xmpl3d86, 86th 'example' data file for CPO3D
Space charge repulsion in a pulsed beam
This simulation is based on xmpl3d07, which shows the space-charge repulsion in a beam that initially converges to a point.
For a 2D analogue and further information, see xmpl2d54.
The 'direct' method of ray tracing is used. The advanced option to vary the tube diameter is used to make the diameter a constant fraction of the
The 'pulsed beam' option is activated with a pulse length of 1E-6ms (the transit time in the tube is 3.6E-5ms and the pulse length is 0.36mm).
Because this is a pulsed beam we have disabled the recalulation of surface charges between iterations (go to databuilder/setting the rays/advanced options). If we do not do this then the surface charges would be recalculated in the presence of the last trajectory space-charges known to the program-namely those at the at the ends of the trajectories.
We cannot use the cathode damping option here to deal deal with the ever-present oscillations in the space-charge densities, so instead we increase the current over a large number of iterations. There are 14 space-charge iterations, the last 3 of which show some consistency. The beam waist has a radius of approximately 0.22, much smaller than the value 1.244 for an ideal continuous beam. The waist is at approximately z = 2.1, different from the value 0.88 obtained with xmpl2d54 (but influenced by the outside trajectories).
If you want to plot contours (of potentials, fields or space-charges) after the ray tracing has finished then you will be asked to specify the time for the contours. If you start with a small time and then step towards the final time (approximately 3.6E-5) then you will see the centres of the contours move progressively from left to right in the z direction.
When the pulsing is effectively switched off by making the final time large, say 1E-4ms, the waist is similar to what is seen in xmpl3d07 for a continuous beam. In fact the results are not expected to be exactly the same, for 3 reasons: (1) in the pulsed beam option the program ignores the 'self-fields' that act on a point in a ray due to the space-charge tubes of that same ray, for reasons given in Help), (2) the surface charges are not recalculation at the ends of iterations (see above), and (3) There are difficulties in assigning the space-charges that exist at the starting times of the