Track Structure

An ion's path through matter does not resemble a "pencil beam" as just indicated but rather a "test tube brush" where the bristles are made up of the

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Fig. 8. Linear energy transfer of protons versus range in water.

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Fig. 8. Linear energy transfer of protons versus range in water.

secondary electrons. This track structure has to be taken into account by any attempt to understand the action of heavy charged particles in a quantitative way. With protons and alpha particles it is now possible to calculate the microscopic pattern of energy deposition by Monte Carlo computations but not yet for heavier ions as the interaction cross are not sufficiently known. Another approach, pioneered by R. Katz and sometimes named "amorphous track model" is to consider "local doses" within the track, i.e. the average energy in cylindrical shells around the ion path. As emission angel and electron energy are related there is a maximum radial extension of the track which is called the "penumbra radius" rp. According to a current model (Kiefer and Straaten, 1986 [4]) the following relation holds rp = 0.0616E17 (4)

where rp is measured in pm and E is the ion specific energy in MeV/u. The penumbra radius does not depend on ion charge but local doses in the track do.

For a given energy the electron density scales with zff and the local dose d(r) is given by the following formula (Kiefer and Straaten, 1986 [4])

with ยก3 = v/c being the ion speed relative to that of light in vacuo, r the radial distance from the track centre in mm, d(r) is given in Gy.

Figure 9 displays an example for 10 MeV/u iron ions. One sees that close to the track centre very high local doses are achieved. This plays an important role for the understanding of the increased biological effectiveness of heavy charged articles because very complex lesions can be created.

1 10 100 1000 10000 Radial extension / nm

Fig. 9. The distribution of local dose in the track of a 10 MeV/u iron nucleus after Kiefer and Straaten (1986) [4].

1 10 100 1000 10000 Radial extension / nm

Fig. 9. The distribution of local dose in the track of a 10 MeV/u iron nucleus after Kiefer and Straaten (1986) [4].

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