Page 168 - Maxwell House

148 Chapter 3

3.3.4 Field Electron Emission

Field electron emission is a quantum effect, and we are not going to discuss it. Note only that
for pure metals it takes place at the
field exceeding 10 V/m and depends
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on many physical factors such as
pressure, temperature, etc. The
discovery and intensive research of
Carbon NanoTube (CNT) led to
creation of nanotubes with diameter as
small as 3 ∙ 10 −10 m (0.3 nm).
Evidently, the electric field strength
around such tiny tips can be
enormous, and it is defined primarily
Figure 3.3.7 CNT array by the nanotube aspect ratio (length-
to-diameter ratio) that can
reach 10 : 1 and more. The electric current produced by a single nanotube depends on applied
8
voltage, and it is usually in the range of several microamperes. Scientists found a way to boost
this current fabricating the high-density array or “forest” of vertically oriented highly
conductive nanotubes attached to a conductive substrate like shown in Figure 3.3.7 .
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3.3.5 How to Treat Problem of Field Singularities in Numerical Simulation?

Unfortunately, the readily available singular solutions of Maxwell’s equations are very
restricted by a few particular geometries like wedges or cones. The only way to get the solution
of most practical problems is numerical
methods. Evidently, the edge effect
makes questionable any numerical
solution because a computer cannot
handle any infinite field near
singularities by definition. Note that
numerical methods typically include
the procedure of mesh or grid
generation. It means that the physical
Figure 3.3.8 Grid model of aircraft and field domain of interest is approximated by
distribution image the set of tiny cells like aircraft model
shown on the right side in Figure
3.3.8 . The spike (red spots) of EM fields are clearly visible near the sharp edges. The aircraft
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symmetry was apparently used during the numerical simulation. That explains why the only
left half of plane is highlighted in color. There are several ways to go around of singularity
problem depending on pursued accuracy:

16 Public Domain Image, source: http://ep.yimg.com/ty/cdn/nanolab2000/ntantenna.jpg
17 Public Domain Image, source: http://www.pointwise.com/apps/f15e.shtml