Section 2.10 of the User's Guide for CPO2D and CPO3D

(or proceed to section 2.11)


Accuracy of ray tracings


The inaccuracy of the final coordinates of a ray depends primarily on the fractional inaccuracy chosen for the ray tracing.

But several other factors also have an effect, including: 

 (1) the inaccuracies of the surface charges,

 (2) the choice of subdivisions (see 2D note or 3D note) for the electrodes (particularly if rays pass close to an electrode),

 (3) the mesh spacing, if the 'mesh' method is being used, and

 (4) the maximum step length or time for the ray tracing (but be careful not to use step lengths or times that are too short, which would increase the computing time unnecessarily, because a large number of evaluation points is used inside each step).


The fractional inaccuracy that is specified by the user is only a guide.


The usual value is 0.1 for quick exploratory tests (see Chapter 3 of the User's Guide), and 0.00001 to 0.0001 for the final answers (except in space-charge problems, where high ray accuracies are usually not justified).


A higher ray accuracy implies a longer computing time. This time can be reduced (sometimes significantly) by minimising the graphics box on the screen (or hiding it with the edit or information boxes).

Please also see the note that gives a strategy for improving the accuracy of rays. 


Technical notes:

The 'fractional inaccuracy' that is chosen will be used by the program to define the accuracy with which the fields are evaluated and also to help to decide on the number of evaluation points inside each step in the ray tracing routine. The well-known Bulirsch-Stoer method is used. We have found this to be the most suitable when a wide range of simulations has to be dealt with. In the way that the program uses the Bulirsch-Stoer method the inaccuracy is somewhere between a single step inaccuracy and a global inaccuracy, and is only an approximate indication of the actual inaccuracy that will be achieved with a particular simulation. In any case the 'inaccuracy' of a ray tracing cannot be clearly defined in general. The inaccuracy of the rays also depends on the maximum step length or time that has been specified. When the motion is relativistic the equations of motion are solved to an inaccuracy slightly better than that corresponding to the 'ray fractional inaccuracy'.


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