CPO3D 62nd example: enhancement factor for a nanotube, 'hemisphere on post'.

The 'post' has a height h = 1 micron (ie 0.001mm) and a radius a = 1nm.

To create a field an anode is placed at an arbitrary 9 micron away, with a potential of 0.01V, giving a 'far field' of 1V/mm.

The field enhancement factor depends only on h/a.

The ray output file contains the field at 10 points at distances of 0.1 to 1.0 nm from the surface of the cap.


 0.00E+00  0.00E+00  5.00E-08  0.00000E+00  0.00000E+00 -5.52368E+02  5.52368E+02

 0.00E+00  0.00E+00  1.00E-07  0.00000E+00  0.00000E+00 -5.02061E+02  5.02061E+02

 0.00E+00  0.00E+00  1.50E-07  0.00000E+00  0.00000E+00 -4.59666E+02  4.59666E+02

 0.00E+00  0.00E+00  2.00E-07  0.00000E+00  0.00000E+00 -4.22842E+02  4.22842E+02

 0.00E+00  0.00E+00  2.50E-07  0.00000E+00  0.00000E+00 -3.90576E+02  3.90576E+02

 0.00E+00  0.00E+00  3.00E-07  0.00000E+00  0.00000E+00 -3.62122E+02  3.62122E+02

 0.00E+00  0.00E+00  3.50E-07  0.00000E+00  0.00000E+00 -3.36889E+02  3.36889E+02

 0.00E+00  0.00E+00  4.00E-07  0.00000E+00  0.00000E+00 -3.14400E+02  3.14400E+02

 0.00E+00  0.00E+00  4.50E-07  0.00000E+00  0.00000E+00 -2.94265E+02  2.94265E+02

 0.00E+00  0.00E+00  5.00E-07  0.00000E+00  0.00000E+00 -2.76161E+02  2.76161E+02

Analysis of the results:

The field at points near to the surface are less accurate because the distance from the nearest segment is comparable with the dimensions of the segment. 

Extrapolate field to z=0 by extrapolation of E(z)*(z+a)**2.  But this extrapolation is not smooth.  So take the lowest value of E(z)*(z+a)**2 (which is at z=1E-7) and divide it 

by a**2, which gives E(a) = 60749.4.  Therefore enhancement factor, gamma = 607.49

The correct value (see xmpl2d42.dat) is 602.29, so the error is 0.9 percent (but the error would be smaller if more than the present 491 segments were to be used).

However, this geometry has been set up only to help in setting up xmpl3d64, where 2 'hemispheres on posts' are used. 

Please also see papers 55 and 59 in the publications list.