τ / v
3
ð2:4:24
0
Þ
Since the relaxation time strongly depends on the velocity of plasma particles, there
should be some unique characters in transport phenomena in plasma.
Consider the physical process where the non-Maxwellian velocity distribution
finally becomes Maxwellian for electron and ion groups. It is important to take
account of the fact that the electron-electron Coulomb collision allows exchange of
momentum and energy in each collision and the same as between ion-ion collision.
However, it is not the case of the collision of electrons by ions because of the big
difference of the masses. The electrons can change momentum easily through the
collision with ions, while energy does not change enough in this case. The ions do
not exchange the momentum and energy substantially at the collision with electrons.
Such fact indicates that the electron and ion groups become Maxwellian distribution
keeping each total energy almost constant, namely, with different temperatures, and
finally after a long time, both gases will be in the Maxwell distributions with the
same temperature.
Now, consider the electron motion via Coulomb collision in the x-y
2-dimensional velocity space. As shown in Fig. 2.13, each electron moves like “a”
or “b” after the collision with an ion, since the electron momentum predominantly
changes after the collision with ion and the energy is almost kept constant. On the
other hand, an electron changes momentum and energy after the collision with
another electrons, namely, its position in Fig. 2.13 will move to any directions
including special cases like a, b, c, and d.
Let us evaluate the relaxation times of electron and ion gases to their Maxwellian
distributions only through the collisions with the same particles, electron gas τ e and
ion gas τ i . The Rutherford scattering cross σ in (2.4.18) should be applied to the
center of mass of binary collision, and the following relaxation times can be
obtained:
V y
V x
a
b
c
d
0
Fig. 2.13 In the velocity space of electrons, the scattering with ions changes the angle by keeping
the absolute value of the velocity (energy), and almost no energy transfer is expected (the change is
the direction a or b), while the collision with other electrons provides not only the angle scattering
but also the energy change shown with the direction c or d
2.4 Electron Coulomb Collision by Ions in Plasma
63
3
ð2:4:24
0
Þ
Since the relaxation time strongly depends on the velocity of plasma particles, there
should be some unique characters in transport phenomena in plasma.
Consider the physical process where the non-Maxwellian velocity distribution
finally becomes Maxwellian for electron and ion groups. It is important to take
account of the fact that the electron-electron Coulomb collision allows exchange of
momentum and energy in each collision and the same as between ion-ion collision.
However, it is not the case of the collision of electrons by ions because of the big
difference of the masses. The electrons can change momentum easily through the
collision with ions, while energy does not change enough in this case. The ions do
not exchange the momentum and energy substantially at the collision with electrons.
Such fact indicates that the electron and ion groups become Maxwellian distribution
keeping each total energy almost constant, namely, with different temperatures, and
finally after a long time, both gases will be in the Maxwell distributions with the
same temperature.
Now, consider the electron motion via Coulomb collision in the x-y
2-dimensional velocity space. As shown in Fig. 2.13, each electron moves like “a”
or “b” after the collision with an ion, since the electron momentum predominantly
changes after the collision with ion and the energy is almost kept constant. On the
other hand, an electron changes momentum and energy after the collision with
another electrons, namely, its position in Fig. 2.13 will move to any directions
including special cases like a, b, c, and d.
Let us evaluate the relaxation times of electron and ion gases to their Maxwellian
distributions only through the collisions with the same particles, electron gas τ e and
ion gas τ i . The Rutherford scattering cross σ in (2.4.18) should be applied to the
center of mass of binary collision, and the following relaxation times can be
obtained:
V y
V x
a
b
c
d
0
Fig. 2.13 In the velocity space of electrons, the scattering with ions changes the angle by keeping
the absolute value of the velocity (energy), and almost no energy transfer is expected (the change is
the direction a or b), while the collision with other electrons provides not only the angle scattering
but also the energy change shown with the direction c or d
2.4 Electron Coulomb Collision by Ions in Plasma
63