THE EGS5 CODE SYSTEM

where ẋ and ẍ (for example) are the x-components of velocity and acceleration, respectively. Noattempt is made to solve these coupled differential equations. Instead, in the example user codecalled UCBEND, we use a simple vector expression for the change in the direction of motion aftera very small translation, ∆l, in a constant magnetic field strength, B, in which the particle energyis assumed to remain constant. Namely,whereˆv = 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 measurementsperformed 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 beproduced from two locations within the structure and were accelerated to kinetic energies of 8.5and 3.5 MeV, respectively, depending on their point of origin. Upon exiting the cavity they passedthrough a 0.015 inch copper window, where they lost energy primarily by ionization and weremultiply scattered. The experimentalists attempted to measure the spectrum of the electronsusing a magnet, a lead slit, and a Faraday cup. A strong peak corresponding to the 8.5 MeV groupwas observed, but the 3.5 MeV peak was not observed. The object of the EGS5 simulation wasto try to understand these observations, particularly with the help of graphics showing particletrajectories.Subroutine HOWFAR of UCBEND was designed using the diagram shown in Figure 4.1. Electronsstart from the origin (at plane 1), transport through the copper window (Region 2), emanate outinto the air (Region 3), and pass through the magnetic field, which is constant and along the positivey-direction (in Region 4 only). They are then bent in the direction of the lead wall (Regions 6 and8) where some of them pass through the slit (Region 7) and get scored (at Plane 10). By varyingthe field strength of the magnet one should be able to re-create the observations for both 3.5 MeVand 8.5 MeV.In order to gain a more complete understanding of the geometry, it is suggested that the readerstudy the listing for UCBEND, which is included with the EGS5 distribution. What is of interesthere is the method that we employ in order to transport the electrons through the magnetic fieldregion. Using Equation 4.3 with ∆l/R