Xmpl2d54, 54th 'example' data file for CPO2D

Space-charge repulsion in a pulsed beam.

Simulation of the space-charge repulsion of an isolated pulsed beam that initially converges to a point, using the 'ray space-charge tube' method.

Similar to xmpl2d11.dat, a non-pulsed beam.

See also xmpl3d86.dat.

Here the beam starts from a plate at a finite distance from the cross-over, and is surrounded by a cylinder at ground potential to try to reduce any external lensing action of the beam on itself. The energy of the electrons is 1eV.

There are 25 rays, all starting from a disc of effective radius 3 at z = -10, and all directed towards the point (r,z) = (0,0). The 'beam' option is used, with a 'uniform' distribution of current across the starting disc.

Each ray therefore carries the same current and each represents the same area of the disc (and so they are not uniformly spaced in the radial direction).

The total initial current is a quarter of that given by the above formula for tan theta = 0.3, namely a quarter of 0.003474 mA. The current is multiplied in stages until the value 0.003474 is reached.

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

beam diameter.

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 0.25, much smaller than the value 1.244 for an ideal continuous beam. The waist is at approximately z = 0.9, different from the value 1.21 obtained with xmpl3d86 (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

trajectories.