Muon Beam Polarimeter for the NF Decay Rings m. apollonio – Imperial College (London) a. blondel – Universite de Geneve d. kelliher – ASTe. C (RAL) 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg 1
• • • the lattice of the DK racetrack ring G 4 beamline 3 D model the method of spin precession resolution in ideal case detector issues (location, …) conclusions 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg 2
lattice g 4 beamline model spin precession ideal case detector issues conclusions Track DK Ring lattice [C. Prior, IDS baseline] Pm = 25 Ge. V/c e. N = 4. 8 mm rad e = 0. 02 mm rad a. N = 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 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg 3
lattice g 4 beamline model spin precession ideal case detector issues conclusions MAGNET eff. length (mm) width (mm) gap (mm) pole tip radius (mm) field/gradient (T/Tm-1) QF 1500 - - 200 +0. 454 QD 1500 - - 200 -0. 464 1 st Bend 4000 1000 200 - -0. 64 QD 800 - - 200 -9. 2 QF 1600 - - 200 +11. 6 MATCHING QD 1600 - - 200 -7. 66 2 nd bend 600 1000 200 - -1. 9 QF 800 - - 200 +4. 1 3 rd bend 2300 1000 200 - +0. 35 bend 2000 1000 200 - -4. 27 QF 500 - - 200 +24. 18 QD 500 - - 200 -23. 77 STRAIGHT ARC 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg 4
lattice g 4 beamline model G 4 beamline MODEL spin precession ideal case detector issues conclusions straight section matching section main open issues on diagnostics - measurement of divergence - measurement beam current - measurement of energy/polarization via spin precession location for the device? arc section 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg 5
lattice g 4 beamline model spin precession ideal case detector issues conclusions - Spin precesses in a ring due to coupling with magnetic fields (bending magnets). B - At every turn spin precession is determined by the SPIN TUNE: turn 0 turn 1 turn 2 Sz(1) w=2 pga a = 1. 16 E-3 -Every muon spin evolves independently: - if ∆E/E = 0, P oscillates between two extremes (± |Pmax|) - if ΔE/E ≠ 0, P decoheres (polarization damping) Sz(0) Sz(2) - modelled behaviour of a beam (1 E 6 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 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg 6
lattice g 4 beamline model spin precession detector issues conclusions 0 d. kelliher – ASTe. C (RAL), m. a. (IC) -Check polarization vs turn pattern: model vs Zgoubi ideal case 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg 7
lattice g 4 beamline model spin precession -Ee spectrum in the muon c. o. m. - function of P ideal case detector issues conclusions 1 2 P=1 m-c. o. m. Pe cosq co mm x=2 E/ cos(Θ) s(Θ ) - Total Electron Energy in the Lab Frame - N 0: initial n. of decays (@ turn 0) - a: decay constant - Em: beam energy - P: average polarization - w: angular spin tune ( Em) P e LAB cosq. LAB ~ 1 2 -4/June/2010 Lab-Frame Ee (Me. V) 2 nd EUROnu meeting - Strasbourg 8
lattice g 4 beamline model spin precession ideal case - What does it happen when we sample a fraction of the Ee spectrum? - How we parametrize the Beam Energy spread? m-decay energy spread detector issues conclusions 3 spin tune “polarization” - Asymmetry A 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 Ge. V or >15 Ge. V) - A(11 Ge. V)~0 no P observable! Ee spectrum We sample [a, b]: - [0, 5] or, - [15, 18]… [0, 5] Ge. V 2 -4/June/2010 NO sensitivity [15, 18] Ge. V 2 nd EUROnu meeting - Strasbourg 9
lattice g 4 beamline model spin precession ideal case detector issues conclusions MEASURABLE SIGNAL - collect electrons at different energy bins, [a, b] Ge. V - try to maximize A (enhanced oscillatory pattern) - measure the TOTAL energy deposited (e. g. in a Cherenkov+calorimeter) -Energy resolution modeled as: s. E/E=√(1. 03…/Ne) [Raja-Tollestrup] Signal fitted to Eq. (3) f(T) = A e-T/t (1+b/7*exp(-(w. DE/E)2/2) * P * cos (f+w. T)) 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 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg 10
![lattice g 4 beamline model spin precession ideal case [0, 5] Ge. V/c N](https://present5.com/presentation/255d782bc0584b65f38bdcc99d673a2e/image-11.jpg "lattice g 4 beamline model spin precession ideal case [0, 5] Ge. V/c N")
lattice g 4 beamline model spin precession ideal case [0, 5] Ge. V/c N 0=30% (1 E 6) detector issues conclusions -18% P 0 DE/E=2. 5% (hw) fit (80 turns) E = 24999 ± 40 Me. V DE/E = 2. 6 ± 0. 1 % tm = 97. 5 ± 0. 15 P [0, 5] Ge. V = (22. ± 0. 7)% [15, 18] Ge. V/c N 0=30% (1 E 6) fit (80 turns) E = 25040 ± 38 Me. V [15, 18] Ge. V DE/E = 2. 57 ± 0. 15 % tm derive actual P from MAX-min excursions 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg = 97. 6 ± 0. 16 P = (10. 8 ± 0. 7)% 11
lattice g 4 beamline model spin precession ideal case detector issues conclusions Statistic Precision of Fit (w. r. t. # of turns) -18% P 0 DE/E=2. 5% (hw) [0. 0, 2. 5] Ge. V/c N 0=16. 0% (1 E 6) fit (80 turns) High A E = 24998 ± 37 Me. V DE/E = 2. 55 ± 0. 09 % tm = 97. 56 ± 0. 14 P = (25. 9 ± 0. 7)% 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg 12
lattice g 4 beamline model spin precession ideal case detector issues conclusions Statistic Precision of Fit (w. r. t. # of turns) -18% P 0 DE/E=2. 5% (hw) [2. 5, 5. 0] Ge. V/c N 0=15. 5% (1 E 6) fit (80 turns) E = 24999 ± 49 Me. V DE/E = 2. 57 ± 0. 12 % tm = 97. 47 ± 0. 14 P = (20. 8 ± 0. 7)% 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg 13
lattice g 4 beamline model spin precession ideal case detector issues conclusions Statistic Precision of Fit (w. r. t. # of turns) -18% P 0 DE/E=2. 5% (hw) [5. 0, 7. 5] Ge. V/c N 0=14. 7% (1 E 6) fit (80 turns) E = 24876 ± 68 Me. V DE/E = 2. 66 ± 0. 15 % tm = 97. 52 ± 0. 14 P = (15. 5 ± 0. 7)% 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg 14
lattice g 4 beamline model spin precession ideal case detector issues conclusions Statistic Precision of Fit (w. r. t. # of turns) -18% P 0 DE/E=2. 5% (hw) [7. 5, 10. ] Ge. V/c N 0=13. 4% (1 E 6) fit (80 turns) Low A E = 25069 ± 126 Me. V DE/E = 2. 33 ± 0. 35 % tm = 97. 65 ± 0. 15 P = ( 7. 5 ± 0. 8)% 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg 15
lattice g 4 beamline 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 Ge. V)? In fact electron is emitted ~parallel to m (due to the high g) The spectral power of the 1 st magnet depends on its FIELD and LENGTH A G 4 Beamline simulation used to determine downstream electron distributions 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg 16
lattice g 4 beamline model spin precession ideal case detector issues conclusions use finite size beams of m+ from Zgoubi [C. Prior, D. Kelliher] - Pm = 25 Ge. V/c DP/P = 1% , DP/P = 2. 5% (*) - e. N = 30 mm rad (*) half width 2 -4/June/2010 m at mid - straight 2 nd EUROnu meeting - Strasbourg m at end of straight 17
lattice g 4 beamline model spin precession ideal case detector issues conclusions Device location and Naming Convention Bending Magnet m beam low E e+ longitudinal monitor transverse monitor high E e+ 2 nd EUROnu meeting - Strasbourg 18 “good” decay “bad” HE decay 2 -4/June/2010
lattice g 4 beamline model spin precession ideal case detector issues conclusions elmon 6 -L elmon 5 -T e from m decays elmon 2 -T … B 3 B 2 B= -4. 27 T/L=2. 0 m B 1 B= -4. 27 T/L=2. 0 m M 3 B=+0. 35 T/L=2. 3 m M 2 B=-1. 9 T/L=0. 6 m M 1 B=-0. 64 T /L=4. 0 m elmon 1 -L force m decay 2 -4/June/2010 elmon 4 -L elmon 3. 1 -L elmon 3 -T 2 nd EUROnu meeting - Strasbourg m beam 19
lattice g 4 beamline 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 Ge. V, ME=[5, 10] Ge. V, LE<5 Ge. V Possible Cases (PRO, CON) - elmon 1 -L: 1 st bending after long straight, small SP selects LE e+ mostly swept away by previous q-poles -elmon 2 -T: small SP, cannot separate HE component -elmon 3 -T: long decay path, decent SP separate LE, ME -elmon 3. 1 -L: inside the last bend of the matching section, small SP (E<0. 7 Ge. V) -elmon 4 -L: need to review the study -elmon 5 -T: need to review the study -elmon 6 -L: between two arc-bending magnets, very good SP 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg 20
lattice g 4 beamline model spin precession ideal case elmon 1 -L detector issues 300 m 1730 . 64 T/ 4 m 260 m 324 240 m 156 conclusions 280 m 734 220 m 200 m L (m) 300 m 180 m L (m) P (Ge. V/c) 160 m 140 m 120 m 100 m 80 m P (Ge. V/c) - only e+ at <20 m generate a clear pattern which is disturbed by e+ decayed far away - also the low bending E<4 Ge. V 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg - need further investigation 21 0 m
lattice g 4 beamline model 13 m 1. 9 T/ 0. 6 m spin precession ideal case detector issues conclusions elmon 3 -T long drift for higher momenta dri ft p ath ~1 3 m 0 mm -2200 mm force m decay 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg 22
lattice g 4 beamline model spin precession ideal case detector issues uniformity check for upstream decays <x> conclusions <P> RMS-x RMS-P dispersion 25 Ge. V/c beam size e=30 mmrad 20 15 10 5 0 2 -4/June/2010 -0. 2 0 [15, 18] Ge. V 0. 2 2 nd EUROnu meeting - Strasbourg 0. 4 0. 6 Impact Point (m) 0. 8 1. 0 1. 2 23
lattice g 4 beamline model spin precession ideal case detector issues conclusions An interesting location for a detector: sideway in an ARC-DIPOLE - study the decay of 10 K muons along the line from B 2 to B 3 included (step 200 mm) - check the effect on P vs detected position on the B 3 -monitor +2. m 0 m -2. 3 m -4. 3 m B 3 elmon 6 -L B 2 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg 24
Impact Point (m) lattice g 4 beamline model spin precession ideal case detector issues conclusions DS-B 2 Decays in B 2 -2500 mm -2700 mm -2900 mm -3100 mm -3300 mm -3500 mm -3700 mm -3900 mm e+ start falling in the acceptance of the channel only at the exit of the bending magnet US-B 2 -4100 mm -4300 mm P (Ge. V/c) 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg 25
lattice g 4 beamline model spin precession ideal case detector issues conclusions L=a+b. Ec DS-drift 0 mm Decays in the gap between B 2 and B 3 e+ are almost all in the acceptance US-drift -2400 mm 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg 26
lattice g 4 beamline model spin precession ideal case detector issues conclusions Decays in B 3 DS-B 2 1300 mm 100 mm 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg US-B 3 27
lattice g 4 beamline model spin precession ideal case detector issues conclusions uniformity check for upstream decays 0 m Uniformity Zone: P vs Impact. Point unchanged in B 3 67% of tot collected e+ -4. 3 m 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg this component can distort the spectrum 28
lattice g 4 beamline model spin precession ideal case detector issues …some back-of-the-envelope calculations 5 x 1020 n/yr (1 yr = 200 days) = 2. 9 x 1013 n/s - 50 Hz (proton) rep. rate = 20 ms (fill) - 0. 6 x 1012 n per fill - NB: every fill = 3 bunch trains (L=440 ns / S=1200 ns) - how many e+ (say) in a 10 m section before the bending element? - 10/1608 * 0. 6 * 1012 = 3. 5*109 - 30% [2. 5 -7. 5 Ge. V/c] 109 (15% [2. 5 -5. 0] 0. 5 x 109) - in conclusions . Nx 10 12 s oes. g t e ma E=[2. g o/ …= ? y 5 Bu ilk, , t 5] then m 2. 5 m 1. 2 x 108 /100 (# of turns = tm): ≈106 per turn per 2. 5 Ge. V-bin achievable 2 ns 440 ns 1200 ns (T) (S) 88 B 3 ns 1640 ns Tperiod = 5. 36 msec tm=520 msec 2 x 104 msec = 50 Hz rep. rate 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg 29
lattice g 4 beamline model spin precession ideal case detector issues conclusions # of decays over the ring 1. 2 E+6 It should not be a problem of statistics … … rather an issue of very high intensity electrons detectable in a 2. 5 Ge. V bin From a device with 2. 5 m U. S. acceptance 0. 5 E+6 turn # 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg 30
lattice g 4 beamline model spin precession ideal case detector issues conclusions challenging? Special magnet? C-dipole? how close can we get? 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg 31
lattice g 4 beamline 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 G 4 Beamline 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: IPAC 10 - Kyoto – 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 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg 32
lattice g 4 beamline model spin depolarisation ideal case detector issues conclusions End / Spares 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg 33
lattice g 4 beamline model First Dipole of the Arc section B= -4. 27 T / L=2. 0 m spin depolarisation ideal case detector issues conclusions First Dipole of the matching section B= -0. 64 T / L=4. 0 m elmon 2 low P e- elmon 1 elmon 5 elmon 4 force m decay 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg 34
lattice g 4 beamline model spin depolarisation ideal case detector issues conclusions [7. 0, 8. 0] Ge. V/c 0. 2 [9, 10] Ge. V/c [10, 11] Ge. V/c [11, 12] Ge. V/c 0 [8. 0, 9. 0] Ge. V/c [12, 13] Ge. V/c [13, 14] Ge. V/c [14, 15] Ge. V/c 0. 4 0. 6 2 -4/June/2010 0. 8 1. 0 1. 2 0 0. 2 0. 4 0. 6 0. 8 1. 0 1. 2 0 0. 2 0. 4 2 nd EUROnu meeting - Strasbourg 0. 6 0. 8 1. 0 1. 2 0 0. 2 0. 4 0. 6 0. 8 1. 0 35 1. 2
lattice g 4 beamline model spin precession ideal case detector issues …some back-of-the-envelope calculations 5. 8 x 1013 n/s n/yr (1 yr = 200 days) = - 50 Hz (proton) rep. rate = 20 ms (fill) - 1. 16 x 1012 n per fill - NB: every fill = 3 bunch trains (L=440 ns / S=1200 ns) - how many e+ (say) in a 10 m section before the bending element? - 10/1608 * 1. 16 * 1012 = 7*109 - 30% [2. 5 -7. 5 Ge. V/c] 2*109 (15% [2. 5 -5. 0] 109) 1021 - in conclusions t igh to Nx 10 12 fl e/ E=[2 e th o …= ? k. 5, g Ta ica 5] then h C 1 m 108 /100 (# of turns = tm): 106 per turn per 2. 5 Ge. V-bin is achievable 2 ns 440 ns 1200 ns (T) (S) 88 B 3 ns 1640 ns Tperiod = 5. 36 msec tm=520 msec 2 x 104 msec = 50 Hz rep. rate 2 -4/June/2010 2 nd EUROnu meeting - Strasbourg 36
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