Ray inaccuracy in the presence of space-charge.

The usual reason for slow speeds is that the requested ray tracing inaccuracy is too small..

A request inaccuracy of less than about 0.001 is rarely justifiable, for the reasons are given below.

An exception is when using a cathode with an anode at high voltage, which requires careful treatment.

Other causes of apparent problems are:

(1) The preferred tube method is not being used when it should be, or if the space-charge cell method is being used the cell spacing is not small enough.

(2) The behaviour of rays near to the axis is important, but the direct method of ray tracing is being used instead of the mesh method (the mesh method is usually better here).

(3) If space-charge cells are used the maximum number of them is limited by the memory space and also by the computing time, so they cannot be arbitrary small.

(4) If space-charge tubes are used their diameter cannot be arbitrary small (see note on the tube method), and there might also be limitations of memory space and computing time.

Other help can be found in the detailed notes at the ends of the test and example files of the relevant type.

The reasons why a request inaccuracy of less than about 0.001 is rarely justifiable are:

(1) The main reason is that the program cannot simulate the space-charges as accurately as the boundary charges, because:

The finite size of the cells or tubes effectively increases the diameter of a beam in a cross-over region.

A low value of the ray tracing inaccuracy would therefore be inconsistent with the inaccuracy of simulation of the space-charge, and would give tracing times that are unnecessarily long without achieving greater accuracy.

(2) Another reason for not selecting a very small ray tracing inaccuracy is that the inaccuracy for calculating the space-charge fields is then set at the same small value by the program. The program then usually has to work very hard to try to achieve this inaccuracy, because the number of cells or tubes is usually large. In any case the program is sometimes not able to calculate the fields due to space-charges as accurately as those due to the boundary charges.