24P123-P
Evaluation Method for Electrical Conductivity of Warm Dense Matter withIsochoric State using Pulsed-Power Discharge
パルスパワー駆動定積 Warm Dense Matter の導電率評価法
Yusuke Amano, Yasutoshi Miki, Takuya Takahashi, Toru Sasaki, Takashi Kikuchi, andNob. Harada
天野 祐介, 三木 康稔, 高橋 拓也, 佐々木 徹, 菊池 崇志, 原田 信弘
Nagaoka University of Technology, Kamitomioka 1603-1, Nagaoka, 940-2188, Japan
長岡技術科学大学〒940-2188 長岡市上富岡1603-1
An evaluation method of electrical conductivity in isochoric warm dense state produced by foam ablation
has been developed by using pulsed-power discharge. The isochoric state can be achieved to surround thefoamed metal with a hollow sapphire capillary as a rigid wall. The temperature and the electricalconductivity of foam/plasma have been evaluated by the emission intensity ratio and the voltage-current
waveforms. Observed electrical conductivity is in agreement with previous experiments and predictions.
As a result, the electrical conductivity in warm dense state with well-defined temperature and density canbe obtained by the proposed method.

1. Introduction
Properties of materials in a warm dense matter(WDM) are of interested to concern an interior ofgiant planets and an imploded fuel pellet of inertial
confinement fusion. The WDM region is definedthat the density range is from 10-3 s (s is the solid
density of matter) to 10s, and temperature varies
from 0.1 to 10 eV. To understand properties of
WDM state, effects of the ion-ion correlation andthe degenerated electrons can be evaluated by thedensity-temperature dependence of electricalconductivity. [1-5, 8]. Generating and evaluating
WDM state, we should create a well-defined state,i.e. estimative density and temperature condition, ina laboratory experiment.
In this study, we propose a measurement
method for electrical conductivity in WDM state byusing pulsed-power discharge with isochoric
heating.
2. Experimental setup
Figure 1 shows a schematic diagram of theproposed method by a pulsed-power discharge
device with isochoric state [8]. To achieve isochoricstate, metallic foam was packed into a hollow
sapphire capillary (5×10 mm). The metallic foam
is copper with from 50 m to 600 m porous sizeand about 90 % porosity. To avoid the surface
creepage on sapphire, turbo-molecular and rotary
pumps are set at bottom of chamber. The density ofWDM can be controlled by the volume of foam
enclosed into the hollow capillary. The capacitors(3×1.87 F) were charged up to 15 kV to ensure thevaporization of foam. Time evolutions of current

Fig. 1 Experimental setup

I(t) and voltage V(t) in foam/plasma were measured
by a Rogowski coil and high voltage probes. The
obtained voltage was composed of resistive andinductive parts. The stray inductance L of thedischarge device was estimated to be 165 nH fromthe preliminary experiment with the short-circuit.
The electrical conductivity (t) of the foam/plasma
is evaluated by the following equation;lI (t )(1)
 (t )  2,
r V (t )  V (t )   L dI (t )
1

2

dt

where, l is the length of the foam/plasma, r is thefoam/plasma radius, V1(t) is the voltage between
gap switch and ground, V2(t) is the voltage between
the return cable and ground.
To evaluate thetemperature without
equation-of-state models, the emission from thefoam/plasma is measured by the spectroscopemounted on a streak camera. The foam/plasma
temperature T is estimated by using line pairmethod;  E(2)ln  21 21    2  ln K ,AgkTB 21 2 

where  is the wavelength, A21 is the spontaneousemission coefficient, 21 is the emission factor ofthe spectral line, E2 is the upper level energy, kB is
the Boltzmann constant, and K is the constant factor,respectively.
3. Experimental results
Figure 2 shows typical results for (a) the voltage
and current waveforms, (b) the input energy andfoam/plasma temperature, and (c) the electricalconductivity in 0.032s. The peak voltage andcurrent are 1 kV and 50 kA, respectively. In case of0.032s, the evaporation energy is estimated to be300 J. From input energy history, the copper foam
is ensured the vaporization at 20 s from beginningof discharges. The foam/plasma temperature wasestimated to be about 5500 K by the input energyand SESAME equation of state (material No. 3333)[7] and spectra of Cu I at 477 nm and 617 nm witheq. (2) [6]. From this comparison, the temperatureis almost same between 8 s and 13 s. As a result,
it is confirmed that the copper foam became theisochoric WDM state by the pulsed-power
discharge device. The electrical conductivity ofcopper foam/plasma is estimated to be 104 S/mfrom the voltage and current waveforms. The
observed electrical conductivity is in agreementwith previous experimental results [2, 5] and thetheoretical predictions [4]. Therefore, it isconcluded that the proposed method can produce
the well-defined WDM state.
4. Conclusions
We have developed a measurement method forelectrical conductivity in isochoric WDM state byusing pulsed-power discharge. Achieving isochoricstate and avoiding skin effect, we have used thefoamed metal surrounded by the hollow sapphire
capillary. The result indicated that the foam/plasma
temperature obtained by the line pair method iscomparable with the temperature estimated by theinput energy history with SESAME. It is indicatedthat the dependence of electrical conductivity
obtained by the proposed method is in agreementwith the previous results.

Fig. 2 Typical results for (a) voltage and current
waveforms, (b) input energy and typical temperature
estimated by line pear method and SESAME equation ofstate table Cu3333, and (c) electrical conductivity

Acknowledgments
We would like to thank Prof. Ken Yukimura for his
useful advice. This work was partly supported by
Grant-in-Aid for Young Scientists (B) from Japan
Society for the Promotion of Science (23740406).
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