High Current Magnetic Lens Simulation

This is a follow up related to my post from yesterday about electron beam magnetic lenses. I was curious about different configurations and operating parameters, so I ran the simulations again and increased the current by a factor of ten.  Everything else in the simulations are exactly the same.  I'll present the resultant graphs below with some notes.  The associated files can be found here.

Cross section of the field through the coil axis

Cross section of the field just above the plane of the coil

The field plots above look exactly the same as the low current plots.  This is because they are plots of relative intensity, just to show the shape of the field.  If the current in the coil is multiplied by ten, the field will be ten times stronger, but will still have the same shape.

Focussing and diffusion

From the graph above it appears that the field is so strong that the electrons are focussed just before entering the coil but still keep spiralling along at different speeds with each beam approaching the axis twice more at slightly different positions.

x velocity through the simulation

We can see here once again that the electron's x velocity decreases significantly as is transits the lens, most of this is however regained after passing through the lens.

velocity magnitude

Ignoring any errors from the numerical simulation, we can see that the velocity of the electron remains constant throughout its interaction with the lens.

Electrons spiralling along the x axis

In this plot we can see the electron as it spirals along the axis.  I do find it surprising that the electrons don't spiral around the axis, instead they just keep kissing the axis.  I think if this was longer solenoid with a more uniform field there may be different results.

Electron trajectories

The high current simulation shows some interesting results.  The electrons that start furtherest from the axis loose a significant portion of their x velocity and are flung off away from the axis after spiralling around next to it.  I am slightly puzzled that the electrons don't spiral around the axis.  What little information I could find in textbooks on this topic have the electrons spiralling around the axis.  They weren't simulations though, and were more of just a conceptual look at the problem.  I may need a more uniform field to see that effect.  Hmmm.