Low- HFOFO Status - Y. Alexahin NFMCC Meeting Oxford, MS, January 14 2010

  9. Choice of the Solenoid Geometry 9 Bz_coil/ Bz0 (left) and B3/Bz0 (right) vs coil inner radius Rin (cm). - Field on coil drops with smaller Rin, but nonlinearity grows. Bz_coil/ Bz0 (left) and B3/Bz0 (right) vs coil half-length L/2 (cm). - Both field on coil and nonlinearity decrease with L, but this leaves no room for RF! Low- HFOFO Status - Y. Alexahin NFMCC Meeting Oxford, MS, January 14 2010

  10. Revised HFOFO-270° 10 600 MHz pillbox RF 2  8cm, Emax=17MV/m (on-axis) Solenoids: L=16cm, Rin=14.5cm, Rout=38cm (Bz_coil/Bz_axis=1.5) Inclination: 2.24mrad: v+, h+, v-, h- Absorbers: 2cm LH2 with 1mm LiH windows, no wedge angle Total length of 4-cell period 4  38cm = 1.52m Bz_axis=12.6T (Bz_coil=19T) for p0=90MeV/c With constant quadrupole field of gradient 1.5T/m mode I II III tune 0.191+0.0015i 3.254+0.0035i 3.288+0.0036i _eq (mm) 0.62 0.29 0.30 B (T)  (cm) y Bz 100Bx z (cm) x 100By z (cm) Low- HFOFO Status - Y. Alexahin NFMCC Meeting Oxford, MS, January 14 2010

  11. Revised HFOFO-270° Momentum Acceptance 11  Static momentum acceptance is fine: (-9%,+27%), but the dynamic acceptance is only 25% (full width) – enough to accommodate the equilibrium momentum spread, but not the incoming beam  To increase dynamic acceptance one can: - reduce solenoid pitch angle (to reduce p) - reduce p0 (to increase 1/2) Both these methods are bad for longitudinal cooling –  Careful optimization is necessary Q3 Q2 p/p0 p0 = 80 p0 = 90 p/p0 - 1 Low- HFOFO Status - Y. Alexahin NFMCC Meeting Oxford, MS, January 14 2010

  12. HFOFO-270° G4BL Simulations 12 x (cm) Precision check: periodic orbit red – MICCD, blue – G4BL z (cm) pz (MeV/c) y (cm) z (cm) z (cm) Low- HFOFO Status - Y. Alexahin NFMCC Meeting Oxford, MS, January 14 2010

  13. HFOFO-270° G4BL Simulations 13 Phase portrait of initially Gaussian beam: blue – after 1st pass, red – after 16th pass (22.8m) px, py are mechanical momenta, p0=90MeV/c stochastics on, decays off px/p0 py/p0 (p - p0)/p0 x (cm) y (cm) t (ns) Low- HFOFO Status - Y. Alexahin NFMCC Meeting Oxford, MS, January 14 2010

  14. HFOFO-270° G4BL Simulations 14 Fitted normalized emittances (final values 0.51mm, 0.36mm, 0.35mm), number of muons (N16/N1=908/5222=17.4%) and Palmer’s 6D cooling efficiency 1N Q6 2,3N pass # N pass # Total 6D cooling efficiency is just Q6=2: 50% cooling 50% shaving pass # Low- HFOFO Status - Y. Alexahin NFMCC Meeting Oxford, MS, January 14 2010

  15. Summary & Outlook 15  FOFO-180 promises large momentum acceptance, DA and small emittances. However, no way to equalize the transverse mode cooling rates has been found yet. Still, there are some possibilities to explore.  HFOFO-270 can provide emittances T ~ 0.35mm, L ~0.5mm with LH2 absorbers, but the transmission is poor. It can be (probably) improved with nonlinear shape of the absorbers reducing ionization losses for low-momentum muons.  If both efforts fail, retreat below 180: the allowed maximum field of 19T (on the coil) will be achieved with smaller cell length  the increase in min and emittances will be moderate Low- HFOFO Status - Y. Alexahin NFMCC Meeting Oxford, MS, January 14 2010

  16. Plans (from MCDW09) 16  Search for the final stage HFOFO configuration (by IPAC10)  Front end with HFOFO (by April 2010 IDS meeting)  Determination of the number of stages and configuration for each stage (by the next MCDW)  Optimization of each stage parameters (2010-2012)  End-to-end simulation with matching between the stages (by 2012) Low- HFOFO Status - Y. Alexahin NFMCC Meeting Oxford, MS, January 14 2010

More Related