THE EGS5 CODE SYSTEM

Fractional Energy Deposited
1
0.8
0.6
0.4
0.2
5 MeV electrons on Cu, Range = 3.796037e-01 cm
D = 1.8980e-01 cm
D = 7.5921e-02 cm
D = 3.7960e-02 cm
D = 1.8980e-02 cm
D = 7.5921e-03 cm
D = 3.7960e-03 cm
D = 1.8980e-03 cm
D = 7.5921e-04 cm
D = 3.7960e-04 cm
0
0.001 0.01 0.1
EfracH
Figure 2.17: Convergence of energy deposition as a function of step-size (in terms of fractional
energy loss) for the broomstick problem with varying diameters D in copper at 5 MeV.
converged value at short paths. The initial scattering strengths K 1 corresponding to the determined
maximum fractional energy losses were computed using Equation 2.372 cast in terms of an integral
over energy instead of over pathlength,
∫ E0
∣ ∣∣∣
K 1 (E 0 ) = dE ′ G 1 (E ′ dE
−1
)
E 1
dx ∣ , (2.393)
where E 0 is the initial energy, E 1 the energy after the determined maximum fractional energy loss,
G 1 the scattering strength and
dE
∣ dx ∣ the stopping power of the medium. Plots of these maximum
values of K 1 to assure convergence as a function of broomstick diameter for several energies in
titanium are shown in Figure 2.19.
The expected nearly linearly relationship between K 1 and t and the appropriate scaling of K 1
with E is clearly evident in Figure 2.19. We also see in that figure, however, several artifacts of
our method. First, we see that our estimation process did not always produce monotonic results,
primarily because of noise in the data due to the Monte Carlo statistics (given the large number of
runs, some outlier points were to be expected). Additionally, the plots exhibit some discrete jumps
because of the finite number of possible K 1 values tested in the parameter study. An additional
artifact can be seen in the top plot of Figure 2.20, which shows converged scattering strength data
vs. characteristic dimension for a variety of elements at 100 MeV. Because we limited the test runs
to a maximum of 30% fractional energy loss, we see a plateauing of the plots for high energies.
Other data sets show a corresponding artifact caused by numerical limits on the minimum step-size
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