29th example file, enhancement factor for a cone.
The tip of the cone is spherical, with radius of 1mm. The half-angle of the cone is arctan(0.5). The cone has a base radius of 50.9mm and a height of 101.6mm. The cone sits on an effectively infinite back plate at 0V. A field is provided by a plate at 6V, separated from the back plate by 600nm. (These dimensions can of course be scaled.)
The asymptotic field is therefore 0.01V/mm.
The results, copied into the output file temp29a.dat, can be processed to give the values of Ez and Ez*z**2 as a function of z, where r = 0, z is the distance from the centre of curvature of the tip, Ez is the z component of the electric field, and all the dimensions are in mm.
|
|
z |
Ez |
Ez*z**2 |
|
|
1.1 |
0.40162 |
0.48596 |
|
|
1.2 |
0.34063 |
0.49051 |
|
|
1.3 |
0.29436 |
0.49747 |
|
|
1.4 |
0.25839 |
0.50644 |
|
|
1.5 |
0.22984 |
0.51714 |
|
|
1.6 |
0.20675 |
0.52928 |
|
|
1.7 |
0.18778 |
0.54268 |
|
|
1.8 |
0.17197 |
0.55718 |
|
|
1.9 |
0.15863 |
0.57265 |
|
|
2.0 |
0.14724 |
0.58896 |
Fitting to a cubic, we find that Ez*z**2 extrapolates to 0.4835 at z = 1, ie at the surface of the tip. The field at the tip is therefore 0.4835 V/mm. The field 'enhancement factor' is therefore 48.4.
The result obtained in the less accurate 3D analysis, see xmpl3d52, is 48.6.
This 'enhancement factor' is a function of the radius of the tip, the angle of the cone and the length of the cone.
See papers 55 and 59 on the publications list.
If the cone is surrounded by other cones the 'enhancement factor' would also be a function of the distance between the cones. This is investigated in file xmpl3d53.