b 0 ¼ 1:1 Â 10
À8 Z
ε eV
cm
½
ð2:4:5Þ
where ε eV is the kinetic energy of the impacting electron. It is noted that scattering
cross section like molecules of about 1 Å corresponds to the collision in plasma with
electron thermal energy of about 1 eV, and the cross section decreases in proportion
to the inverse of square of the energy of impacting electron.
The 90 degree scatter mean free path is consequently proportional to the square of
energy in the form.
ℓ
R
90 ¼
1
n i σ R
90
¼ 2:6 Â 10
15 ε eV
ð Þ
2
Zn e
cm
½
ð2:4:6Þ
where n e in [cm
À3 ]. Note that this mean free path is about 80 times longer than
Coulomb mean free path as seen soon later. For example, in magnetic confinement
fusion, the plasma with the density of 10
14 cm
À3 and the temperature of about
10 keV are confined in a torus device. The electron mean free path of (2.4.6) is
roughly 6500 km or 100 km. It is clear that such high-temperature fusion plasma is
collisionless plasma.
In order to evaluate the transport properties by Coulomb collision in plasma,
small-angle scattering whose impact parameter is larger than (2.4.5) should be
considered quantitatively. Rutherford scattering differential cross section is used to
integrate all contribution of different angle scattering and the contribution by
integrating over all velocities. However, a new problem appears, that is, the
integration over the total impact parameter leads the divergence of the total scattering
cross section. The Coulomb charge shielding schematically shown in Fig. 2.12a
around a certain ion should be taken into account for small-angle scattering as
described.
Fig. 2.12 The image of Debye shielding. (a): Schematic image of a snapshot of electrons and ions
near a certain ion. The electrons are attracted by the Coulomb force of the ion, while ions are
repulsed by this force. (b): The image of the Debye sphere where a huge number of electron and
ions are distributed statistically. The green color means the distribution of negative charge. At the
radius of Debye sphere, the 1/r Coulomb charge in vacuum is shielded, and the central ion has no
effect outside of the Debye sphere
2.4 Electron Coulomb Collision by Ions in Plasma
55
À8 Z
ε eV
cm
½
ð2:4:5Þ
where ε eV is the kinetic energy of the impacting electron. It is noted that scattering
cross section like molecules of about 1 Å corresponds to the collision in plasma with
electron thermal energy of about 1 eV, and the cross section decreases in proportion
to the inverse of square of the energy of impacting electron.
The 90 degree scatter mean free path is consequently proportional to the square of
energy in the form.
ℓ
R
90 ¼
1
n i σ R
90
¼ 2:6 Â 10
15 ε eV
ð Þ
2
Zn e
cm
½
ð2:4:6Þ
where n e in [cm
À3 ]. Note that this mean free path is about 80 times longer than
Coulomb mean free path as seen soon later. For example, in magnetic confinement
fusion, the plasma with the density of 10
14 cm
À3 and the temperature of about
10 keV are confined in a torus device. The electron mean free path of (2.4.6) is
roughly 6500 km or 100 km. It is clear that such high-temperature fusion plasma is
collisionless plasma.
In order to evaluate the transport properties by Coulomb collision in plasma,
small-angle scattering whose impact parameter is larger than (2.4.5) should be
considered quantitatively. Rutherford scattering differential cross section is used to
integrate all contribution of different angle scattering and the contribution by
integrating over all velocities. However, a new problem appears, that is, the
integration over the total impact parameter leads the divergence of the total scattering
cross section. The Coulomb charge shielding schematically shown in Fig. 2.12a
around a certain ion should be taken into account for small-angle scattering as
described.
Fig. 2.12 The image of Debye shielding. (a): Schematic image of a snapshot of electrons and ions
near a certain ion. The electrons are attracted by the Coulomb force of the ion, while ions are
repulsed by this force. (b): The image of the Debye sphere where a huge number of electron and
ions are distributed statistically. The green color means the distribution of negative charge. At the
radius of Debye sphere, the 1/r Coulomb charge in vacuum is shielded, and the central ion has no
effect outside of the Debye sphere
2.4 Electron Coulomb Collision by Ions in Plasma
55