Search Results (20 total)

The study of the linear stage of the incompressible Rayleigh-Taylor instability in elastic-plastic solids is performed by considering thick plates under a constant acceleration that is also uniform except for a small sinusoidal ripple in the horizontal plane. The analysis is carried out by using an analytical model based on the Newton second law and it is complemented with extensive two-dimensional numerical simulations. The conditions for marginal stability that determine the instability threshold are derived. Besides, the boundary for the transition from the elastic to the plastic regime is obtained and it is demonstrated that such a transition is not a sufficient condition for instability. The model yields complete analytical solutions for the perturbation amplitude evolution and reveals the main physical process that governs the instability. The theory is in general agreement with the numerical simulations and provides useful quantitative results. Implications for high-energy-density-physics experiments are also discussed.

This paper presents numerical simulations that have been carried out to study the thermodynamic and hydrodynamic responses of a solid copper cylindrical target that is facially irradiated along the axis by one of the two Large Hadron Collider (LHC) 7 TeV/c proton beams. The energy deposition by protons in solid copper has been calculated using an established particle interaction and Monte Carlo code, FLUKA, which is capable of simulating all components of the particle cascades in matter, up to multi-TeV energies. These data have been used as input to a sophisticated two-dimensional hydrodynamic computer code BIG2 that has been employed to study this problem. The prime purpose of these investigations was to assess the damage caused to the equipment if the entire LHC beam is lost at a single place. The FLUKA calculations show that the energy of protons will be deposited in solid copper within about 1 m assuming constant material parameters. Nevertheless, our hydrodynamic simulations have shown that the energy deposition region will extend to a length of about 35 m over the beam duration. This is due to the fact that first few tens of bunches deposit sufficient energy that leads to high pressure that generates an outgoing radial shock wave. Shock propagation leads to continuous reduction in the density at the target center that allows the protons delivered in subsequent bunches to penetrate deeper and deeper into the target. This phenomenon has also been seen in case of heavy-ion heated targets [N. A. Tahir, A. Kozyreva, P. Spiller, D. H. H. Hoffmann, and A. Shutov, Phys. Rev. E 63, 036407 (2001)]. This effect needs to be considered in the design of a sacrificial beam stopper. These simulations have also shown that the target is severely damaged and is converted into a huge sample of high-energy density (HED) matter. In fact, the inner part of the target is transformed into a strongly coupled plasma with fairly uniform physical conditions. This work, therefore, has suggested an additional very important application of the LHC, namely, studies of HED states in matter.

An analytical model for the linear Richtmyer-Meshkov instability in solids under conditions of high-energy density is presented, in order to describe the evolution of small perturbations at the solid-vacuum interface. The model shows that plasticity determines the maximum perturbation amplitude and provides simple scaling laws for it as well as for the time when it is reached. After the maximum amplitude is reached, the interface remains oscillating with a period that is determined by the elastic shear modulus. Extensive two-dimensional simulations are presented that show excellent agreement with the analytical model. The results suggest the possibility to experimentally evaluate the yield strength of solids under dynamic conditions by using a Richtmyer-Meshkov-instability-based technique.

This Letter demonstrates the transporting and focusing of laser-accelerated 14 MeV protons by permanent magnet miniature quadrupole lenses providing field gradients of up to 500  T/m. The approach is highly reproducible and predictable, leading to a focal spot of (286×173)  μm full width at half maximum 50 cm behind the source. It decouples the relativistic laser-proton acceleration from the beam transport, paving the way to optimize both separately. The collimation and the subsequent energy selection obtained are perfectly applicable for upcoming high-energy, high-repetition rate laser systems.

Richtmyer-Meshkov flow is studied by means of an analytical model which describes the asymptotic oscillations of a corrugated interface between two perfectly elastic solids after the interaction with a shock wave. The model shows that the flow stability is due to the restoring effect of the elastic force. It provides a simple approximate but still very accurate formula for the oscillation period. It also shows that as it is observed in numerical simulations, the amplitude oscillates around a mean value equal to the post-shock amplitude, and that this is a consequence of the stress free conditions of the material immediately after the shock interaction. Extensive numerical simulations are presented to validate the model results.

We present an analytical model for the Rayleigh-Taylor instability that allows for an approximate but still very accurate and appealing description of the instability physics in the linear regime. The model is based on the second law of Newton and it has been developed with the aim of dealing with the instability of accelerated elastic solids. It yields the asymptotic instability growth rate but also describes the initial transient phase determined by the initial conditions. We have applied the model to solid/solid and solid/fluid interfaces with arbitrary Atwood numbers. The results are in excellent agreement with previous models that yield exact solutions but which are of more limited validity. Our model allows for including more complex physics. In particular, the present approach is expected to lead to a more general theory of the instability that would allow for describing the transition to the plastic regime.

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.

The Large Hadron Collider (LHC) at CERN will generate two extremely powerful 7 TeV proton beams. Each beam will consist of 2808 bunches with an intensity per bunch of 1.15×10¹¹ protons so that the total number of protons in one beam will be about 3×10¹⁴ and the total energy will be 362 MJ. Each bunch will have a duration of 0.5 ns and two successive bunches will be separated by 25 ns, while the power distribution in the radial direction will be Gaussian with a standard deviation, σ=0.2  mm. The total duration of the beam will be about 89  μs. Using a 2D hydrodynamic code, we have carried out numerical simulations of the thermodynamic and hydrodynamic response of a solid copper target that is irradiated with one of the LHC beams. These calculations show that only the first few hundred proton bunches will deposit a high specific energy of 400  kJ/g that will induce exotic states of high energy density in matter.

This paper presents two-dimensional hydrodynamic simulations of implosion of a multilayered cylindrical target that is driven by an intense heavy ion beam which has an annular focal spot. The target consists of a hollow lead cylinder which is filled with hydrogen at one tenth of the solid density at room temperature. The beam is assumed to be made of 2.7-GeV/u uranium ions and six different cases for the beam intensity (total number of particles in the beam, N) are considered. In each of these six cases the particles are delivered in single bunches, 20 ns long. The simulations have been carried out using a two-dimensional hydrodynamic computer code BIG-2. A multiple shock reflection scheme is employed in these calculations that leads to very high densities of the compressed hydrogen while the temperature remains relatively low. In this study we have used two different equation-of-state models for hydrogen, namely, the SESAME data and a model that includes molecular dissociation that is based on a fluid variational theory in the neutral fluid region which is replaced by Padé approximation in the fully ionized plasma region. Our calculations show that the latter model predicts higher densities, higher pressures but lower temperatures compared to the SESAME model. The differences in the results are more pronounced for lower driving energies (lower beam intensities).

The subject of high-energy density (HED) in matter is of considerable interest to many branches of physics. Intense beams of energetic heavy ions are a promising tool for creating large samples of HED matter which can be used to study the equation-of-state properties of such exotic states of matter experimentally. The Gesellschaft für Schwerionenforschung (GSI), Darmstadt, is a unique laboratory worldwide which has a heavy ion synchrotron facility, SIS18 (with a magnetic rigidity of 18 Tm), that delivers intense heavy ion beams. Using the beams generated at this present facility, interesting experimental work has been carried out in the field of HED matter [D. H. H. Hoffmann , Nucl. Instrum. Methods Phys. Res., Sect. B 161–162, 9 (2000)]. The GSI is planning to significantly expand its accelerator capabilities with construction of a new synchrotron ring, SIS100, which will have a magnetic rigidity of 100 Tm. This new facility will deliver a uranium beam which will have orders of magnitude higher intensity than the existing facility and will also have the possibility of multibeam acceleration. This paper presents two-dimensional hydrodynamic simulations of different target geometries including solid as well as hollow cylinders that are irradiated with beams having different shapes of the focal spot which will be available at the SIS100 facility. These include a circular focal spot, an annular focal spot, and an elliptic focal spot, respectively. The purpose of this study is to determine the region of the physical parameters including density, temperature, and pressure that can be accessed using the SIS100 beam. This information, we hope, will be useful for designing experiments on the studies of thermophysical properties of matter including the designing of appropriate diagnostic tools.

A hollow intense heavy ion beam with an annular focal spot has many important applications. The Gesellschaft für Schwerionenforschung, Darmstadt is planning to develop a radio frequency wobbler that will rotate the beam at extremely high frequencies and thus create an annular (ring shaped) focal spot. In this paper, we present an analytical model that determines the minimum rotation frequency of the wobbler in order to achieve a high degree of irradiation symmetry (an asymmetry of a few percent) of the target. Estimates for a typical heavy ion imploded target are also presented.

An analytical model for the implosion of a multilayered cylindrical target driven by an intense heavy ion beam has been developed. The target is composed of a cylinder of frozen hydrogen or deuterium, which is enclosed in a thick shell of solid lead. This target has been designed for future high-energy-density matter experiments to be carried out at the Gesellschaft für Schwerionenforschung, Darmstadt. The model describes the implosion dynamics including the motion of the incident shock and the first reflected shock and allows for calculation of the physical conditions of the hydrogen at stagnation. The model predicts that the conditions of the compressed hydrogen are not sensitive to significant variations in target and beam parameters. These predictions are confirmed by one-dimensional numerical simulations and thus allow for a robust target design.

This paper presents two-dimensional numerical simulations of hydrodynamic response of a solid lead cylindrical target that is irradiated by an intense uranium beam having a particle energy of 1 GeV/u and that consists of 10¹² particles. Different time profiles have been considered for the beam power that include a case where the beam consists of five identical parabolic bunches with equal separation between neighboring bunches as well as a beam that consists of a single bunch. For the single bunch case we consider two different values for pulse length, namely, 1000 and 50 ns, respectively. Moreover we allow for two different values for the beam radius that is 0.5 and 1.0 mm, respectively. These calculations show that in order to achieve a high degree of beam-target coupling, it is absolutely essential to use a single bunched beam that has a reasonably short pulse length, which is 50 ns in this case. Such a large beam-target coupling efficiency is highly desirable for creating high-density strongly coupled plasmas as well as for studies that involve fragmentation of the projectile ions as the beam passes through solid matter. If the pulse length is assumed to be too long, substantial hydrodynamic expansion of the target material occurs during the early stages of irradiation that leads to significant reduction in the energy deposition by the ions that are delivered in the later part of the pulse. In case of the five-bunch configuration, heating caused by the first bunch is so strong that the target is completely distorted. As a result, the ions that are delivered in the later four bunches pass through the target without any interaction.

Employing a two-dimensional simulation model, this paper presents a suitable design for an experiment to study metallization of hydrogen in a heavy-ion beam imploded multilayered cylindrical target that contains a layer of frozen hydrogen. Such an experiment will be carried out at the upgraded heavy-ion synchrotron facility (SIS-18) at the Gesellschaft für Schwerionenforschung, Darmstadt by the end of the year 2001. In these calculations we consider a uranium beam that will be available at the upgraded SIS-18. Our calculations show that it may be possible to achieve theoretically predicted physical conditions necessary to create metallic hydrogen in such experiments. These include a density of about 1 g/cm³, a pressure of 3–5 Mbar, and a temperature of a few 0.1 eV.

A specifically tailored plasma lens could shape a high-energy, heavy-ion beam into the form of a hollow cylinder without loss of beam intensity. It has been experimentally confirmed that both a positive as well as a negative radial gradient of the current density in the active plasma lens can be the underlying principle. Calculations were performed that yield the ideal current density distribution for both cases. A numerical simulation of an experiment with an intense ion beam highlights that the shaping of the beam increases the achievable compression in a lead sample.

This paper presents two-dimensional numerical simulations of the hydrodynamic response of solid as well as hollow cylindrical targets made of lead that are irradiated by an intense beam of uranium ions which has an annular focal spot. Using a particle tracking computer code, it has been shown that a plasma lens can generate such a beam with parameters used in the calculations presented in this paper. The total number of particles in the beam is 2×10¹¹ and the particle energy is about 200 MeV/u that means a total energy of approximately 1.5 kJ. This energy is delivered in a pulse that is 50 ns long. These beam parameters lead to a specific energy deposition of 50–100 kJ/g and a specific power deposition of 1–2 TW/g in solid matter. These calculations show that in case of the solid lead cylinder, it may be possible to achieve more than 4 times solid lead density along the cylinder axis at the time of maximum compression. The pressure in the compressed region is about 20 Mbar and the temperature is a few eV. In the case of a hollow cylinder, one also achieves the same degree of compression but now the temperature in the compressed region is much higher (over 10 eV). Such samples of highly compressed matter can be used to study the equation-of-state properties of high-energy-density matter. It is expected that by the end of the year 2001, after completion of the upgrade of the existing facilities, the above beam parameters will be available at the Gesellschaft für Schwerionenforschung (GSI), Darmstadt. This will open up the possibility to carry out very interesting experiments on a number of important problems including the investigation of the EOS of high-energy-density matter.

In this paper is presented, with the help of sophisticated two-dimensional hydrodynamic simulations, a suitable design with optimized parameters for a heavy-ion beam-matter interaction experiment that will be carried out at the Gesellschaft für Schwerionenforschung (GSI) Darmstadt by the end of the year 2001 when the upgrade of the existing accelerator facility will be completed. Our simulations show that this upgraded heavy-ion beam is capable of generating strong shocks in solid targets that compress the target material to supersolid densities and generate multi-mbar pressures. This will open up, at the GSI, the possibility of investigation of the equation-of-state properties of matter under such extreme conditions. Numerical simulations can predict the experimental results with reasonable accuracy, which is helpful in designing the diagnostic tools for the experiment.

It is expected that after the completion of a new high current injector, the heavy-ion synchrotron (SIS) at the Gesellschaft für Schwerionforschung (GSI) Darmstadt will accelerate U⁺²⁸ ions to energies of the order of 200 MeV/u. The use of a powerful rf buncher will reduce the pulse length to about 50 ns, and employment of a multiturn injection scheme will provide 2×10¹¹ particles in the beam that correspond to a total energy of the order of 1 kJ. This upgrade of the SIS, hopefully, will be completed by the end of the year 2001. These beam parameters lead to a specific power deposition of the order of 1–2 TW/g in solid matter that will provide temperatures of about 10 eV. Such low specific power deposition will induce hydrodynamic effects in solid materials, and one may design appropriate beam-target interaction experiments that could be used to investigate the equation of state of matter under extreme conditions. The purpose of this paper is to propose suitable target designs with optimized parameters for the future GSI experiments with the help of one and two-dimensional hydrodynamic simulations. Cylindrical geometry is the natural geometry for highly focused ion beams, and therefore cylindrical targets are the most appropriate for this type of interaction experiments. The numerical simulations presented in this paper show that one can experimentally measure the characteristic sound speed in beam heated targets which is an important physical parameter. Moreover, one can study the propagation of ion-beam-induced shock waves in the solid materials. Different values for the specific power deposition, namely, 10, 25, 50, and 100 kJ/g, have been used. In some cases the pulse length is assumed to be 40 ns while in others it is considered to be 50 ns. Various materials including lead, aluminum, and solid neon have been used.

In this paper we present an analysis of the theory of the energy deposition of ions in cold materials and hot dense plasmas together with numerical calculations for heavy and light ions of interest to ion-beam fusion. We have used the gorgon computer code of Long, Moritz, and Tahir (which is an extension of the code originally written for protons by Nardi, Peleg, and Zinamon) to carry out these calculations. The energy-deposition data calculated in this manner has been used in the design of heavy-ion-beam-driven fusion targets suitable for a reactor, by its inclusion in the medusa code of Christiansen, Ashby, and Roberts as extended by Tahir and Long. A number of other improvements have been made in this code and these are also discussed. Various aspects of the theoretical analysis of such targets are discussed including the calculation of the hydrodynamic stability, the hydrodynamic efficiency, and the gain. Various different target designs have been used, some of them new. In general these targets are driven by Bi⁺ ions of energy 8–12 GeV, with an input energy of 4–6.5 MJ, with output energies in the range 600–900 MJ, and with gains in the range 120–180. The peak powers are in the range of 500–750 TW. We present detailed calculations of the ablation, compression, ignition, and burn phases. By the application of a new stability analysis which includes ablation and density-gradient effects we show that these targets appear to implode in a stable manner. Thus the targets designed offer working examples suited for use in a future inertial-confinement fusion reactor.