Nothing on this page measures what it reports. A radius comes from three points, a position from a wire number, a coordinate from a drift time — every instrument here reports an inference.
🎯 Why this matters
Because each number is inferred, its uncertainty is inherited from the step that produced it. Improving one of these detectors nearly always means changing what gets counted rather than counting the same thing more carefully.§1.13b left one thing unfinished: a chamber photograph shows a curved track, and turns a radius into a momentum — but nobody measures a radius. You measure a handful of points. This page starts by closing that gap — the trick is a quantity called the sagitta sagitta the height of a circular arc above its own chord, s ≈ L²/8R; the quantity actually measured when a track's curvature is extracted from a few points, because it is a stable difference of coordinates rather than an ill-conditioned circle fit. defined in §1.13c — open in glossary — and then leaves photography behind for good: the rest of it is the family of detectors that replaced film with wires, amplifiers and a clock.
Example 1.15 — how you actually get from three points
🪜 From three measured points to a momentum
Step 1 of 6 — The problem
Why you may do this: A circle through three points is elementary geometry, but the radius comes out as a ratio of nearly equal large numbers — numerically horrible when the arc is almost straight, which is exactly the case that matters. So do not compute R directly.
For a 1 GeV track in 1.5 T, R is 2.2 m and the chamber is 0.5 m across. You are fitting a circle to an arc that spans 13° of it.
Bettini Example 1.15 and Fig. 1.22, worked step by step. The geometry is trivial; the reason to do it this way is numerical, and the book does not say so.
Read it as a design equation, not a result: it tells you how big a detector has to be to measure a given momentum to a given accuracy.
Every symbol, one at a time
Hover or tap a symbol above — it lights up in the equation and its meaning, units and type appear here.
💡 What this really says — a spectrometer resolves 1/p, so the error on p grows with p
A magnetic spectrometer measures curvature, and curvature is . So the quantity you actually resolve is , uniformly — which means the relative error on itself grows in proportion to :
At some momentum the sagitta drops below your point resolution and the track is simply a straight line with error bars. That momentum is what “the reach of the tracker” means. Everything about spectrometer design — bigger magnets, wider trackers, finer sensors — is an attempt to push that number up, and each of the three costs money differently.
🧲 Momentum from a bent track
R = p/(0.3 B) = 2.222 m s = 0.3 B L²/(8 p) = 14.0625 mm (exact R[1−cos(θ/2)] = 14.0477 mm) θ = L/R = 225.00 mrad σ_s = σ√(3/2) = 0.1225 mm δp/p = σ_s/s = 0.87 %
✓ A usable measurement. Double p and the sagitta halves, so δp/p grows linearly with p — the opposite of a calorimeter, whose σ/E improves as 1/√E (§1.13d).
Field fills the tracking volume, so the track is an arc. You fit a circle to measured points; with only three, the sagitta IS the measurement: s = (y₁+y₃)/2 − y₂, whose error is σ√(3/2).
🔢 Worked example — where a 1.5 T, 0.5 m tracker gives up
Take T, m, and points measured to mm, so mm.
| 1 GeV | 2.22 m | 14.06 mm | 0.87 % |
| 10 GeV | 22.2 m | 1.41 mm | 8.7 % |
| 100 GeV | 222 m | 0.141 mm | 87 % |
The sagitta at 100 GeV is comparable to the point resolution itself: the measurement has failed. Note that the failure is not sudden and it is not a threshold — it is a straight line through the origin on a plot of against , and you simply choose where along it you are willing to stop.
Contrast a calorimeter (§1.13d), whose resolution improves as because it counts shower particles. That is why every large experiment measures low-momentum particles with the tracker and high-energy ones with the calorimeter: the two curves cross.
Ionisation detectors: one idea, five instruments
An ionisation detector is two or more electrodes with a fluid — gas or liquid — between them. A charged particle leaves ion–electron pairs; the field sweeps them apart before they recombine; the motion of the charge induces a current in the electrodes. Electrons drift much faster than ions, so theirs is the fast signal.
📐 Physics you need first — drift, and why gas amplifies
Drift, not acceleration. An electron in a gas under a field does not accelerate freely; it is scattered constantly by the gas molecules and reaches a steady average velocity, the drift velocity . Typical values are tens of mm per microsecond for electrons and a thousand times slower for the ions, which are heavy and lumbering. This is the same physics as carrier drift in a semiconductor, with the same name and the same mobility .
Multiplication. Between two collisions an electron picks up energy , where is its mean free path. Make large enough that this exceeds the ionisation energy of the gas, and the electron ionises on impact: now there are two, then four. The number grows exponentially with distance — the Townsend avalanche — and the exponent depends steeply on .
So the whole design problem is: where is the field strong? In a coaxial geometry with a thin wire the answer is “only very near the wire”, because . That is not a detail. It is what makes gas detectors possible: the volume is a quiet drift region almost everywhere, and an amplifier only in the last hundred micrometres.
⚡ One device, five times — the gas ionisation family
G. Charpak, CERN, from 1967 (Charpak et al. 1968); first instrumented chambers, Amato & Petrucci 1968
Why it exists: One proportional counter per wire, sharing a gas volume. The field shape carves the volume into a cell per wire, so several square metres can be read out — straight into a computer, with no film and no scanners.
- Gain
- ≈ 10⁵
- Reads out
- x from which wire fired; z by construction. A second chamber rotated 90° gives y
- Resolution
- σ = pitch/√12 — for a 2 mm pitch, 0.58 mm
- Costs you
- digital: the answer is a wire number, so the resolution is quantisation noise and nothing else
- E(r) in a coaxial cell
⚙️ Engineer’s bridge — the wire is the front-end amplifier
Every one of these devices is a charge-sensitive analogue front end built out of geometry instead of transistors:
| The chamber | Its electronics analogue |
|---|---|
| ionisation electrons drifting in a uniform field | a sample propagating down a delay line at a known velocity |
| the field near the wire | a gain stage placed at exactly one point in that line |
| Townsend multiplication, gain ~10⁵ | a pre-amplifier with a gain you set by a voltage |
| the wire pitch | the sampling interval |
| which wire fired | the quantised output — an ADC code |
| drift time | the analogue residual, recovered by a TDC |
That last row is the whole trick of the drift chamber, and it is a familiar one: you have a coarse quantiser (the wire) and a fine timing measurement, so you use the timing to interpolate inside one quantisation bin. Sub-LSB resolution from a time measurement is exactly what a time-to-digital converter, a delta-sigma modulator or a vernier delay line does. The chamber got there in 1971.
Where it breaks: the wire is not a linear amplifier. Gas gain depends exponentially on the field and on the gas density, so it drifts with temperature and atmospheric pressure and has to be tracked in situ rather than specified. It also saturates: at high ionisation density the space charge of the avalanche screens the wire and the response goes nonlinear, which is precisely where dE/dx measurement is most wanted. An op-amp has a gain–bandwidth product on a datasheet; a proportional wire has a working point that the weather moves.
The Geiger counter: a detector that refuses to measure
The simplest ionisation counter (Geiger 1908, in its modern form Geiger & Mueller 1928) is a grounded metal tube with an insulated central wire of order 100 μm diameter at about +1000 V, filled with argon plus an alcohol vapour whose job is to quench the discharge.
Click a numbered marker for what that piece does.
The proportional counter: the same tube, tamed
S. Curran’s gas-filled proportional counter (Glasgow, 1948) uses the same cylindrical geometry at a lower voltage with a much thinner anode wire. The primary electrons still drift in and still avalanche, but the avalanche now stays inside a small region around the anode instead of propagating along it. The total separated charge is then proportional to the primary ionisation — proportional charge amplification proportional charge amplification gas multiplication confined to a small region around a thin anode wire, so the total separated charge stays proportional to the primary ionisation; the difference between a proportional counter and a Geiger counter is only where the avalanche is allowed to stop. defined in §1.13c — open in glossary — so the pulse height finally means something.
Then comes a genuinely surprising result. The voltage pulse is produced by the motion of charges of both signs: electrons rushing to the anode (fast, high drift velocity) and positive ions crawling away from it (slow). Intuition says the fast electrons dominate. They do not.
Rossi & Staub (1949). The contribution of each charge is proportional to the potential difference it traverses, not to how fast it gets there.
Every symbol, one at a time
Hover or tap a symbol above — it lights up in the equation and its meaning, units and type appear here.
💡 What this really says — why the slow charges win
Induced charge is not about speed. A charge moving through a potential difference induces a signal proportional to , however long it takes. And the potential in a coaxial cell goes as , so:
- the electrons are born at μm and travel inward to μm — a span of in log-radius;
- the ions are born at the same place and travel outward all the way to mm — a span of .
Ratio 16. The electrons are fast but they are already nearly at the anode, so there is almost no potential left for them to fall through. Being close to the electrode is worthless; the signal is the journey, not the speed.
This is the Shockley–Ramo theorem, and it applies unchanged to silicon detectors in §1.13d and to every solid-state radiation sensor. It also explains a practical annoyance: the useful part of the pulse comes from the slowest carriers, so chamber signals have long ion tails that the electronics must clip.
Chambers with several parallel anode wires had been used since the 1950s, mostly for energy measurements. A pulse is induced on the neighbouring wires too — but for those wires the ions are approaching rather than receding, so the induced pulse has the opposite (positive) polarity. The read-out electronics can discard it on sign alone, with no shielding between wires. That single fact is what makes wires only 2 mm apart practical.
Multi-wire proportional chambers: the end of film
G. Charpak began developing MWPCs multi-wire proportional chamber Charpak's 1967 tracking detector: a plane of anode wires a couple of millimetres apart, each its own proportional counter, giving one coordinate with resolution pitch/√12; it replaced film because integrated circuits made thousands of read-out channels affordable. defined in §1.13c — open in glossary for tracking at CERN in 1967. The idea needed nothing new in gas physics — it needed integrated circuits, which became commercially affordable at exactly the right moment.
The geometry is a plane of anode wires 10–30 μm thick at a pitch of typically 2 mm, sandwiched between two cathode planes several millimetres away. The field shape carves the gas volume into one cell per wire: the ionisation from a given segment of track drifts to that cell’s wire and avalanches there, with a gain of order .
📏 Where the resolution comes from — and why an engineer already knows it
The MWPC’s output is a wire number. Any track passing anywhere within a cell gives the same answer, so the position error is the spread of a uniform distribution of width equal to the pitch :
That is the standard deviation of a uniform distribution on — the identical formula to quantisation noise in an ADC, where the error of rounding to the nearest LSB has r.m.s. . An MWPC is a one-dimensional flash ADC whose comparators are wires, and its resolution is its LSB over root twelve. Nothing about gas enters.
The book quotes 0.6 mm, which is 0.577 rounded.
The coordinate perpendicular to the wires comes from which wire fired; normal to the plane is fixed by construction. The third coordinate requires at least a second chamber with its wires rotated 90°. Large areas — several square metres — became practical, and the data went straight into a computer. After §1.13b, that is the sentence that matters: no film, no scanning tables, no rooms of people.
⚙️ Engineer’s bridge — Charpak’s real bottleneck was Moore’s law
Every wire needs its own channel: a charge amplifier for negative-polarity pulses and pulse-shape discrimination in the analogue stage, then digitisation, delay, logic and storage. Thousands of channels per chamber.
The book is precise about the timing, and it is worth dwelling on. Integrated circuits carrying hundreds of transistors per chip became cheap in 1968, driven substantially by US aerospace programmes — and the first MWPCs with associated electronics were built by Amato and Petrucci that same year. Charpak’s chambers were not waiting on physics. They were waiting on semiconductor economics.
The relationship never ended. Every subsequent jump in this chapter — drift-time digitisation, the TPC’s megachannel read-out, silicon strips (§1.13d), the LHC trigger (§9.14) — is enabled by the integration scale of the year it was designed. CERN’s investment in custom integrated circuits is a large part of why the MWPC succeeded, and it is essentially an in-house ASIC programme.
Where it breaks: “wait for electronics to get cheaper” works only while the channel count grows more slowly than the cost per channel falls. In tracking it does not — going from wires at millimetre pitch to pixels at 100 μm multiplied the channels by while the per-channel cost fell by rather less, which is why CMS has 70 million channels and a power budget measured in tens of kilowatts inside a volume that must also be nearly transparent. Moore’s law was necessary and never sufficient.
Drift chambers: use the clock you were throwing away
A drift chamber drift chamber an MWPC that also measures the electron drift time, converting it to a distance through a constant drift velocity; 4 ns timing at 50 mm/μs gives 200 μm, about three times better than the wire pitch alone. defined in §1.13c — open in glossary (Heintze and Walenta, Heidelberg 1971) is an MWPC that also records when the signal arrived. One coordinate is still the wire; the second, perpendicular to the wire in the plane of the chamber, is the drift time multiplied by the drift velocity.
For that to work, the drift velocity must be constant across the cell, which requires a uniform field — obtained by putting field wires on the two sides of each cell at gradually diminishing potentials — and a gas mixture chosen so that saturates. The anode–cathode distance is then several centimetres rather than millimetres.
🔢 Worked example — 4 nanoseconds buys you a factor of three
With a typical drift velocity of 50 mm μs⁻¹ and drift-time measurement good to 4 ns:
Against the MWPC’s 577 μm that is a factor 2.9 — the book’s “about three times better”. And it comes from a cheaper resource: 4 ns timing was ordinary electronics in 1971, whereas halving the wire pitch to 1 mm would have doubled the channel count for only a factor .
Integrating the current from the wire instead of just timing it gives the total induced charge, hence , hence particle identification (§1.11) — from the same wire, at no extra cost in channels.
A complete spectrometer
Put chambers before and after a dipole magnet and you have an instrument that measures momentum and the sign of the charge.
Click a numbered marker for what that piece does.
The product BL — properly ∫B·dl — is the magnet's BENDING POWER, or the particle's RIGIDITY when you look at it from the particle's side.
Every symbol, one at a time
Hover or tap a symbol above — it lights up in the equation and its meaning, units and type appear here.
The quantity , more generally , has a name because it is the only combination that matters: a short strong magnet and a long weak one with the same bending power bending power ∫B·dl through a magnet, the only combination of field and length that matters for deflection: θ ≈ 0.3∫B·dl/p. Seen from the particle rather than the magnet, the same quantity is called rigidity. defined in §1.13c — open in glossary bend a given momentum by the same angle.
⚠️ The book’s 100 mrad
p. 59 works the example: a magnet of bending power T m and a particle of GeV. It says the particle “is bent by 100 mrad, corresponding to a lateral shift, for example at 5 m after the magnet, of 50 mm”.
Equation (1.121) gives
and the sentence contradicts itself: 100 mrad at 5 m would be 500 mm, not 50. The 50 mm is right and the 10 mrad is right; the printed “100 mrad” is the slip. Nothing downstream is affected — with a 100 μm resolution on a 50 mm shift you get either way — but the arithmetic does not close as printed.
Set the widget above to the “∫Bdl = 1 T m at 30 GeV” preset to watch it come out at 10.0 mrad.
Time projection chambers: three dimensions from one volume
The time projection chamber time projection chamber a cubic-metre gas volume in a uniform field giving all three track coordinates plus dE/dx from one exposure: wire number, drift time and charge division along the wire; its tens-of-microseconds drift makes it unusable at LHC luminosity. defined in §1.13c — open in glossary (W. W. Allison and colleagues at Oxford from 1972; D. Nygren in the USA from 1976) abandons cells altogether. Anode and cathode are parallel planes metres apart, and the anode carries parallel sense wires at about 2 mm spacing. An ionising particle leaves a trail through cubic metres of gas; the electrons drift the whole way to the endplate; and there:
- , perpendicular to the wires, comes from which wire — as in an MWPC;
- , along the drift field, comes from the drift time — as in a drift chamber;
- , along the wire, comes from charge division: read both ends of the wire and take the ratio, good to about 10 % of the wire length;
- and the specific ionisation on top of all that, giving particle identification.
A single gas volume, no film, full three-dimensional images. Cylindrical TPCs became the standard central detector of collider experiments, immersed in a magnetic field so that the momenta come out too.
⚙️ Engineer’s bridge — why there is no TPC at the LHC
The book states flatly that a TPC “is not possible at LHC due to its high luminosity”. The reason is a number you can compute in one line.
A 2 m drift at 50 mm μs⁻¹ takes 40 μs. The LHC delivers a bunch crossing every 25 ns. So one TPC exposure spans
each with tens of interactions, all superimposed in the same drifting gas with no way to tell them apart. The TPC is a frame-based sensor with a 40 μs exposure being asked to work at 40 MHz — a rolling-shutter problem, and a 1600-fold one.
The failure is architectural, not technological. Note the family resemblance to the bubble chamber (§1.13b), which also imaged everything in a volume and also died of rate. Each generation of detector buys resolution by integrating over a volume and over time, and each is eventually killed by the next machine’s luminosity.
Where it breaks: it is worth being careful about what killed the TPC, because “each generation is killed by luminosity” is too neat. The TPC is not obsolete — ALICE runs the largest one ever built, because heavy-ion collisions deliver a few hundred events per second with thousands of tracks each, and there the trade inverts: an enormous number of tracks per event and a modest event rate is exactly what a TPC is for. What kills a detector is not luminosity but the product of rate and occupancy, and the same machine can be hostile to a technology in one experiment and ideal for it in another.
Electro-luminescence mode
Both drift chambers and TPCs can be run so that the field near the sense wires is lower: not enough to multiply the charge, but enough for the drifting electrons to excite the gas, which then emits light. In xenon about 1000 photons per drifting electron are produced. Introduced for drift chambers by Conde and Policarpo (1967) and for TPCs by Nygren (2009) and Gómez-Cadenas et al. (2012).
The payoff is statistical: charge amplification has large avalanche-gain fluctuations, and excitation does not, so the energy resolution is far better. For tracking, the light is read by a two-dimensional array of photo-sensors in the – plane, with the drift time still supplying .
🔬 Experiment card — an EL TPC prototype (Fig. 1.27, NEXT)
Apparatus
5 kg of xenon gas at 1 MPa, read out by silicon photomultipliers of 1 mm² area arranged in a square pattern with 10 mm spacing, plus the drift time for the third coordinate.What is measured
The three projections (–, –, –) of the track of a single 2.4 MeV electron brought to rest in the gas, with the grey level along the track proportional to the specific ionisation.What it shows
Two things at once, both from earlier in this chapter. The track visibly wanders — multiple Coulomb scattering (§1.8), severe because the electron is light and slow. And the ionisation is near-minimum along most of the path but piles up at the very end: the Bragg peak, which is nothing more than the rise of Bethe–Bloch (§1.11) as the particle runs out of speed.Why it matters
That end-of-range signature is a topological signal: it is how a detector like this tells one electron from two, which is the whole basis of neutrinoless double-β searches (§10.5).The family, side by side
| Device↕ | Year↕ | What comes out↕ | Resolution↕ | What it cost↕ |
|---|---|---|---|---|
| Geiger counter | 1908 / 1928 | yes-no, and when | ≈ 1 μs in time; no position | everything else — the output is independent of what was deposited |
| Proportional counter | 1948 | charge ∝ primary ionisation | energy; still no position | the voltage must be held below the Geiger regime |
| MWPC | 1967–68 | which wire (one coordinate) | pitch/√12 = 0.58 mm at 2 mm pitch | |
| Drift chamber | 1971 | wire + drift time (two coordinates), plus dE/dx | 200 μm from 4 ns timing | needs a uniform field and a saturating gas |
| Time projection chamber | 1972–81 | x, y, z and dE/dx from one volume of cubic metres | tens of μs per exposure — unusable above a certain luminosity |
Read down the last column. Every step buys information with a different currency — voltage stability, channel count, timing precision, exposure time — and the one that eventually runs out is <strong>exposure time</strong>. §1.13d picks the story up with silicon, where the drift distance is a hundred micrometres instead of two metres.
Reproduce it
import numpy as np
# proportional counter: Rossi & Staub (1949)
ra, r0, rc = 20e-6, 30e-6, 20e-3 # anode, avalanche, cathode radii
R = np.log(rc/r0)/np.log(r0/ra)
print(f"proportional counter: ion/electron signal ratio = {R:.2f}"
f" -> ions carry {R/(1+R)*100:.1f} %")
pitch = 2.0 # mm
print(f"MWPC, {pitch:.0f} mm pitch: sigma = {pitch/np.sqrt(12):.3f} mm"
f" (the book rounds to 0.6)")
vd, dt = 50.0, 4.0 # mm/us, ns
sig_z = vd*dt/1000 # mm
print(f"drift chamber: {vd:.0f} mm/us x {dt:.0f} ns = {sig_z*1000:.0f} um, "
f"i.e. {pitch/np.sqrt(12)/sig_z:.1f}x better than the MWPC")
BL, p, D, sig = 1.0, 30.0, 5.0, 0.1 # T m, GeV, m, mm
theta = 0.3*BL/p
print(f"Eq 1.121 with BL = {BL:.0f} T m, p = {p:.0f} GeV: "
f"theta = {theta*1e3:.1f} mrad (the book prints 100)")
print(f" lateral shift at {D:.0f} m = {theta*D*1e3:.1f} mm"
f" <- this is the book's own number, and it needs 10 mrad")
print(f" with {sig} mm resolution: dp/p = {sig/(theta*D*1e3)*100:.2f} %")
B, L, sig = 1.5, 0.5, 0.1 # T, m, mm per point
sig_s = sig*np.sqrt(1.5) # 3-point sagitta error
print(f"sagitta, B = {B} T, L = {L} m, sigma = {sig} mm (3 points):")
for p in (1.0, 10.0, 100.0):
s = 0.3*B*L**2/(8*p)*1000 # mm
print(f" {p:5.0f} GeV: s = {s:6.3f} mm, dp/p = {sig_s/s*100:5.2f} %")
drift, vd, bx = 2.0, 50.0, 25.0 # m, mm/us, ns
t = drift*1000/vd
print(f"TPC: {drift:.0f} m drift at {vd:.0f} mm/us = {t:.0f} us = "
f"{t*1000/bx:.0f} LHC bunch crossings of {bx:.0f} ns")proportional counter: ion/electron signal ratio = 16.04 -> ions carry 94.1 %
MWPC, 2 mm pitch: sigma = 0.577 mm (the book rounds to 0.6)
drift chamber: 50 mm/us x 4 ns = 200 um, i.e. 2.9x better than the MWPC
Eq 1.121 with BL = 1 T m, p = 30 GeV: theta = 10.0 mrad (the book prints 100)
lateral shift at 5 m = 50.0 mm <- this is the book's own number, and it needs 10 mrad
with 0.1 mm resolution: dp/p = 0.20 %
sagitta, B = 1.5 T, L = 0.5 m, sigma = 0.1 mm (3 points):
1 GeV: s = 14.062 mm, dp/p = 0.87 %
10 GeV: s = 1.406 mm, dp/p = 8.71 %
100 GeV: s = 0.141 mm, dp/p = 87.09 %
TPC: 2 m drift at 50 mm/us = 40 us = 1600 LHC bunch crossings of 25 ns Erratum — the deflection angle on p. 59, contradicted by its own sentence
The text reads: “A particle of momentum GeV is bent by 100 mrad, corresponding to a lateral shift, for example at 5 m after the magnet, of 50 mm.”
Those two numbers cannot both be right. A 100 mrad deflection gives mm, not 50. Eq. (1.121) settles which one is wrong:
and mm. The 50 mm is right; the angle is the slip. The momentum resolution that follows, δp/p ≈ 0.2 % for a 100 μm position resolution, is unaffected — it depends on the shift, not on the angle.
🔑 If you remember only three things
-
One tube, five instruments, and the knob is the voltage. Turn it far enough and the Geiger counter saturates, which buys a signal every time at the cost of ever knowing how much charge arrived.
-
The third coordinate is a clock. Drift time turns a plane of wires into a three-dimensional image, so a TPC’s resolution is set by timing electronics rather than by geometry.
-
A tracker gives up at high momentum, not at low. The track straightens as it gets stiffer, so the fastest particle is the hardest one to measure.
Where this goes next
- §1.13d replaces the two-metre drift with a hundred micrometres of depleted silicon, and then stops tracking particles altogether and starts absorbing them.
- §9.14 is what all of this becomes at the LHC, trigger included.
- §4.10 and §8.6 are the measurements that the vertex resolution of the next page made possible.
✅ Check yourself — wires, drift and the bending power
0/6 answered · 0 correct
1.In the widget, set B = 1.5 T, L = 0.5 m, σ = 0.1 mm and sweep p from 1 to 100 GeV. What happens to δp/p, and why?
2.In a proportional counter the ions supply about 94 % of the signal and the electrons only 6 %, even though the electrons are a thousand times faster. Why?
3.An MWPC with 2 mm wire pitch has a resolution of 0.58 mm. Where does the √12 come from?
4.A drift chamber gets 200 μm from 50 mm/μs drift velocity and 4 ns timing. What is the engineering lesson relative to just building a finer MWPC?
5.A TPC gives full 3-D tracks plus dE/dx from one gas volume. Why is there none at the LHC?
6.The book says a 30 GeV particle in a magnet of ∫Bdl = 1 T m is bent by 100 mrad, giving a 50 mm shift 5 m downstream. What is wrong?