Diffusion and space point resolution in a TPC Master seminar: - - PowerPoint PPT Presentation
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
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– Ionization Process – Drift of particles – Diffusion – Signal Creation
– MWPC – GEM
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Note: Only one half of the TPC drift chamber = 400 V/cm for ALICE TPC
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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:
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Charged particles will ionize the gas in the TPC. Its important to distinguish between primary and secondary ionization Primary ionization Secondary electrons
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Number of primary electrons is poisson distributed. For the ALICE TPC with Ne/CO2 [90,10]: (Simulations) mean free path Number of electrons per cm
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With enough energy primary electrons can produce secondary electrons. On average: Because secondary electrons are created in vicinity of the primary electrons. → electrons form cluster
Cluster size distribution
Energy loss in given collision First ionization potenial Effectiv energy to produce an electron ion pair
Energy E Range R 1 keV 30 mum 10 keV 1.5 mm 30 keV 1 cm 60 keV 3 cm Range of primary electrons:
Range primary for argon:
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Equation of Motion (Langevin equation) in gas given by: K: Friction constant E: ele. Field B: mag. Field m: electron mass Define characteristic time: In the microscopic picture it's the average time between two collisions For large times, steady state and constant velocity. For vanishing B- field:
1.Blum, Rolandi, Riegler: Particle Detection with drift chambers
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Everything is more complicate with a B- field:
Cyclotron frequency
Component in E x B direction Component in E * B direction
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 Ar-CH4(90-10) ALEPH TPC 7 1.5 T
: Unitvektor in direction of E or B field
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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
velocity from the electric field. 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 collisions
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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
N: Number density Sigma: cross section
Goal: Drift velocity differs little with the field → coordinate measurements less depend on field changes For ALICE TPC filled with argon or neon
1.Blum, Rolandi, Riegler: Particle Detection with drift chambers
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Ramsauer Minimum
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Ion drift differ from electron drift due to there larger mass. → no isotropic scattering Therefore the drift velocity is given as:
m: mass ion M: mass gas atom .m*: reduce mass
Limit for low E fields like in ALICE:
For ALICE TPC filled with neon
1.Blum, Rolandi, Riegler: Particle Detection with drift chambers
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Electrons and ions are scattered in the gas molecules. In the simplest case deviation is same in all direction. With : electron mobility : mean free path
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The Diffusion width in for example x direction is now given by (L travel distance) Goal: High E field at small electron energies → small diffusion width Thermal limit is given by: For ALICE TPC
: Electron energy
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Mobility variation inside an electron cloud traversing in the z direction
Effect: Diffusion in direction of drift field is different than in traverse direction:
1.Blum, Rolandi, Riegler: Particle Detection with drift chambers
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Diffusion for different gas mixtures Electron energy for different gases For ALICE TPC
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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
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
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1 cm ~ 60 electrons ~ 600.000 electrons
Example : 1cm gas counter, filled with neon 60 electrons can not be detect easily Noise of the electronics → 700 – 1000 e → Therefore increasing number of electrons via gas amplification
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Important for the accuracy of the coordinate measurements is the gas gain fluctuation, not the gas gain! In ALICE TPC: Exponential gas gain fluctuation Exponential signal , were small signals being most probable P n Gas Gain fluctuation for GEM detectors
n: Number of electrons a: Constant
MWPC:
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Example Multi wire proportional chambers:
Electrons will create avalanche near the wire → creation of ions and therefore induced signal on the pads
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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.
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General Concept of GEM's: GEM's for the Run 3 alice upgrade
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Disadvantage of GEM → electron signal on only one pad → No Center of Gravity
2 mm (3 mm)
Pad width: 6 mm Width of the Pad response function:
Outer readout chambers
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– Electronic noise – Diffusion – Gas gain fluctuation – Angular pad effect – Landau fluctuation – E x B effect
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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
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Charge deposit on
h: Pad width Q: deposit charge on the pad The center of gravity can be calculated by: pad For ALICE with MWPC Intrinsic resolution of COG because
.h = 0.6 cm Pad response function
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Each electron is multiplied near the wire. This multiplication has large fluctuation, which were described before. → Therefore the center of gravity of the electron cloud can be changed. g: gas amplification Resolution is given by: Diffusion No gas gain fluctuation Gas gain fluctuation
2.http://irfu.cea.fr/Spp/ILCTPC/home/talks/2008/080520_K.Fujii_GasGainFluctuation.pdf
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Accuracy in coordinate measurements are limited by a track angle which will spread the ionization at the wire. Electrons distributed in clusters, not randomly. → position of clusters is determined by the primary electrons
Pad row track Cluster 0.6 cm
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Electrons will now drift with an effective angle toward the wire. Cyclotron frequency b: distance between wires Close to the wire E and B field → Component of el. field perpendicular to the mag. Field → resulting E x B force → displacement of the electrons
1.Blum, Rolandi, Riegler: Particle Detection with drift chambers
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Diffusion, gas gain fluctuation, angular pad effect, landau fluctuation and electric noise
Space point resolution as function of the drift length and the inclination angle Space point resolution as function of the maximum charge deposit in a cluster
With magnetic field Without magnetic field
Short pad Medium pad Long pad
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Intrinsic resolution for MWPC and GEMS
worse→ narrow Pad Response Function for GEMs.
Pad size: 0.75 x 0.4 cm² Pad size: 1.0 x 0.6 cm² Pad size: 1.5 x 0.6 cm²
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Space point resolution important to determine also the momentum resolution. → Measure the track curvature General uncertainty: For N equidistant measurements the momentum resolution is described by the Gluckstern formula r
s y
B L: projected length of the track onto the bending plane
Not sure if I should use this!!!!
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– Fundamental limit of the accuracy
– e. g. momentum resolution