06 Dose
Spencer–Attix cavity dose
D_med = D_gas × (L̄/ρ)_gas^med × P. Restricted stopping-power ratio with cutoff Δ.
Listen
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Simulation
Spencer–Attix cavity dose — Change the numbers; the scene follows.
Where it works
Water phantom
Ion chamber
In the water tank under the linac, at the ion chamber — reference dosimetry happens here.
Open this machineFormula
Variables
Results
D_med
Medium dose
0.01119Gy
Explanation
What it means
Bragg–Gray assumes the cavity does not perturb the electron fluence and uses unrestricted stopping powers. Spencer–Attix is the practical version: δ-rays above a cutoff Δ (matched to cavity size, ~10 keV for a Farmer) are treated as part of the electron field, and restricted stopping powers L_Δ are used. Every TG-51 / TRS-398 kQ is, under the hood, a Spencer–Attix ratio evaluated in Monte Carlo. This is a working relation in Dosimetry.
Where it is used
Clinically it sits on the Water phantom — Ion chamber. In the water tank under the linac, at the ion chamber — reference dosimetry happens here. Dosimetry is the chamber in water under the linac, or the well counter in the hot lab: TG-51, TRS-398, kerma, and recombination. These numbers are the calibration the rest of the department borrows.
Water phantom · Open this machineHow to use it
Enter dose in gas (from J / m, with W/e), the restricted stopping-power ratio, and a combined perturbation P (Pwall Pfl Pgr Pcel…). Read D_med. A Co-60 Farmer in water has (L̄/ρ) ≈ 1.127 and P ≈ 0.99. Change one input and watch the curve and the simulation follow.
Symbols
- D_gasGas dose0.01 Gy
- (L̄/ρ)Stopping-power ratio1.127
- PPerturbation product0.993
Worked example
A typical case from the default values: D_gas = 0.01 Gy (Gas dose); (L̄/ρ) = 1.127 (Stopping-power ratio); P = 0.993 (Perturbation product). Substituting into the relation gives D_med = 0.01119 Gy. These are teaching numbers — align them with your machine.
Typical values give
- D_med = 0.01119Gy
Where it comes from
The displayed formula is the working relation. D_med = D_gas × (L̄/ρ)_gas^med × P. Restricted stopping-power ratio with cutoff Δ. Usual reference: Spencer & Attix 1955 / Attix. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: Spencer & Attix 1955 / Attix
Assumptions & limits
Δ is not an input — you must supply an (L̄/ρ) that already corresponds to a chosen Δ. Fano’s theorem says a density (not Z) perturbation of a homogeneous medium does not change fluence; real chambers violate that via the wall and electrode.
Pitfalls
kQ is for that chamber and that beam quality — not a neighbour's value. Polarity and recombination are measured, not copied. A ⁶⁰Co N_D,w is not an MV calibration until kQ is applied. Δ is not an input — you must supply an (L̄/ρ) that already corresponds to a chosen Δ. Fano’s theorem says a density (not Z) perturbation of a homogeneous medium does not change fluence; real chambers violate that via the wall and electrode.
Keep this
Trace every gray back to a protocol, a chamber, and a quality index. Δ is not an input — you must supply an (L̄/ρ) that already corresponds to a chosen Δ. Fano’s theorem says a density (not Z) perturbation of a homogeneous medium does not change fluence; real chambers violate that via the wall and electrode.
In this specialty