Tracking Detectors: Tracking Detectors: Proportional and Drift ChambersProportional and Drift Chambers

Prof. Robin D. ErbacherUniversity of California, Davis

References: R. Fernow, Introduction to Experimental Particle Physics, Ch. 9, 10 D. Green, The Physics of Particle Detectors, Ch. 8 K. Kleinknecht, Ch. 3 http://pdg.lbl.gov/2004/reviews/pardetrpp.pdf

How we measure particle momenta & ID (in some cases): 2 types of tracking detectors

Radiative Energy LossOptical behavior of medium: characterized by complex dielectric constant

Sometimes instead of ionizing an atom or exciting matter, the photon can escape the medium: (transition, C, etc).

Nuclear InteractionsWe have seen that the electromagnetic interaction is responsible for:

• Energy loss of charged particles• Small angle scattering of charged particles• Production and interaction of photons

In some processes, the nuclear interaction dominates:• Particle creation reactions• Interactions at high energy / large momentum transfer• Interactions of neutral particles other than photons

Nuclear cross section:

Goes as A2/3 times Compton wavelength2 of proton

Brem. cross section:

Goes as Z2 due to coherence, 3 penalty due to 3 vertices

For A~3(Li), they’re comparable, for A>3, X0(Brem) dominates

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σN ~ A2

3Dp2

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σB ~ Zα( )2αDe

2

Strong InteractionsHadrons are subject to the strong interaction in matter. The neutron: ideal probe since no real em interactions.

For attenuation in matter, the absorption cross section is:

σabs = σT - σel - σq

Here σel is coherent elastic scattering off a nucleus, and

σq is quasielastic scattering from individual nucleons.

Absorption lengths of particles:

For particle production, σT(pp, pn)~ln(s), σT(n-nucl)~A2/3.The e+e- or e-nucleon initial state can couple to hadronic final state via a virtual , and apart from resonances, the e+e- hadronic production cross section falls off as s-1.

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λN =A

NAσ abs

Strong Interactions

• What is λn? The mean distance (in cm, or g/cm2) a particle travels in a material before encountering a nucleus

• Nuclei act as hard-sphere scattering centers

• Cross section is proportional to nuclear radius squared, or Z2/3

material

X0 (g/cm2) λn (g/cm2)

H2 63 52.4

Al 24 106

Fe 13.8 132

Pb 6.3 193

Nuclear interaction length:

lead ~ steel: 17 cm

Weak InteractionsThe 2nd fundamental nuclear interaction: weak interaction.Important for interactions, decays of quasistable particles.

Neutrinos are direct probes of the weak interaction, but do not interact with matter very easily.

Weak interaction can play role in charged lepton interactions: does not preserve parity. Thus, signatures separating weak from em interaction are parity-violating. Asymmetries: polarized e-N scattering (SLAC) and muon pair production in e+e- collisions at PETRA.

Two major classes of weak interaction known:Charged current: e-nucleon via W e (lepton # cons.)Neutral current: e-nucleon via Z0, final state lepton neutral: e

Tracking:Proportional Counters

and Drift Chambers

Charged Particle Tracking• Two main types: gas wire chambers, silicon

• (We heard about silicon last time)

• Innermost detectors: want precise trackingSi!

• Outer detectors: silicon too expensive!

• Basic design: ionization chamber with HV sense wire:

amplification of103 - 105 in high field near wire

Ionization Wire ChambersWire Chambers: Probably the most commonly used detection devices in high energy physics experiments.

The Basics of Wire Chambers:

• Charged particles travels through a volume of gas

• Gas is ionized by the passage of the particle

• Ionization drifts & diffuses in an electric (and magnetic) field toward an electrode

• Collection and amplification of anode signal charge, and charge induced on cathode creates detectable signals

• Measurement of points on trajectory determines p

Processes in GasesWhen a charged particle passes through gases subject to an E field, it loses energy by:• Elastic scattering (small)• Excitation: gas atoms/molecules excite then deexcite by emission• Ionization (most important)

Ionization: One or more electrons are liberated from atoms of the medium, leaving positive ions and electrons. Energy imparted to atom exceeds ionization potential of gas.

Ionization Potentials of Vapors -Clifton G. Found, G.E.Phys. Rev. 16, 41-53 (1920)©1920 The American Physical Society

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i = A(V + V0)3

2

Langmuir' s Eqn

Ionizationpotential

Primary Ionization Potential

Ionization Potentials of Vapors -Clifton G. Found, G.E.Phys. Rev. 16, 41-53 (1920) ©1920 The American Physical Society

Secondary and Total Specific IonizationAverage energy lost in creating ion pair ~30 eV.

Primary ionization: number of ionizing collisions per unit length for the incident particle. (Poisson distribution)

Secondary ionization: some of the electrons ( rays) have energy to cause more ionization.

Total specific ionization: total # ions actually created per unit length. (Landau distribution: long tails)

Deexcitation: Further ionization from deexcitation of meta-stable atoms (Penning effect). Example: Ne* + Ar Ne + Ar+ + e-

Peak fraction of E lost can double by adding 0.1% Ar gas.

Number of Ions v. Voltage

Simplest case:Parallel plate capacitor

Ionization chamber: Voltage increased such that the charge arriving on plates = charge formed Proportional region: Initial electrons accelerated enough to ionize more; avalanche pulse proportional to primary ionization; reaches ~108

After Ionization, What Next?Once ion pairs are created, many processes can occur:Recombination, charge exchange, attachment, absorption.Want electrons/ions to recover after signals have been read out.

Recombination of positive/negative ions to neutrals: X+ + Y- X + Y +

Electrons can be removed by recombination as well:X+ + e- X +

Add gas w/ large electron affinity:energy difference of lowest (ground) state of neutral and lowest state of

corresponding negative ion. X + e- X- + Water vapor, O2, ethanol, SF6, CCl4, freon

Charge Exchange

Another way to eliminate positive ions is throughCharge Exchange.

Ionization potential of the ion is greater than some molecule mixed with the gas, usually polyatomic gas like ethanol or methylal.

Gas quenches the ion multiplication by neutralizing ions of the main chamber gas: dissipates ionization energy by dissociating into smaller fragments and absorbs s emitted in radiative deexcitation process.

This is called a quenching gas.

Proportional ChambersConsider a simple cylindrical proportional tube of outer radius b at voltage V0 and inner (wire) of radius a at voltage zero.

Electric field inside the chamber:

a

b

V0

V=0

Charged particle -> ionization. e- move toward anode. High fields near wire->mulitiplication of e-s by collisions: at small r the energy gain can exceed ionization potential. Runaway process, like avalanche in PMTs.

Gas gain: Change dN(r) in # electrons at r in multiplication process, &

depends on first Townsend coefficient : inverse distance b/w collisions

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E = 2λ /r, V0 = 2λ ln(b /a), V(r) = V0

ln(r /a)

ln(b /a), E(r) =

V0

r ln b /a( )

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dN(r) = N(r)αdr, N(r) = N0eαr, α ~ 1/ L

ion

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Lion

Mean free path for ionization:

Typical Gas gain~105. For > r~20 pairs, or 108, Geiger region: runaway!

Pulse FormationIn the ionization chamber region, we have a gain of unity. For these field strengths, the dominant signals are due to electrons.

For proportional chambers, primary ionization electrons are multiplied due to high fields near wire, E(r)~1/r. Electrons collect on anode, ions remain, ‘sheathing” wire, moving slowly toward cathode. Moving chargesenergy changescapacitively-induced signal, dV.

Suppose multiplication takes place at N radii away r~Na. Voltage on anode due to e- and ions: V- and V+. Let qs be source charge. The induced voltage due to e- and ion motion is:

Signal due to ions dominates, as they travel all the way to the cathode.

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dV =qs

CV0

E(r)dr, V - = dVa

Na

∫ , V + = −dV( )Na

b

∫

V - =qs

C

ln(N )

ln(b /a), V + =

qs

C

ln(b /Na)

ln(b /a)>>V -

Drift Velocity and MobilityA gas with molecules of mass M has a thermal velocity vT:

For N2, vT~0.1 cm/σ (Earth escape v~1.1 cm/s). For electrons, vT~4-40 cm/σ, below the binding energy of atoms.

Wire chambers operate in an electric field: consider the drift velocity for electrons and ions in a uniform electric field. Let the mean time between collisions, , be , and the acceleration be a~eE/M. Then

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vT = 3kTM

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L /vT

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vd ~ aτ ~eE

M

L

vTUsing that the mean free path is proportional to the collision cross section: we express the drift velocity in terms of mobility.Mobility: drift velocity per unit reduced electric field E/.

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L−1≅ N0ρσ / A

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vd ~eE

M

A /N0ρσ

vT

=μE

ρHere

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≡vd

Eρ

Multiwire Proportional ChambersThe MWPC was invented by Charpak at CERN. Principle of proportional counter is extended to large areas.

Stack several wire planes up in different direction to get position location.

1992 Prize

Avalanche developing

Precision Drift Tracking

• Next idea: stack up proportional wire drift tubes, measure time of arrival of the ionization pulse

• Find track from tangents to circles

• Can get about 150 μm position resolution

• But: too much material!

Large Area Drift ChambersThe “open cell” drift chamber uses field and sense wires: field wires create shape of electric field, sense wires detect time of arrival of pulse.

This is the design of the CDF drift chamber - the cells are tilted to take

into account ExB drift!

Drift ChambersThere is an unequivocal correlation of the time difference t between the particle passage and the rising edge of the anode signal with the distance between the point of primary ionization and the anode wire in a proportional chamber.t0=initial ionization, t1=avalanche near wire begins

If the drift velocity is vD a constant, it becomes linear. Example: With constant vD~55 mm/σ, a time measurement of 4 ns can give spatial resolution ~200 m! (Typical resolutions for MWPC~0.5 mm)

To keep vD constant, keep field along direction of path constant. Impossible to do with MWPC layout! Zero field between anode wires.Change geometry: add field wire -HV between two anode wires +HV:

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z = vD (t)dtt0

t1∫ (where z is drift path)

-HV1-HV1

+HV2

Negative potentialNegative potential

Drift region Drift region

Chamber GeometriesPlanar: Large planar detectors resolution limited by spatial positioning of wires, and gravity sagging. ~100-300 m. Smaller limited by TDC resolution (>40 m) and e- diffusion.

Cylindrical: Four main types are proportional, cylindrical, jet, and TPC (time projection chamber). Used in colliding beam experiments, in conjunction with solenoidal fields.The regular cylindrical is open celled, whereas the jet chamber has radial partitions. The TPC is unique in that the electrons drift along the E and B field lines, and z coordinate is more accurate than the rest.

Proportional: These are the familiar (mainly rectangular) counters with anode wires sandwiched between cathode sheets. Simple, but not as good resolution without cathode strip readout.

Chamber Geometries

Proportional: wires between planes Jet Drift Chamber

Cylindrical Drift Chamber

+HV+HV-HV

B

EE

+++

+++

+++

+++

Time Projection Chamber