Initial recombination in the track of heavy charged particles: Numerical solution for air filled ionization chambers

Figures & data

Figure 1. Comparison between the different charge carrier distributions used. The Kiefer–Chatterjee (KC) and the Scholz–Kraft (SK) charge carrier distribution share the same r _min = 4 nm, the width of the Gaussian style charge carrier distribution is b = 20 μm.

Figure 2. Numerical solution of the diffusion and recombination partial differential equation (PDE) for 420 MeV/u carbon ions with a linear energy transfer of LET = 9.4 keV/μm using the Gaussian (JAFFE), the Kiefer–Chatterjee (KC), and the Scholz–Kraft (SK) charge carrier distribution for the best fitting b or r_min (indicated in the plot) as initial condition compared to measurements. The numerical calculations are displayed as lines whereas the experimental data is displayed as open circles.

Table I. Approximate fit parameters of the core radius r_min (KC and SK) or width b (Gaussian CCD, see Equation 3) and the correction in the relative saturation charge extracted from Figures 2, 5 and 6.

Energy [MeV/u]	420	240	75
LET [keV/μm]	9.4	13	29
KC fit to absolute values	6 μm	10 μm	25 μm
KC fit to curvature	0.1 μm	0.4 μm	20 μm
KC resulting correction	1.2%	1.4%	0.1%
SK fit to absolute values	30 nm	40 nm	700 nm
SK fit to curvature	0.1 nm	0.1 nm	40 nm
SK resulting correction	1%	1.6%	1.35%
Gaussian fit to absolute values	12 μm	15 μm	28 μm
Gaussian fit to curvature	6.8 μm	13 μm	27 μm
Gaussian resulting correction	0.43%	0.09%	0.02%

KC, Kiefer–Chatterjee; LET, linear energy transfer; SK, Scholz–Kraft.

Figure 3. Diffusion of a Scholz–Kraft (SK) and Gaussian style charge carrier distribution for a 240 MeV/u carbon ion. The values for the core radius or the width are taken from the fit to the absolute values.

Figure 4. Diffusion of a Kiefer–Chatterjee (KC) and Gaussian style charge carrier distribution for a 240 MeV/u carbon ion. The values for the core radius or the width are taken from the fit to the absolute values.