THE EGS5 CODE SYSTEM

• Sum the weighted energy deposition (WT(NP)*EDEP).
The easiest way to see that the weights have been properly assigned in the statements above is
by example. Assume that the incident particle has a kinetic energy of 1000 MeV and that one of
the progeny has energy 100 MeV and the other has 900 MeV. Then clearly the 100 MeV particle
will be chosen 10% of the time and will have a weight of 1000
100
, whereas the 900 MeV particle will
be chosen 90% of the time and will have a weight of 1000
900
. But the total particle count will average
out to two (ı.e. 0.1 × 1000
1000
100
+ 0.9 ×
900 = 2).
This scheme has been found to increase the speed of shower calculations by a factor of 300 at
33 GeV. However, because the biasing can be somewhat severe at times during the calculation,
the weights that are assigned tend to become rather large, and the net result is that the overall
1
efficiency (
variance×time
) is not usually 300 times better. Nevertheless, factors of 20 or more are
generally obtained for many problems[75]and this technique can be invaluable.
As an example, at one time it took about one minute of CPU time on the IBM-3081 to completely
generate one 50 GeV shower in a large absorber. When simulating “real” beams of particles having
spatial and/or angular distributions, analog EGS calculations gave only 60 incident events in one
hour runs, which was inadequate. The use of leading particle biasing with a factor of 300 increase
in speed, on the other hand, produced 18,000 events/hour, which was sufficient.
As a final note, it should be understood that leading particle biasing, or any importance sampling
scheme for that matter, should not be attempted in an arbitrary manner. For example, one should
not use leading particle biasing for the “O-ring” problem above since, even though many more
incident shower events will certainly be generated, the weights that are assigned to the low energy
particles heading in the direction of the “O-ring” region will tend to be quite high, and no significant
reduction in the variance will result. Quite the contrary, biasing of this sort can lead to very
erroneous results, and one should really have a full grasp (ı.e. pre-knowledge) of the important
aspects of the radiation transport before attempting to apply any of these variance reduction
methods with EGS5 (or any Monte Carlo program for that matter).
4.2 UCBEND - Charged Particle Transport in a Magnetic Field
Charged particle motion in a magnetic field is governed by the Lorentz force equation
⃗F = q⃗v × ⃗ B = d⃗p
dt
where ⃗ B is the magnetic field strength vector, ⃗v is the velocity vector, and q is the electric charge
of the particle. This equation can be expanded into its Cartesian components to give
mẍ = q(ẏB z − żB y )
(4.1)
mÿ = q(żB x − ẋB z ) (4.2)
m¨z = q(ẋB y − ẏB x )
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