Fermi temperature, and the collision frequency is calculated through electronphonon interaction in the lower temperature. In the case of electron-phonon interaction, the electron collision frequency depends on the ion temperature determining
the phonon amplitude, and the electron-ion collisional temperature relaxation time
should be well modeled in non-plasma state. Since the phonon amplitude increases
in proportion to the ion temperature, the collision frequency increases at first as the
increase of ion temperature and then decreases when the collision frequency as
plasmas becomes dominant as the form (2.6.14). In addition, the electron and ion
temperatures are very different, and equation of state (EOS) should be modeled
independently.
The collision of electrons by phonon in dense matter has been studied relating to
the electron collision in the partially degenerated matter in white dwarfs and at the
surface of neutron stars. When the electron temperature is below the Fermi temperature, the free electrons are predominantly scattered by the phonons or lattice
vibrations, and the collision frequency in such case has been derived in the approximated form [5]:
ν ep ¼ 2k s
e
2 T i
ħ
2 v F
ð3:2:1Þ
where k s is a numerical constant and v F is the Fermi velocity. It is noted that the solid
aluminum Fermi temperature (¼mv F
2 ) is 11.7 eV, and (3.2.1) is applicable for the
lower temperature than about 10 eV. In contrast, (2.6.14) is good for higher
temperature than the Fermi temperature in the dense aluminum. Both models,
however, becomes nonphysical if the mean free path obtained with these collision
frequencies becomes shorter than the average ion distance r 0 defined by:
4π
3
r
3
0 n i ¼ 1
Note that this radius r 0 is usually called ion sphere radius. Taking account of such
physics, the collision frequency from the solid material to ablating plasmas can be
modeled as shown in Fig. 3.9 [5]. In Fig. 3.9, the thick solid curve is used for
simulation, while the thin solid curve obtained from the interpolation formula of
(2.6.14) and (3.2.1):
ν
À1
¼ ν
À1
ei þ ν
À1
ep
ð3:2:2Þ
In Fig. 3.9, the collision frequency in the ambiguous region sandwiching the Fermi
temperature is given by a simple relation that the mean free path is the ion sphere
radius, namely, ν ¼ v e /r 0 . In addition, a collision frequency derived from the surface
reflectivity at room temperature is used as the limiting value of collision frequency in
the lowest temperature region as shown in Fig. 3.9.
3.2 Self-Consistent Analysis of Short Pulse Absorption
89
the phonon amplitude, and the electron-ion collisional temperature relaxation time
should be well modeled in non-plasma state. Since the phonon amplitude increases
in proportion to the ion temperature, the collision frequency increases at first as the
increase of ion temperature and then decreases when the collision frequency as
plasmas becomes dominant as the form (2.6.14). In addition, the electron and ion
temperatures are very different, and equation of state (EOS) should be modeled
independently.
The collision of electrons by phonon in dense matter has been studied relating to
the electron collision in the partially degenerated matter in white dwarfs and at the
surface of neutron stars. When the electron temperature is below the Fermi temperature, the free electrons are predominantly scattered by the phonons or lattice
vibrations, and the collision frequency in such case has been derived in the approximated form [5]:
ν ep ¼ 2k s
e
2 T i
ħ
2 v F
ð3:2:1Þ
where k s is a numerical constant and v F is the Fermi velocity. It is noted that the solid
aluminum Fermi temperature (¼mv F
2 ) is 11.7 eV, and (3.2.1) is applicable for the
lower temperature than about 10 eV. In contrast, (2.6.14) is good for higher
temperature than the Fermi temperature in the dense aluminum. Both models,
however, becomes nonphysical if the mean free path obtained with these collision
frequencies becomes shorter than the average ion distance r 0 defined by:
4π
3
r
3
0 n i ¼ 1
Note that this radius r 0 is usually called ion sphere radius. Taking account of such
physics, the collision frequency from the solid material to ablating plasmas can be
modeled as shown in Fig. 3.9 [5]. In Fig. 3.9, the thick solid curve is used for
simulation, while the thin solid curve obtained from the interpolation formula of
(2.6.14) and (3.2.1):
ν
À1
¼ ν
À1
ei þ ν
À1
ep
ð3:2:2Þ
In Fig. 3.9, the collision frequency in the ambiguous region sandwiching the Fermi
temperature is given by a simple relation that the mean free path is the ion sphere
radius, namely, ν ¼ v e /r 0 . In addition, a collision frequency derived from the surface
reflectivity at room temperature is used as the limiting value of collision frequency in
the lowest temperature region as shown in Fig. 3.9.
3.2 Self-Consistent Analysis of Short Pulse Absorption
89