Way *above* the highest resonant frequency the dielectric constant takes
on a simple form (factoring out
and doing the sum to the
lowest surviving order in
. As before, we start out
with:
&epsi#epsilon;(&omega#omega;) & = & &epsi#epsilon;_0 (1 + N e^2m
&sum#sum;_i f_i(&omega#omega;_i^2 - &omega#omega;^2 - i &omega#omega;&gamma#gamma;_i) )

& = & &epsi#epsilon;_0 (
1 - N e^2&omega#omega;^2 m
&sum#sum;_i f_i(1 + i&gamma#gamma;_i&omega#omega; -
&omega#omega;_i^2&omega#omega;^2) )

& &ap#approx;& &epsi#epsilon;_0 (
1 - NZ e^2&omega#omega;^2 m )

& &ap#approx;& &epsi#epsilon;_0 (1 -
&omega#omega;_p^2&omega#omega;^2)
where

(11.68) |

This is called the

The wave number in this limit is given by:

(11.69) |

(or ). This is called a

In certain physical situations (such as a plasma or the ionosphere) all the electrons are essentially ``free'' (in a degenerate ``gas'' surrounding the positive charges) and resonant damping is neglible. In that case this relation can hold for frequencies well below (but well above the static limit, since plasmas are low frequency ``conductors''). Waves incident on a plasma are reflected and the fields inside fall off exponentially away from the surface. Note that

(11.70) |

shows how electric flux is expelled by the ``screening'' electrons.

The reflectivity of metals is caused by essentially the same mechanism. At high frequencies, the dielectric constant of a metal has the form

(11.71) |

where is the ``plasma frequency'' of the conduction electrons. is the ``effective mass'' of the electrons, introduced to describe the effects of binding phenomenologically.

Metals reflect according to this rule (with a very small field penetration length of ``skin depth'') as long as the dielectric constant is negative; in the ultraviolet it becomes positive and metals can become transparent. Just one of many problems involved in making high ultraviolet, x-ray and gamma ray lasers -- it is so hard to make a mirror!