Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet

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2.2 Free modes of decay-
Whereas external fields can exci-te only the TE-mode within the
conductor, there exist free modes of current decay for both TE-
and TM-fields, Consider the typical potential
where @ and f stand for OE, $M and f,, fM, respectively. First it
L
wlll be shown that the decay constants B (ei.genvalues) must be
positive quantities. Inserting (2.23) in (2.9) and (2.10) we ob-
tain
fECz) =. { K ~ - f3~~0(z)l 'fE(z), (2.24)
where K' = K' -1- K'. The ej-genfunctions have -to satisfy the boundary
X Y
conditions
fE = (km) = 0, f (to) = 0, fr(m) = 0
M M
If there is a perfect conductor at finite depth d then
(2.26)
fE(d) = 0, fi(d) = 0 (2.2Ea)
Multiplying (2.24) and (2.25) by f" aid of" and integrating over z'
E M
from -m to +m and 0 to -, respectively, we obtain on integrating
by parts and using (2.26)
Hence, all decay constants f3 are real and positive. The currcnt
flow for TE-decays is in horizontal planes, whereas the TM-decay
currcnts flow predominantly in vertical planes.
Example :
u = O
0 + 0,-
- z - 0