SLD Central Drift Chamber

Drift clock

0.000 μs

The particles cross the whole chamber in ~3 ns; the ionization they leave needs up to 3.7 μs to drift the 29.5 mm half-cell at 7.9 μm/ns. Replay is slowed ~10⁵× so the two time scales are visible: tracks flash, then hits latch one by one as their charge arrives at a wire.

TDC spectrum (live)

Arrival times of all latched hits. It fills flat because the drift velocity is constant in the CO₂ gas — this is exactly the spectrum a real chamber integrates to calibrate its time→distance relation.

One cell, magnified

A — axial superlayer (measures r–φ only) U — stereo +41 mrad V — stereo −41 mrad hit color = drift distance (short→long)

Stereo shift: with the exaggeration toggle on, U hits displace one way in φ and V hits the other, by δφ = tan(41 mrad)·tanλ (λ = track dip angle). Axial hits don’t move. Measuring that U/V split is how the chamber gets z along the track — the real shift is ~40× smaller than drawn.

tracks 10 replay speed 4 stereo shift ×40

Cell readout

Axial (A) cell: wires strung parallel to the beam. The wire sits at the same φ for every z — a hit gives a precise r–φ point but carries no z information from the drift time alone.

Stereo (U/V) cell: the whole cell is strung skewed by ±41 mrad, so its transverse position slides by z·tan(41 mrad) ≈ 41 μm per mm of z — ±37 mm at the endplates, more than half a cell width. Move the z slider: the cell (solid) slides past its z = 0 outline (dashed) while the track stays put, so the measured drift distance changes with z. Comparing stereo and axial measurements of the same track solves for z.

sense wires (8 per cell, 5 mm pitch) guard / field wires drifting electron clusters (~48/cm) avalanche (gain ~2×10⁵)

The two waveforms below the cell are the two ends of the hit wire — same pulses, different sizes. Tab 3 dissects why.

track angle 12° z of this section 0.00 m

Estimator

Why the ratio measures z. The avalanche injects charge Q at position z on a resistive wire (tungsten, 337.5 Ω over 1.8 m, terminated by 30 Ω preamps: ρ = R_in/R_w = 0.089). The wire is a current divider: each end receives charge in inverse proportion to the resistance it sees, so Q_R/Q = (z/L + ρ)/(1 + 2ρ) — linear in z. Invert it and you have ẑ.

Why the pulse shapes differ. Both ends see the same avalanche current, so to first order the pulses are copies scaled by the division ratio — the areas carry the z information. Second order: the wire is an RC line, so the pulse reaching the far end is slightly dispersed (slower rise, lower peak, same area). That is why SLD divides integrated charge, which ignores dispersion, rather than pulse heights.

What limits it. Johnson noise of the wire itself: σ_Q ≈ 3.3 fC per end (0.45 μs gate) on a 0.67 pC hit → σ_z ≈ 7.4 mm = 0.41% of the wire — the benchmark tool’s number. Fire a burst to see the scatter build that band.

true z 0.54 m noise

TDC readout

Where t₀ comes from. The SLC delivers beam crossings at known times, so the accelerator itself provides the start signal. The chamber measures the stop: the waveform sampler (200 MHz, 5 ns bins) watches each wire and marks when the summed pulse first crosses threshold (~3 electrons).

Time → distance. In this gas v_d is constant, so dˆ = v_d·(t_stop − t₀). What smears it: the first cluster isn’t exactly at the point of closest approach (ionization statistics, ~48 clusters/cm), diffusion adds σ = 68√d μm, and the 5 ns sampling contributes ~10–13 μm. Fire repeatedly and watch the residual strip build up a σ of a few tens of μm — the 100 μm budget of the real chamber includes alignment and field distortions on top.

Left–right ambiguity. A drift time alone cannot tell which side of the wire the track passed (dashed mirror track). SLD resolves it with the staggered guard wires, the 5° cell tilt, and the track fit across 8 wires.

impact parameter d 12 mm