It is noted that the absorption for the intensity less than 10
17 W/cm
2 is mainly due
to the classical absorption already mentioned in Chap. 3. The rapid increase of the
absorption fraction over 10
19 W/cm
2 is consistent with the absorption fraction in
Fig. 7.8 for the energy contrast 2 Â 10
À4 . For explaining the experimental data, the
pre-formed plasma and ion motion effects are studied with 2D PIC code. It is
informative to show the result of absorption fraction η ab for 3 Â 10
20 W/cm
2 resulted
by the PIC code. Case A, η ab ¼ 37% for ion fixed, no pre-plasma. Case B, η ab ¼ 68%
for mobile ion, no pre-plasma. Case C, η ab ¼ 63% for ion fixed, pre-plasma with
L > λ. Comparing these three simulation results, it is said that the pre-plasma
enhances the absorption fraction and the ion motion help to form the plasma cloud
near the surface of solid target. Of course, the pre-formed plasma and mobile ions
help the increase of the absorption rate.
In Fig. 7.8, the comparison has been done for three different lasers with the short
pulse duration of about 50 fs, while the pulse duration of the Callisto laser is 150 fs,
three times longer. Let us roughly evaluate how long it takes that the ions move over
about laser wavelength λ due to the ambipolar field by electrons under the
ponderomotive force. The ion motion is governed by the ambipolar field force,
and it should balance with the ponderomotive force as follows:
m i
du i
dt
¼ þeE
0 ¼ ÀeE À
∂
∂x
U PM
ð7:1:1Þ
Inserting the ponderomotive potential in (3.7.10) into (7.1.1), the dimensional
analysis provides the following characteristic velocity of the ion fluid:
V PM ~ c
ffiffiffiffiffiffiffiffiffiffiffiffi ffi
m e
m i
γ
h i
r
ð7:1:2Þ
The time for ions to move over λ ¼ 800 nm is typically about 160 fs for the root of
the mass ratio 60 and <γ>~1 from (7.1.2). This means the pulse duration of 150 fs is
very critical value for the ion motion becomes important and the expanding plasma is
created during the laser duration.
7.3 Absorption Enhancement by Hot Electron
Re-circulation
It became clear that the absorption rate of ultra-short intense laser is sensitive to
pre-formed plasma scale-length and pulse duration. In addition, it is experimentally
and computationally demonstrated that the absorption rate is also sensitive to laser
focal spot size, target thickness, and pulse duration [9]. In order to clarify the
248
7 Relativistic Laser and Solid Target Interactions
17 W/cm
2 is mainly due
to the classical absorption already mentioned in Chap. 3. The rapid increase of the
absorption fraction over 10
19 W/cm
2 is consistent with the absorption fraction in
Fig. 7.8 for the energy contrast 2 Â 10
À4 . For explaining the experimental data, the
pre-formed plasma and ion motion effects are studied with 2D PIC code. It is
informative to show the result of absorption fraction η ab for 3 Â 10
20 W/cm
2 resulted
by the PIC code. Case A, η ab ¼ 37% for ion fixed, no pre-plasma. Case B, η ab ¼ 68%
for mobile ion, no pre-plasma. Case C, η ab ¼ 63% for ion fixed, pre-plasma with
L > λ. Comparing these three simulation results, it is said that the pre-plasma
enhances the absorption fraction and the ion motion help to form the plasma cloud
near the surface of solid target. Of course, the pre-formed plasma and mobile ions
help the increase of the absorption rate.
In Fig. 7.8, the comparison has been done for three different lasers with the short
pulse duration of about 50 fs, while the pulse duration of the Callisto laser is 150 fs,
three times longer. Let us roughly evaluate how long it takes that the ions move over
about laser wavelength λ due to the ambipolar field by electrons under the
ponderomotive force. The ion motion is governed by the ambipolar field force,
and it should balance with the ponderomotive force as follows:
m i
du i
dt
¼ þeE
0 ¼ ÀeE À
∂
∂x
U PM
ð7:1:1Þ
Inserting the ponderomotive potential in (3.7.10) into (7.1.1), the dimensional
analysis provides the following characteristic velocity of the ion fluid:
V PM ~ c
ffiffiffiffiffiffiffiffiffiffiffiffi ffi
m e
m i
γ
h i
r
ð7:1:2Þ
The time for ions to move over λ ¼ 800 nm is typically about 160 fs for the root of
the mass ratio 60 and <γ>~1 from (7.1.2). This means the pulse duration of 150 fs is
very critical value for the ion motion becomes important and the expanding plasma is
created during the laser duration.
7.3 Absorption Enhancement by Hot Electron
Re-circulation
It became clear that the absorption rate of ultra-short intense laser is sensitive to
pre-formed plasma scale-length and pulse duration. In addition, it is experimentally
and computationally demonstrated that the absorption rate is also sensitive to laser
focal spot size, target thickness, and pulse duration [9]. In order to clarify the
248
7 Relativistic Laser and Solid Target Interactions