Wave Propagation in Linear Media | re-examined

3.5 A dispersive system: the lossless plasma
3.5 A dispersive system: the lossless plasma
After the above re ections to ensure the plausibility of (3.29), we may apply it to dispersive
and evanescent systems. Remaining with our transmission line model, we assume it this time
to be lled with a lossless plasma. This has no e ect on the wave type, but only on its
propagation velocity. We still consider a TEM wave, and so the equivalent circuit is still
valid, although c becomes frequency-dependent. If we neglect the motion of ions and focus
on the contribution of the electrons, the relative dielectric constant is given by
with the plasma frequency [94]
"r =1, !p
!
!p =
s q 2 n0
"0m
2
(3.41)
: (3.42)
In this formula, q is the elementary charge, n0 the electron density, m the electron mass and
"0 the dielectric constant ofvacuum. Hence we have
and the dispersion relation
X 0 =!L 0 ; B 0 = !C 0 1 , !p
!
k(!) = !p
c
s !
!p
2
2
; c = 1
p L 0 C 0
(3.43)
,1: (3.44)
We see immediately that the wavenumber becomes imaginary in the evanescent region !