1. Proportional Counters

2. 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

3. Avalanche Many electrons reach the anode for each initial pair.
Typically 104 electrons
An “avalanche”

4. Proportional Region
Ionization chambers at increased voltage move from an ionization plateau to the proportional region.
Counters operating in this region are proportional counters.

5. 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

6. 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.

7. 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.

8. 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)

9. 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

10. Equipotentials

11. 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

12. 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.

13. 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.

14. Drift Residuals
With multiple drift cells resolution can be determined through residuals.
Three displacements
Ideal residual equals 0
s = 0.31 mm

15. 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.

16. Charge Ratios
The signal is not as linear in this coordinate.

17. 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

18. 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

19. 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

20. 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.