as suggested in a stellar evolution theory; (2.3.19) provides the limit of the mass of a
massive star M which can be a stationary star. This limiting mass is called
Eddington limit.
2.3.2 Electron Current in Matters
To make the calculation more general, consider the finite resistivity even in
conducting metals and plasmas. It is noted that the high-temperature plasma is of
very good conductor, but still small resistivity remained due to electron binary
collisions with heavy ions. This is a kind of viscosity fluid, and the frictional force
should be included in (2.3.1).
Start with (2.3.1), neglect small force by magnetic field, and include the effect of
electron collision by the background ions. The equation to derive the free electron
current in non-relativistic condition is given to be:
m
d
dt
v ¼ ÀeE À mνv
ð2:3:20Þ
where ν is the collision frequency of electron with the background ions. In order to
obtain the induced current by laser field such as in (2.2.18), assume complex
expression to (2.3.20) and assume that E is in the x direction inducing the velocity
v. The following electron velocity is obtained:
v ¼ Ài
e
mω
1
1 þ iν=ω
E
ð2:3:21Þ
Assuming that all electrons have the same velocity, the following DC current is
derived for ω ¼ 0:
j ¼ Àenv ¼
e
2 n e
mν
E ¼
e
2 n e
m
τE
where n e is the electron density, and the collision time τ(1/ν) is also introduced. It
is familiar that metals are good conductor due to a lot of free electrons inside. The
electrical conductivity σ is defined by:
j ¼ σE
ð2:3:22Þ
The DC conductivity σ DC is obtained in the form:
50
2 Laser Absorption by Coulomb Collision