Heavy-ion-beam-induced hydrodynamic effects in solid targets

Cylindrical convergence effects on the Rayleigh-Taylor instability in elastic and viscous media

Convergence effects on the perturbation growth of an imploding surface separating two nonideal material media (elastic and viscous media) are analyzed in the case of a cylindrical implosion in both the Rayleigh-Taylor stable and unstable configurations. In the stable configuration, the perturbation damping effect due to angular momentum conservation becomes destroyed for sufficiently high values of the elastic modulus or of the viscosity of the media. For the unstable configuration, Rayleigh-Taylor instability can be suppressed by the elasticity or mitigated by the viscosity, but without practically affecting the perturbation growth due to the geometrical convergence. However, the convergence effects manifest themselves in a manner somewhat different from the classical Bell-Plesset effect by making the process more sensitive to the media compressibility than in the case involving ideal media.

Elastic-plastic Rayleigh-Taylor instability at a cylindrical interface

The boundaries of stability are determined for the Rayleigh-Taylor instability at a cylindrical interface between an ideal fluid in the interior and a heavier elastic-plastic solid in the outer region. The stability maps are given in terms of the maximum dimensionless initial amplitude ξ_{th}^{*} that can be tolerated for the interface to remain stable, for any particular value of the dimensionless radius B of the surface, and for the different spatial modes m of the perturbations. In general, for the smallest dimensionless radius and larger modes m, the interface remains stable for larger values of ξ_{th}^{*}. In particular, for m>1 and B→0, it turns out ξ_{th}^{*}→1, and a cylindrical geometry equivalent to Drucker's criterion is found, which indeed ends up being independent of the interface geometry.

Simulations of beam-matter interaction experiments at the CERN HiRadMat facility and prospects of high-energy-density physics research

In a recent publication [Schmidt et al., Phys. Plasmas 21, 080701 (2014)], we reported results on beam-target interaction experiments that have been carried out at the CERN HiRadMat (High Radiation to Materials) facility using extended solid copper cylindrical targets that were irradiated with a 440-GeV proton beam delivered by the Super Proton Synchrotron (SPS). On the one hand, these experiments confirmed the existence of hydrodynamic tunneling of the protons that leads to substantial increase in the range of the protons and the corresponding hadron shower in the target, a phenomenon predicted by our previous theoretical investigations [Tahir et al., Phys. Rev. ST Accel. Beams 25, 051003 (2012)]. On the other hand, these experiments demonstrated that the beam heated part of the target is severely damaged and is converted into different phases of high energy density (HED) matter, as suggested by our previous theoretical studies [Tahir et al., Phys. Rev. E 79, 046410 (2009)]. The latter confirms that the HiRadMat facility can be used to study HED physics. In the present paper, we give details of the numerical simulations carried out to understand the experimental measurements. These include the evolution of the physical parameters, for example, density, temperature, pressure, and the internal energy in the target, during and after the irradiation. This information is important in order to determine the region of the HED phase diagram that can be accessed in such experiments. These simulations have been done using the energy deposition code fluka and a two-dimensional hydrodynamic code, big2, iteratively.

Large Hadron Collider at CERN: Beams generating high-energy-density matter

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.

Necessity of bunch compression for heavy-ion-induced hydrodynamics and studies of beam fragmentation in solid targets at a proposed synchrotron facility

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 10(12) 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.

Metallization of hydrogen using heavy-ion-beam implosion of multilayered cylindrical targets

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/cm(3), a pressure of 3-5 Mbar, and a temperature of a few 0.1 eV.

Equation-of-state properties of high-energy-density matter using intense heavy ion beams with an annular focal spot

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 2x10(11) 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 fur 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.

Shock compression of condensed matter using intense beams of energetic heavy ions

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 fur 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.