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Muon Beam Polarimeter for the NF Decay Rings

This presentation discusses the design and simulation of a muon beam polarimeter for the NF Decay Rings. Topics covered include the lattice of the DK racetrack ring, G4beamline 3D model, spin precession method, resolution in ideal case, detector issues, and conclusions.

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Muon Beam Polarimeter for the NF Decay Rings

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  1. Muon Beam Polarimeter for the NF Decay Rings m. apollonio – Imperial College (London) a. blondel – Universite de Geneve d. kelliher – ASTeC (RAL) 2nd EUROnu meeting - Strasbourg

  2. the lattice of the DK racetrack ring • G4beamline 3D model • the method of spin precession • resolution in ideal case • detector issues (location, …) • conclusions 2nd EUROnu meeting - Strasbourg

  3. lattice g4beamline model spin precession ideal case detector issues conclusions Track DK Ring lattice [C. Prior, IDS baseline] Pm= 25 GeV/c eN = 4.8 mm rad e = 0.02 mm rad aN = 30 mm rad (accept) a= 0.127 mm rad Twiss Parameters (MADX) straights: sx = 51 mm sx’ = 0.4 mrad arcs: sx = 16 mm sx’ = 0.13 mrad 1/g = 4 mrad sx’ * g ~ 0.1 2nd EUROnu meeting - Strasbourg

  4. lattice g4beamline model spin precession ideal case detector issues conclusions 2nd EUROnu meeting - Strasbourg

  5. latticeg4beamline model spin precession ideal case detector issues conclusions straight section matching section arc section G4beamline MODEL main open issues on diagnostics - measurement of divergence - measurement beam current - measurement of energy/polarization via spin precession location for the device? 2nd EUROnu meeting - Strasbourg

  6. lattice g4beamline model spin precession ideal case detector issues conclusions • - Spin precesses in a ring due to coupling with magnetic fields • (bending magnets). • At every turn spin precession is determined by the SPIN TUNE: • w = 2 p g a • a = 1.16E-3 • Every muon spin evolves independently: • if ∆E/E = 0, P oscillates between two extremes (± |Pmax|) • if ΔE/E ≠ 0, P decoheres (polarization damping) • modelled behaviour of a beam (1E6 muons) all with their spin and energy (DE/E =[0.01-0.05]) • Lorentz Boost • - Modulation in P produces a modulation in E(e+) • I assume P= 18% is left when filling the DK ring B turn0 turn1 turn2 Sz(1) Sz(0) Sz(2) 2nd EUROnu meeting - Strasbourg

  7. lattice g4beamline model spin precession ideal case detector issues conclusions • Check polarization vs turn pattern: • model vs Zgoubi 0 d. kelliher – ASTeC (RAL), m.a. (IC) 2nd EUROnu meeting - Strasbourg

  8. lattice g4beamline model spin precession ideal case detector issues conclusions • Ee spectrum in the muon c.o.m. • function of P 1 2 • Total Electron Energy in the Lab Frame • N0: initial n. of decays (@ turn 0) • a: decay constant • Em: beam energy • P: averagepolarization • w: angular spin tune (Em) Pe P = 1 m-c.o.m. cosq cos(Θ) x=2E/mm cos(Θ) Pe LAB cosqLAB ~ 1 Lab-Frame 2nd EUROnu meeting - Strasbourg Ee (MeV)

  9. lattice g4beamline model spin precession ideal case detector issues conclusions • What does it happen when we sample a fraction of the Ee spectrum? • How we parametrize the Beam Energy spread? 3 • AsymmetryA characterizes the maximal change in Ee (between +P and –P) • it should be maximized for a better Em / P determination • A more pronounced for some energy ranges (<5 GeV or >15GeV) • A(11 GeV)~0  no P observable! m-decay energy spread spin tune “polarization” • Ee spectrum • We sample [a,b]: • [0,5] or, • [15,18]… [0,5] GeV [15,18] GeV NO sensitivity 2-4/June/2010 2nd EUROnu meeting - Strasbourg

  10. lattice g4beamline model spin precession ideal case detector issues conclusions • MEASURABLE SIGNAL • collect electrons at different energy bins, [a,b] GeV • try to maximize A (enhanced oscillatory pattern) • - measure the TOTAL energy deposited • (e.g. in a Cherenkov+calorimeter) • Energy resolution modeled as: sE/E=√(1.03…/Ne) • [Raja-Tollestrup] • Signal fitted to Eq. (3) • f(T) = A e-T/t(1+b/7*exp(-(wDE/E)2/2) * P * cos (f+wT)) • w(g): is the SPIN tune from which g can be inferred • b=b(w) • t:muon decay slope [in n. of turns] • P: polarisation of the beam 2nd EUROnu meeting - Strasbourg

  11. lattice g4beamline model spin precession ideal case detector issues conclusions [0,5] GeV/c N0=30% (1E6) fit (80 turns) E = 24999 ± 40 MeV DE/E = 2.6 ± 0.1 % tm = 97.5 ± 0.15 P = (22. ± 0.7)% -18% P0 DE/E=2.5% (hw) [0, 5] GeV [15,18] GeV/c N0=30% (1E6) fit (80 turns) E = 25040 ± 38 MeV DE/E = 2.57 ± 0.15 % tm = 97.6 ± 0.16 P = (10.8 ± 0.7)% [15, 18] GeV derive actual P from MAX-min excursions 2nd EUROnu meeting - Strasbourg

  12. lattice g4beamline model spin precession ideal case detector issues conclusions Statistic Precision of Fit (w.r.t. # of turns) -18% P0 DE/E=2.5% (hw) [0.0,2.5] GeV/c N0=16.0% (1E6) fit (80 turns) E = 24998 ± 37 MeV DE/E = 2.55 ± 0.09 % tm = 97.56 ± 0.14 P = (25.9 ± 0.7)% High A 2nd EUROnu meeting - Strasbourg

  13. lattice g4beamline model spin precession ideal case detector issues conclusions Statistic Precision of Fit (w.r.t. # of turns) -18% P0 DE/E=2.5% (hw) [2.5,5.0] GeV/c N0=15.5% (1E6) fit (80 turns) E = 24999 ± 49 MeV DE/E = 2.57 ± 0.12 % tm = 97.47 ± 0.14 P = (20.8 ± 0.7)% 2nd EUROnu meeting - Strasbourg

  14. lattice g4beamline model spin precession ideal case detector issues conclusions Statistic Precision of Fit (w.r.t. # of turns) -18% P0 DE/E=2.5% (hw) [5.0,7.5] GeV/c N0=14.7% (1E6) fit (80 turns) E = 24876 ± 68 MeV DE/E = 2.66 ± 0.15 % tm = 97.52 ± 0.14 P = (15.5 ± 0.7)% 2nd EUROnu meeting - Strasbourg

  15. lattice g4beamline model spin precession ideal case detector issues conclusions Statistic Precision of Fit (w.r.t. # of turns) -18% P0 DE/E=2.5% (hw) [7.5,10.] GeV/c N0=13.4% (1E6) fit (80 turns) E = 25069 ± 126 MeV DE/E = 2.33 ± 0.35 % tm = 97.65 ± 0.15 P = ( 7.5 ± 0.8)% Low A 2nd EUROnu meeting - Strasbourg

  16. lattice g4beamline model spin precession ideal case detector issues conclusions This is somewhat ideal ... we need to collect the electrons! How do we turn it into a realistic device for our case? suggested [Blondel – ECFA 99-197(1999)] to use the first bending magnet after the decay straight section to SELECT electron energy bins: what does that mean today with a realistic lattice (25 GeV)? In fact electron is emitted ~parallel to m (due to the high g) The spectral power of the 1st magnet depends on its FIELD and LENGTH A G4Beamline simulation used to determine downstream electron distributions 2nd EUROnu meeting - Strasbourg

  17. lattice g4beamline model spin precession ideal case detector issues conclusions use finite size beams of m+ from Zgoubi [C. Prior, D. Kelliher]- Pm = 25 GeV/c DP/P = 1% , DP/P = 2.5% (*)- eN = 30 mm rad m at mid - straight m at end of straight (*) half width 2nd EUROnu meeting - Strasbourg

  18. lattice g4beamline model spin precession ideal case detector issues conclusions low E e+ Device location and Naming Convention m beam Bending Magnet high E e+ transverse monitor longitudinal monitor “good” decay “bad” HE decay 2nd EUROnu meeting - Strasbourg

  19. lattice g4beamline model spin precession ideal case detector issues conclusions elmon6-L elmon5-T elmon4-L elmon3.1-L elmon3-T elmon2-T elmon1-L e from m decays … B3 B2 B= -4.27T/L=2.0m B1 B= -4.27T/L=2.0m M3 B=+0.35T/L=2.3m M2 B=-1.9T/L=0.6m M1 B=-0.64T /L=4.0m m beam force m decay 2nd EUROnu meeting - Strasbourg

  20. lattice g4beamline model spin precession ideal case detector issues conclusions • Choice of location  compromise among several factors • - spectral power of magnet (determines covered energy range) • upstream free decay path (ideally “magnet free”) • some cases here considered: • Naming convention: HE>10 GeV, ME=[5,10] GeV, LE<5GeV • Possible Cases (PRO, CON) • - elmon1-L:1st bending after long straight, small SP selects LE e+ mostly swept • away by previous q-poles • elmon2-T: small SP, cannot separate HE component • elmon3-T:long decay path, decent SP  separate LE,ME • elmon3.1-L: inside the last bend of the matching section, small SP (E<0.7 GeV) • elmon4-L: need to review the study • elmon5-T: need to review the study • elmon6-L:between two arc-bending magnets, very good SP 2nd EUROnu meeting - Strasbourg

  21. lattice g4beamline model spin precession ideal case detector issues conclusions elmon1-L .64T/ 4m 300m 1730 280m 734 260m 324 240m 156 220m 200m 300 m L (m) 180m 160m 140m L (m) 120m 100m 80m P (GeV/c) P (GeV/c) • only e+ at <20m generate a clear pattern which is disturbed by • e+ decayed far away • also the low bending  E<4 GeV • need further investigation 0 m 2nd EUROnu meeting - Strasbourg

  22. lattice g4beamline model spin precession ideal case detector issues conclusions 13 m elmon3-T long drift for higher momenta 1.9T/ 0.6m drift path ~ 13 m 0 mm -2200 mm force m decay 2nd EUROnu meeting - Strasbourg

  23. lattice g4beamline model spin precession ideal case detector issues conclusions <x> <P> RMS-x RMS-P uniformity check for upstream decays RMS-P dispersion 25 20 15 10 5 0 GeV/c [15,18] GeV beam size e=30 mmrad Impact Point (m) 2nd EUROnu meeting - Strasbourg -0.2 0 0.2 0.4 0.6 0.8 1.0 1.2

  24. lattice g4beamline model spin precession ideal case detector issues conclusions An interesting location for a detector: sideway in an ARC-DIPOLE - study the decay of 10K muons along the line from B2 to B3 included (step 200mm) - check the effect on P vs detected position on the B3-monitor +2.m 0m -2.3m -4.3m elmon6-L B3 B2 2nd EUROnu meeting - Strasbourg

  25. lattice g4beamline model spin precession ideal case detector issues conclusions DS-B2 Decays in B2 e+ start falling in the acceptance of the channel only at the exit of the bending magnet Impact Point (m) -2500 mm -2700 mm -2900 mm -3100 mm -3300 mm -3500 mm -3700 mm -3900 mm US-B2 -4100 mm -4300 mm P (GeV/c) 2nd EUROnu meeting - Strasbourg

  26. lattice g4beamline model spin precession ideal case detector issues conclusions L=a+bEc DS-drift 0mm Decays in the gap between B2 and B3 e+ are almost all in the acceptance US-drift -2400mm 2nd EUROnu meeting - Strasbourg

  27. lattice g4beamline model spin precession ideal case detector issues conclusions Decays in B3 DS-B2 1300 mm US-B3 100 mm 2nd EUROnu meeting - Strasbourg

  28. lattice g4beamline model spin precession ideal case detector issues conclusions uniformity check for upstream decays Uniformity Zone: P vs ImpactPoint unchanged in B3 0m -4.3m 67% of tot collected e+ this component can distort the spectrum 2nd EUROnu meeting - Strasbourg

  29. lattice g4beamline model spin precession ideal case detector issues conclusions 88 B 2ns 3ns …some back-of-the-envelope calculations 5x1020n/yr (1yr = 200 days) = 2.9x1013n/s • 50 Hz (proton) rep. rate = 20 ms (fill)  • 0.6 x 1012n per fill • NB: every fill = 3 bunch trains (L=440ns / S=1200ns) • how many e+ (say) in a 10m section before the bending element? • 10/1608 * 0.6 * 1012 = 3.5*109 • 30%[2.5-7.5GeV/c] 109 (15% [2.5-5.0]  0.5x109) • in 2.5m  1.2x108  /100 (# of turns = tm): ≈106 per turn per 2.5GeV-bin achievable Buy eggs milk, tomatoes .. Nx1012 / …= ? E=[2.5,5] then (T) (S) 440ns 1200ns 1640ns Tperiod = 5.36 msec tm=520 msec 2x104msec = 50Hz rep.rate 2nd EUROnu meeting - Strasbourg

  30. lattice g4beamline model spin precession ideal case detector issues conclusions # of decays over the ring It should not be a problem of statistics … … rather an issue of very high intensity 1.2E+6 0.5E+6 electrons detectable in a 2.5 GeV bin From a device with 2.5 m U.S. acceptance turn # 2nd EUROnu meeting - Strasbourg

  31. lattice g4beamline model spin precession ideal case detector issues conclusions challenging? Special magnet? C-dipole? how close can we get? 2nd EUROnu meeting - Strasbourg

  32. lattice g4beamline model spin precession ideal case detector issues conclusions • method of Energy/Polarization Monitoring via spin precession revived for the IDS Race Track Decay Ring • Use of G4Beamline for a more realistic rendering of the events • Zgoubi to realistically describe P • Need to introduce a proper 3-body decay … • detailed study on how distributed decays (upstream of a dipole) change an e+ spectrum • think of a better geometry/technology for a possible detector • evaluate e+ rate in interested areas • Clarify some key issues: • What is the degree of Polarisation? • which realistic signal in a realistic detector? • How to analyze the polarisation pattern? (fit, Fourier …) and which precision obtainable? • Best Location? • Special Magnet and Hi-Rad detector IPAC10 - Kyoto 2nd EUROnu meeting - Strasbourg

  33. lattice g4beamline model spin depolarisation ideal case detector issues conclusions End / Spares 2nd EUROnu meeting - Strasbourg

  34. latticeg4beamline model spin depolarisation ideal case detector issues conclusions First Dipole of the matching section B= -0.64T / L=4.0m First Dipole of the Arc section B= -4.27T / L=2.0m elmon2 elmon1 low P e- elmon5 elmon4 force m decay 2nd EUROnu meeting - Strasbourg

  35. latticeg4beamline model spin depolarisation ideal case detector issues conclusions [7.0,8.0] GeV/c [8.0,9.0] GeV/c [9,10] GeV/c [10,11] GeV/c [11,12] GeV/c [12,13] GeV/c [13,14] GeV/c [14,15] GeV/c 0 0.2 0.4 0.6 0.8 1.0 1.2 0 0.2 0.4 0.6 0.8 1.0 1.2 0 0.2 0.4 0.6 0.8 1.0 1.2 0 0.2 0.4 0.6 0.8 1.0 1.2 2nd EUROnu meeting - Strasbourg

  36. lattice g4beamline model spin precession ideal case detector issues conclusions 88 B 2ns 3ns …some back-of-the-envelope calculations 1021n/yr (1yr = 200 days) = 5.8x1013n/s • 50 Hz (proton) rep. rate = 20 ms (fill)  • 1.16 x 1012n per fill • NB: every fill = 3 bunch trains (L=440ns / S=1200ns) • how many e+ (say) in a 10m section before the bending element? • 10/1608 * 1.16 * 1012 = 7*109 • 30%[2.5-7.5GeV/c] 2*109 (15% [2.5-5.0]  109) • in 1m  108  /100 (# of turns = tm): 106 per turn per 2.5GeV-bin is achievable Take the flight to Chicago Nx1012 / …= ? E=[2.5,5] then (T) (S) 440ns 1200ns 1640ns Tperiod = 5.36 msec tm=520 msec 2x104msec = 50Hz rep.rate 2nd EUROnu meeting - Strasbourg

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