Setting up cathode segments


It is very easy to specify a cathode in the space-charge versions CPO2DS and CPO3DS. The user can specify either that

(1) the N segments that comprise the cathode are the first N segments in the list of segments or

(2) the N electrodes that comprise the cathode are the first N electrodes in the list of electrodes.

The cathode can therefore have any shape, size or potential, and the parameters can be easily changed.


Nothing else is needed to define the shape of the cathode.  The Boundary Element Method is ideally suited to cathode and space-charge simulations.


One ray starts from the centre of each cathode segment. Each ray represents a model particle that moves in the total electric field as if it were a single electron but carries the charge and current of many adjacent electrons. The current carried by a ray is proportional to the area of the parent segment and also depends of course on the field at the segment.

A common mistake made by new users is to specify too many cathode segments in the initial stages of setting up a simulation.  This results in computing times that are unnecessarily too long.  Usually the number of segments in the rest of the system is also too large.  So start with a system that has fewer segments and rays than you will use in the final stage of a simulation.


Warning: If the choice is to define the number of cathode segments directly then in CPO3DS the program might change the number of segments (that is, subdivisions) of an electrode (because it cannot subdivide a spherical surface or disc into an arbitrary number of segments). It might also order the segments in a way not expected by the user. So the user MUST LOOK at the screen plots to see from which segments the cathode rays come. The more experienced user can look at the processed data file to check on the first N segments (look for the second set of electrode specifications). If the actual number of cathode segments turns out to be larger than the specified value of N then some of the segments will not be emitting electrons. Conversely if the number of cathode segments is smaller than N then electrons will be emitted from unintended places!


Another warning: The cathode region must not overlap with any other electrodes, or else Child's Law and Langmuir's relationships are invalidated. This is not checked by the program.

Yet another warning:  If you are using cpo2ds to simulate cathodes of non-zero temperature then we advise that you try using cpo3ds instead.  The reason is that using cpo2ds means that the rays are necessarily non-meridional which forces the use of routines borrowed from cpo3ds to integrate the trajectories, thus increasing the computing time.  There is a program for converting the 2D electrode data to the 3D format.  Remember to use the 3 planes of reflection symmetry, x==0, y=0, x=y.


Extra detailed information:

It is usually (but not always) preferable for all the segments of a cathode to have approximately the same area. The reason for this is that the current that a ray carries is proportional to the area of the parent segment and it is also proportional to the current density (mA/mm**2) that is determined by the program (and that is often approximately constant over the active part of the surface of the cathode for each set of rays).

For example for a cathode on the axis of a 2D cylindrically symmetric system this is easily achieved by using the segment subdivision type '2' or '-2'.

Several of the types of 3D electrode available in this program are automatically divided into segments of equal, or approximately equal, area. For example, 'spherical' electrodes are divided equally if they have a closed end. Also 'evenly divided disc' electrodes are divided equally, and 'triangular', 'spherical triangle', 'end spherical triangle', 'end conical or cylindrical triangle', 'end disc triangle', 'rectangle', 'rectangle x,y,z', 'cylinder rectangle' and 'cylindrical' electrodes are divided up into segments of the same, or nearly the same, area, but the segments could sometimes be long and thin. 'Conical', 'conical triangle' and 'disc' electrodes are not divided into equal areas.

End of extra detailed information: