THE EGS5 CODE SYSTEM

Since the CSDA range is uniquely defined monotonic function of energy, its inverse, the energy ofan 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 isstraightforward.Implementation We begin with the energy loss integration, for which case we are looking forthe largest ∆E for which1 − 1 ( ∣∣∣∣ ∆E dEt 2 dx (E −10)∣ +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 representsthe analytical value we wish to preserve within a relative error tolerance given by ɛ E . We use aniterative process, beginning with a value of ∆E that is 50% of E 0 and step down in 5% incrementsuntil the inequality is satisfied. We next look at scattering power, starting with the value of ∆Erequired by the stopping power integration. In this case, we numerically compute the integral ofstored values of G 1 (E 0 ) times the stopping power for K 1 (∆E) and compare that value to that fromthe energy hinge trapezoidal integration,∆E2( ∣∣∣∣ 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 lessthan ɛ E .A treatment for the maximum hinge steps which preserve the mean free path (using Equations2.386 and 2.384) and total scattering probability (using Equations 2.385 and 2.387) for hardcollisions to within ɛ E is still being developed.2.15.8 Multiple Scattering Step-size Specification Using Fractional Energy LossParametersTo control multiple scattering step-sizes, it would seem logical for EGS5 to require specificationof cos Θ, because K 1 is very close to 1 − 〈cos Θ〉 (see Equation 2.375). However, because electronscattering power changes (increases) much more rapidly than stopping power as an electron slowsbelow an MeV or so, fixing K 1 for the entire electron trajectory results in taking much, muchsmaller steps for lower energy electrons than the fixed fractional energy loss method using ESTEPEof EGS4, given the same step size at the initial (higher) energy. For example, the value of K 1corresponding to a 2% energy loss for a 10 MeV electron in water corresponds to a 0.3% energy lossat 500 keV. Thus a step-size control mechanism based on constant scattering strength would forceso many small steps at lower energies that EGS5 could be slower than EGS4 for certain problems,111