Proportional Counters

Amplifying Field 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 I + 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 Cylindrical geometry is common for proportional counters. Grounded outer cathode High voltage anode The avalanche is limited to a region near the wire. I + - 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 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. 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 grounded shell 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

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.