Cathode with a high anode voltage.

This note deals with systems such as x-ray tubes in which electrons start with low energies -especially from a thermionic cathode- and finish with energies that are orders of magnitude higher (for example 100keV). This is one of the most challenging simulations.

Firstly the 'fractional inaccuracy for potentials used in ray tracing' must be small enough to deal satisfactorily with the potentials and fields within the cathode region. Usually the smallest inaccuracy should be selected (see note on accuracy for ray tracing with cathodes). One reason for this is that the errors in the potentials and fields are of the order of the product (potentials fractional inaccuracy)*(maximum voltage difference). Another reason is that the boundary elements are calculated using the smallest inaccuracy and then the potentials at the centres of the cathode segments (and all the other segments) are exactly equal to the applied voltages -and so they will again be exactly equal later if the smallest inaccuracy is used, but not if higher inaccuracies are used.

(But note that the other inaccuracy involved in ray tracing -the 'fractional inaccuracy for ray tracing'- does not usually have to be very small.)

The 'zero total charge' option should be disabled.

The cathode depth 'd' must not be too small (see notes on region near cathode). A suitable value for 'd' is in the region of the average width of the cathode segments.

The segments in the vicinity of the cathode should be significantly shorter than their distance from the cathode, see general note on accuracies of potentials.

It is often advisable to 'anchor' the potential of the cathode by adding an addition electrode inside the real cathode and close to it. It might also be advisable to 'anchor' neighbouring electrodes in a similar way.

It might be necessary to use smaller inaccuracies for the charges and the rays tracing (that is, smaller than the usual minimum allowed values).

This can be achieved by entering a negative value for the charge inaccuracy in the primary data file. For example if a charge inaccuracy of 10**-8 (that is, 0.00000001) is required then enter the value -10**-8. This can be done in the 'Edit file' mode or by directly editing the file. It cannot be done by the databuilder (and so the databuilder cannot be used). The later inaccuracies, for evaluating potentials etc, and for ray tracing, can then also be as small as 10**-8 (but again the data builder cannot be used because it would restore the preset value). The smallest inaccuracy is 100 times smaller than the usual inaccuracy, which is 10**-7 for CPO2D and 10**-6 for CPO3D.

When the anode voltage is 10000 or more the program automatically makes sure that the inaccuracy for potential and field evaluation is at least 10 times smaller than the ray tracing inaccuracy.

To obtain the most accurate results it is sometimes necessary to divide the system into low and high-energy halves -see the note on two-stage solutions.