# Cavity Theory

Cavity theory is the basis of operation for ionization chambers used in reference dosimetry. Cavity theory relates measured dose in a cavity, such as an ion chamber, to dose at the same point in the medium in absence of the cavity.

### Bragg-Gray Cavity Theory

Bragg-Gray (BG) theory relates dose to the medium, Dmed, to dose to the cavity fill gas, Dgas, via the ratio of mass collision stopping powers between the medium and gas, .

#### Bragg-Gray Assumptions

1. Charged particle equilibrium (CPE) or transient charged particle equilibrium (TCPE) exist
2. All electrons causing ionization in the cavity arise from phantom material
3. Secondary electron spectrum is unchanged by presence of the cavity
4. Energy of secondary electrons created inside the cavity are deposited locally
• Neglects secondary electrons (delta rays) generated within the cavity as a result of interactions with scattered electrons

#### Bragg-Gray Limitations

Because of contradictory and non-physical assumptions, Bragg-Gray theory is only an approximate solution for physical systems.

Assumptions 2 and 3 imply a need for a small cavity volume while requirement 4 requires a large volume to collect all electrons. These conditions cannot be met simultaneously.

Requirement 3, that the spectrum be unchanged, would mean that no energy could be collected to rigorously meet this theory. This is generally disregarded as the effect is minimal with a small cavity.

### Spencer-Attix Cavity Theory

The Spencer-Attix formulation of cavity theory resolves the issues of the Bragg-Gray so that it applies for small cavities.

•  is the ratio of restricted mass collision stopping power from the medium to the cavity fill gas.
• Restricted mass collision stopping power uses a cutoff energy, Δ, which removes the requirement that secondary electrons deposit their energy locally.

#### Spencer-Attix Requirements

1. Requires charged particle equilibrium (CPE) or transient charged particle equilibrium (TCPE)
2. All electrons causing ionization in the cavity arise from phantom material
3. Secondary electron spectrum is unchanged by presence of the cavity

### Burlin Cavity Theory

The Burlin formulation generalizes cavity theory for large and small cavities.

• is the ratio of restricted mass collision stopping power from the medium to the cavity fill gas.
• d is a parameter related to cavity size
• d = 1 for small cavities
• d approaches 0 for large cavities
• is the ratio of mass energy absorption coefficients from the medium to gas.

#### Burlin Requirements

1. Charged particle equilibrium (CPE) exists in medium and cavity

#### Restricted Mass Collision Stopping Power (L/ρ)

Restricted mass collision stopping power introduces a cutoff energy, Δ, typically taken to be 10-20keV.

• Electrons with energy <Δ are assumed to deposit their energy where created
• Electrons with energy >Δ dissipate their energy through the Continuous Slowing Down Approximation (CSDA)

Key Point: Bragg-Gray cavity theory provides an approximate theory of operation for ionization but requires contradictory assumptions. Spencer-Attix and Burlin theories improve upon this by assuming that low energy electrons deposit their energy locally.

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