σ DC ¼
e
2 n e
m
τ
ð2:3:23Þ
It is easy to understand this relation, because the conductivity is higher in less
collision in material, and higher density of free electrons. The well-known basic
relation of Ohm law for an electric device is given in the form:
V ¼ RI
ð2:3:24Þ
where V is an applied voltage, I is electric current, and R is resistivity in the unit of
Ω. Comparing (2.3.22) to the relation of a device (2.3.24), the local electrical
resistivity η should be:
η ¼ 1=σ ΩÁ cm
½
Š
ð2:3:25Þ
In the case of alternating electric field like laser radiation in plasmas, the AC
conductivity is given as Drude model in the form:
σ AC ¼ σ DC
1
1 þ iωτ
ð2:3:26Þ
1
1 þ iωτ
¼
1
1 þ ω 2 τ 2 À i
ωτ
1 þ ω 2 τ 2
The real and imaginary parts of DC conductivity of (2.3.26) are shown in Fig. 2.10 as
a function of frequency. It is noted that the real part of the conductivity drops near the
frequency equal to the collision frequency. In the limit of no friction, the
conductivity becomes pure imaginary in the form:
Fig. 2.10 The real and
imaginary parts of the factor
from DC to AC conductivity
in Drude model defined in
(2.3.18) is plotted. The
imaginary part is at the
maximum for the frequency
ωτ ¼ 1
2.3 Electron Current Induced by Laser Fields
51