06 Dose
Recombination P_ion (pulsed)
Two-voltage technique for pulsed beams (linac): P_ion from V_H, V_L, M_H, M_L.
Listen
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Simulation
Recombination P_ion (pulsed) — 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
P_ion
Pulsed (linac)
1.0054
P_ion^{cont}
Continuous (Co-60 / kV)
1.0081
Explanation
What it means
Ion recombination is measured with the two-voltage method. For pulsed linac beams TG-51 uses P_ion = [1−(V_L/V_H)²]/[M_L/M_H − (V_L/V_H)²]. Continuous beams (Co-60, kV) use a linear voltage ratio instead of squares. 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
Take M at the clinical voltage (V_H) and at half voltage (V_L). P_ion should be 1.001–1.03. Above 1.05, drop dose-per-pulse (flattening filter free, large fields) or raise voltage. Change one input and watch the curve and the simulation follow.
Symbols
- V_HHigh voltage300 V
- V_LLow voltage150 V
- M_HReading at V_H12.5 nC
- M_LReading at V_L12.45 nC
Worked example
A typical case from the default values: V_H = 300 V (High voltage); V_L = 150 V (Low voltage); M_H = 12.5 nC (Reading at V_H); M_L = 12.45 nC (Reading at V_L). Substituting into the relation gives P_ion = 1.0054; P_ion^{cont} = 1.0081. These are teaching numbers — align them with your machine.
Typical values give
- P_ion = 1.0054
- P_ion^{cont} = 1.0081
Where it comes from
The displayed formula is the working relation. Two-voltage technique for pulsed beams (linac): P_ion from V_H, V_L, M_H, M_L. Usual reference: AAPM TG-51. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: AAPM TG-51
Assumptions & limits
Boag theory, same polarity, no charge multiplication. Does not replace a Jaffé plot when P_ion is large. Initial recombination (not Boag) can appear in proton beams.
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. Boag theory, same polarity, no charge multiplication. Does not replace a Jaffé plot when P_ion is large. Initial recombination (not Boag) can appear in proton beams.
Keep this
M_H is the reading at the higher voltage V_H. P_ion should be slightly above 1. TG-51 recommends P_ion < 1.05.
In this specialty