on the laser intensity is well described by a fitting formula given in [16]
where Coulomb log is modified to include the field strength v os /v e dependence in
ν
DO
ei in (2.6.14).
3.5 Electron Plasma Waves and Collisionless Absorption
In the discussion so far, the absorption of laser energy stems from the collisions of
electrons oscillating by the laser electric field, and the study of such classical laser
absorption demanded the correct evaluation of the collision frequency of electrons
by the ions in plasma or solid materials. When the plasma temperature is high
enough, such collisions merely happen, and the classical absorption rate tends to
inefficient. In such collisionless plasmas, the plasma waves are easily excited, and
the coupling of laser wave and the plasma waves will become important in the
energy conversion from laser to the plasma waves. In the limit of cold plasmas, the
plasma waves are the so-called electron plasma oscillation as shown soon, while
with finite temperature, this oscillation induces electron pressure perturbation and
propagates in the form of waves. Before discussion of the wave-wave coupling, the
plasma oscillations and plasma waves are derived. Since such oscillations and waves
are induced and propagated in plasma due to the long-range Coulomb force and they
are formed with the collective interactions among many electrons, such phenomena
like waves are called collective phenomena in plasmas.
In the case where small amplitude longitudinal waves are excited in plasmas, the
basic equation is the linearized equation of (2.2.11). The current by electron oscillations is obtained for the electrostatic field E in (2.3.3) by assuming one-direction x:
j x ¼ Àen 0 v,
1
ε 0
∂j x
∂t
¼ ω
2
pe E x
Then, (2.2.11) reduces the form in the oscillation direction, x:
∂E
∂t 2 þ ω
2
pe E ¼ 0
ð3:5:1Þ
where ω pe is the electron plasma frequency defined in (2.3.31), and it is constant with
a constant density, n e ¼ n 0 . (3.5.1) is the equation of a harmonic oscillator, while
each oscillation of electron layer is interacting each other via electric field in the
continuous plasma media.
The dispersion relation of (3.5.1) is simply obtained and shows the waves
oscillating with the frequency ω in the form:
104
3 Ultra-Short Pulse and Collisionless Absorption
where Coulomb log is modified to include the field strength v os /v e dependence in
ν
DO
ei in (2.6.14).
3.5 Electron Plasma Waves and Collisionless Absorption
In the discussion so far, the absorption of laser energy stems from the collisions of
electrons oscillating by the laser electric field, and the study of such classical laser
absorption demanded the correct evaluation of the collision frequency of electrons
by the ions in plasma or solid materials. When the plasma temperature is high
enough, such collisions merely happen, and the classical absorption rate tends to
inefficient. In such collisionless plasmas, the plasma waves are easily excited, and
the coupling of laser wave and the plasma waves will become important in the
energy conversion from laser to the plasma waves. In the limit of cold plasmas, the
plasma waves are the so-called electron plasma oscillation as shown soon, while
with finite temperature, this oscillation induces electron pressure perturbation and
propagates in the form of waves. Before discussion of the wave-wave coupling, the
plasma oscillations and plasma waves are derived. Since such oscillations and waves
are induced and propagated in plasma due to the long-range Coulomb force and they
are formed with the collective interactions among many electrons, such phenomena
like waves are called collective phenomena in plasmas.
In the case where small amplitude longitudinal waves are excited in plasmas, the
basic equation is the linearized equation of (2.2.11). The current by electron oscillations is obtained for the electrostatic field E in (2.3.3) by assuming one-direction x:
j x ¼ Àen 0 v,
1
ε 0
∂j x
∂t
¼ ω
2
pe E x
Then, (2.2.11) reduces the form in the oscillation direction, x:
∂E
∂t 2 þ ω
2
pe E ¼ 0
ð3:5:1Þ
where ω pe is the electron plasma frequency defined in (2.3.31), and it is constant with
a constant density, n e ¼ n 0 . (3.5.1) is the equation of a harmonic oscillator, while
each oscillation of electron layer is interacting each other via electric field in the
continuous plasma media.
The dispersion relation of (3.5.1) is simply obtained and shows the waves
oscillating with the frequency ω in the form:
104
3 Ultra-Short Pulse and Collisionless Absorption