particles, and it is the reason why statistical model of (2.4.7) can be applied. This
ideal plasma condition is:
Λ ¼ 4πnλ
3
D $
4π
3
nλ
3
D >> 1
The sphere made of the radius of Debye length is called Debye sphere. The typical
values of lnΛ are around 10 and change very slowly to density and temperature. In
the region where relatively low temperature and high-density region, the present
ideal plasma assumption cannot be applied and (2.4.18) should be modified by
taking account of the strongly coupling in nonideal plasma.
The b min in the Coulomb logarithm has been evaluated classically while
impacting electron has a finite size given by the uncertain principle, namely, de
Broglie length. So, it is reasonable to think that the electron minimum impact should
be larger than the de Broglie length:
b
qm
min ¼
ħ
2mv
It is better to define an effective bmin as:
b min ¼ max b
cl
min , b
qm
min
È
É
where b min
cl
¼ b 0 in (2.4.17). This condition is calculated to be for the thermal
velocity v ¼ (T e /m)
1/2
:
T e ! 20Z
2 eV
½
It is very clear that the quantum effect is dominant in most of plasma.
The electron collision frequency averaged over Maxwell distribution is obtained
as:
ν ei ¼ n i σ C v
h
i¼
Z
2π
ln Λ
n e λ
3
D
ω pe
ð2:4:20Þ
The electron mean free path due to Coulomb scattering by ions in plasma is given
from (2.4.18) by taking the average for Maxwell distribution:
ℓ ei ¼
1
n i σ C
h i
¼
2π
Z ln Λ
n e λ
3
D λ D
where the mean free path of an electron with the velocity v is given with (2.4.6) in
the form:
60
2 Laser Absorption by Coulomb Collision
ideal plasma condition is:
Λ ¼ 4πnλ
3
D $
4π
3
nλ
3
D >> 1
The sphere made of the radius of Debye length is called Debye sphere. The typical
values of lnΛ are around 10 and change very slowly to density and temperature. In
the region where relatively low temperature and high-density region, the present
ideal plasma assumption cannot be applied and (2.4.18) should be modified by
taking account of the strongly coupling in nonideal plasma.
The b min in the Coulomb logarithm has been evaluated classically while
impacting electron has a finite size given by the uncertain principle, namely, de
Broglie length. So, it is reasonable to think that the electron minimum impact should
be larger than the de Broglie length:
b
qm
min ¼
ħ
2mv
It is better to define an effective bmin as:
b min ¼ max b
cl
min , b
qm
min
È
É
where b min
cl
¼ b 0 in (2.4.17). This condition is calculated to be for the thermal
velocity v ¼ (T e /m)
1/2
:
T e ! 20Z
2 eV
½
It is very clear that the quantum effect is dominant in most of plasma.
The electron collision frequency averaged over Maxwell distribution is obtained
as:
ν ei ¼ n i σ C v
h
i¼
Z
2π
ln Λ
n e λ
3
D
ω pe
ð2:4:20Þ
The electron mean free path due to Coulomb scattering by ions in plasma is given
from (2.4.18) by taking the average for Maxwell distribution:
ℓ ei ¼
1
n i σ C
h i
¼
2π
Z ln Λ
n e λ
3
D λ D
where the mean free path of an electron with the velocity v is given with (2.4.6) in
the form:
60
2 Laser Absorption by Coulomb Collision