THE EGS5 CODE SYSTEM

Since the CSDA range is uniquely defined monotonic function of energy, its inverse, the energy of
an electron with a given CSDA range, E C (R), can be trivially determined. Thus we have
∆E(t) = E 0 − E C (R C (E 0 ) − t) (2.391)
By interpolating tabulated values of R C (E) and E C (R), relating energy loss to distance traveled is
straightforward.
Implementation We begin with the energy loss integration, for which case we are looking for
the largest ∆E for which
1 − 1 ( ∣∣∣∣ ∆E dE
t 2 dx (E −1
0)
∣ +
dE
∣ dx (E 1) ∣
∣−1 ) < ɛ E (2.392)
where t = R C (E 0 ) − R C (E 1 ), the pathlength as determined from the range tables, and represents
the analytical value we wish to preserve within a relative error tolerance given by ɛ E . We use an
iterative process, beginning with a value of ∆E that is 50% of E 0 and step down in 5% increments
until the inequality is satisfied. We next look at scattering power, starting with the value of ∆E
required by the stopping power integration. In this case, we numerically compute the integral of
stored values of G 1 (E 0 ) times the stopping power for K 1 (∆E) and compare that value to that from
the energy hinge trapezoidal integration,
∆E
2
( ∣∣∣∣ dE
−1
)
dx ∣ (E 0 )G 1 (E 0 ) +
dE
−1
∣ dx ∣ (E 1 )G 1 (E 1 )
If the difference is greater than ɛ E , we reduce ∆E by 5% and continue until the difference is less
than ɛ E .
A treatment for the maximum hinge steps which preserve the mean free path (using Equations
2.386 and 2.384) and total scattering probability (using Equations 2.385 and 2.387) for hard
collisions to within ɛ E is still being developed.
2.15.8 Multiple Scattering Step-size Specification Using Fractional Energy Loss
Parameters
To control multiple scattering step-sizes, it would seem logical for EGS5 to require specification
of cos Θ, because K 1 is very close to 1 − 〈cos Θ〉 (see Equation 2.375). However, because electron
scattering power changes (increases) much more rapidly than stopping power as an electron slows
below an MeV or so, fixing K 1 for the entire electron trajectory results in taking much, much
smaller steps for lower energy electrons than the fixed fractional energy loss method using ESTEPE
of EGS4, given the same step size at the initial (higher) energy. For example, the value of K 1
corresponding to a 2% energy loss for a 10 MeV electron in water corresponds to a 0.3% energy loss
at 500 keV. Thus a step-size control mechanism based on constant scattering strength would force
so many small steps at lower energies that EGS5 could be slower than EGS4 for certain problems,
111