53nd example: enhancement factor for a cone in an array of cones.
The geometry is the same as in files xmpl3d52 and xmpl2d29, except that an array of 9 cones is used.
The spacing between the tips of the cones is 200mm in the x and y directions.
An extra back plate has been included, at an empirical potential of -0.089V, in order to produce a potential of approximately 0V in the holes on the base plate (ie in the parts of the base plate that are not covered by segments).
Using the same analysis as the previous two files:
|
|
z |
Ez |
Ez*z**2 |
|
|
1.1 |
0.36712 |
0.44422 |
|
|
1.2 |
0.30945 |
0.44561 |
|
|
1.3 |
0.26680 |
0.45089 |
|
|
1.4 |
0.23387 |
0.45839 |
|
|
1.5 |
0.20785 |
0.46766 |
|
|
1.6 |
0.18689 |
0.47844 |
|
|
1.7 |
0.16970 |
0.49043 |
|
|
1.8 |
0.15540 |
0.50350 |
|
|
1.9 |
0.14335 |
0.51749 |
|
|
2.0 |
0.13308 |
0.53232 |
Extrapolating, the field at the tip is therefore 0.4446 V/mm. The field 'enhancement factor' is therefore 44.5.
The result obtained previously for an isolated cone was 48.4, see xmpl2d29.dat. The present result is 92 percent of the value for an isolated cone.
When the anode plate is put further away, at z = 1500, the enhancement factor decreases by approximately 0.1 percent (which might be due to the inaccuracy of the present simulation).
This 'enhancement factor' is a function of the radius of the tip, the angle of the cone, the length of the cone and the array spacing.
See papers 55 and 59 on the publications list.