a Gesellschaft für Schwerionenforschung, Planckstrasse 1, Darmstadt, Germany

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1 Nuclear Instruments and Methods in Physics Research A 544 (25) Studies of heavy ion-induced high-energy density states in matter at the GSI Darmstadt SIS-18 and future FAIR facility N.A. Tahir a,, A. Adonin b, C. Deutsch c, V.E. Fortov d, N. Grandjouan e, B. Geil f, V. Grayaznov d, D.H.H. Hoffmann a,g, M. Kulish d, I.V. Lomonosov d, V. Mintsev d, P. Ni g, D. Nikolaev d, A.R. Piriz h, N. Shilkin d, P. Spiller a, A. Shutov d, M. Temporal h, V. Ternovoi d, S. Udrea g, D. Varentsov g a Gesellschaft für Schwerionenforschung, Planckstrasse 1, Darmstadt, Germany b Institut für Angewandte Physik, Frankfurt University, 6325 Frankfurt, Germany c Laboratoire de Physik des Gaz et des Plasmas, Universite Paris-Sud, 9145 Orsay, France d Institute for Problems in Chemical Physics, Chernogolovka, Russia e LULI, UMR 765, Ecole Polytechnique-CNRS-CEA-Universite Paris VI, Palaiseau, France f Institut für Festkörperphysik, TU Darmstadt, Darmstadt, Germany g Institut für Kernphysik, TU Darmstadt, Darmstadt, Germany h E.T.S.I Industrials, Universidad de Castilla-La Mancha, 1371 Ciudad Real, Spain Available online 11 March 25 Abstract This paper presents numerical simulation results of heating and compression of matter using intense beams of energetic heavy ions. In this study we consider different beam parameters that include those which are currently available at the heavy ion synchrotron, SIS18 at the Gesellschaft fu r Schwerionenforschung (GSI), Darmstadt and those which will be available in the near future as a result of the upgraded facility. In addition to this, we carried out detailed calculations considering parameters of high-intensity beam which will be generated at the GSI future Facility for Antiprotons and Ion Research (FAIR facility) that has been approved by the German Government. These simulations show that by using the above ion beam parameter range, it will be possible to carry out very useful studies on the thermophysical properties of high-energy density (HED) states in matter. This scheme would make it possible to investigate those regions of the phase diagram that are either very difficult to access or even are unaccessible using the traditional methods of shock waves. Moreover, employing a hollow ion beam which has an annular (ring shaped) focal spot, it would be possible to achieve a low entropy compression of a test material like hydrogen, which is enclosed in a cylindrical shell of a high-density material such as lead or gold. These experiments Corresponding author. GSI Darmstadt, Planckstr.1, Darmstadt, Germany. Tel.: ; fax: address: n.tahir@gsi.de (N.A. Tahir) /$ - see front matter r 25 Elsevier B.V. All rights reserved. doi:1.116/j.nima

2 will enable one to study the interiors of Giant planets, Jupiter and Saturn as well as to investigate the problem of hydrogen metallization. r 25 Elsevier B.V. All rights reserved. PACS: i; 52.4.Mj; 52.5.Lp N.A. Tahir et al. / Nuclear Instruments and Methods in Physics Research A 544 (25) Keywords: Intense heavy ion beams; High-energy density matter; Equation-of-state; Strongly coupled plasmas; Planetary science 1. Introduction The Gesellschaft fu r Schwerionenforschung (GSI), Darmstadt is a unique laboratory worldwide that has the capability to generate intense heavy ion beams at a heavy ion synchrotron facility, SIS18 which has a magnetic rigidity of 18 Tm. Currently, this facility can deliver a uranium beam with an intensity N ¼ ions; having a particle energy of a few hundred MeV=u: The particles are delivered in a single bunch which is a few hundred nanosecond long. It is expected that when the upgrade of the SIS18 will be completed, the beam intensity will be increased to 2: ions per bunch while the bunch length will be reduced to about 5 ns and the particle energy will be 197 MeV=u [1]. The fullwidth at half-maximum (FWHM) of the Gaussian beam intensity profile along the radial direction, which for the calculational purposes is considered as the effective beam diameter will be 1. mm. GSI is also in the process to establish a new accelerator facility named Facility for Antiprotons and Ion Research (FAIR) that would include construction of a new synchrotron SIS1, which will have a magnetic rigidity of 1 Tm. The SIS18 will be used as injector for the SIS1 and four to eight bunches from the SIS18 will be transferred to the SIS1 consecutively, where the ions will be further accelerated before the beam is finally delivered onto a target. The SIS1 beam will therefore consist of uranium ions with a wide range of available particle energy ð4 MeV=u22:7 GeV=uÞ: The bunch length corresponding to this energy range is expected to be 9 2 ns. Recently, a letter of intent (LOI) named highenergy-density matter Generated by Heavy Ion Beams (HEDgeHOB) [2], has been written by the members of the GSI Plasma Physics Group together with more than 1 international collaborators from about 3 universities and scientific institutions from all over the world. In this LOI, two different schemes have been proposed to study the problem of high-energy-density (HED) states in matter using the intense heavy ion beams that will be generated at the FAIR facility. In the first scheme named Heavy Ion Heating and Expansion (HIHEX), the material is isochorically heated by the beam. The heated material can then expand isentropically and depending on deposited energy, will reach different interesting physical states from that of an expanded hot liquid, critical point region and two-phase liquid gas region to strongly coupled plasmas and warm dense matter (WDM) states. These states are either very difficult to achieve or are unaccessible using traditional methods. An additional advantage of the HIHEX experiment compared to some traditional methods is that it is not limited to a specific type of target material, but any material of interest like for example, metals, minerals or oxides can be studied [3]. In case of the exploding wire experiments which are somewhat similar to the proposed HIHEX scheme, on the other hand, one is limited to use conductor material only [4]. In addition to that, due to the large flexibility in beam spot size and geometry, one may use plane as well as cylindrical geometry in these studies. The second type of experiments named Laboratory Planetary Sciences (LAPLAS) are designed to achieve low entropy compression of a sample material like hydrogen, using a hollow beam that has a ring-shaped (annular) focal spot. Numerical simulation and analytic modeling have shown that using the beam parameters that will be available at the future FAIR facility, it will be possible to achieve the physical conditions that are expected

3 18 N.A. Tahir et al. / Nuclear Instruments and Methods in Physics Research A 544 (25) to exist in the interior of Giant planets, Jupiter and Saturn. Moreover, with the help of these experiments, one should be able to study the problem of hydrogen metallization [5 8]. In Section 2, we schematically describe the HIHEX and LAPLAS setup, while in Section 3, the numerical simulation results are presented. The conclusions drawn from this work are noted in Section Description of the HIHEX and LAPLAS experimental setup Fig. 1. Schematic diagram of the cylindrical HIHEX experimental setup. In this section, we show schematically the experimental setup for the HIHEX and LAPLAS schemes The HIHEX scheme The main idea of the HIHEX experiment is to exploit the intrinsic feature of the heavy ion beamvolumetric character of heating, in contrast to generating a shock wave. A large volume of a sample material is heated by the intense heavy ion beam quasi-isochorically, inducing a HED, highentropy state. The heated material will then expand isentropically, passing through many interesting physical states. The expansion of the target material can be limited by a surrounding container that can also be filled with a buffer gas at different initial pressures. The measurements of the target physical properties are carried out during the heating as well as the expansion phase. In case of confined target configuration, the diagnostics are also performed at the final stage, shortly after the thermalization of the target material in the container. It is proposed that the complexity of the physical problem can be simplified by reducing the hydrodynamic response of the target material to one-dimensional case. We therefore propose to consider plane as well as cylindrical targets as both have certain advantages. In Figs. 1 and 2, we show the schematic view of the layout of the HIHEX experiments in cylindrical and plane geometry, respectively. It is seen in Fig. 1 that the target consists of a thin cylinder (wire) of a test material that is surrounded by a Fig. 2. Schematic diagram of the plane HIHEX experimental setup. cylindrical shell (wall) of a strong transparent material like LiF or sapphire. The wire can be supported in many possible ways, for example, can be held by the thin conductivity measurement probes at the two ends. Also there is a gap between the test material and the wall. 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 much less than that of the ion beam which in fact is the FWHM of the Gaussian power distribution in the

4 N.A. Tahir et al. / Nuclear Instruments and Methods in Physics Research A 544 (25) beam focal spot along the radial direction. Fulfillment of these conditions ensures a fairly uniform energy deposition along the target radius as well as the length. Typically, for the case of uranium 35 1 GeV=u ions, the focal spot size (FWHM) is mm and the ion range in lead corresponding to this energy band is mm while the length of the wire would be 6 8% of the range. The beam and the target could be aligned to a precision of about 1 mm which is sufficient for the success of the experiment. Heating of the wall by the beam is avoided by using a beam blocker (diaphragm) which is installed before the target assembly. The thickness of the diaphragm is sufficiently large to completely stop the ions. To minimize the fringe effects, the target length is considered to be much larger than the radius. Typically, a ratio of 1 between the length and the radius is reasonable. This would ensure a one-dimensional response of the target during the expansion phase. The heated material from the sample would freely expand in the radial direction into the gap until it will collide with the wall where it will be reflected. Multiple reflections between the wall and the target axis will create fairly uniform physical conditions throughout the sample. Measurement of the physical parameters including density (volume), pressure, temperature, expansion velocity, electric conductivity and others will be carried out. It is also important to note that by adjusting the size of the gap, the final density can be easily controlled. Details about the development of diagnostic tools for these experiments can be found in the LOI HEDgeHOB [2]. Fig. 2 shows the HIHEX configuration using plane geometry. In this case, one uses a thin foil of a test material which is irradiated along the length. To optimize the specific energy deposition, we use a beam with an elliptic focal spot as shown in the figure. The width of the beam is significantly larger than the foil thickness and the ion range is longer than the foil length which allows for uniform material heating. As stated in the previous case, such a beam-target configuration would lead to a simple one-dimensional target expansion. The two plates of the transparent material placed on either side of the foil act as walls that confine and homogenize the expanding test material as a result of multiple shock reflection The LAPLAS scheme Fig. 3 shows the conceptual design of the proposed LAPLAS experiment. The purpose of this experiment is to achieve a low-entropy compression of a test material, like frozen hydrogen or water that will lead to a high degree of compression while the temperature in the sample will be relatively low. As shown in Fig. 3, the target consists of a cylinder of the sample material that is surrounded by a thick shell of a heavy material, typically gold or lead. One face of the target is irradiated with an intense heavy ion beam which has an annular focal spot. It is assumed that the inner radius of the annulus is larger than the radius of the sample material which is a necessary condition to avoid direct heating of the sample material by the ion beam. Moreover, we assume that the outer radius of the focal spot ring is smaller than the outer radius of the surrounding Fig. 3. Schematic diagram of the LAPLAS experimental setup.

5 2 N.A. Tahir et al. / Nuclear Instruments and Methods in Physics Research A 544 (25) shell. It is seen from Fig. 3 that a layer of cold material from the surrounding shell known as payload is created between the sample material and the beam heated region. As a result of compression, the payload density becomes about twice the solid density whereas the density in the beam-heated region decreases due to the shock waves moving inwards and outwards. The payload plays an important role in placing the compression on the desired adiabat. It is also seen that a cold shell remains around the beam-heated region as a tamper that confines the implosion for a longer time. The high pressure in the beam-heated region launches a shock inwards that passes through the payload and is subsequently transmitted into the sample material. The shock compresses the sample material and is reflected at the target axis and travels outwards. The reflected shock is re-reflected at the material boundary and again moves inwards. This process of multiple-shock reflection continues while the payload shell continuously moves inwards, thereby compressing the sample material slowly. Numerical simulations show [5] that such a scheme leads to a low-entropy compression of the sample material Diagnostic techniques to be used In the proposed HIHEX and LAPLAS experiments, the physical properties of the material will be directly measured in order to determine the equation-of-state (EOS) properties of HED states in matter. It is therefore necessary to develop the essential diagnostic tools for this purpose. The target density will be measured using X-ray backlighting. One of the proposed X-ray source is the PHELIX laser. The target density can also be estimated using the energy loss dynamic scheme in which the heavy ion beam that heats the target can be used to diagnose the target by measuring the change in the energy of the escaping ions [9]. However, this scheme can only be used if the pulse length is sufficiently long. In case of short pulses, it will be necessary to have two beams simultaneously. One high-intensity, strongly bunched beam to heat the target and second, a low-intensity beam with a duration of the order of a microsecond that will be used for the diagnostic purposes. Numerical simulations using such a two-beam scheme have been reported elsewhere [1]. The target temperature will be measured using pyrometric techniques and the pressure delivered onto the transparent wall will be measured using laser interferometry including VISAR. Ideally, one should be able to make all these measurements simultaneously in a single experiment. A set of the measured volume, temperature and pressure will determine the EOS of the material completely. Moreover, in heavy ion experiments the deposited energy is known with a reasonable accuracy. 3. Numerical simulation results In this section, we present the numerical simulation results of hydrodynamic and thermodynamic response of the target material using different target designs as well as different beam parameters. These simulations have been carried out using a two-dimensional hydrodynamic computer code BIG-2 [11]. This code is based on a godunov-type scheme that has a second-order accuracy in space for solving the hydrodynamic equations. It uses rectangular grid and includes heat conduction and uses EOS data in tabular form. Normally, we use a semi-empirical model for the EOS described elsewhere [12], but one may also use other models. It also includes energy deposition by the projectile ions taking into account the beam geometry Simulations of recent experiments using plane HIHEX In this subsection, we present numerical simulation results of recently performed experiments on heating of matter by intense heavy ion beams at the High Temperature Experimental Area (HHT) of the GSI Darmstadt. These experiments have been performed during December 23 and the most intense beam of uranium that has ever been achieved was used. The beam parameters are as follows.

6 N.A. Tahir et al. / Nuclear Instruments and Methods in Physics Research A 544 (25) Intensity (arb. units) e-7 4e-7 6e-7 8e-7 1e-6 Time (s) Fig. 4. Experimentally recorded temporal profile of the beam intensity. As a result of accelerator development and better optimization of the accelerator parameters, a maximum beam intensity of particles of 238 U þ73 having a particle energy of 35 MeV=u was achieved. The recorded temporal profile of the beam intensity is presented in Fig. 4 which shows that the profile is approximately a Gaussian with a FWHM of about 24 ns. Such a high-intensity bunched beam has never been previously generated at the GSI accelerator facility. The focal spot of the beam had an elliptic shape and the beam power distribution along the focal spot radius (semi-major axis and semi-minor axis of the ellipse) was Gaussian with a FWHM of.85 and 1.6 mm along the x and y directions, respectively. In these experiments, we used the plane HIHEX target design shown in Fig. 2. The target consists of a thin foil of test material (lead) which has a thickness of 25 mm and is placed vertically along the ion beam at the origin. Since the thickness of the foil is much smaller than the horizontal beam spot size whereas the vertical beam extension is large, this target geometry provides homogeneous volume heating of the foil. This configuration also leads to a quasi one-dimensional expansion character of the heated matter. As seen in Fig. 2, two sapphire plates are placed parallel to the foil on either side at a suitable distance in order to limit the hydrodynamic expansion and to confine the heated material, thereby defining the final volume. The gap between the foil and the walls was filled with helium gas at different pressures. In order to avoid direct heating of the sapphire wall by the ion beam, a beam blocker (diaphragm) of tungsten is placed in front of the foil whose thickness was sufficient to stop the ion beam completely. The main diagnostic tool used in these experiments was a fast multi-channel pyrometer that recorded the brightness temperature of the heated material [13]. Other physical parameters of the material like density and pressure were not measured in these experiments. Moreover, it was not possible to measure the spatial distribution of temperature in the target. However, detailed numerical simulations of the problem have been carried out using the BIG-2 code [14] that has provided very useful information about the deposited energy and the target physical conditions that may exist during the experiment. In the particular experiment whose simulation results are presented in the following, the foil thickness was.25 mm while the gas pressure in the gap was.5 bar and the width of the gap was.746 mm. Our simulations show that the beam deposits a specific energy of.6 kj/g in solid lead that leads to a temperature of the order of 36 K. The heated lead material expands, thereby compressing the helium gas. In Fig. 5, we plot the simulated material velocity along the transverse direction at different times. It is seen that the Velocity (km/s) ns 8 ns 1 ns 12 ns 15 ns 2 ns Transverse coordinate (cm) Fig. 5. Material velocity from the lead foil vs. transverse direction at different times.

7 22 N.A. Tahir et al. / Nuclear Instruments and Methods in Physics Research A 544 (25) velocity increases with time and the expanding lead material hits the sapphire wall at about t ¼ 12 ns with a peak velocity of 1.2 km/s. The temperature in that region increases to about 6 K after the collision, which is close to the value measured in the experiment at that instant of time Simulations of near future experiments using cylindrical HIHEX It is expected that in the near future the SIS18 will deliver a uranium beam with an intensity, N of the order of 1 1 particles. In this subsection, we present calculations considering cylindrical HI- HEX design using this beam intensity. The particle energy is assumed to be 5 MeV=u while the pulse duration, t ¼ 3 ns: The beam power deposition profile along the radial direction is considered to be Gaussian with a FWHM ¼ 1. mm which for calculation purposes we define as the effective beam diameter. The temporal beam power profile is assumed to be parabolic. For the test material we consider four different metals, namely, lead, gold, copper and zinc. The ranges of 5 MeV=u uranium ions in these materials are given in Table 1. These ranges have been calculated using the SRIM code [15]. The accuracy of the SRIM code in this energy range is of the order of 5%. In order to allow for quasiuniform deposition along the target length, in case of Pb, Zn and Cu we consider the length of the target ¼ 2 3 mm while for Au we assume a 1 mm long wire. The radius of the wire is taken to be 3 mm which is much smaller than the FWHM of the Gaussian and therefore the energy deposition along the radial direction is almost uniform. In order to limit the lateral expansion of the test material, two thin discs of W; each 5 mm thick, are placed on either side of the wire. The wire is enclosed in a thick shell of LiF and the inner radius of this surrounding shell is varied between.7 and 1. mm while the outer radius is assumed to be 3.5 mm. This configuration is shown in Fig. 6 where we plot the target density on a length radius plane assuming lead as the test material at time ¼ ns, using the BIG-2 code. At the end of the pulse at 3 ns, the beam deposits a specific energy of the order of 1.7 kj/g that leads to a temperature of about 95 K, a pressure of the order of 2 kbar and the density has been reduced to about 4:5 g=cm 3 : If Fig. 7, we plot the same parameters as in Fig. 6, but at t ¼ 45 ns: It is seen that the lead wire has significantly expanded and target cavity is almost filled with lead, although the expanding material has not yet collided with the capillary wall. It is seen that average material density in this region is 2:8 g=cm 3 ; the average pressure is 4 kbar and the temperature is 7 K. The estimated critical point values for these parameters for lead are 3:1 g=cm 3 ; 2.3 kbar and 55 K, respectively. One can, therefore, achieve the critical point region for lead in these experiments that will allow to check the theoretically calculated values for the respective parameters. Target Radius (mm) W Density (g/cm 3 ) t = ns LiF ρ = 2.64 W Table 1 Range of 5 MeV=u uranium ions in different materials Target material Lead 5.93 Gold 3.42 Zinc 7.7 Copper 5.71 Range in mm Pb ρ = Target Length (mm) Fig. 6. Density on a length radius plane showing one half of the target at t ¼ ns using the BIG-2 [11] code. The ion beam is incident from right to left with the maxima of the Gaussian distribution coinciding with r ¼ : A diaphragm is also used to avoid the heating of the LiF wall by the beam.

8 N.A. Tahir et al. / Nuclear Instruments and Methods in Physics Research A 544 (25) W t = 45 ns W GeV/u U ions, N = 5x1 11, Bunch length = 5 ns Target Radius (mm) LiF ρ = 2.64 (g/cm 3 ) P = 4 kbar T = 7 K Pb ρ = 2.8 (g/cm 3 ) Target Length (mm) Fig. 7. Same as in Fig. 6, but at t ¼ 45 ns:. Density (g/cm 3 ) t = 137 ns t = 142 ns t = 16 ns t = 165 ns t = 168 ns t = 179 ns Radius (cm) Fig. 8. Hydrogen density vs. radius at L ¼ 2:5 mm (middle of the target) at different times during the implosion. Table 2 Estimated critical point parameters for different metals Temperature (K) Pressure (kbar) Density ðg=cm 3 Þ Lead Gold Zinc Copper In Table 2, we provide estimated values for the critical point parameters for lead, gold, zinc and copper. Our simulations show that using the beam parameters considered in the present calculations, one can access the critical point region for all these metals Simulations of LAPLAS experiments The potential of using this concept is twofold. One to study the problem of hydrogen metallization and second to investigate the material properties under the conditions that are expected to exist at the interior of large planets. In this subsection, we present simulation results of implosion of proposed LAPLAS experiment concept shown in Fig. 3. Typical beam-target parameters are as below. We consider a cylinder of frozen hydrogen as test material that is enclosed in a shell of lead. The radius of the hydrogen cylinder is assumed to be.4 mm while the outer radius of the lead shell is considered to be 3. mm. The right face of this target is irradiated with a hollow beam of uranium with a particle energy of 1 GeV=u and an intensity of while the pulse duration is assumed to be 5 ns. The cylinder length, L is considered to be 5 mm, which is much less than the range of 1 GeV=u uranium ions in solid lead that ensures a fairly uniform energy deposition in the target. The inner radius of the beam focal spot in this case is.6 mm while the outer radius is 1.6 mm. In Fig. 8, we plot the target density in hydrogen vs. radius at the middle of the target ðl ¼ 2:5 mmþ at different times during the implosion. The process of multiple shock reflection between the target axis and the hydrogen lead boundary and the corresponding increase in the hydrogen density is clearly seen in this figure. The optimum implosion conditions are shown in Fig. 9 where we plot the density, pressure and temperature vs. radius in the hydrogen at t ¼ 216 ns: It is seen that the average density is of the order of 1 g=cm 3 ; the pressure is about 3 Mbar while the average temperature is of the order of.3 ev. These are theoretically predicted physical conditions for hydrogen metallization. We have also carried out a parameter study using beam intensity in the range of and the corresponding density range that is achieved is 1 2 g=cm 3 ; the pressure range is 3 15 Mbar and the temperature range is.3 1. ev. These physical

9 24 N.A. Tahir et al. / Nuclear Instruments and Methods in Physics Research A 544 (25) Dens. (g/cm 3 ), Pressure (Mbar), Temp. (ev) Time = 216 ns Density Pressure Temperature T / 1 K molecular ionic Fluid Neptune isentrope Superionic Metallic Radius (cm) 2 Fig. 9. Density, temperature and pressure vs. radius at the time of maximum compression in the hydrogen. 1 Solid 8 km 16 km 5 K. 3 GPa conditions are expected to exist in the interior of the Giant planets, Jupiter and Saturn. Other important planets in our solar system that should be studied are Neptune and Uranus. Based on the precise information provided by the Voyager on the gravitational fields of these planets, several models have been developed about their structure [16,17]. These two neighbor planets are expected to have a similar structure. In Fig. 1, we present a picture based on one such model that shows the structure of Neptune. It is seen that this planet has an atmosphere of hydrogen and helium Ice He H 2 25 km 2 K, 2 GPa Fig. 1. A schematic diagram of Neptune [16,17] P/GPa Fig. 11. Phase diagram of water [18]. and its outer part consists of a thick layer of water under very exotic conditions. Next to the water layer there is an inner core made of a mixture of metal and rock which contains naturally occurring radioactive materials like U 238 ; Th 232 and K 4 : The heat generated by the radioactivity of these materials diffuses outwards and a temperature profile is created through the layer of water. In Fig. 11, we present a phase diagram of water over a wide range of pressure and temperature that includes the region of physical conditions that are believed to exist in Neptune and Uranus water layers. The line marked with Neptune isentrope shows the temperature distribution in the water region. It is seen that at the inner surface of the water, next to the core, the temperature is 5 K and the pressure is 3 Mbar while at the outer surface of the planet the temperature decreases to 2 K while the pressure becomes.1 Mbar. The water density is believed to be of the order of 4 g=cm 3 : This phase diagram has been obtained using an ab initio Car Purinello molecular dynamic simulations [18]. Numerical simulations have shown that using the LAPLAS experimental setup, considering

10 N.A. Tahir et al. / Nuclear Instruments and Methods in Physics Research A 544 (25) water in the target shown in Fig. 3 as test material, one can achieve physical conditions that cover the entire phase diagram of water shown in Fig. 11. In this simulation study, we assume the beam intensity N ¼ : A very challenging problem concerning the LAPLAS experiments is the generation of a beam with a righ-shaped focal spot. One possibility is to use an RF-wobbler that will rotate the beam with a very high frequency (of the order of gigahertz). The beam rotation will introduce non-uniformities in the deposited energy that will introduce asymmetries in driving pressure. Success of implosion requires a high degree of pressure symmetry (1% asymmetry). Detailed analytic and numerical studies have shown that in order to achieve the required level of symmetry in the driving pressure, one would require 1 revolutions provided the beam temporal profile is a smooth function like a parabolic or a Gaussian distribution. In case of a box shape distribution, on the other hand, one would require 1 revolutions to achieve the above symmetry level. For details, see Ref. [19]. Another important problem is development of a facility to prepare cryogenic targets. Another proposal for generating a ring-shaped focal spot is by transverse beam shaping using nolinear ion optics [2]. 4. Conclusions This paper describes two different schemes named HIHEX and LAPLAS, that can be used to study the thermophysical properties of HED matter employing intense beams of energetic heavy ion. The first scheme is based on isochoric heating and subsequent isentropic expansion of the heated material that will pass through different interesting physical states of HED matter. An experimental study of thermophysical properties of these exotic states of matter will be a very important contribution to this field. Numerical simulations have shown that using the parameters of the present heavy ion synchrotron, SIS18 at the GSI and the future SIS1 machine that will be constructed within the GSI FAIR project will enable one to study those parts of the phase diagram that are either very difficult to access or even are unaccessible using the traditional methods. The second scheme is designed to achieve a lowentropy compression of a test material like frozen hydrogen that is enclosed in a cylindrical shell of a heavy material like lead or gold which is driven by a hollow intense beam with an annular (ringshaped) focal spot. Numerical simulations have demonstrated that using the parameters of the beam that will be generated at the FAIR facility, one should be able to achieve the physical conditions in the hydrogen sample that are believed to exist at the interior of the giant planets, Jupiter and Saturn. In addition to this, one would be able to investigate the problem of hydrogen metallization. Another very interesting problem in the field of planetary sciences is to study the structure of Neptune and Uranus who are believed to be made of thick layers of water under very exotic conditions. Numerical simulations have shown that if one uses water as a test material in a LAPLAS configuration, one would be able to achieve the physical conditions of water that are expected to exist in these two planets. Acknowledgements The authors wish to thank the BMBF for providing financial support to do this work. References [1] R.W. Mu ller, P. Spiller, Strategy for achieving high target power density with a modified SIS18 and the new high current injector, GSI Report, GSI-96-7, [2] HEDgeHOB: High Energy Density Matter with Intense Heavy Ion Beams and Lasers at GSI, Letter of Intent, 24. [3] D.H.H. Hoffmann, V.E. Fortov, I.V. Lomonosov, V. Mintsev, N.A. Tahir, D. Varentsov, J. Wieser, Phys. Plasmas 9 (22) [4] G.R. Gathers, Rep. Prog. Phys. 49 (1986) 341. [5] N.A. Tahir, D.H.H. Hoffmann, A. Kozyreva, A. Tauschwitz, A. Shutov, J.A. Maruhn, P. Spiller, U. Neuner, J. Jacoby, M. Roth, R. Bock, H. Juranik, R. Redmer, Phys. Rev. E 63 (21) [6] N.A. Tahir, H. Juranik, A. Shutov, R. Redmer, A.R. Piriz, M. Temporal, D. Varentsov, S. Udrea, D.H.H. Hoffmann,

11 26 N.A. Tahir et al. / Nuclear Instruments and Methods in Physics Research A 544 (25) C. Duetsch, I.V. Lomonosov, V.E. Fortov, Phys. Rev. B 67 (23) [7] A.R. Piriz, R.F. Portugues, N.A. Tahir, D.H.H. Hoffmann, Phys. Rev. E 66 (22) 427. [8] M. Temporal, A.R. Piriz, N. Grandjouan, N.A. Tahir, D.H.H. Hoffmann, Laser Part. Beams 21 (23) 65. [9] D. Varentsov, N.A. Tahir, I.V. Lomonosov, D.H.H. Hoffmann, J. Wieser, V.E. Fortov, Euro. Phys. Lett. 64 (23) 57. [1] N.A. Tahir, A. Shutov, D. Varentsov, P. Spiller, S. Udrea, D.H.H. Hoffmann, I.V. Lomonosov, J. Wieser, M. Kirk, A.R. Piriz, V.E. Fortov, R. Bock, Phys. Rev. Spe. Top. Accel. Beams 6 (23) 211. [11] V.E. Fortov, B. Goel, C.-D. Munz, A.L. Ni, A. Shutov, O.Yu. Vorobiev, Nucl. Sci. Eng. 123 (1996) 169. [12] A.V. Bushman, V.E. Fortov, Sov. Tech. Rev. B. Therm. Phys. 1 (1987) 219. [13] D. Varentsov, A.Adonin, V.E. Fortov, V.K. Gryaznov, D.H.H. Hoffmann, M. Kulish, I.V. Lomonosov, V. Mintsev, P. Ni, D. Nikolaev, N. Shilkin, A. Shutov, P. Spiller, N.A. Tahir, V. Ternovoi, S. Udrea, GSI Plasma Physics Annual Report, GSI-24-3, 24, p. 14. [14] N.A. Tahir, A. Adonin, C. Deutsch, V.E. Fortov, V.K. Gryaznov, D.H.H. Hoffmann, M. Kulish, I.V. Lomonosov, V. Mintsev, P. Ni, A.R. Piriz, D. Nikolaev, N. Shilkin, A. Shutov, P. Spiller, M. Temporal, V. Ternovoi, S. Udrea, GSI Plasma Physics Annual Report, GSI-24-3, 24, p. 43. [15] J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Ranges of Ions in Solids, Pergamon Press, New York, [16] M. Podolak, A. Weizman, M. Marley, Planetary Space Sci. 48 (1995) [17] M. Podolak, A. Weizman, M. Marley, Planetary Space Sci. 43 (2) 143. [18] C. Cavazzoni, Ph.D. Thesis, International School for Advanced Studies, Rome, [19] A.R. Piriz, M. Temporal, J.J. Lopez Cela, N.A. Tahir, D.H.H. Hoffmann, Plasma Phys. Controlled Fusion 45 (23) [2] D. Varentsov, D.H.H. Hoffmann, N.A. Tahir, GSI Plasma Physics Annual Report, GSI-23-2, 23, p. 2.