Formation of spikes and bubbles in the linear phase of Rayleigh-Taylor instability in elastic-plastic media

The generation of spikes and bubbles, a typical characteristic of the nonlinear regime in the Rayleigh-Taylor instability, is found to occur as well during the linear regime in an elastic-plastic solid medium caused, however, by a very different mechanism. This singular feature originates in the differential loads at different locations of the interface, which makes that the transition from the elastic to the plastic regime takes place at different times, thus producing an asymmetric growth of peaks and valleys that rapidly evolves in exponentially growing spikes, while bubbles can also grow exponentially at a lower rate.

Production of diamond using intense heavy ion beams at the FAIR facility and application to planetary physics

Diamonds are supposedly abundantly present in different objects in the Universe including meteorites, carbon-rich stars as well as carbon-rich extrasolar planets. Moreover, the prediction that in deep layers of Uranus and Neptune, methane may undergo a process of phase separation into diamond and hydrogen, has been experimentally verified. In particular, high power lasers have been used to study this problem. It is therefore important from the point of view of astrophysics and planetary physics, to further study the production processes of diamond in the laboratory. In the present paper, we present numerical simulations of implosion of a solid carbon sample using an intense uranium beam that is to be delivered by the heavy ion synchrotron, SIS100, that is under construction at the Facility for Antiprotons and Ion Research (FAIR), at Darmstadt. These calculations show that using our proposed experimental scheme, one can generate the extreme pressure and temperature conditions, necessary to produce diamonds of mm3 dimensions.

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.

Linear analysis of Rayleigh-Taylor instability in viscoelastic materials

Rayleigh-Taylor instability (RTI) has become a powerful tool for determining the mechanical properties of materials under extreme conditions. In this paper, we first present the exact and approximate linear dispersion relations for RTI in viscoelastic materials based on the Maxwell and Kelvin-Voigt models. The approximate dispersion relation produces good predictions of growth rates in comparison with the exact one. The motion of the interface in Maxwell flow is mainly controlled by viscosity and elasticity dominates this behavior in Kelvin-Voigt flow. Since elasticity plays a distinct role from viscosity, cutoff wavelengths arise only in Kelvin-Voigt flow. The variation of the maximum growth rates and their corresponding wave numbers are also carefully studied. For both types of materials, viscosity suppresses the growth of instability, while elasticity speeds it up. This is at odds with the well-known understanding that elasticity suppresses hydrodynamic instabilities. The dependence of the maximum growth rate on slab thickness is also investigated for RTI in both types of flow, since the metal slab as a pusher has been extensively employed in high-energy-density physics. The model presented here allows study of more realistic situations by considering convergent effects and shock wave interactions, for the traditional potential flow theory is not suitable. To summary, it is able to provide guidances for future experimental designs for studies of materials under high strain and high strain rate conditions, as well as allow us to study RTI theoretically in more complicated conditions.

Rayleigh-Taylor instability in elastic-plastic solid slabs bounded by a rigid wall

The linear evolution of the incompressible Rayleigh-Taylor instability for the interface between an elastic-plastic slab medium and a lighter semi-infinite ideal fluid beneath the slab is developed for the case in which slab is attached to a rigid wall at the top surface. The theory yields the maps for the stability in the space determined by the initial perturbation amplitude and wavelength, as well as for the transition boundary from the elastic to the plastic regimes for arbitrary thicknesses of the slab and density contrasts between the media. In particular, an approximate but very accurate scaling law is found for the minimum initial perturbation amplitude required for instability and for the corresponding perturbation wavelength at which it occurs. These results allows for an interpretation of the recent experiments by Maimouni et al. [Phys. Rev. Lett. 116, 154502 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.154502].

Studies of equation of state properties of high-energy-density matter generated by intense ion beams at the facility for antiprotons and ion research

The work presented in this paper shows with the help of two-dimensional hydrodynamic simulations that intense heavy-ion beams are a very efficient tool to induce high energy density (HED) states in solid matter. These simulations have been carried out using a computer code BIG2 that is based on a Godunov-type numerical algorithm. This code includes ion beam energy deposition using the cold stopping model, which is a valid approximation for the temperature range accessed in these simulations. Different phases of matter achieved due to the beam heating are treated using a semiempirical equation-of-state (EOS) model. To take care of the solid material properties, the Prandl-Reuss model is used. The high specific power deposited by the projectile particles in the target leads to phase transitions on a timescale of the order of tens of nanosecond, which means that the sample material achieves thermodynamic equilibrium during the heating process. In these calculations we use Pb as the sample material that is irradiated by an intense uranium beam. The beam parameters including particle energy, focal spot size, bunch length, and bunch intensity are considered to be the same as the design parameters of the ion beam to be generated by the SIS100 heavy-ion synchrotron at the Facility for Antiprotons and Ion Research (FAIR), at Darmstadt. The purpose of this work is to propose experiments to measure the EOS properties of HED matter including studies of the processes of phase transitions at the FAIR facility. Our simulations have shown that depending on the specific energy deposition, solid lead will undergo phase transitions leading to an expanded hot liquid state, two-phase liquid-gas state, or the critical parameter regime. In a similar manner, other materials can be studied in such experiments, which will be a very useful addition to the knowledge in this important field of research.

Stability boundaries for the Rayleigh-Taylor instability in accelerated elastic-plastic solid slabs

The linear theory of the incompressible Rayleigh-Taylor instability in elastic-plastic solid slabs is developed on the basis of the simplest constitutive model consisting in a linear elastic (Hookean) initial stage followed by a rigid-plastic phase. The slab is under the action of a constant acceleration, and it overlays a very thick ideal fluid. The boundaries of stability and plastic flow are obtained by assuming that the instability is dominated by the average growth of the perturbation amplitude and neglecting the effects of the higher oscillation frequencies during the stable elastic phase. The theory yields complete analytical expressions for such boundaries for arbitrary Atwood numbers and thickness of the solid slabs.

Linear Rayleigh-Taylor instability in an accelerated Newtonian fluid with finite width

The linear theory of Rayleigh-Taylor instability is developed for the case of a viscous fluid layer accelerated by a semi-infinite viscous fluid, considering that the top interface is a free surface. Effects of the surface tensions at both interfaces are taken into account. When viscous effects dominate on surface tensions, an interplay of two mechanisms determines opposite behaviors of the instability growth rate with the thickness of the heavy layer for an Atwood number A_{T}=1 and for sufficiently small values of A_{T}. In the former case, viscosity is a less effective stabilizing mechanism for the thinnest layers. However, the finite thickness of the heavy layer enhances its viscous effects that, in general, prevail on the viscous effects of the semi-infinite medium.

Rayleigh-Taylor instability in accelerated elastic-solid slabs

We develop the linear theory for the asymptotic growth of the incompressible Rayleigh-Taylor instability of an accelerated solid slab of density ρ_{2}, shear modulus G, and thickness h, placed over a semi-infinite ideal fluid of density ρ_{1}<ρ_{2}. It extends previous results for Atwood number A_{T}=1 [B. J. Plohr and D. H. Sharp, Z. Angew. Math. Phys. 49, 786 (1998)ZAMPA80044-227510.1007/s000330050121] to arbitrary values of A_{T} and unveil the singular feature of an instability threshold below which the slab is stable for any perturbation wavelength. As a consequence, an accelerated elastic-solid slab is stable if ρ_{2}gh/G≤2(1-A_{T})/A_{T}.