23P166-B
Comparison of fluid behavior of implosion dynamics derived by difference ofequation-of-state
状態方程式モデルの違いによる慣性核融合爆縮過程の流体挙動の比較
Yu Komatsu, Toru Sasaki, Takashi Kikuchi, Nob. Harada, Hideo Nagatomo1)
小松悠, 佐々木徹, 菊池崇志, 原田信弘, 長友英夫
Nagaoka University of Technology, Kamitomioka 1603-1, Nagaoka, Niigata, 940-2188, Japan
長岡技術科学大学 〒940-2188 新潟県長岡市上富岡町1603-1
1)
Institute of Laser Engineering, Osaka University, Yamadaoka 2-6, Suita, Osaka, 565-0871, Japan
大阪大学レーザーエネルギー学研究センター 〒565-0871 大阪府吹田市山田丘2-6
Comparing hydrodynamic simulation with various equation of state (EOS), we obtained difference of EOS
for implosion dynamics. To evaluate the implosion process, we used the two-dimensional radiationhydrodynamics simulation code with QEOS, ideal gas EOS, and SESAME. The maximum density for theideal gas EOS is higher than that for the QEOS. The sound velocity of the SESAME is faster than that for
the QEOS. These results indicated that each EOS model affected the implosion dynamics in inertial
confinement fusion (ICF) .

1. Introduction
During the implosion process of ICF, the target
material passes through a transition from solid toplasma. To generate inertial fusion energy, weshould clearly understand the hydrodynamics offuel pellet in wide density-temperature regime.
The implosion dynamics is dominated bycomplex physical phenomena, such as strong
shock wave, thermodynamics, atomic process,radiation transport, and so on. Recently, warm
dense state, which is one of a thermodynamic
regime defined by 0.01-1 times solid density withtemperature of 0.1-10 eV, is pointed to thedifference of existing equation-of-state models.
The reason why the region includes thephase-transition from solid to plasma states,degenerated electrons, and coupled ions. To
understand the effect on implosion dynamics withwarm-dense-matter’s EOS, we demonstrate toevaluate the changing implosion dynamics due todifference EOS models.
The purpose of this study is to compare to thefluid behavior of implosion dynamics for thevarious EOS models by numerical simulations.
2. Simulation code and EOS models
To evaluate the implosion process, we used thetwo-dimensionalradiationhydrodynamics
simulation code, PINOCO [1]. The EOS equipped
in PINOCO is based on the quotidian EOS (QEOS)[2] with a fitting formula [3].
QEOS[2,3] and SESAME [4] are usually usednumerical simulations of ICF. QEOS stands for
quotidian equation of state. The cold and electron

thermal property are based on semi-empiricalbonding correction and the Thomas-Fermi model,respectively. The ion thermal properties evaluatedwith Cowan’s model. Thermodynamic derivatives
such as specific heat, sound speed can be easy touse from composed formulas.
SESAME is tabular data of the pressure andinternal energy per unit mass as a function oftemperature and density for each material [4]. The
pressure and internal energy of SESAME should beinterpolation of the finite number of data. Therefore,
the thermodynamic derivatives should be careful
due to discontinuity of models.
Figure 1 shows pressure curves at constanttemperature. The pressure for ideal gas EOS islower then that for QEOS and SESAME in a highdensity and low temperature regime. There is adifference in low temperature and near the solid
density regime even if between QEOS andSESAME.
Spherical implosion of CH shell target wassimulated. The thickness and radius of the shell are
6.8 µm and 241.2 µm. Background density andshell density are 1.0x10-6 g/cm3 and 1.0 g/cm3,respectively. To clarify the implosion dynamics
from difference of EOS models, we neglect theradiation transport. The target is irradiated by
uniform laser which energy and pulse width are 2.0
kJ and 1.0 ns with Gaussian, full width at half
maximum (FWHM).
3. Results
Figure 2 shows the density profile for QEOS andideal gas EOS in radial direction. The results

(a)QEOSFig. 1. Comparison of QEOS, ideal gas EOS, andSESAME pressure curves at constant temperature.

indicated that the implosion dynamics of both EOS
cases are different structure around the shock front.
Thus, from these time evolutions, the implosion
velocity for the ideal gas EOS is faster than that for
the QEOS. The difference of hydrodynamicstructure is occurred by the degenerated pressure atover the solid density, which is log10 ρ ~ 0 as shownin Fig. 1.
The maximum density for the ideal gas EOS isachieved 3560 g/cm3 and that for the QEOS isobtained 741 g/cm3.The compressibility κ isexpressed as follows,1  ∂ρ  1 1,
κ=   =ρ  ∂p T ρ Cs(1)where, ρ is the density, p is the pressure, and CS is
the sound velocity. Therefore, the EOS models
affect the maximum density.
Figure 3 shows the density profile for QEOS andSESAME in radial direction. In the interior of shell,
the shock velocity of SESAME is faster than thatfor QEOS. SESAME has Maxwell construction atwarm dense regime, which is under the soliddensity. Thus, the propagation structure in interiorof shell is quite different between both EOSmodels.
4. Conclusions
We investigated the implosion dynamics with theQEOS, ideal gas EOS, and SESAME by using
PINOCO. The maximum density between QEOSand SESAME changed by the degenerated pressure.
The propagation structure in interior of shell
between QEOS and SESEAME changed by
Maxwell construction at warm dense regime.
Through these comparisons, we will construct thevaluable EOS for ICF.
References[1] H. Nagatomo, et al., Phys. Plasmas 14, (2007)056303.
[2] R. M. More, et. al., Phys. Fluids 31, (1988) 3059.

(b)ideal gas EOS

Fig. 2. Time-evolution of density profiles for radial
direction. (a) QEOS and (b) ideal gas EOS. The solidline indicates the initial time of t=0 ns, the doted colorlines denote 1.9 ns, 2.1 ns, and 2.3 ns, respectively. 2.51
ns for QEOS and 2.42 ns for ideal gas EOS show themaximum compression.
(a)QEOS(b)SESAME

Fig. 3. Time-evolution of density profiles for radial
direction. (a) QEOS and (b) SESAME. The solid lineindicates the initial time of t=0 ns, the doted color lines
denote 0.5 ns, 1.0 ns, 1.5 ns, and 1.71 ns, respectively.
[3] K. Takami and H. Takabe, Technol. Rep. Osaka Univ.
40, (1990) 159.
[4] S. P. Lyon, et al., Group T-1, LA-CP-98-100 (1988).