Diffusion and space point resolution in a TPC Master seminar: „Particle tracking and identification at high rates“ 25.11.2016 Michael Ciupek 1
Overview ● Introduction ● From Ionization to Signal Creation – Ionization Process – Drift of particles – Diffusion – Signal Creation ● Fundamental Limit for Space Point Resolution ● Resolution of ALICE TPC – MWPC – GEM ● Momentum resolution ● Summary 2
Structure of the TPC Note: Only one half of the TPC drift chamber E = 400 V/cm for ALICE TPC cccccc 3 1. https://www.lctpc.org/e8/e57671
Working principle of the TPC Two coordinates given by projection on the pad plane Third coordinate from drift time and drift velocity Momentum measurements due to curvature of the track because of a mag. Field: 4 1. Jens Wiechula: TPC lectures/seminar
Ionization process 5
Ionization Charged particles will ionize the gas in the TPC. Its important to distinguish between primary and secondary ionization Primary ionization Secondary electrons 6 1. Jens Wiechula: TPC lectures/seminar
Primary Ionization For the ALICE TPC with Ne/CO2 [90,10]: Number of primary (Simulations) electrons is poisson distributed. Number of electrons per cm mean free path 7 1. ALICE TPC Technical Design Report ; 2. Blum, Rolandi, Riegler: Particle Detection with drift chambers
Secondary Ionization / Cluster Size Distribution Because secondary electrons are With enough energy primary created in vicinity of the primary electrons can produce secondary electrons. electrons. → electrons form cluster Range of primary electrons: Energy loss in given collision First ionization potenial Range primary for argon: Effectiv energy to produce an Energy E Range R electron ion pair 1 keV 30 mum 10 keV 1.5 mm On average: 30 keV 1 cm Cluster size distribution 60 keV 3 cm 8 1. Blum, Rolandi, Riegler: Particle Detection with drift chambers
Drift of particles 9
Equation of motion with friction (macroscopic picture) Equation of Motion (Langevin equation) in gas given by: For large times, steady state and constant velocity. K: Friction constant E: ele. Field B: mag. Field m: electron mass Define characteristic time: For vanishing B- field: In the microscopic picture it's the average time between two collisions 10 1.Blum, Rolandi, Riegler: Particle Detection with drift chambers
Equation of motion with friction (macroscopic picture) Everything is more complicate with a B- field: Component in Component in E * B E x B direction direction Cyclotron : Unitvektor in direction of E or B frequency field Examples: Ne- CO2 (90-10) ALICE TPC Run 1 0.34 0.5 T Ne-Co2-N2 (85-10-5) ALICE TPC Run 1/3 0.32 0.5 T Ar-Co2 (90-20) Run2 0.43 0.5 T Ar-CH4(90-10) STAR TPC 2.3 0.5 T 11 Ar-CH4(90-10) ALEPH TPC 7 1.5 T 1. Jens Wiechula: TPC lectures/seminar 2.Blum, Rolandi, Riegler: Particle Detection with drift chambers
Drift of Electrons Electrons in a gas will drift with a constant velocity u in a external electric field. Electrons will scatter isotropically due to their light mass and forgot there preferential direction. The electron will pick up the velocity from the electric field. e - Tau: time between two collisions → A equilibrium between picked up energy and scattering losses is obtained and therefore a constant drift velocity is observed. Fractional energy loss per 12 collisions 1. Jens Wiechula: TPC lectures/seminar ; 2.Blum, Rolandi, Riegler: Particle Detection with drift chambers
Drift of Electrons Additionally we have to include thermal energy, but due to high electric energies thermal energy can be neglected. The drift velocity is then given by Goal: Drift velocity differs little with the field → coordinate measurements less depend on field changes For ALICE TPC filled with argon or neon N: Number density Sigma: cross section 13 1.Blum, Rolandi, Riegler: Particle Detection with drift chambers
Ramsauer Minimum 14 1. Ernst Hellbär: Ion Movement and Space-Charge Distortions in the ALICE TPC (Masterthesis)
Drift of Ions Ion drift differ from electron drift due to there larger mass. → no isotropic scattering Therefore the drift velocity is given as: Limit for low E fields like in ALICE: m: mass ion 15 For ALICE TPC filled with neon M: mass gas atom .m*: reduce mass 1.Blum, Rolandi, Riegler: Particle Detection with drift chambers
Diffusion 16
Diffusion Electrons and ions are scattered in the gas molecules. In the simplest case deviation is same in all direction. With : electron mobility 17 : mean free path 1. Jens Wiechula: TPC lectures/seminar ; 2.Blum, Rolandi, Riegler: Particle Detection with drift chambers
Diffusion Thermal limit is The Diffusion width in for example given by: x direction is now given by (L travel distance) Goal: High E field at small electron energies → small diffusion width For ALICE TPC : Electron energy 18 1. Jens Wiechula: TPC lectures/seminar ; 2.Blum, Rolandi, Riegler: Particle Detection with drift chambers
Electric anisotropy Reason for anisotropy → electron mobility is different in the center of the cloud and in the edges → Due to e – e interactions Effect: Diffusion in direction of drift field is different than in traverse direction: Mobility variation inside an electron 19 cloud traversing in the z direction 1.Blum, Rolandi, Riegler: Particle Detection with drift chambers
Diffusion (Drift gas choice) Diffusion for different gas mixtures For ALICE TPC Electron energy for 20 different gases 1. Ernst Hellbär: Ion Movement and Space-Charge Distortions in the ALICE TPC (Masterthesis) ; 2.Blum, Rolandi, Riegler: Particle Detection with drift chambers
Magnetic anisotropy In presence of a magnetic field the diffusion in traverse direction will reduced, it follows: Lorentz force will bend particles in B field direction. Influence on resolution in traverse direction 21 Traverse resolution as function of B-field and track length 1.Blum, Rolandi, Riegler: Particle Detection with drift chambers ; 2. http://www.desy.de/~garutti/LECTURES/ParticleDetectorSS12/L4_gasDetectors.pdf
Signal Creation 22
Number of electrons: Example : 1cm gas counter, filled with neon 1 cm ~ 60 electrons ~ 600.000 electrons 60 electrons can not be detect easily Noise of the electronics → 700 – 1000 e → Therefore increasing number of electrons via gas amplification 23 1. Jens Wiechula: TPC lectures/seminar
Gas gain fluctuation MWPC: P Important for the accuracy of the coordinate measurements is the gas gain fluctuation, not the gas gain! n In ALICE TPC: Exponential gas gain fluctuation Exponential signal , were small signals being most probable Gas Gain fluctuation for GEM detectors n: Number of electrons a: Constant 24 1. Jens Wiechula: TPC lectures/seminar ; 2.Blum, Rolandi, Riegler: Particle Detection with drift chambers
Signal creation (MWPC) Example Multi wire proportional chambers: Electrons will create avalanche near the wire → creation of ions and therefore induced 25 signal on the pads 1. http://www.desy.de/~garutti/LECTURES/ParticleDetectorSS12/L4_gasDetectors.pdf
Space point reconstruction (Alice - TPC) Calculate the center of gravity in pad direction and time direction → x/y and z coordinate This is only one possible approach to calculate the position of the cluster. 26 1. Jens Wiechula: TPC lectures/seminar
Signal creation (GEM) General Concept of GEM's: GEM's for the Run 3 alice upgrade 27 1. http://www.desy.de/~garutti/LECTURES/ParticleDetectorSS12/L4_gasDetectors.pdf 2. Technical Design Report for the Upgrade of the ALICE Time Projection Chamber
Pad Response for MWPC and GEM Disadvantage of GEM → electron signal on only one Outer pad readout → No Center of Gravity chambers (3 mm) 2 mm Pad width: 6 mm Width of the Pad response function: - MWPC: 3 mm - GEM: 0.2 mm 28 1. https://web.physik.rwth-aachen.de/~tpcmgr/downloads/talks/ICATPP-como03-roth.pdf
Fundamental Limit for Space Point Resolution 29
Fundamental Limit for Space Point Resolution ● Many effects will have an impact on the accuracy of the coordinate measurements – Electronic noise – Diffusion – Gas gain fluctuation – Angular pad effect – Landau fluctuation – E x B effect 30
Defining Coordinate system Inclination angle between track and the wire normal Inclination angle between track and direction of the pad rows Schematic view of the detection process in TPC 31 1. Y.Belikov, M.Ivanov, K.Safarik: TPC tracking and particle identification in high-density environment
Intrinsic resolution The center of gravity can be calculated by: Pad response function Intrinsic resolution of COG because of noise: pad Charge .h = deposit on 0.6 one pad cm h: Pad width Q: deposit charge on the pad For ALICE with MWPC 32 1. Y.Belikov, M.Ivanov, K.Safarik: TPC tracking and particle identification in high-density environment
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