PRL 95, 035001 (2005)
PHYSICAL REVIEW LETTERS
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Proposal for the Study of Thermophysical Properties of High-Energy-Density Matter Using
Current and Future Heavy-Ion Accelerator Facilities at GSI Darmstadt
N. A. Tahir,1 C. Deutsch,2 V. E. Fortov,3 V. Gryaznov,3 D. H. H. Hoffmann,4,1 M. Kulish,3 I. V. Lomonosov,3 V. Mintsev,3
P. Ni,4 D. Nikolaev,3 A. R. Piriz,5 N. Shilkin,3 P. Spiller,1 A. Shutov,3 M. Temporal,5 V. Ternovoi,3
S. Udrea,4 and D. Varentsov4
1
Gesellschaft für Schwerionenforschung, Planckstraße 1, 64291 Darmstadt, Germany
Laboratoire de Physik des Gaz et des Plasmas, Universite Paris-Sud, 91405 Orsay, France
3
Institute of Problems of Chemical Physics, Chernogolovka, Russia
4
Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt, Germany
5
ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
(Received 16 February 2005; revised manuscript received 3 May 2005; published 11 July 2005)
2
The subject of high-energy-density (HED) states in matter is of considerable importance to numerous
branches of basic as well as applied physics. Intense heavy-ion beams are an excellent tool to create large
samples of HED matter in the laboratory with fairly uniform physical conditions. Gesellschaft für
Schwerionenforschung, Darmstadt, is a unique worldwide laboratory that has a heavy-ion synchrotron,
SIS18, that delivers intense beams of energetic heavy ions. Construction of a much more powerful
synchrotron, SIS100, at the future international facility for antiprotons and ion research (FAIR) at
Darmstadt will lead to an increase in beam intensity by 3 orders of magnitude compared to what is
currently available. The purpose of this Letter is to investigate with the help of two-dimensional numerical
simulations, the potential of the FAIR to carry out research in the field of HED states in matter.
DOI: 10.1103/PhysRevLett.95.035001
PACS numbers: 52.27.Gr, 52.25.Kn
A study of the fundamental properties of high-energydensity (HED) matter is of considerable importance as it
has very wide applications to basic as well as to numerous
branches of applied physics. In addition to that, it has great
potential for lucrative industrial applications. Theoretical
calculations have demonstrated that an intense heavy-ion
beam can be a very efficient tool to study the equation-ofstate (EOS) properties of HED matter using the heavy-ion
heating and expansion (HIHEX) technique [1] that employs isochoric heating of a sample material by the ion
beam that is subsequently allowed to expand isentropically.
While going through the expansion process, the sample
material will pass through many interesting physical states
that are either very difficult to access or for some materials
even inaccessible, using the traditional method of shock
compression.
Figure 1 presents the EOS surface of lead in pressurevolume-temperature variables that is calculated using a
semiempirical model [2]. The picture shows the parameter
space in which different phases of matter will exist and
where different phase transitions will take place. On this
surface, we also plot experimental data that have been
obtained using different techniques, including diamondanvil-cell [3], isobaric expansion, or exploding wire technique [4], and shock compression of solid [5–7] and porous [8] material. A few release isentropes [9] of the
shocked matter are presented as well. Moreover, lines
with a constant degree of ionization and the plasma
nonideality parameter are indicated on this figure.
The colored line, below the Hugoniot curves H1 and HP
that represent the shock adiabats in the case of solid and
0031-9007=05=95(3)=035001(4)$23.00
porous materials, respectively, in Fig. 1, shows the isochoric heating path that will be followed by the beam
heated matter, and the colored surface below this line
indicates the region of the phase diagram that will be
FIG. 1 (color). Equation-of-state surface for lead in P-V-T
variables (logarithmic scale). The painted area bounded by
corresponding isochore and isentrope shows the parameter region accessible with SIS18 and SIS100 heavy-ion beams (the
HIHEX experiment). Also shown: M, melting region; H, principal and porous Hugoniot curves; DAC, diamond-anvil-cells
data; IEX, isobaric expansion (‘‘exploding wires’’) data; S,
release isentropes; R, boundary of two-phase liquid-gas region
with the critical point, isolines of ionization degree , and
plasma nonideality parameter .
035001-1
 2005 The American Physical Society
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PHYSICAL REVIEW LETTERS
much less than that of the ion beam, which in fact is the full
width at half maximum (FWHM) of the Gaussian power
distribution in the beam focal spot along the transverse
direction. Fulfillment of these conditions ensures a fairly
uniform energy deposition along the target radius as well
as the length. The heated material expands in the radial
direction only as the fringe effects are minimized considering the cylinder length to be much larger than the radius
so that the problem is reduced to a one-dimensional radial
expansion. Typically, the cylinder length is a few millimeters, while the radius is of the order of a few hundred
micron.
First, we present results using a 1 GeV=u uranium beam
having N 2:5 1010 , 50 ns, and a focal spot diameter FWHM 2 mm. The target is assumed to be a
solid lead cylinder having a length l 2 mm and a radius
r 300 m. In Fig. 3(a) we present the material state at
t 25 ns, during the target irradiation with a specific
energy deposition Es of 0:45 kJ=g. It is seen that solid
lead has been converted to a liquid state having a temperature of about 3400 K and a pressure of 78 kbar. Figure 3(b)
is plotted at t 50 ns, when the beam has just delivered its
total energy (Es 0:9 kJ=g). The sample material is still
in a liquid state but at a higher temperature and pressure of
6100 K and 125 kbar, respectively.
Figure 4 also shows the material state, but at t 225 ns.
It is seen that the target has undergone substantial expan-
Material State at t = 25 ns
0.3
Liquid
a)
0.2
Specific Energy = 0.45 kJ/g
Temperature = 3400 K
Pressure = 78 kbar
0.1
0
0.5
0
1.0
1.5
2.0
Length (mm)
Material State at t = 50 ns
0.3
Radius (mm)
accessible in the HIHEX experiments using the upgraded
SIS18 beam and a more powerful beam that will be generated at the future facility for antiprotons and ion research
(FAIR) [10].
Currently, the uranium beam generated by the existing
synchrotron, SIS18, has an intensity of 4 109 ions with a
particle energy of up to 1 GeV=u delivered in a single
bunch, a few hundred nanoseconds long. It is expected
that when the SIS18 upgrade is completed, the beam
intensity will increase to 2 1011 ions, while the bunch
length will be reduced to about 50 ns. A new synchrotron,
SIS100, which will be built at the future FAIR, will provide
a much more powerful uranium beam with an intensity of
2 1012 ions per bunch. The particle energy will be in the
range of 400 MeV=u–2:7 GeV=u, and, depending on the
energy, the bunch length will be in the range 20 –100 ns.
The beam intensity at the above two facilities is
expected to increase gradually, and the respective maximum beam intensities will be achieved over a period of
several years. It is thus important to know if one can
perform useful experiments during the intermediate
stages of the facility upgrades. For this purpose, we have
carried out extensive numerical simulations of thermodynamic and hydrodynamic responses of a sample material
(lead) using the two-dimensional computer code BIG-2
[11], considering a wide range of beam intensities
(1010 –1011 ions=bunch). The proposed experiment design
showing the beam-target configuration is presented in
Fig. 2.
The target consists of a thin cylinder (wire) of a test
material that is surrounded by a cylindrical shell or wall of
a strong transparent material such as LiF or sapphire. The
target can be supported in many possible ways; for example, it can be freely suspended with the surrounding
wall or it can be held by thin conductivity measurement
probes at the two ends of the target. The beam is incident
on one face of the target and the ions penetrate into the
target along its length. The length of the cylinder is considered to be much smaller than the range of the ions so
that the Bragg peak does not lie inside the target and the
energy deposition is uniform along the ion trajectories.
Moreover, we assume that the diameter of the target is
Radius (mm)
PRL 95, 035001 (2005)
Liquid
b)
0.2
Specific Energy = 0.90 kJ/g
Temperature = 6100 K
0.1
Pressure = 125 kbar
0
0
0.5
1.0
1.5
2.0
Length (mm)
FIG. 2. Beam-target geometry of the proposed experiment.
PW (petawatt) laser beam for x-ray backlighting.
FIG. 3. Material state of a solid lead cylinder, l 2 mm, r 300 m, N 2:5 1010 , 50 ns, Eions 1 GeV=u, and
spot size FWHM 2 mm, (a) at t 25 ns and (b) at t 50 ns.
035001-2
Radius (mm)
Material State at t = 225 ns
TABLE II.
0.5
Intensity
0.4
1011
Sample physical conditions at t 50 ns.
FWHM (mm) E (kJ=g) P (kbar)
1
2
3
4
1
2
3
4
1
2
3
1
2
3
1
2
Two−Phase Liquid−Gas Region
0.3
0.2
0.1
7:5 1010
0
0
0.5
1.0
1.5
2.0
Length (mm)
FIG. 4.
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PHYSICAL REVIEW LETTERS
PRL 95, 035001 (2005)
5 1010
Same as in Fig. 3, but at t 225 ns.
sion that leads to reduction in density, temperature, and
pressure, and the sample material enters a two-phase
liquid-gas state.
Tables I and II show the material physical conditions and
material state at t 25 and 50 ns, respectively, meaning
during and after beam heating, for various beam intensities
and beam spot sizes. It is seen that in all these cases, the
sample material has been converted into liquid (L) and a
wide range of pressure and temperature is achievable.
In Fig. 5 we plot the density, temperature, and pressure
vs radius at t 400 ns using a beam intensity of
1011 ions=bunch and a beam spot size FWHM 3 mm. It is seen that the achieved values of the corresponding variables are very close to the calculated critical point
parameters of lead [12], which are TC 5500 K, PC 2:3 kbar, and C 3:1 g=cm3 .
Figure 6 shows the material density vs radius at t 120 ns for the same beam intensity as in Fig. 5, but using
FWHM 1 mm. The achieved values show that the sample material will be in a strongly coupled plasmas state
with a coupling parameter of the order of 4 [13].
2:5 1010
1010
14.0
3.6
1.6
0.9
10.5
2.6
1.2
0.7
7.0
1.8
0.8
3.5
0.9
0.4
1.4
0.35
5 1010
2:5 1010
1010
7.10
1.81
0.81
0.46
5.5
1.4
0.65
0.35
3.65
0.91
0.41
1.8
0.45
0.2
0.73
0.18
575
220
120
78
485
177
96
64
365
130
72
220
78
45
110
42
State
36 000
11 700
5728
3424
30 000
9200
4410
2640
21 700
6376
3070
11 700
3400
1645
5175
1495
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
3
1
2
3
4
1
2
3
4
1
2
3
1
2
3
1
2
T (K)
3
7:5 1010
FWHM (mm) E (kJ=g) P (kbar)
Dens. (g/cm ), Temp.(x10 K), Press.(kbar)
1011
State
56 000
21 000
10 000
6256
47 000
17 000
8060
4825
36 300
11 600
5600
21 000
6100
3000
9452
2733
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
Table III shows the final material states, namely, expanded hot liquid (EHL), gaseous (G), two-phase liquidgas (2PLG) and strongly coupled plasma (SCP), that can be
achieved using different beam intensities and focal spot
sizes.
Efficient diagnostics is the backbone to the success and
usefulness of any experiment. In the proposed HIHEX
scheme, the EOS will be determined by direct measurement of the basic physical parameters of the sample material including density, temperature, and pressure. Because
of the high density and exotic behavior of the electrons in
the HED sample, the standard diagnostic techniques will
fail. Moreover, these exotic states are available in the
laboratory in a highly transient state that requires a high
temporal resolution of the diagnostics (typically of the
TABLE I. Sample physical conditions at t 25 ns.
Intensity
830
360
200
103
710
290
106
104
550
215
117
347
125
70
180
65
T (K)
t = 400ns
6
Density
Temperature
Pressure (kbar)
5
Critical Point Region
4
3
2
1
0
0
0.25
0.5
0.75
1
1.25
1.5
Radius (mm)
FIG. 5. , T, and P vs radius at t 400 ns; solid lead cylinder,
l 2 mm, r 500 m, N 1:0 1011 ions, 50 ns,
Eions 1 GeV=u, and spot size FWHM 3 mm.
035001-3
t = 120 ns
3
4
Dens.(g/cm ), Temp. (x10 K)
5
TABLE III. Final achievable material state.
Intensity
Density
Temperature
1011
4
3
Plasma Parameter = 4
7:5 1010
2
1
0
0
5 1010
0.1
0.2
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PHYSICAL REVIEW LETTERS
PRL 95, 035001 (2005)
0.3
0.4
0.5
0.6
0.7
0.8
Radius (mm)
FIG. 6. and T vs radius at t 120 ns, using the same beam
parameters except spot size FWHM 1 mm.
order of a nanosecond). Measurements will be made during
as well as after beam heating of the target.
For the temperature measurements, a fast multichannel
pyrometer is being developed. The large dynamic range
(about 10 000) of this instrument due to its photodetectors,
specially designed amplifiers, and large number of channels will allow one to measure target temperatures over a
wide range (from 1000 K to more than 60 000 K). The
spatial resolution of the system will be as good as
50–100 m, which is sufficient to perform experiments
using targets with typical dimensions of 1 mm.
The density distribution in the sample will be determined by ion and proton radiography. The ions will be
provided by an additional diagnostic beam that will be
delivered by the SIS18, while the protons will be generated
by the petawatt high-energy laser for heavy ion experiments (PHELIX) that is being constructed at the
Gesellschaft für Schwerionenforschung (GSI). The ion
and proton beams for radiography will be incident perpendicular to the target. In addition to that, x-ray backlighting
and the shadowgraphy technique will be used to measure
the volume of the expanding material.
The expansion velocity of the material and the material
pressure will be measured using laser interferometric
methods, especially the velocity interferometer system
for any reflector (VISAR) technique [14]. The metal-toinsulator transition will be investigated by performing
conductivity measurements employing contact as well as
noncontact methods.
Conclusions.—Numerical simulations have shown that
the intense uranium beams that will be available at the GSI
Darmstadt upgraded heavy-ion synchrotron SIS18 and at a
much more powerful synchrotron SIS100, which will be
built at the future FAIR, could be a very efficient tool to
study the EOS properties of HED matter in a parameter
range that is inaccessible employing other techniques such
2:5 1010
1010
FWHM (mm)
Material State
1
2
3
4
1
2
3
4
1
2
3
1
2
3
1
2
SCP
SCP
CP
2PLG
SCP
G
2PLG
2PLG
SCP
EHL
2PLG
G
2PLG
2PLG
2PLG
2PLG
as shock compression of matter. Using our proposed
HIHEX technique, one can access the states of expanded
hot liquid, the two-phase liquid-gas region, the critical
point region, and the strongly coupled plasmas. It is also
to be noted that, using the exploding wire technique to
study EOS [4], one can investigate a sample of conducting
material only. In the case of our proposed HIHEX method,
the choice of the sample material is unrestricted, which
underscores the power and usefulness of this method.
[1] D. H. H. Hoffmann et al., Phys. Plasmas 9, 3651 (2002).
[2] A. V. Bushman and V. E. Fortov, Sov. Tech. Rev. B 1, 219
(1987).
[3] C.-S. Yoo, H. Cynn, and P. Söderlind, Phys. Rev. B 57,
10 359 (1998).
[4] G. R. Gathers, Rep. Prog. Phys. 49, 341 (1986).
[5] R. G. McQueen et al., in High Velocity Impact
Phenomena, edited by R. Kinslow (Academic Press,
New York, 1970), pp. 293– 417 and appendixes on
pp. 515–568.
[6] J. M. Walsh et al., Phys. Rev. 108, 196 (1957).
[7] LASL Shock Hugoniot Data, edited by S. P. Marsh
(University of California Press, Berkeley, 1980).
[8] Y. B. Zeldovich and Y. P. Raizer, Physics of Shock Waves
and High Temperature Phenomena (Academic Press, New
York, 1966), Vol. I–II.
[9] V. E. Fortov and I. T. Yakubov, Physics of Non-Ideal
Plasmas (World Scientific, London, 1999).
[10] W. F. Henning, Nucl. Instrum. Methods Phys. Res., Sect. B
214, 211 (2004).
[11] V. E. Fortov et al., Nucl. Sci. Eng. 123, 169 (1996).
[12] V. E. Fortov et al., Nucl. Instrum. Methods Phys. Res.,
Sect. A 415, 604 (1998).
[13] V. K. Gryaznov, Zh. Eksp. Teor. Fiz. 114, 1242 (1998).
[14] G. Kanel et al., J. Appl. Phys. 79, 8310 (1996).
035001-4