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A first step in the dosimetry of fast-ion beams is the determination of accurate Bragg (ionization) functions. Bragg functions for several substances have been measured and calculated for 3480 MeV carbon ions. In the measurements, the ions first traverse an absorber in which the energy is reduced to either 1900 or 1200 MeV, then a "range gauge" followed by a thin ionization chamber. Functions are calculated with an analytical method using convolutions of straggling functions. This approach gives results without the stochastic variations implicit in Monte Carlo methods. The comparison of measured and calculated functions shows how reliable the calculations are. An important part of the calculations is the determination of the total range of the ions. The range can be determined from the Bragg function. The measured range is given by the sum of the thickness of the absorber and the residual range measured with the range gauge. For water, the range is about 150 mm, and the precision of the measurements is +/-0.05 mm. Because the ion energy at the surface of the absorber fluctuates with time, measurements with water are used to define this energy. Thus the ranges (or average stopping powers) in absorbers are obtained relative to those in water. Measured ranges R(m) are compared with ranges R(0) calculated with a current version of the Bethe theory. For light absorbers (atomic number Z < 20), differences between R(m) and R(0) are less than +/-0.3 mm; for Z > 20 differences are between 0 and +/-0.6 mm. This agreement between calculated and measured ranges confirms the value I = 80 eV for water measured earlier for protons. The ionization by nuclear fragments is obtained from the difference between measured and calculated ionization functions, and has little influence on the ranges of the primary ions.

To verify international uniformity in carbon beam dosimetry, an intercomparison programme was carried out at the heavy ion medical accelerator (HIMAC). Dose measurements with ionization chambers were performed for both unmodulated and 6 cm modulated 290 MeV/nucleon carbon beams. Although two different dosimetry procedures were employed, the evaluated values of absorbed dose were in good agreement. This comparison established a common framework for ionization chamber dosimetry between two different carbon beam therapy facilities.