A pulsed power facility has been designed for studying the warm dense matter regime. It is based on the pulsed Joule heating technique, originally proposed by Korobenko and Rakhel [Int. J. Thermophy. 20, 1257 (1999)], where a 3.96 µF capacitor bench is used for inducing a solid to plasma phase transition to metallic foils confined into a sapphire cell. The first experiments have been conducted on pure aluminum. Experimental data have been collected using electrical and optical diagnostics. Direct measurements of tension, current, pressure, and particle velocity allow us to evaluate the equation of state (EOS) and the DC conductivity of expanded aluminum. The results are compared to hydrodynamic simulations performed with various EOS models. As a result, collected data on aluminum highlight the relevance of our experimental procedure for improving EOS modeling in the warm dense matter regime.

1.
R. H.
Lee
,
D.
Kalantar
, and
J.
Molitoris
, “
Warm dense matter: An overview
,”
LLNL Report No. UCRL-TR-203844
(Lawrence Livermore National Laboratory, 2004).
2.
M.
Kaikanov
,
K.
Baigarin
,
A.
Tikhonov
,
A.
Urazbayev
,
J. W.
Kwan
,
E.
Henestroza
,
G.
Remnev
,
B.
Shubin
,
A.
Stepanov
,
V.
Shamanin
, and
W. L.
Waldron
, “
An accelerator facility for WDM, HEDP, and HIF investigations in Nazarbayev university
,”
J. Phys.: Conf. Ser.
717
,
012099
(
2016
).
3.
R.
Cheng
,
Y.
Lei
,
X.
Zhou
,
Y.
Wang
,
Y.
Chen
,
Y.
Zhao
,
J.
Ren
,
L.
Sheng
,
J.
Yang
,
Z.
Zhang
,
Y.
Du
,
W.
Gai
,
X.
Ma
, and
G.
Xiao
, “
Warm dense matter research at HIAF
,”
Matter Radiat. Extremes
3
,
85
93
(
2018
).
4.
A. F.
Akkerman
,
A. V.
Bushman
,
B. A.
Demidov
,
M. V.
Ivkin
,
A. L.
Ni
,
V. A.
Petrov
,
L. I.
Rudakov
, and
V. E.
Fortov
, “
Dynamics of shock waves excited by a high-current relativistic electron beam in aluminum targets
,”
Sov. Phys. JETP
62
,
489
493
(
1985
), http://jetp.ras.ru/cgi-bin/dn/e_062_03_0489.pdf.
5.
J. E.
Coleman
and
J.
Colgan
, “
Collisional heating and adiabatic expansion of warm dense matter with intense relativistic electrons
,”
Phys. Rev. E
96
,
013208
(
2017
).
6.
J.
Gardelle
,
B.
Cassany
,
N.
Szalek
,
A.
Galtié
,
B.
Bicrel
,
D.
Hébert
,
I.
Bertron
, and
K.
Pepitone
, “
High power electron beam interaction with an aluminum target: Measurements and simulations
,”
J. Appl. Phys.
126
,
153301
(
2019
).
7.
N. A.
Tahir
,
R.
Schmidt
,
M.
Brugger
,
R.
Assmann
,
A.
Shutov
,
I. V.
Lomonosov
,
V.
Gryaznov
,
A. R.
Piriz
,
S.
Udrea
,
D. H. H.
Hoffmann
,
V. E.
Fortov
, and
C.
Deutsch
, “
Generation of warm dense matter and strongly coupled plasmas using the High Radiation on Materials facility at the CERN Super Proton Synchrotron
,”
Phys. Plasmas
16
,
082703
(
2009
).
8.
A.
Mančić
,
A.
Lévy
,
M.
Harmand
,
M.
Nakatsutsumi
,
P.
Antici
,
P.
Audebert
,
P.
Combis
,
S.
Fourmaux
,
S.
Mazevet
,
O.
Peyrusse
,
V.
Recoules
,
P.
Renaudin
,
J.
Robiche
,
F.
Dorchies
, and
J.
Fuchs
, “
Picosecond short-range disordering in isochorically heated aluminum at solid density
,”
Phys. Rev. Lett.
104
,
035002
(
2010
).
9.
D.
Hoarty
,
T.
Guymer
,
S.
James
,
E.
Gumbrell
,
C.
Brown
,
M.
Hill
,
J.
Morton
, and
H.
Doyle
, “
Equation of state studies of warm dense matter samples heated by laser produced proton beams
,”
High Energy Density Phys.
8
,
50
54
(
2012
).
10.
A.
Zylstra
,
J.
Frenje
,
P.
Grabowski
,
C.
Li
,
G.
Collins
,
P.
Fitzsimmons
,
S.
Glenzer
,
F.
Graziani
,
S.
Hansen
,
S.
Hu
,
M. G.
Johnson
,
P.
Keiter
,
H.
Reynolds
,
J.
Rygg
,
F.
Séguin
, and
R.
Petrasso
, “
Measurement of charged-particle stopping in warm dense plasma
,”
Phys. Rev. Lett.
114
,
215002
(
2015
).
11.
M.
Ishino
,
N.
Hasegawa
,
M.
Nishikino
,
T.
Pikuz
,
I.
Skobelev
,
A.
Faenov
,
N.
Inogamov
,
T.
Kawachi
, and
M.
Yamagiwa
, “
Very low electron temperature in warm dense matter formed by focused picosecond soft x-ray laser pulses
,”
J. Appl. Phys.
116
,
183302
(
2014
).
12.
V.
Dervieux
,
B.
Loupias
,
S.
Baton
,
L.
Lecherbourg
,
K.
Glize
,
C.
Rousseaux
,
C.
Reverdin
,
L.
Gremillet
,
C.
Blancard
,
V.
Silvert
,
J.-C.
Pain
,
C.
Brown
,
P.
Allan
,
M.
Hill
,
D.
Hoarty
, and
P.
Renaudin
, “
Characterization of near-LTE, high-temperature and high-density aluminum plasmas produced by ultra-high intensity lasers
,”
High Energy Density Phys.
16
,
12
17
(
2015
).
13.
N.
Jourdain
,
L.
Lecherbourg
,
V.
Recoules
,
P.
Renaudin
, and
F.
Dorchies
, “
Ultrafast thermal melting in Nonequilibrium warm dense copper
,”
Phys. Rev. Lett.
126
,
065001
(
2021
).
14.
M. D.
Knudson
,
D. L.
Hanson
,
J. E.
Bailey
,
C. A.
Hall
,
J. R.
Asay
, and
W. W.
Anderson
, “
Equation of state measurements in liquid deuterium to 70 GPa
,”
Phys. Rev. Lett.
87
,
225501
(
2001
).
15.
A.
Benuzzi-Mounaix
,
F.
Dorchies
,
V.
Recoules
,
F.
Festa
,
O.
Peyrusse
,
A.
Levy
,
A.
Ravasio
,
T.
Hall
,
M.
Koenig
,
N.
Amadou
,
E.
Brambrink
, and
S.
Mazevet
, “
Electronic structure investigation of highly compressed aluminum with k edge absorption spectroscopy
,”
Phys. Rev. Lett.
107
,
165006
(
2011
).
16.
V. B.
Mintsev
and
V. E.
Fortov
, “
Transport properties of warm dense matter behind intense shock waves
,”
Laser Part. Beams
33
,
41
50
(
2015
).
17.
D.
Yanuka
,
S.
Theocharous
,
S.
Efimov
,
S. N.
Bland
,
A.
Rososhek
,
Y. E.
Krasik
,
M. P.
Olbinado
, and
A.
Rack
, “
Synchrotron based X-ray radiography of convergent shock waves driven by underwater electrical explosion of a cylindrical wire array
,”
J. Appl. Phys.
125
,
093301
(
2019
).
18.
J. E.
Coleman
,
H. E.
Morris
,
M. S.
Jakulewicz
,
H. L.
Andrews
, and
M. E.
Briggs
, “
Hydrodynamic disassembly and expansion of electron-beam-heated warm dense copper
,”
Phys. Rev. E
98
,
043201
(
2018
).
19.
S.
Laffite
,
S. D.
Baton
,
P.
Combis
,
J.
Clerouin
,
M.
Koenig
,
V.
Recoules
,
C.
Rousseaux
, and
L.
Videau
, “
Velocity Interferometer blanking due to preheating in a double pulse planar experiment
,”
Phys. Plasmas
21
,
082705
(
2014
).
20.
A.
Ravasio
,
G.
Gregori
,
A.
Benuzzi-Mounaix
,
J.
Daligault
,
A.
Delserieys
,
A. Y.
Faenov
,
B.
Loupias
,
N.
Ozaki
,
M.
Rabec le Gloahec
,
T. A.
Pikuz
,
D.
Riley
, and
M.
Koenig
, “
Direct observation of strong ion coupling in laser-driven shock-compressed targets
,”
Phys. Rev. Lett.
99
,
135006
(
2007
).
21.
S. H.
Glenzer
,
O. L.
Landen
,
P.
Neumayer
,
R. W.
Lee
,
K.
Widmann
,
S. W.
Pollaine
,
R. J.
Wallace
,
G.
Gregori
,
A.
Höll
,
T.
Bornath
,
R.
Thiele
,
V.
Schwarz
,
W.-D.
Kraeft
, and
R.
Redmer
, “
Observations of plasmons in warm dense matter
,”
Phys. Rev. Lett.
98
,
065002
(
2007
).
22.
C. A.
Hall
,
J. R.
Asay
,
M. D.
Knudson
,
W. A.
Stygar
,
R. B.
Spielman
,
T. D.
Pointon
,
D. B.
Reisman
,
A.
Toor
, and
R. C.
Cauble
, “
Experimental configuration for isentropic compression of solids using pulsed magnetic loading
,”
Rev. Sci. Instrum.
72
,
3587
3595
(
2001
).
23.
J.-P.
Davis
, “
Experimental measurement of the principal isentrope for aluminum 6061-T6 to 240 GPa
,”
J. Appl. Phys.
99
,
103512
(
2006
).
24.
R. F.
Smith
,
J. H.
Eggert
,
M. D.
Saculla
,
A. F.
Jankowski
,
M.
Bastea
,
D. G.
Hicks
, and
G. W.
Collins
, “
Ultrafast dynamic compression technique to study the kinetics of phase transformations in bismuth
,”
Phys. Rev. Lett.
101
,
065701
(
2008
).
25.
D. K.
Bradley
,
J. H.
Eggert
,
R. F.
Smith
,
S. T.
Prisbrey
,
D. G.
Hicks
,
D. G.
Braun
,
J.
Biener
,
A. V.
Hamza
,
R. E.
Rudd
, and
G. W.
Collins
, “
Diamond at 800 GPa
,”
Phys. Rev. Lett.
102
,
075503
(
2009
).
26.
G. R.
Gathers
, “
Thermophysical properties of liquid copper and aluminum
,”
Int. J. Thermophys.
4
,
209
226
(
1983
).
27.
G. R.
Gathers
, “
Fast transient thermophysical measurements at Livermore
,”
Int. J. Thermophys.
11
,
693
708
(
1990
).
28.
P.
Renaudin
,
C.
Blancard
,
J.
Clérouin
,
G.
Faussurier
,
P.
Noiret
, and
V.
Recoules
, “
Aluminum equation-of-state data in the warm dense matter regime
,”
Phys. Rev. Lett.
91
,
075002
(
2003
).
29.
V. N.
Korobenko
and
A. D.
Rakhel
, “
Technique for measuring thermophysical properties of refractory metals at supercritical temperatures
,”
Int. J. Thermophys.
20
,
1257
1266
(
1999
).
30.
V. N.
Korobenko
,
A. D.
Rakhel
,
A. I.
Savvatimskiy
, and
V. E.
Fortov
, “
Measurement of the electric conductivity of tungsten in a continuous liquid-to-gas transition
,”
Plasma Phys. Rep.
28
,
1008
1016
(
2002
).
31.
A. W.
DeSilva
and
A. D.
Rakhel
, “
Electrical resistivity and thermodynamic properties of dense tungsten plasma
,”
Int. J. Thermophys.
26
,
1137
1149
(
2005
).
32.
V. N.
Korobenko
,
A. D.
Rakhel
,
A. I.
Savvatimski
, and
V. E.
Fortov
, “
Measurement of the electrical resistivity of hot aluminum passing from the liquid to gaseous state at supercritical pressure
,”
Phys. Rev. B
71
,
014208
(
2005
).
33.
V. N.
Korobenko
and
A. D.
Rakhel
, “
Electrical resistivity and equation of state measurements on hot expanded aluminum in the metal-nonmetal transition range
,”
Phys. Rev. B
75
,
064208
(
2007
).
34.
A. M.
Kondratyev
,
V. N.
Korobenko
, and
A. D.
Rakhel
, “
Experimental study of liquid carbon
,”
J. Phys.: Condens. Matter
28
,
265501
(
2016
).
35.
S. F.
Garanin
and
S. D.
Kuznetsov
, “
Overheating instability of a thin conductor with respect to stratification
,”
J. Appl. Phys.
123
,
133301
(
2018
).
36.
V. N.
Korobenko
and
A. D.
Rakhel
, “
Observation of a first-order metal-to-nonmetal phase transition in fluid iron
,”
Phys. Rev. B
85
,
014208
(
2012
).
37.
A. D.
Rakhel
, “
Equation of state of fluid aluminum in the metal–nonmetal transition region
,”
J. Phys.: Condens. Matter
30
,
295602
(
2018
).
38.
R.
Forman
,
G.
Piermarini
,
J. D.
Barnett
, and
S.
Block
, “
Pressure measurement made by the utilization of ruby sharp-line luminescence
,”
Science
176
,
284
285
(
1972
).
39.
M.
Millot
,
J.-M.
Broto
, and
J.
Gonzalez
, “
High-field Zeeman and Paschen-Back effects at high pressure in oriented ruby
,”
Phys. Rev. B
78
,
155125
(
2008
).
40.
J.
Clérouin
,
P.
Noiret
,
V.
Korobenko
, and
A.
Rahkel
, “
Direct measurements and ab initio simulations for expanded fluid aluminum in the metal-nonmetal transition range
,”
Phys. Rev. B
78
,
224203
(
2008
).
41.
O. T.
Strand
,
D. R.
Goosman
,
C.
Martinez
, and
T. L.
Whitworth
, “
Accuracy and precision in photon Doppler velocimetry
,”
Rev. Sci. Instrum.
77
(
8
),
083108
(
2006
).
42.
D. H.
Dolan
, “
Accuracy and precision in photonic Doppler velocimetry
,”
Rev. Sci. Instrum.
81
,
053905
(
2010
).
43.
L. M.
Barker
and
R. E.
Hollenbach
, “
Shock-wave studies of PMMA, fused silica, and sapphire
,”
J. Appl. Phys.
41
,
4208
4226
(
1970
).
44.
P.
Horn
and
Y.
Gupta
, “
Wavelength shift of the ruby luminescence R lines under shock compression
,”
Appl. Phys. Lett.
49
,
856
858
(
1986
).
45.
X.
Shen
and
Y.
Gupta
, “
Effect of crystal orientation on ruby R-line shifts under shock compression and tension
,”
Phys. Rev. B
48
,
2929
2940
(
1993
).
46.
R.
Hankey
and
D.
Schuele
, “
Third-order elastic constants of Al2O3
,”
J. Acoust. Soc. Am.
48
,
190
202
(
1970
).
47.
H. K.
Mao
,
P. M.
Bell
,
J. W.
Shaner
, and
D. J.
Steinberg
, “
Specific volume measurements of Cu, Mo, Pd, and Ag and calibration of the ruby R1 fluorescence pressure gauge from 0.06 to 1 Mbar
,”
J. Appl. Phys.
49
,
3276
3283
(
1978
).
48.
Y.
Gupta
and
X.
Shen
, “
Potential use of the ruby R2 line shift for static high-pressure calibration
,”
Appl. Phys. Lett.
58
,
583
585
(
1991
).
49.
S.
Sharma
and
Y.
Gupta
, “
Theoretical analysis of R-line shifts of ruby subjected to different deformation conditions
,”
Phys. Rev. B
43
,
879
893
(
1991
).
50.
J. K.
Hyun
,
S. M.
Sharma
, and
Y. M.
Gupta
, “
Ruby R-line shifts for shock compression along (1102)
,”
J. Appl. Phys.
84
(
4
),
1947
1952
(
1998
).
51.
V.
Korobenko
and
A.
Rahkel
, “
Transition of expanded liquid iron to the nonmetallic state under supercritical pressure
,”
J. Theor. Phys.
112
,
649
655
(
2011
).
52.
V. N.
Korobenko
and
A. D.
Rakhel
, “
Direct measurements of thermodynamic functions and electrical resistivity of fluid tungsten over a wide range of densities
,”
Phys. Rev. B
88
,
134203
(
2013
).
53.
H.
Lamb
,
J.
Glaisher
, and
L.
Whitbread
, “
XIII. On electrical motions in a spherical conductor
,”
Philos. Trans. R. Soc. London
174
,
519
549
(
1883
).
54.
L.
Landau
and
E.
Lifchitz
,
Physique Théorique: Mécanique Des Fluides
, 3rd ed. (
Mir - Ellipses
,
1994
).
55.
G.
Prudhomme
, “
Etude du nuage de particules ejectees sous choc: apports de la velocimetrie heterodyne
,” Doctoral thesis, Ecole Nationale Supérieure Des Arts et Métiers – ENSAM, 2014.
56.
D.
Hébert
,
J.
Gardelle
,
G.
Poette
,
G.
Robert
,
V.
Dubois
, and
P.
Legrand
, “
Development of an equation of state to characterize an electron beam interacting with an aluminum target
,”
J. Appl. Phys.
133
,
125901
(
2023
).
57.
J. P.
Colombier
,
P.
Combis
,
F.
Bonneau
,
R.
Le Harzic
, and
E.
Audouard
, “
Hydrodynamic simulations of metal ablation by femtosecond laser irradiation
,”
Phys. Rev. B
71
,
165406
(
2005
).
58.
J.-P.
Cuq-Lelandais
,
M.
Boustie
,
L.
Berthe
,
T.
de Rességuier
,
P.
Combis
,
J.-P.
Colombier
,
M.
Nivard
, and
A.
Claverie
, “
Spallation generated by femtosecond laser driven shocks in thin metallic targets
,”
J. Phys. D: Appl. Phys.
42
,
065402
(
2009
).
59.
S.
Bardy
,
B.
Aubert
,
T.
Bergara
,
L.
Berthe
,
P.
Combis
,
D.
Hébert
,
E.
Lescoute
,
Y.
Rouchausse
, and
L.
Videau
, “
Development of a numerical code for laser-induced shock waves applications
,”
Opt Laser. Technol.
124
,
105983
(
2020
).
60.
M.
Scius-Bertrand
,
L.
Videau
,
A.
Rondepierre
,
E.
Lescoute
,
Y.
Rouchausse
,
J.
Kaufman
,
D.
Rostohar
,
J.
Brajer
, and
L.
Berthe
, “
Laser induced plasma characterization in direct and water confined regimes: New advances in experimental studies and numerical modelling
,”
J. Phys. D: Appl. Phys.
54
,
055204
(
2020
).
61.
S.
Lyon
and
J.
Johnson
, “
Sesame: The Los Alamos National Laboratory equation of state database
,” LANL Report No. LA-UR-92-3407 (Los Alamos National Laboratory, 1992).
62.
A.
Bushman
,
I.
Lomonosov
, and
V.
Fortov
,
Equations of State of Metals at High Energy Densities, Institute of Chemical Physics
(
Russian Academy of Sciences
,
Chernogolovka
,
1987
).
63.
D.
Wallace
, “
Thermoelasticity of stressed materials and comparison of various elastic constants
,”
Phys. Rev.
162
,
776
789
(
1967
).
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