EXERCISE 4: THE E×B (WIEN) FILTER, PART 2

As an extension of Exercise 3, now assume that the particles entering the field region at the origin have a normal distribution of velocities directed purely along the z-axis. The center of the distribution is vz,pass and its width is 0.1vz,pass.

(a) Allow 40,000 particles from this distribution to enter the field region at the origin. What is the resulting histogram of the scaled velocities vz/vz,pass of the particles transmitted through a circular aperture of radius R=1.0 mm centered on the z-axis? How does it compare to the histogram of the initial velocities?

(b) Repeat part (a) for an aperture of radius R=0.5 mm.

It is worth noting that an actual source of ions will not only be characterized by a distribution of velocities, but also distribution of directions (no ion beam is strictly mono-directional, just like a laser beam is not strictly mono-directional). This is an additional fact that would have to be considered to accurately simulate the performance of a real Wien filter.