Test2d14, 14th 'benchmark test' data file for CPO2D
Cylindrical diode, small inner cathode
The coaxial cathode and anode have radii of 0.01cm and 1cm respectively, and the voltage difference is 1V. The theoretical space-charge limited total current is 0.013601 mA/mm. After 5 iterations the value given by the program has an error of 5%, in a total computing time of less than a minute. The result converges after a total of 15 iterations to give an error of 1.4%
The data are the same as in file test2d11.dat, except that
(1) the symmetry is 'planar' instead of 'cylindrical',
(2) x = 0 is a plane of voltage symmetry,
(3) the initial maximum current density is 0.2,
(4) the damping factor has been increased to 0.8, and
(5) the number of iterations is 5.
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.
The theoretical space-charge limited total current is 0.013601 mA/mm (see I Langmuir and K B Blodgett, Phys. Rev. vol 22, 347, 1923 -and using the modern values of the fundamental constants that appear in the formulas). The current that appears on the screen and in the output data file is the total current divided by 4 (because of there are 2 planes of reflection symmetry) and so should be 0.003400 mA. In fact in this example it is 0.003573 (giving an error of 5%) in the last iteration, with a total computing time of less than a minute. The next 2 iterations give errors of up to 13%, and then the result converges after a total of 15 iterations to 0.003448, giving an error of 1.4%
Doubling the number of segments and the number of interpolation points in the cathode region (and also halving the ray inaccuracy and the maximum step length) gives the current 0.003421 mA, that is, an error of 0.6%, but with an increase in computing time of approximately 5.