Detectors in Nuclear and Particle Physics

Transcription

1 Detectors in Nuclear and Particle Physics Prof. Dr. Johanna Stachel Deartment of Physics und Astronomy University of Heidelberg June 17, 2015 J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

2 6. Momentum Measurements 6 Momentum Measurements Forward Sectrometer J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

3 6. Momentum Measurements Deflection of track of charged article in magnetic sectrometer Lorentz force circular orbit of curvature radius ρ in homogeneous magnetic field mv 2 ρ = q v B = qv B v : comonent of v to B and for B ρ = ρ = units: for ρ in m in GeV/c B in T q in units of e 2 q B qb : analogue ρ = 0.3 qb or = 0.3 qρb J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

4 Forward Sectrometer 6.1 Forward Sectrometer Mainly in fixed target exeriments (but also LHCb) or ALICE forward muon sectrometer _ L beam _ x Target z tracking chambers diole magnet + + B = (0, B y, 0) magnetic field gives (additional) -kick tyically, Lorentz force always aroximately in x-direction and x = 0.3 L q B or for magnetic field not constant over entire ath x = 0.3 q L BdL J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

5 Momentum Measurements Forward Sectrometer ALICE (Di)-Muon Sectrometer Diole magnet Muon chambers Muon absorber and filter J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

6 Forward Sectrometer Examle: roton of = 10 GeV/c z BdL = 6 Tm x = 1.8 GeV/c θ x = 10 about the limit for this aroximation x θ/2 ρ z θ h for ρ L θ L ρ = LqB y or x = sin θ θ = LqB y q L 0 B y dl J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

7 Forward Sectrometer Momentum resolution = qρb y = q L θ B y d dθ = qlb y 1 θ 2 = θ d = dθ θ σ = σ θ θ minimum: two measured oints before and two after deflection accuracy of angular measurement accuracy of momentum measurement in ractice always 3 or more measurements, since detectors need to be aligned relative to each other (best done with straight tracks) in case all measured oints have identical resolution σ x : n/2 oints before n/2 oints after deflection lever arm h (see Fig. revious age) σ θ = 8 n σ x h σ = 8/n σx h qlb y = 8/n σx h x contribution of sace oint resolution to momentum resolution σ tyical form = const with const = i.e. 1% % Examle: 6 measurements each with σ x = 200 µm, h = 5 m, deflection 1 σ θ x = x = deflection) for = 10 GeV /c = = J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

8 Forward Sectrometer Effect of multile scattering multile Coulomb scattering along article trajectory of length L contributes to -broadening erendicular to direction of roagation ms = sin θ rms θ rms = q 19.2 MeV/c β L X 0 Δ x ms where X 0 is the radiation length. In the direction of deflection (x) this means: x ms q 19.2 MeV/c = β L q 13.6 MeV/c L = 2 X 0 β for sufficiently large momenta indeendent of contribution to momentum resolution: ( ) σ = ms x x ms = 13.6 MeV/c L/X0 e B y dl where x is the deflection due to magnetic field (see above). X 0 J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

9 Forward Sectrometer total momentum resolution Examle: as above e BdL = x = 0.17 GeV/c L = 15 m material: air, X 0 = 304 m ( ) σ = 1.8% ms ( ) σ vs. = 0.03% defl multile scattering dominates at small momenta ( σ ) 2 = ( σ ) 2 ms + ( σ ) 2 defl momentum resolution in magnetic sectrometer J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

10 Forward Sectrometer Examle: ( σ ) 2 = (1.8%) 2 + (0.06% ) 2 σ [%] 3. both together σ σ defl σ 2 ms [GeV/c] J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

11 Forward Sectrometer Multile scattering articularly relevant if magnetized iron is used, as frequently done for measurements of muon momentum advantage: high B-field, stos π, K before they decay into µ disadvantage: worsens momentum resolution by multile scattering X Fe 0 = 1.76 cm, B = 1.8 T, L = 3 m, x = 1.6 GeV/c ( ) σ = 11% ms deending on desired momentum range, accuracy of deflection measurement can be chosen accordingly J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

12 6.2 Normally 4π coverage desired, leading to secial sectrometer configuration diole disfavored - deflects beam which must be comensated - not nice symmetry for 4π exeriment Solenoid B long cylindrical coil I beam axis B B along beam direction, no deflection measure momentum comonent erendicular to beam J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

13 y φ need to measure at least 3 oints of track circular in xy-lane ρ (radius of curvature) or and ϕ measurement of θ: = x beam and B-field along z-axis article roduced with momentum comletely characterized by x, y, z, where x and y can be written as: = tan θ sin θ comlete measurement of article momentum, ϕ : x = cos ϕ y = sin ϕ r θ z J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

14 Sagitta Method x S L Sagitta S = ρ ρ cos θ ( 2 = ρ 1 cos θ ) 2 θ/ 2 ρ = 2ρ sin 2 θ 4 for small θ S ρθ2 8 with θ = qbl and sin θ/2 θ/2 = L/2 ρ S = ql2 B 8 B in T, L in m, in GeV/c, q in e S(m) = 0.3 ql2 B 8 J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

15 Measurement of at least 3 oints with coordinates x 1, x 2, x 3 S = x 2 x 1 + x σ S = 2 σ x σ = σ S S = 3/2 σx 8 0.3qBL 2 Measurement of N equally saced oints: examle σ = σ x 0.3qBL NIM 24 (1963) 381 (N + 4) B = 0.5 T L = 2 m σ x = 400 µm N = 150 similar to ALICE TPC, usage of former L3 Magnet σ J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

16 L3 σ S = 90 µm σ = 2.5% at 45 GeV (tyical Z 0 decay roduct) J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

17 Construction site ALICE the solenoid and the iron return yoke Largest magnet, about 7000 t iron (like Eiffel tower) current in magnet 30 ka average lightning energy stored in magnetic field equivalent to exlosion of 45 kg TNT bomb J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

18 ALICE first 13 TeV collisions J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

19 Toroid B I on axis vanishing B-field no deflection of beam fill with iron-core e.g. for muon measurement in end cas Examle: H1 forward muon sectrometer J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

20 H1 exeriment at HERA Central solenoid lus forward muon toroid to measure high energy muons between 3 and 17 drift chamber lanes before and after toroid Toroidal magnet: 12 segments with 15 turns each (Cu), 150 A B = 1.6 T filled with Fe core J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

21 Momentum Measurements - ro = 2.9 m deflection in olar angle momentum σ = 24 36% for = GeV/c dominated by multile scattering σ = ri = 0.65 m 12 m J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

22 Momentum Measurements ATLAS - A Toroidal LHC AaratuS J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

23 air core toroid central barrel L = 26 m, D i = 9.4 m, D 0 = 19.5 m Momentum Measurements J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

24 Momentum Measurements 8 flat coils, R suer-conducting, 70 km suer-conducting cable 20 ka, BdL = 3 9 Tm energy stored in magnetic field 1490 MJ J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

25 Momentum Measurements ATLAS cavern J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

26 Momentum Measurements F with current on forces on coils radially inward J. Stachel (Physics University Heidelberg) B-field monitored by 5000 Hall robes attached to muon chambers Detectorhysics June 17, / 333

27 Momentum Measurements η = 1.4 η = 1.05 Princile of momentum measurement of muon tracks with monitored drift-tube array: η = layers, each consisting of 2 multilayers η = 2.4 total 1200 muon chambers of m2 η = 3.0 total channels J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

28 ATLAS monitored drift tube arrays drift tubes Al-Mn 3 cm 400 µm wall thickness m long 50 µm wire centered in tube to 20 µm oeration at 3 bar drift time 600 ns gas gain < (only streamers to avoid aging ) gas: Ar/C 2 H 6 /CO 2 /N 2 86 : 5 : 4 : 5 Multilayer In-lane alignment Longitudinal beam Cross late J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

29 osition resolution ATLAS monitored drift tube array difficulty: wires gravitational sag of long tubes and single tube osition resolution 80 µm σ t / t = 10% at 1000 GeV J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333

30 Need to know exactly where tubes and wires are! Rasnick System CCD cameras align each muon chamber to 0.05 mm recision Alignment system for 3 layers of MDT s J. Stachel (Physics University Heidelberg) Detectorhysics June 17, / 333