Test2d20, 20th 'benchmark test' data file for CPO2D
Cylindrical Pierce gun.
The following data were obtained when the memory and speed of PC's was much more limited than at present, so the available number of segments was small and the requested inaccuracies were fairly high to give a quick demonstration.
Derived from file test2d12.dat for a planar Pierce gun.
For convenience (because the accurate solution of the cylindrical Pierce gun is not readily available) the same geometry and voltages are used, as an approximation.
The theoretical Child's Law current density is w*(V^1.5)/L**2,
where w=.0023340 mA/mm**2. In the present problem, V=10, L=10, so the current density should be .73808 microamp/mm**2 and the current should be 9.2750 micro-amp, if the cylindrically symmetric system had the same potential distribution as the planar system (which it does not).