CPO3D 63rd example: enhancement factor for 2 nearby nanotubes, both of form 'hemisphere on post'.

The 'posts' have a height h = 0.5 micron (ie 0.0005mm) and a radius a = 1nm, as in xmpl3d63 and xmpl3d65.

They are each at a distance 4E-5mm from the centre, so the distance between them is therefore 80nm.

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

The field enhancement factor depends only on h/a and s/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 of one of the nanotubes.


       x          y          z         ex         ey         ez      etotal (V/mm)

 0.00E+00  4.00E-05  5.00E-08  0.00000E+00 -6.47149E-02 -2.65867E+02  2.65867E+02

 0.00E+00  4.00E-05  1.00E-07  0.00000E+00 -1.18480E-01 -2.39702E+02  2.39703E+02

 0.00E+00  4.00E-05  1.50E-07  0.00000E+00 -1.60996E-01 -2.19044E+02  2.19044E+02

 0.00E+00  4.00E-05  2.00E-07  0.00000E+00 -1.96945E-01 -2.01323E+02  2.01323E+02

 0.00E+00  4.00E-05  2.50E-07  0.00000E+00 -2.27962E-01 -1.85851E+02  1.85851E+02

 0.00E+00  4.00E-05  3.00E-07  0.00000E+00 -2.54853E-01 -1.72241E+02  1.72241E+02

 0.00E+00  4.00E-05  3.50E-07  0.00000E+00 -2.78161E-01 -1.60197E+02  1.60198E+02

 0.00E+00  4.00E-05  4.00E-07  0.00000E+00 -2.98412E-01 -1.49483E+02  1.49484E+02

 0.00E+00  4.00E-05  4.50E-07  0.00000E+00 -3.16018E-01 -1.39905E+02  1.39905E+02

 0.00E+00  4.00E-05  5.00E-07  0.00000E+00 -3.31362E-01 -1.31302E+02  1.31303E+02

Analysis of these 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=1.5E-7) and divide it 

by a**2, which gives E(a) = 28968.6.  Therefore enhancement factor, gamma = 289.69.

Please see the footnotes to the data file for a considerable amount of further information.

Please also see papers 55 and 59 in the publications list.Further results, all for h/a = 500: