1. 7-8/1/2010UKNF - Imperial College London1 Diagnostic for the Decay Ring : Energy Monitoring m. apollonio – Imperial College London

2. 7-8/1/2010UKNF - Imperial College London2 the lattice of the DK racetrack ring G4beamline 3D model the method of spin depolarisation resolution in ideal case detector issues (location, …) conclusions

3. 7-8/1/2010UKNF - Imperial College London3 Track DK Ring lattice [C. Prior, IDS baseline] P  = 25 GeV/c  N = 4.8 mm rad  = 0.02 mm rad a N = 30 mm rad (accept) a  = 0.127 mm rad Twiss Parameters (MADX) straights:  x = 51 mm  x’ = 0.4 mrad arcs:  x = 16 mm  x’ = 0.13 mrad 1/  = 4 mrad  x’ *  ~ 0.1 lattice g4beamline model spin depolarisation ideal case detector issues conclusions

4. 7-8/1/2010UKNF - Imperial College London4 main open issues on diagnostics - measurement of divergence - measurement of energy via beam (de)polarisation location for the device? G4beamline MODEL lattice g4beamline model spin depolarisation ideal case detector issues conclusions straight section matching section arc section - measurement beam current

5. 7-8/1/2010UKNF - Imperial College London5 MAGNETeff. length (mm) width (mm) gap (mm) pole tip radius (mm) field/gradient (T/Tm-1) STRAIGHT QF1500--200+0.454 QD1500--200-0.464 MATCHING 1 st Bend40001000200--0.64 QD800--200-9.2 QF1600--200+11.6 QD1600--200-7.66 2 nd bend6001000200--1.9 QF800--200+4.1 3 rd bend23001000200-+0.35 ARC bend20001000200--4.27 QF500--200+24.18 QD500--200-23.77 lattice g4beamline model spin depolarisation ideal case detector issues conclusions

6. 7-8/1/2010UKNF - Imperial College London6 - Energy can be measured using the Polarisation of the Muon Beam [ Raja-Tollestrup – FERMILAB-Pub-97 / 402] IF some P is saved after all the massage in the machines... - I assume P = 27% is left when filling the DK ring - Spin precesses in a ring due to coupling with magnetic fields (bending magnets). NB: the trick does NOT work in a bow-tie shape - At every turn spin precession is determined by the SPIN TUNE:  = 2  a a = 1.16E-3 This determines a modulation in P - NB: if  E/E =0   same for all muons  P keeps oscillating if  E/E !=0  P goes to 0 after n turns e+ spectrum from  -decay is a function of P : d 2 N/dx dcos  = N0[(3-2x)x 2 – P (1-x)x 2 cos  ] (CM) - I have modelled the behaviour of a beam made of 100000 muons, all with their spin and energy (  E/E =[0.01-0.05]) - Lorentz Boost - Modulation in P produces a modulation in E(e+) Sz(0) Sz(1) turn0 turn1 Sz(2) turn2 lattice g4beamline model spin depolarisation ideal case detector issues conclusions

7. 7-8/1/2010UKNF - Imperial College London7 E (MeV) Cos (  LAB) Centre of Mass frame: P=+100% LAB frame after Lorentz boost X=2Ee/m  (CM) x=2E e /m  PePe cos  P e LAB cos  LAB ~ 1 0.99996 lattice g4beamline model spin depolarisation ideal case detector issues conclusions

8. 7-8/1/2010UKNF - Imperial College London8 DP/P = 3% Pol=27% fine mesh = 10 samples / turn TURN P modulation (spin precession) and damping (  E/E !=0) lattice g4beamline model spin depolarisation ideal case detector issues conclusions POL (%) turn #

9. 7-8/1/2010UKNF - Imperial College London9 MEASURABLE SIGNAL collect electrons at three different energy bins [0,5] GeV [5,10] GeV [10,25] GeV measure the TOTAL energy deposited (e.g. in a calorimeter) Energy resolution modeled as:  E/E=SQRT(1.03…/Ne) [Raja-Tollestrup] obtain a signal which shows: - an oscillation due to Polarisation - a decay slope due to continuous muon decays - a modulation/damping due to  E/E fit the signal at every TURN with a function: f(T) = A e -BT (C exp -(G T 2 ) cos(D+E T) + F) G: contains  P/P E: is the SPIN tune from which  can be inferred B: describes muon decay slope lattice g4beamline model spin depolarisation ideal case detector issues conclusions

10. 7-8/1/2010UKNF - Imperial College London10 31% in [0,5] GeV/c 100000 initial muon decays lattice g4beamline model spin depolarisation ideal case detector issues conclusions turn # Ee (GeV)

11. 7-8/1/2010UKNF - Imperial College London11 28% in [5,10] GeV/c lattice g4beamline model spin depolarisation ideal case detector issues conclusions

12. 7-8/1/2010UKNF - Imperial College London12 41% in [10,25] GeV/c lattice g4beamline model spin depolarisation ideal case detector issues conclusions

13. 7-8/1/2010UKNF - Imperial College London13 This is somewhat ideal... we need to collect the electrons! How do we turn it into a realistic device for our case? It has been 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  (due to the high  ) The spectral power of the 1 st magnet depends on its FIELD and LENGTH A G4Beamline simulation can tell us where electrons impinge after decaying somewhere along the orbit lattice g4beamline model spin depolarisation ideal case detector issues conclusions

14. 7-8/1/2010UKNF - Imperial College London14 use a “realistic” beam of   from Zgoubi [C. Prior] - P  = 25 GeV/c  P/P = 1% -  N = 30 mm rad lattice g4beamline model spin depolarisation ideal case detector issues conclusions  at mid - straight  at end of straight

15. 7-8/1/2010UKNF - Imperial College London15 … 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  beam e from  decays elmon5 elmon4 elmon3 elmon2 elmon1 force  decay lattice g4beamline model spin depolarisation ideal case detector issues conclusions

16. 7-8/1/2010UKNF - Imperial College London16 elmon5 elmon4 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- force  decay lattice g4beamline model spin depolarisation ideal case detector issues conclusions

17. 7-8/1/2010UKNF - Imperial College London17 elmon5 sensible plane lattice g4beamline model spin depolarisation ideal case detector issues conclusions

18. 7-8/1/2010UKNF - Imperial College London18 lattice g4beamline model spin depolarisation ideal case detector issues conclusions elmon4 sensible plane Dipole Length = 2m magnet gap

19. 7-8/1/2010UKNF - Imperial College London19 drift path ~ 13 m elmon3 long drift for higher momenta force  decay lattice g4beamline model spin depolarisation ideal case detector issues conclusions

20. 7-8/1/2010UKNF - Imperial College London20 Elmon3 – DS of M2  consider Ee = [2.5-7.5] e+ out of the aperture lattice g4beamline model spin depolarisation ideal case detector issues conclusions

21. 7-8/1/2010UKNF - Imperial College London21 OUT OF detector acceptance How does TOT Ee changes turn by turn? lattice g4beamline model spin depolarisation ideal case detector issues conclusions TOT Ee in [2.5,7.5] GeV/c bin fit on 40 turns TOT Ee in [2.5,7.5] GeV/c bin fit on 80 turns TOT Ee in [12.5,25] GeV/c bin fit on 80 turns TOT Ee in [12.5,25] GeV/c bin fit on 40 turns

22. 7-8/1/2010UKNF - Imperial College London22 consider an initial sample of ~100000 e- [0,25] bin [2.5,7.5] = 30% measure E (  E/E) with (de)polarisation after n turn E = 25009+/-44 after 40 turns (24986+/-23, 100 turns)  E/E = 0.89+/-0.36 after 40 turns (0.93+/-0.07, 100 turns) Q.: how many electrons can I collect at turn=0? [2.5,7.5] GeV/c – Energy Bias [2.5,7.5] GeV/c – DE/E lattice g4beamline model spin depolarisation ideal case detector issues conclusions [12.5,25] GeV/c – Energy Bias = (E-25)/25 [12.5,25] GeV/c – DE/E OUT OF detector acceptance

23. 7-8/1/2010UKNF - Imperial College London23 10 21 /yr (1yr = 200 days) = 5.8x10 13 /s - 50 Hz (proton) rep. rate = 20 ms (fill)  -1.16 x 10 12  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 * 10 12 = 7*10 9 - 30% [2.5-7.5GeV/c]  2*10 9 2x10 4  sec = 50Hz rep.rate t  =520  sec 2ns 3ns 88 B lattice g4beamline model spin depolarisation ideal case detector issues conclusions 440ns1200ns (T)(S) Tperiod = 5.36  sec 1640ns

24. 7-8/1/2010UKNF - Imperial College London24 decay region >10m lattice g4beamline model spin depolarisation ideal case detector issues conclusions ideal decay point Open issues: - which electrons are relevant for the measurement? i.e. which decay points upstream of the bending dipole? - 1m? 10m? 100m upstream? A B

25. 7-8/1/2010UKNF - Imperial College London25 to do list: a- introduce polarisation(*) of the beam  Zgoubi b- use Zgoubi-generated files as input for G4beamline c- force the decay over a continuous volume (length) = some technicalities with g4bl to be solved d- build the e+spectrum at elmon(i) e- perform fit and evaluate precision/biases lattice g4beamline model spin depolarisation ideal case detector issues conclusions (*) so far a self made model

26. 7-8/1/2010UKNF - Imperial College London26 Conclusions method of Energy Monitoring via depolarisation revived for the IDS Race Track Decay Ring Use of G4Beamline for a more realistic rendering of the events Zgoubi to realistically describe P 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 lattice g4beamline model spin depolarisation ideal case detector issues conclusions

27. 7-8/1/2010UKNF - Imperial College London27 to do list: a- force the decay over a continuous volume (length) = some technicalities with g4bl to be solved b- build the e+spectrum at elmon(i) c- introduce polarisation (verify if P is taken into account in g4bl) d- perform fit and evaluate precision/biases lattice g4beamline model spin depolarisation ideal case detector issues conclusions