|Cross section of the field through the coil axis|
|Cross section of the field just above the plane of the coil|
|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|
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.
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.