Two-stage solutions.

After Dec 2006 it is possible to divide a complicated system into two (or more) parts, export the calculated potentials and fields of the first part and then import these into the second part.

Here are the recommendations given before Dec 2006:

It is sometimes necessary to divide a system into two (or more) stages, each separately simulated. The final ray information at the exit of the first stage is then used as the initial ray information at the entrance of the second stage.

The final ray data at the exit of the first stage is the correct format for re-use as initial ray data if the ‘nearly-zero’ printing level is used.

There are several reasons for needing to use a two-stage (or multi-stage) solution, including:

Too many segments are needed for a single solution.

One stage can use more planes of reflection symmetry than the other stage.

The range of voltages is too high, as in an x-ray tube (see below).

If the stages have a field-free region between them then the procedure is simple.

On the other hand, when there is no intermediate field-free region, an artificial membrane should be used. For example to simulate an x-ray tube it is sometimes necessary to divide the system into low and high-energy halves, with the following steps:

(1) Choose a test plane that separates the system into a low energy and a high energy part. The maximum voltage difference in the 'low energy' part should be much smaller than in the 'high energy' part, preferably of the order of 100V.

(2) Find the boundary charges for the whole system and then output the potentials distribution at the selected test plane between the low energy and high energy parts.

(3) Use program 20, or something similar, to generate the segments (and their applied potentials) of an electrode that can be used to replace the selected test plane, to physically separate the two parts.

(3) Set up the first part of the system, terminated by the new electrode. The overall potential distribution in the first part should now be the same as it was when the whole system was used.

(4) Trace rays up to the new electrode, and output information on the rays at a test plane that coincides with the new electrode.

(5) Set up the second part of the system, terminated by the new electrode, and use the ray output information from the previous step to start rays from the new electrode.

It might be necessary to iterate this process if space-charges are present.

Other variations of this procedure might be necessary to give accurate results -for example by using two new electrodes, on either side of the middle test plane, the one inside the first part being used to terminate the second part and vice-versa.