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MULTI one dimensional radiation hydrodynamic code
The MULTI (MULTIgroup MULTIlayer) code developed by R. Ramis et al. [1], simulates the hydrodynamics of a one dimensional plasma coupled with a radiation field. The code is based on a finite set of difference equations, which result from the physical model describing the coupling of the plasma with the radiation, as follows :
• the spatial variation of the plasma fluid motion, and of the radiation transport through it, are described in discrete cells, while the temporal variation is calculated in discrete time steps sampling the evolution of the plasma–radiation coupling.
• the frequency domain is optimally divided in discrete groups. This is achieved by the multigroup approach of the plasma emissivity and opacity, which is a powerful extension of the simplified single mean opacity approximation used to solve the non grey radiation transfer problem [6].
Radiation confinement in the interior of an open spherical gold cavity
The confinement of the radiation field in the interior of a cavity can be viewed as the composite result following from the heating of its wall and the radiation reemission accompanying this heating. Though these phenomena are strongly correlated, we approach them separately in the following paragraphs. First, we analyze the energy exchange inside the cavity, which determines the heating of each wall element. Then, we study the behavior of a single wall element due to the radiation incident on it, which determines its radiation reemission. Finally, we calculate the total radiation heating the absorption foil. Radiation transfer through a plasma–Cavities thermal radiation and solid foil heating Chapter 2
Energy exchange in the cavity interior
The energy exchange inside the cavity is described in Figure 2.2. This figure shows a spherical cavity with open sections having a direct correspondence with the cavities used in the experiment. In particular, the cavity contains two holes with area AH (i.e. the diagnostic holes, one of which is covered by the absorption foil, AH = AF), and an external source occupying an area AS, and which irradiates the interior of the cavity with a flux ( , ) 0 S r t r . For the cavity used in the experiment this radiation flux corresponds to the x–ray emission at the rear side of the conversion foil heated by the main beam. If the wall material of the cavity participating in the radiation confinement has an area AW, the simple geometrical formula follows C W S H A = A + A + 2A (2.24).
where AC is the equivalent area of a closed spherical cavity with the same radius. Let us consider a differential wall element at an arbitrary point P(r ) r . The radiation energy incident on this element is the sum of the radiation emitted from the source Ss and the radiation emitted from all the other wall elements Si. This energy is balanced by the energy absorbed by the wall element Sw, and the reemitted energy from it Sr. The energy balance in term of radiation fluxes is written S (r, t) S (r, t) S (r, t) S (r, t).
Radiation reemission of the cavity wall–Basko scaling law
The interaction of the x–ray radiation field confined in the interior of the cavity and a single cavity wall element can be described with Figure 2.3 [12]. Here, we assume a planar solid material coming in contact at t = 0 with an x–ray radiation field (Fig. 2.3(a)). For a high–Z material, as gold, the heating of the wall forms an optical thick plasma layer on its surface, which absorbs totally the incident x–ray radiation. Thus, the deposited energy on the wall surface is transmitted into the body of the material by diffusion [13,14]. For high temperatures the dominant heat transport mechanism is the radiation conduction. A non linear supersonic heat wave propagates into the solid material (Fig. 2.3(b)). As the thickness of the heated region increases its propagation velocity decreases, while at the same time a plasma expansion wave is formed in the solid–vacuum interface (Fig. 2.3(c)). When the velocity of the heat wavefront becomes sonic, it is overtaken by the expansion wave front and a shock wave is formed. This situation with the heat wave preceded by a shock wave and the simultaneous expansion of the plasma is known as the ablative heat wave.
The ablative heat wave formed into a planar medium due to the non linear radiation heat conduction was studied in [13]. In particular, it was proved that for a high–Z material, as gold, the non linear heating problem is self–similar, if the specific internal energy ε, and the mean Rosseland free path lR, of the material are non linear functions of its temperature T, and density ρ.
Total radiation flux coupled with the absorption foil
Now, we can calculate the total radiation flux heating the absorption foil. A simplified scheme illustrating the radiation coupling with the absorption foil is given in Figure 2.4. This figure shows that the flux heating the absorption foil is the sum of : (1) the directly coupled flux due to the radiation emitted from the rear of the conversion foil, and (2) the coupled flux due to the radiation emitted from the cavity wall. For the flux heating the absorption foil due to the cavity wall emission, starting from Eq. (2.26) one obtains in a similar manner with Eq. (2.33).
Table of contents :
Chapter 1 Elements of plasma atomic physics
1.1 Introduction
1.2 Plasma atomic processes
1.2.1 Detailed balance principle
1.2.2 Bound–bound processes
1.2.3 Bound–free processes
1.2.4 Free–free processes (Bremsstrahlung radiation)
1.3 Plasma statistical physics
1.3.1 Local Thermodynamic Equilibrium
1.3.2 Non–Local Thermodynamic Equilibrium–Collisional Radiative Model
1.4 Calculation of complex plasma spectrum–Superconfigurations approach
1.5 Atomic codes of plasma physics
1.5.1 The code HULLAC
1.5.2 The code SCO
1.5.3 The code TRANSPEC/AVERROES
Chapter 2 Radiation transfer through a plasma–Cavities thermal radiation and solid foil heating
2.1 Introduction
2.2 Radiation transfer problem
2.2.1 Hydrodynamics–radiation equations coupling
2.2.2 MULTI one dimensional radiation hydrodynamic code
2.3 Radiation confinement in the interior of an open spherical gold cavity
2.3.1 Energy exchange in the cavity interior
2.3.2 Radiation reemission of the cavity wall–Basko scaling law
2.3.3 Total radiation flux coupled with the absorption foil
Chapter 3 Laser and Instrumentation
3.1 Introduction
3.2 LULI2000 laser facility
3.2.1 Laser beam chains
3.2.2 Focalization of the laser beam–KDP crystal and random phase plate
3.3 Targets description
3.3.1 Gas–jet for spectral emission characterization
3.3.2 Spherical gold cavity for absorption spectra measurements
3.4. Diagnostic instruments
3.4.1 Bragg crystal spectrograph
3.4.2 Transmission grating XUV spectrograph
3.4.3 Thomson scattering diagnostic
3.5 Auxiliary devices and other diagnostics
3.5.1 Streak Camera
3.5.2 CCD Cameras
3.5.3 Kodak DEF film
3.5.4 Pinhole cameras
3.5.5 Streak camera differential pumping system
Chapter 4 X–ray emission spectroscopy of xenon and krypton plasmas in NLTE conditions
4.1 Introduction
4.2 Experimental setup
4.2.1 Laser beam and gas–jet targets
4.2.2 Diagnostic instruments
4.3 X–ray spectra data processing
4.3.1 Emission spectra in the keV range
4.3.2 XUV emission spectra
4.4 Determination of the plasma parameters–Thomson scattering spectra analysis
4.4.1 Helium plasma parameters
4.4.2 Xenon and krypton plasmas parameters
4.5 Characterization of the x–ray emission spectra in the keV range
4.5.1 Xenon plasma emission spectra
4.5.2 Krypton plasma emission spectra
4.6 Analysis of the x-ray spectra with TRANSPEC/AVERROES
4.6.1 Calculation of the synthetic emission x–ray spectra in the keV range
4.6.2 Calculation of the XUV emission spectra
4.7 Conclusions
Chapter 5 XUV absorption spectroscopy of radiatively heated ZnS and Al plasmas
5.1 Introduction
5.2 Experimental setup and data processing
5.2.1 Laser beams and targets description
5.2.2 Diagnostic Instruments
5.2.3 Experimental data processing
5.3 Experimental methods
5.3.1 Deduction of the plasma transmission
5.3.2 Al and ZnS plasmas absorption spectra
5.4 Hydrodynamics of the radiatively heated Al absorption foil
5.4.1 Calculation of the radiation heating the Al foil
5.4.2 Hydrodynamic simulation of the Al foil expansion
5.5 Analysis of the Al plasma absorption spectrum
5.5.1 Characterization of the Al absorption spectrum
5.5.2 Comparison of the HULLAC synthetic Al spectrum with the measured absorption
5.6 Analysis of the ZnS plasma absorption spectrum
5.6.1 Characterization of the ZnS absorption spectrum
5.6.2 Hydrodynamic simulation of the ZnS foil
5.6.3 Comparison of the SCO synthetic ZnS spectrum with the measured absorption.
5.7 Conclusions
Conclusions and perspectives
Appendix A Elements of the Thomson scattering theory
Appendix B Mach–Zehnder interferometry experiment
Appendix C Publications
