THE EGS5 CODE SYSTEM

where ẋ and ẍ (for example) are the x-components of velocity and acceleration, respectively. No
attempt is made to solve these coupled differential equations. Instead, in the example user code
called UCBEND, we use a simple vector expression for the change in the direction of motion after
a very small translation, ∆l, in a constant magnetic field strength, B, in which the particle energy
is assumed to remain constant. Namely,
where
ˆv = ˆB(ˆv 0 · ˆB) + [ˆv 0 − ˆB(ˆv 0 · ˆB)] cos α − ˆv 0 × ˆB sin α (4.3)
α = ∆l/R,
R = radius of curvature = qp/B,
p = particle momentum,
ˆB = magnetic field unit vector,
ˆv 0 = particle direction unit vector (before)
= U 0 î + V 0 ĵ + W 0ˆk,
ˆv = particle direction unit vector (after)
= Uî + V ĵ + W ˆk.
The problem that we attempt to solve with UCBEND relates to a series of spectral measurements
performed at SLAC [100]. An RF cavity was tested and found to emit high levels of radiation.
Because the cavity was subjected to very high power levels, surface electrons were found to be
produced from two locations within the structure and were accelerated to kinetic energies of 8.5
and 3.5 MeV, respectively, depending on their point of origin. Upon exiting the cavity they passed
through a 0.015 inch copper window, where they lost energy primarily by ionization and were
multiply scattered. The experimentalists attempted to measure the spectrum of the electrons
using a magnet, a lead slit, and a Faraday cup. A strong peak corresponding to the 8.5 MeV group
was observed, but the 3.5 MeV peak was not observed. The object of the EGS5 simulation was
to try to understand these observations, particularly with the help of graphics showing particle
trajectories.
Subroutine HOWFAR of UCBEND was designed using the diagram shown in Figure 4.1. Electrons
start from the origin (at plane 1), transport through the copper window (Region 2), emanate out
into the air (Region 3), and pass through the magnetic field, which is constant and along the positive
y-direction (in Region 4 only). They are then bent in the direction of the lead wall (Regions 6 and
8) where some of them pass through the slit (Region 7) and get scored (at Plane 10). By varying
the field strength of the magnet one should be able to re-create the observations for both 3.5 MeV
and 8.5 MeV.
In order to gain a more complete understanding of the geometry, it is suggested that the reader
study the listing for UCBEND, which is included with the EGS5 distribution. What is of interest
here is the method that we employ in order to transport the electrons through the magnetic field
region. Using Equation 4.3 with ∆l/R