ωτ << 1 ! ν ab ¼
ω
2
pe
ν
¼ τω
2
pe
ð2:3:34Þ
It should be noted that for the given collision and plasma frequencies, the
dependence of the absorption rate becomes opposite one to the collision frequency
in two limiting regimes of the frequency of the external fields. It is strange intuitively
the absorption rate of (2.3.34) is proportional to the collision frequency inversely.
This is the case of DC conductivity, and electrons obtain large amount of energy
before the energy is converted to the thermal energy, random velocities, before each
collision.
2.4 Electron Coulomb Collision by Ions in Plasma
It is clear that in order to know how efficiently laser heats the plasmas, it is necessary
to obtain the collision frequency of the plasmas.
The gas theory can be applicable not only to neutral gas but also plasmas both of
which consist of thermal particles. Most properties of electron collision in plasmas
can be derived according to the particle collisions in gas. As long as, therefore, the
plasma is locally in thermodynamic equilibrium, the thermodynamics properties,
statistical behavior, and hydrodynamics can be formulated from the analogy of gas.
In what follows, the resemblance and difference in case of plasma compared to
neutral molecular gas are explained by comparing the mean free paths due to
collisions.
Although molecules in air cannot be seen by the naked eyes, it is made of a group
of molecules with 80% nitrogen and 20% oxygen. The molecules interact with each
other by molecular polarization force and collide like billiard balls. The radius at
which the molecule force becomes strong is the effective distance of Van der Waals
force, and for oxygen molecules, it is about 1.5 Å. Since the number density of
molecules in air is about 3 Â 10
19 cm
À3 , the mean free path of air is roughly
evaluated as:
ℓ air ¼
1
πr 2 n
¼ 5 Â 10
À5
cm
½
ð2:4:1Þ
where r ¼ 1.5 Å is assumed. The average molecular thermal velocity is roughly the
speed of sound. Setting average molecular thermal velocity is v ¼ 330 [m/s]; then it
is calculated easily that the each molecule collides another molecules 6.6 Â 10
8
times per second. This means that since the molecules very frequently exchange
energy and momentum with other molecules, air is in thermodynamic equilibrium at
any time much less than a second. Therefore, it is reasonable to use Maxwell
distribution to the velocity distribution of the group of air molecules. In such
molecular gas or liquids, collisional mean free path is too short, and, for example,
the diffusion time due to the collisions is very long as see later. As the result, not
2.4 Electron Coulomb Collision by Ions in Plasma
53
ω
2
pe
ν
¼ τω
2
pe
ð2:3:34Þ
It should be noted that for the given collision and plasma frequencies, the
dependence of the absorption rate becomes opposite one to the collision frequency
in two limiting regimes of the frequency of the external fields. It is strange intuitively
the absorption rate of (2.3.34) is proportional to the collision frequency inversely.
This is the case of DC conductivity, and electrons obtain large amount of energy
before the energy is converted to the thermal energy, random velocities, before each
collision.
2.4 Electron Coulomb Collision by Ions in Plasma
It is clear that in order to know how efficiently laser heats the plasmas, it is necessary
to obtain the collision frequency of the plasmas.
The gas theory can be applicable not only to neutral gas but also plasmas both of
which consist of thermal particles. Most properties of electron collision in plasmas
can be derived according to the particle collisions in gas. As long as, therefore, the
plasma is locally in thermodynamic equilibrium, the thermodynamics properties,
statistical behavior, and hydrodynamics can be formulated from the analogy of gas.
In what follows, the resemblance and difference in case of plasma compared to
neutral molecular gas are explained by comparing the mean free paths due to
collisions.
Although molecules in air cannot be seen by the naked eyes, it is made of a group
of molecules with 80% nitrogen and 20% oxygen. The molecules interact with each
other by molecular polarization force and collide like billiard balls. The radius at
which the molecule force becomes strong is the effective distance of Van der Waals
force, and for oxygen molecules, it is about 1.5 Å. Since the number density of
molecules in air is about 3 Â 10
19 cm
À3 , the mean free path of air is roughly
evaluated as:
ℓ air ¼
1
πr 2 n
¼ 5 Â 10
À5
cm
½
ð2:4:1Þ
where r ¼ 1.5 Å is assumed. The average molecular thermal velocity is roughly the
speed of sound. Setting average molecular thermal velocity is v ¼ 330 [m/s]; then it
is calculated easily that the each molecule collides another molecules 6.6 Â 10
8
times per second. This means that since the molecules very frequently exchange
energy and momentum with other molecules, air is in thermodynamic equilibrium at
any time much less than a second. Therefore, it is reasonable to use Maxwell
distribution to the velocity distribution of the group of air molecules. In such
molecular gas or liquids, collisional mean free path is too short, and, for example,
the diffusion time due to the collisions is very long as see later. As the result, not
2.4 Electron Coulomb Collision by Ions in Plasma
53