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

V

E

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

)/ln( abr

VE

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.

• For 90% Ar, 10% CO2

– A = 14 / (cm-Torr)

– B = 180 V/(cm-Torr)

Gas Gain

• Gain in the proportional region is exponential with the wire radius a.

• The Townsend coefficient depends on the field E.

– Adjusted by pressure P

aKeG

EBPAeP

/

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 kVcathode pads anode wire

D0 central muon drift cell

grounded shell

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

pw VVV 0

)/)((

1

0

0

EBPaV

dV

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

= 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

= 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.