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Proportional Counters Amplifying Field I + • Gas counters at the ionization plateau collect virtually all ion pairs produced. • At higher field the electrons gain energy to ionize other atoms. – More electrons than initial count of ion pairs – Gas amplification E - V Avalanche • Many electrons reach the anode for each initial pair. – Typically 104 electrons – An “avalanche” Proportional Region • Ionization chambers at increased voltage move from an ionization plateau to the proportional region. – Counters operating in this region are proportional counters. Cylindrical Chamber I + - • Cylindrical geometry is common for proportional counters. – Grounded outer cathode – High voltage anode V E r ln( b / a) • The avalanche is limited to a region near the wire. V Single Track • A single track in a chamber creates many avalanches. – All contribute to one pulse • Timing is based on first avalanche arrival. – Usually nearest point in the field. • Accurate time-to distance conversion requires uniform field. Multiwire Proportional Chamber • An array of proportional readout wires can be placed in an array. – Invented in 1968 by Georges Charpak – Used in many discoveries – Received the 1992 Nobel Prize • Provides excellent position resolution for charged particle tracks. Gas Gain • Gain in the proportional region is exponential with the wire radius a. • The Townsend coefficient a depends on the field E. – Adjusted by pressure P G Keaa a P Ae - BP / E • For 90% Ar, 10% CO2 – A = 14 / (cm-Torr) – B = 180 V/(cm-Torr) Parallel Cathode Chamber • A parallel plate chamber may have a single anode wire at center. grounded shell • The cathodes are at high positive voltage Vp compared to the case. – 2-3 kV • The anode is at a higher voltage Vw compared to the case and wire. – 4-5 kV cathode pads anode wire D0 central muon drift cell Equipotentials Gain Comparison • The gas gain can be measured by comparing pulse height to voltage difference. – Field approximated by cylindrical formula. – Expect 204 V for factor of e – 250 V yields factor of e V0 Vw - V p dV0 1 V0 (aa )( BP / E ) Drift Velocity • The important function of a proportional wire chamber is to measure the distance. – Particle to wire – Need drift velocity • The drift velocity also is a factor of the voltage difference. Drift Linearity • Conversion of time to distance is easiest with strong linearity. • Particles are measured externally and compared to test cell. • At right, noise dominates over non-linearity. Drift Residuals • With multiple drift cells resolution can be determined through residuals. – Three displacements – Ideal residual equals 0 s = 0.31 mm Cathode Pads • Measurement along the length of the wire gives a third dimension. – Timing on wire gives 9 cm to 28 cm resolution • Dividing the charge on the pads acts like a vernier to subdivide the longitudinal coordinate. – Repeat pattern longer than wire resolution. Charge Ratios • The signal is not as linear in this coordinate. Pad Residuals • Resolution is improved by staggering the phase of the pad pattern. • Residuals can be applied compared to get resolution. – External wire chambers used for figure at right s = 2.7 mm Gas Fill • The avalanche relies in electrons moving toward the anode. • Electronegative gases like O2 pick up electrons. – O2- drifts toward anode – No avalanche • Preferred gases are noble gases and hydrocarbons – Hydrocarbons are flammable – Noble gases excite and emit photons • Gas mixes can quench photons and extra electrons but remain non-flammable Oxygen Contamination • Oxygen is an electronegative impurity. – Reduced gain – Increases with impurity – Equivalent to 110 V drop at wire • Gain also decreases with distance. – Greater attachment of ions Water Contamination • Water added to the gas causes non-linearities to the drift times. – Electronegative impurity – 3000 ppm at left – Different than O2 • Effect of water is dependent on the field strength.