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1. scattering, particles reaching the downstream end of the cavity have different energies and directions than they would have in the continuous medium. This too affects backscattered fluence . So, fluence in the cavity is not the same as in the continuous medium. A similar argument is made for a cavity of Z lower than the medium. Therefore, the best that can be said is ΦT cav Φ T med: The smaller the cavity and the more similar its Z is to the Z of the medium, the more accurate is the approximation. This second BG condition is more readily satisfied for heavy particles than for electrons because heavy particles experience very small scattering angles.

2. For heavy particle beams, dose to the cavity can be due to heavy particles entering the cavity and to electrons entering the cavity from the medium. The volume of gas in practical chambers is small and lacks CPE. Charged particles tend to cross the volume rather than stop in it. Situations like this do not meet the definition of W because particles do not lose all their energy in the gas. If W is essentially independent of particle energy it has the same value whether or not the particles come to rest. This is easily demonstrated for heavy particles for which there is no bremsstrahlung radiation. Consider a beam of N heavy particles each of energy T incident on a volume of gas large enough to stop the particles as in Fig. 12.1(a). This meets the definition of W. Then, since all energy lost is to collisions ,

3. BRAGG–GRAY (BG) CAVITY THEORY Bragg and Gray set out to determine dose to a medium (such as water) irradiated by gamma rays. An air cavity of known volume in the form of an ionization chamber was placed in the medium. Dose to the air was measured from the collected charge. Gray [1] developed a method for converting this dose to dose to the continuous medium; that is, the medium without the cavity. The following is an adaptation of Gray’s work. His method was based on two conditions about the cavity. The first BG condition is that the size of the cavity is much smaller than the range of particles entering it. Dose to the cavity is, therefore, due solely to charged particles crossing it. In this way, energy lost to the cavity can be calculated from stopping power

4. In Fig. 12.1(b) the beam of N heavy particles cross a small volume of gas. This volume does not meet the definition of W since the particles do not stop in it. The N particles exit the gas with an average energy T0 and Nδ δ rays escape with an average energy Tδ . The energy NT NT NδTδ , which is also the energy absorbed. Similar to W, let W 0 be the average collision energy lost in the gas per ion pair when not all the energy is lost. So,

5. . This condition also requires that dose to the cavity from photon and neutron interactions in the cavity must be negligible. The second BG condition is that the cavity is so small that it does not disturb the distribution of the particles crossing it in terms of their directions and velocities. The cavity must, therefore, have the same scattering properties as the medium. When this is true, the fluence of particles in the cavity is the same as in the continuous medium. Gray recognized that since the cavity is not exactly the same as the medium it scatters particles differently. At any point in the continuous medium there are forward-moving particles and backward-moving particles that were backscattered from the

6. medium beyond the point. Now insert a cavity in the medium as in Fig. 12.2 and consider the forward fluence . If the cavity is higher Z than the medium the forward fluence of particles in the cavity is less than the forward fluence in the continuous medium because more particles are backscattered at the high Z interface than are backscattered in the continuous medium. The change in forward fluence in the cavity also affects backscattering at the downstream end of the cavity. And, due to different

7. CAVITY THEORY A cavity is anything embedded in a medium. To measure dose at a point in a medium requiresinsertion of a detector in the medium. The detector is a cavity and a common cavity material is air. Cavity theory relates dose to the cavity to dose to the medium. For photon beams, dose to thecavity can be due to electrons entering the cavity from the medium and to photon interactions in t he cavity . For neutron beams, dose to the cavity can be due to charged particles (protons, alpha particles , nuclei) entering the cavity from the medium and to neutron interactions in the cavity. For electron beams, dose to the cavity is due to primary and secondary electrons entering the cavity from the medium.