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The frequency distribution of the lineal energy,  y , of a 30-MeV proton beam was measured as a function of the radial distance from the beam path, and the dosed mean of    y  ,y  ¯D,    was obtained to investigate the radial dependence ofy  ¯D.    A wall-less tissue-equivalent proportional counter, in a cylindrical volume with simulated diameters of 0.36, 0.72 and 1.44 µm was used for the measurement of  y  distributions,  yf ( y ). The measured values of  yf ( y ) summed in the radial direction agreed fairly well with the corresponding data taken from the microdosimetric calculations using the PHITS code. They  ¯Dvalue of the 30-MeV proton beam presented its smallest value at  r  = 0.0 and gradually increased with radial distance, and they  ¯Dvalues of heavy ions such as iron showed rapid decrease with radial distance. This experimental result demonstrated that the stochastic deposited energy distribution of high-energy protons in the microscopic region is rather constant in the core as well as in the penumbra region of the track structure.

Measurement of the stochastic radial dose distribution for a 30-MeV proton beam using a wall-less tissue-equivalent proportional counter