52nd 'example' data file for CPO2D

A non-meridional beam in repeated space-charge iterations.

Also illustrates helical motion in an electrostatic field.


Developed from xmpl2d51.dat, a simple non-meridional beam. Please see the notes there.


The simulation is very simple here and is intended only to illustrate the option of iterated non-meridional beams. A He+ beam is set up and is then iterated once, followed by an electron beam.



There is no magnetic field.

The initial non-meridional beam is of He atoms, energy 10 keV, current 0.04 mA. This beam is iterated once and creates a potential of approximately 1V along the axis. This is followed by a non-meridional beam of electrons, energy 1 eV.


This example file also illustrates helical motion in an electrostatic field. Looking at the r*cos(phi) view, it can be seen that the electrons are attracted to the He+ beam and spiral around and through it in a helical motion.


To increase the axial potential of the He+ beam we can increase the multiplying factor for the iterated beam (go to setting rays/space-charge options/repeat space-charge options/edit factor). Then the electron rays move closer to the axis.


Looking at this in more detail, the strength s of the electric field outside a uniform beam is proportional to 1/r, and then we would expect an electron of angular momentum L to have a helical radius proportional to sqrt(L/s). Inside a uniform beam the field is proportional to r and the radius becomes proportional to the 4th root of L*L/s, and so is only weakly dependent on s. The present beam is of course only approximately uniform, but a quick test shows that the above dependences hold approximately for particular electron rays.