Cent. Eur. J. Phys. • 11(5) • 2013 • 575-579
DOI: 10.2478/s11534-013-0218-0
Central European Journal of Physics
Plastic plasma interaction with plasmas with growing
atomic number
Research Article
Andrzej Kasperczuk1 , Tadeusz Pisarczyk1∗ , Tomasz Chodukowski1 , Zofia Kalinowska1 ,
Sergey Gus’kov2 , Nikolai Demchenko2 , Jiri Ullschmied3 , Eduard Krousky4 , Miroslav Pfeifer4 , Jiri Skala4 ,
Daniel Klir5 , Jozef Kravarik5 , Pavel Kubes5 , Jakub Cikhardt5 , Karel Rezac5 , Pawel Pisarczyk6
1 Institute of Plasma Physics and Laser Microfusion,
23 Hery St., 00-908 Warsaw, Poland
2 P.N. Lebedev Physical Institute of RAS,
53 Leninsky Ave., 119 991 Moscow, Russia
3 Institute of Plasma Physics ASCR, v.v.i.,
Za Slovankou 3, 182 00 Prague 8, Czech Republic
4 Institute of Physics ASCR, v.v.i.,
Na Slovance 2, 182 21 Prague 8, Czech Republic
5 Czech Technical University in Prague, FEE
Prague, Czech Republic
6 Warsaw University of Technology, ICS,
15/19 Nowowiejska St., 00-665 Warsaw, Poland
Received 09 March 2013; accepted 02 April 2013
Abstract:
This paper describes the investigation of the influence of target material atomic number (Z ) on the laserproduced plasma pressure. For this reason, several target materials representing a wide range of atomic
numbers (Z = 3.5 − 73), i.e. plastic (C H), Al, C u, Ag, and T a, were used. The results presented show
that the plasma pressure decreases with growing atomic number but in a limited range of Z only. For
higher Z , starting approximately from Z = 47 (Ag), the plasma pressure becomes constant, as confirmed
by interferometric measurements and x-ray plasma imaging.
PACS (2008): 52.38.-r; 52.57.-z
Keywords:
plasma pressure • plastic plasma • plasma
© Versita sp. z o.o.
1.
Introduction
∗
E-mail: [email protected]
Inertial confinement fusion (ICF) is an approach to fusion
that relies on the inertia of the fuel mass to provide confinement. In a direct drive ICF target the efficiency of laser
radiation absorption requires the ablation pressure to be
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Plastic plasma interaction with plasmas with growing atomic number
In our previous papers [e.g. [4]] we have demonstrated
that the laser-produced plasma pressure depends on the
atomic number of target material. The experiments carried
out at the PALS iodine laser facility for three target materials, namely plastic (C H, Z = 3.5), Al (13), and C u (29),
indicated that the plasma pressure decreases with growing Z . As the target irradiation geometry in the PALS
experiments is annular-like, a part of the laser-produced
plasma collides on the axis, generating convergent plasma
streams. However, this mechanism acts well only in the
case of heavy target materials. If the target consisted of
light materials like plastic or Al, no plasma jets were observed, despite that, the initial laser intensity distribution
was the same. Nevertheless, the above phenomenon allowed us to create high-quality Al plasma jets using C H
plasma as a compressor [5, 6]. Besides that, we used a
combination of C u and C H targets to improve the parameters of C u plasma jets, as well as to obtain more complex
plasma configurations, where a C u plasma pipe served as
a nozzle for the C H plasma [7].
In connection with the above activities the question arose
whether the decrease of plasma pressure with growing Z
is permanent or not. In order to answer this, in addition
to the previously used target materials (C H, Al, and C u),
we exploited two heavier target materials, Ag (47) and T a
(73), to investigate the largest range of atomic numbers
as possible.
2. Experimental set-up and conditions
The experiment was carried out with the use of the PALS
laser facility. For plasma generation we used a laser beam
of diameter 290 mm, which was focused by means of an
aspherical lens with a focal length of 600 mm for the third
harmonic of the laser radiation used (λ = 0.438 µm). The
following parameters for target irradiation have been chosen: laser energy EL = 130 J, focal spot diameter (ΦL )
600 µm (the focal point being located inside the target),
and pulse duration 250 ps (full width at half maximum). In
the reported experiments two kinds of targets were used:
y [mm]
a) 1
7 ns
7 ns
Al
0 Al
Shot: 41214/3
Shot: 41214/2
1
b) 1
7 ns
7 ns
Al
y [mm]
as large as possible and the use of materials with low
atomic number (Z ), such as DT-ice. The ablator employs
various plastics and beryllium, are employed as an ablator. For examples see monographs [1]-[3]). As the atomic
number of the target increases, the laser-produced plasma
energy losses grow due to thermal emission. It leads to
a drop in coupling efficiency of the laser energy in the
target and leads to the ablation pressure decreasing. The
degree of plasma pressure reduction with growing Z is an
important issue.
Al
0 CH
CH
Al
Al
Shot: 41216/3
Shot: 41216/2
1
0
1
Figure 1.
2
z [mm]
3
4
0
1
2
z [mm]
3
Interferograms and x-ray images of the plasma produced
on Al and Al+C H targets, taken at t = 7 ns (a - pure Al
target, b - Al target with C H insert).
• massive targets made of Al, C u, Ag, and T a, as
well as
• the same targets but with a cylindrical C H insert
of diameter Φin = 200 µm.
The plasma stream configurations were studied by means
of a three-frame laser interferometric system with automatic image processing. Each of the interferometric channels was equipped with an independent interferometer of
the folding-wave type. In parallel to interferometry, a
four-frame x-ray pinhole-camera with a 80 µm diameter
pinhole was used, registering soft x-ray plasma radiation
in the range of 10 - 1000 eV. The exposure time of the
x-ray camera was below 2 ns.
3.
Experimental results
In Figs. 1 - 4 interferograms and x-ray plasma images
at t = 7 ns, are presented for all the targets used. For
comparison, the results corresponding to the targets without and with the CH insert are grouped in pairs. One can
see that the pure Al plasma stream differs essentially from
those launched on heavier targets. Whereas the plasma
streams in the latter cases have a very narrow shape with
a diameter of 200 - 300 µm, the Al plasma stream diameter is about three times greater. Despite that, the influence of the C H insert on the plasma stream structure is
clearly seen in all the cases. One can see that the diameter of these plasma streams grows due to the influence of
C H plasma pressure. It is obvious that a greater plasma
stream diameter provides evidence of a lower pressure of
the surrounding plasma.
Thanks to very sharp borders of the plasma streams in the
interferograms, the influence of C H insert on the resulting
plasma shape can be presented in a numerical form. Because of differences in the plasma stream configurations
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4
Andrzej Kasperczuk et al.
y [mm]
a) 1
6
7 ns
7 ns
Cu
0 Cu
5
Shot: 41209/2
Shot: 41209/2
1
4
y [mm]
b) 1
7 ns
Cu
0 CH
CH
Cu
η3
Cu
Shot: 41211/2
Shot: 41211/2
1
0
Figure 2.
1
2
z [mm]
3
y [mm]
0
4
1
2
z [mm]
4
0
Shot: 41242/3
7 ns
Ag
0 CH
CH
Ag
Ag
Shot: 41248/2
Shot: 41248/2
Figure 3.
1
2
z [mm]
3
4
0
1
2
z [mm]
3
4
Interferograms and x-ray images of the plasma produced
on Ag and Ag+C H targets, taken at t = 7 ns (a - pure Ag
target, b - Ag target with C H insert).
corresponding to various target materials, the ratio of diameters of plasma streams generated with and without the
C H insert was taken as a common factor (η) for all the
cases. In Fig. 5 the diagram of η = dA+C H /dA (where d
means the plasma stream diameter, while A stands for the
target materials used) as a function of the atomic number
of the target materials is plotted. The diameters of the
plasma streams were measured in the interferograms at
a) 1
0 Ta
Ta
Shot: 41226/4
Shot: 41226/2
7 ns
7 ns
Ta
Ta
0 CH
CH
40
Z
50
60
70
80
Plot of η = dA+C H /dA as a function of the target material
atomic number, where d means the plasma stream diameter at distance of 1.5 mm from the target, and A stands
for the target materials used (C H, Al, C u, Ag, and T a).
an arbitrary chosen distance of 1.5 mm from the target.
The diagram starts from unity, which corresponds to C H
target with C H insert. Then, η gradually grows up to Z =
47. It corresponds to the plasma pressure decrease with
growing Z . However, the increase of η ends for Z ≥ 47,
where the value of η becomes constant. It means that the
pressures of the Ag and T a plasmas are roughly equal
to one another. This fact leads to the conclusion that the
pressure reaches minimum just for Ag plasma and does
not change for plasmas with higher Z anymore.
Ta
Ta
Shot: 41241/3
Shot: 41241/2
1
Figure 4.
30
4. Discussion of the experimental
results
1
0
20
To make sure that the plasma pressure becomes constant
above Z = 47, we also employed a T a target with an
Ag insert of 200 µm in diameter. At the same pressure of
the Ag and T a plasmas the plasma stream launched on
that target should take a narrow form like those launched
on pure Ag and T a targets. The results are presented in
Fig. 6 where, for comparison, the plasma streams of pure
Ag and T a plasmas are shown too. One can see that the
shapes of all the plasma streams are very similar, which
speaks in favor of correctness of the diagram in Fig. 6.
7 ns
7 ns
b) 1
10
7 ns
Ag
1
y [mm]
0
Figure 5.
0
Al
1
Ag
0 Ag
Shot: 41242/2
y [mm]
2
CH
Ta
Ag
7 ns
7 ns
1
b) 1
y [mm]
3
Interferograms and x-ray images of the plasma produced
on C u and C u+C H targets, taken at t = 7 ns (a - pure C u
target, b - C u target with C H insert).
a) 1
Cu
7 ns
Cu
1
2
z [mm]
3
4
0
1
2
z [mm]
3
Interferograms and x-ray images of the plasma produced
on T a and T a+C H targets, taken at t = 7 ns (a - pure T a
target, b - T a target with C H insert).
4
The following expression, widely used for determination of
ablation pressure, can be applied to determine the scale of
ablation pressure in the region with critical plasma density, where a sonic point essentially occurs. This determined scale is correct in the frame in which the laser radiation is mainly absorbed. The coupling parameter for
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Plastic plasma interaction with plasmas with growing atomic number
Figure 6.
Sequences of interferograms showing the plasma stream structures for Ag, T a, and T a+Ag targets.
the incident laser radiation must be smaller than 1014
Wµm2 /cm2 (IL and λ are laser radiation intensity and
wavelength, respectively) and the targets must be made
of light materials.
atomic number of target material is contained in the values
of both critical density and coupling efficiency. According
to (1) and (2), the extract of such dependence is given by:
P ∝ ρcr
Kab IL
ρcr
P∝
2/3
,
A
,
Zm λ2
1/3
(Kab − Kr )2/3 .
(3)
(1)
where ρcr is the critical plasma density
ρcr ≈ 1.83 × 10−3
A
Z m λ2
(2)
where A and Zm are the atomic mass and average charge
of the plasma ions, respectively; Kab = Eab /EL is the absorption efficiency which represents the ratio of absorbed
laser energy (Eab ) and laser energy (Eab ). To extend such
an approach to the case of an arbitrary atomic number of
target material, the coupling efficiency Kc should be used
instead of the absorption coefficient Kab in (1). The coupling efficiency represents the efficiency of the laser energy transformation into the internal plasma energy. This
takes into account the energy losses due to plasma thermal radiation: Kc = Kab − Kr , where Kr = Er /Eab . Kr
is the x-ray conversion efficiency, Er is the energy converted to thermal radiation energy and Eab is the absorbed
laser energy. So, the ablation pressure dependence on the
Expression (3) gives the possibility of qualitative evaluation of the pressure dependence on the atomic number Z .
At temperatures in the range of 300 - 1000 eV, which are
typical for the incident laser intensity of 1013−14 W /cm2 ,
the ionization degree of light and relatively light atoms
(from H up to Al or Si) is close to the total. In this case
the ratio A/Zm practically does not depend on the atomic
number, remaining close to 2. Meanwhile the conversion
efficiency Kr increases with increasing the atomic number due to increasing the average charge of ions. So,
the plasma ablation pressure in the case of target light
material decreases with increasing Z . For heavy atoms
the ionization degree will be saturated at the level of
Zm = 20 − 25. That leads to an increase of the ratio
A/Zm with increasing Z . At the continuous increase of
Kr with growing Z (x-ray conversion efficiency in a laserproduced plasma launched on a planar Au target reaches
the value of 0.7 - 0.8 (see Ref. [8]). The increase of the
ratio A/Zm leads to a slowing down of the decrease of the
ablation pressure and plasma pressure saturation.
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Andrzej Kasperczuk et al.
5.
Conclusions
The PALS laser system gives particular possibilities for
realization of the presented investigations because it
allows simply to create very narrow plasma structures
(plasma jets). Then, the plasma jets could be used as
a convenient tool for determination of mutual relationship
between pressures of plasmas with different atomic numbers. This paper confirms a tendency of the plasma pressure to decrease with growing atomic number of targets.
However, it is also demonstrated that the plasma pressure
decrease is stopped at a relatively high value of atomic
number. Then, the plasma pressure is saturated on a certain level. In our experiment the saturation starts from
Z = 47. The theoretical consideration presented above
has shown that the plasma pressure is a complex function
of two factors: the plasma energy losses due to thermal
radiation and the degree of plasma ionization. Because
both of these depend on target irradiation conditions, their
change can result in certain quantitative differences in
the plasma pressure dependence versus Z . However, the
character of this dependence should be conserved. This
paper also also explains why it is impossible to launch
the plasma jet on low-Z material target like plastic (C H)
or Al (see Fig. 1). The high inner pressures of C H and
Al plasmas are likely to be responsible for the observed
extensive radial spread of these plasmas. They influence
concentration of the plasma at the axis and prevent the
formation of plasma jets, as should be the case for higherZ plasmas. Even though the above presented results are
qualitative only, they bring information on the pressure
relationship in different laser-produced plasmas, which is
of importance not only from a physical point of view, but
also for various technical applications. For example, combinations of different plasmas can create desirable plasma
structures (see [5–7]).
References
[1] J.J. Duderstadt, G.A. Moses, Inertial Confinement Fusion (Wiley, New York, 1982)
[2] S. Atzeni, J. Meyer-ter-Vehn, The physics of inertial
fusion (Oxford Univ. Press, Oxford, 2004)
[3] V.B. Rozanov et al., Energy from inertial fusion (IAEA,
Vienna, 1995)
[4] A. Kasperczuk et al., Plasma Phys. Control. Fusion 53,
095003 (2011)
[5] A. Kasperczuk et al., Laser Part. Beams 30, 1 (2012)
[6] A. Kasperczuk et al., Phys. Plasmas 19, 092106 (2012)
[7] A. Kasperczuk et al., Phys. Plasmas 18, 044503 (2011)
[8] J.D. Lindl, Phys. Plasmas 2, 3933 (1995)
Acknowledgement
This work was supported in part by the Access to Research Infrastructure activity in the 7th Framework Program of the EU Contract No. 284464, Laserlab Europe
III and by Ministry of Science and Higher Education in
Poland, co-supported within the framework of project No.
2734/7.PR2013/2, by the Czech Science Foundation under the grant No. P205/10/0814, and by the project
PALS LM2010014 of the Ministry of Education, Youth and
Sports of the Czech Republic. The participation of S.Yu.
Gus’kov and N.N. Demchenko in this work was supported
by RFBR projects No 12-02-92101-JF and No 11-0201305.
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