Runaway Instability Research Articles

Nonconservative forcing and diffusion in refractive optical traps

Refractive optical trapping forces can be nonconservative in the vicinity of a stable equilibrium point even in the absence of radiation pressure. We discuss how nonconservative 3D force fields, in the vicinity of an equilibrium point, reduce to circular forcing in a plane; a simple model of such forcing is the refractive trapping of a sphere by a four rays. We discuss in general the diffusion of an anisotropically trapped, circularly forced particle and obtain its spectrum of motion. Equipartition of potential energy holds even though the nonconservative flow does not follow equipotentials of the trap. We find that the dissipated nonconservative power is proportional to temperature, providing a mechanism for a runaway heating instability in traps.

Failure, instability, and the second work increment in loose silty sand

Triaxial tests have been performed to demonstrate the conditions for stability and instability in loose silty sand. Drucker (1951) and Hill (1958) stability conditions in terms of the sign of the second work increment were employed in the design of the stress paths used in the triaxial compression and extension tests performed with quasi-constant shear stress while the mean normal stress was reduced until failure occurred. It is shown that the sand is completely stable under drained conditions for any stress path and irrespective of the sign of the second work increment. This is demonstrated by completely stopping the change in stresses and observing the stable behavior in the range of stresses where the sand contracts and where it dilates. Once the effective stress failure surface is passed, the sand becomes unstable, and the sign of the second work increment is always negative. Run-away instability can occur inside the failure surface for loose silty sand under undrained conditions for which the sand tends to contract, pore pressures continue to develop, and the second work increment is negative. Liquefaction may follow if the loose silty sand is sufficiently loose.

Stability of general-relativistic accretion disks

Self-gravitating relativistic disks around black holes can form as transient structures in a number of astrophysical scenarios such as binary neutron star and black hole-neutron star coalescences, as well as the core collapse of massive stars. We explore the stability of such disks against runaway and nonaxisymmetric instabilities using three-dimensional hydrodynamics simulations in full general relativity using the Thor code. We model the disk matter using the ideal fluid approximation with a $\ensuremath{\Gamma}$-law equation of state with $\ensuremath{\Gamma}=4/3$. We explore three disk models around nonrotating black holes with disk-to-black hole mass ratios of 0.24, 0.17, and 0.11. Because of metric blending in our initial data, all of our initial models contain an initial axisymmetric perturbation which induces radial disk oscillations. Despite these oscillations, our models do not develop the runaway instability during the first several orbital periods. Instead, all of the models develop unstable nonaxisymmetric modes on a dynamical time scale. We observe two distinct types of instabilities: the Papaloizou-Pringle and the so-called intermediate type instabilities. The development of the nonaxisymmetric mode with azimuthal number $m=1$ is accompanied by an outspiraling motion of the black hole, which significantly amplifies the growth rate of the $m=1$ mode in some cases. Overall, our simulations show that the properties of the unstable nonaxisymmetric modes in our disk models are qualitatively similar to those in the Newtonian theory.

Influence of Self-Gravity on the Runaway Instability of Black-Hole–Torus Systems

Results from the first fully general relativistic numerical simulations in axisymmetry of a system formed by a black hole surrounded by a self-gravitating torus in equilibrium are presented, aiming to assess the influence of the torus self-gravity on the onset of the runaway instability. We consider several models with varying torus-to-black-hole mass ratio and angular momentum distribution orbiting in equilibrium around a nonrotating black hole. The tori are perturbed to induce the mass transfer towards the black hole. Our numerical simulations show that all models exhibit a persistent phase of axisymmetric oscillations around their equilibria for several dynamical time scales without the appearance of the runaway instability, indicating that the self-gravity of the torus does not play a critical role favoring the onset of the instability, at least during the first few dynamical time scales.

On the runaway instability of self-gravitating torus around black holes

Black holes surrounded by self-gravitating tori are astrophysical systems which may naturally form following the core collapse of a massive star or the merger of two neutron stars. We present here results from fully general relativistic numerical simulations of such systems in order to assess the influence of the torus self-gravity on the onset of the so-called runaway instability. This instability, which might drive the rapid accretion of the disk on shorter timescales than those required to power a relativistic fireball, potentially challenges current models of gamma-ray bursts. Our simulations indicate that the self-gravity of the torus does not actually favour the onset of the instability.

Cold versus hot shear banding in bulk metallic glass

We present an analysis of the shear-banding dynamics in a bulk metallic glass (BMG), including the temperature rise in the band, the sliding speed of the band, and the time elapsed as well as the step size of the shear offset growth in a stop-and-go cycle. This model analysis quantitatively demonstrates that the major shear band can remain cold and slide in a stick-slip manner. We predict that the shear step (distance covered by a stop-and-go cycle) scales with the sample size and machine stiffness. We also illustrate the conditions when such serrated shear is unsustainable and a hot shear band directly develops in a runaway instability (catastrophe). These findings provide physical insight into the shear-instability processes and offer useful information for improving the plasticity of BMGs. The calculation results are used to explain several intriguing recent experimental observations, including the stick slip of the dominant shear-band and the sample-size effects on the plastic-flow behavior of BMGs.

Spontaneous dissipation of elastic energy by self-localizing thermal runaway

Thermal runaway instability induced by material softening due to shear heating represents a potential mechanism for mechanical failure of viscoelastic solids. In this work we present a model based on a continuum formulation of a viscoelastic material with Arrhenius dependence of viscosity on temperature and investigate the behavior of the thermal runaway phenomenon by analytical and numerical methods. Approximate analytical descriptions of the problem reveal that onset of thermal runaway instability is controlled by only two dimensionless combinations of physical parameters. Numerical simulations of the model independently verify these analytical results and allow a quantitative examination of the complete time evolutions of the shear stress and the spatial distributions of temperature and displacement during runaway instability. Thus we find that thermal runaway processes may well develop under nonadiabatic conditions. Moreover, nonadiabaticity of the unstable runaway mode leads to continuous and extreme localization of the strain and temperature profiles in space, demonstrating that the thermal runaway process can cause shear banding. Examples of time evolutions of the spatial distribution of the shear displacement between the interior of the shear band and the essentially nondeforming material outside are presented. Finally, a simple relation between evolution of shear stress, displacement, shear-band width, and temperature rise during runaway instability is given.

Characteristics of the runaway electron beam instability in the HT-7 tokamak

AbstractRunaway electron ream instabilities have been observed in Ohmic plasmas in the HT-7 tokamak. The instability regime is characterized by relaxations in the electron cyclotron emission due to the relativistic anomalous Doppler resonance effect which transfers energy from parallel to perpendicular motion. Two types of instabilities in the slide-away regime have been observed in the HT-7 tokamak. The scaling of the threshold value for the instabilities to occur has been derived. It is found that the threshold value is linearly dependent on the plasma current and independent of the toroidal magnetic field strength.

Effect of gas puffing on current ramp-down ohmic discharges in HT-7 tokamak

A new behaviour of current ramp-down ohmic deuterium discharges has been observed by additional deuterium fueling/gas puffing in HT-7 tokamak. It has been investigated, that the additional gas puffing converts the fast pitch angle scattering (FPAS) event to normal pitch angle scattering (NPAS) event characterized by higher electron energies and shifting the trigger time of the event, which is dependent on the pulse injection time. The attempt has also been made to investigate the scaling of critical values for runaway electrons generation and determination of their related energies along with trigger parameters of the instability and conversion relation between NPAS and FPAS events by ramping-down plasma current and changing the toroidal magnetic field in low-density ohmic discharges. The direct and inverse relationship has been observed for critical trigger value ω p e / ω c e of runaways generation with the plasma current and the toroidal magnetic field strength respectively. The runaway instability regime is characterized by relaxations in the electron cyclotron emission due to relativistic anomalous Doppler resonance (ADR) effect, which transfers energy from parallel to perpendicular motion.

Room-temperature atmospheric argon plasma jet sustained with submicrosecond high-voltage pulses

In this letter, an experimental study is presented to characterize a room-temperature plasma jet in atmospheric argon generated with submicrosecond voltage pulses at 4kHz. Distinct from sinusoidally produced argon discharges that are prone to thermal runaway instabilities, the pulsed atmospheric argon plasma jet is stable and cold with an electron density 3.9 times greater than that in a comparable sinusoidal jet. Its optical emission is also much stronger. Electrical measurement suggests that the discharge event is preceded with a prebreakdown phase and its plasma stability is facilitated by the short voltage pulses.

Rotating black hole surrounded by self-gravitating torus in the puncture framework

We present a formulation for computing equilibria composed of a rotating black hole and a massive self-gravitating torus in general relativity. Such a system is a plausible outcome formed after stellar core collapse of massive and supermassive stars as well as after a merger of a black hole-neutron star binary. In our formulation, the black hole is modeled in the puncture framework. The numerical solutions for equilibria are computed for rapidly rotating black holes and for a wide range of mass ratio of the black hole and torus. The equilibria obtained in this paper can be used for studying nonaxisymmetric instabilities, runaway instability, and magnetorotational instability of a self-gravitating accretion torus around a rotating black hole in numerical relativity. We also remark that the relation among the area, mass, and spin of rotating black holes are slightly modified by the torus.

Thermoporomechanics of creeping landslides: The 1963 Vaiont slide, northern Italy

The catastrophic Vaiont landslide (Southern Alps, Italy) of 9 October 1963 moved 2.7 × 108 m3 of rock that collapsed in an artificial lake, causing a giant wave that killed 1917 people. The landslide was preceded by 2–3 years of creep that ended with the final collapse of the rock mass slipping at about 30 m s−1. Assuming that creep was localized in a clay‐rich water‐saturated layer, in this study we propose shear heating as the primary mechanism for the long‐term phase of accelerating creep. We study only the creeping phase of the slide, and we model this phase using a rigid block moving over a thin zone of high shear strain rates. Introducing a thermal softening and velocity strengthening law for the basal material, we reformulate the governing equations of a water‐saturated porous material, obtaining an estimate for the collapse time of the slide. Our model is calibrated upon real velocity measurements from the Vaiont landslide and provides an estimation of the critical time of failure up to 169 days before the collapse. We also show that the slide became critical ∼21 days before the collapse, when shear heating started localizing in the clay‐rich layer, inducing a tendency for slip localization and thermal runaway instability in a plane. The total loss of strength in the slipping zone during the last minutes prior to the slide is explained by the onset of thermal pressurization, triggered by the temperature rise within the clay‐rich layer.

Magnetically Limited X-Ray Filaments in Young Supernova Remnants

We discuss the damping of strong magnetic turbulence downstream of the forward shock of young supernova remnants (SNRs). We find that strong magnetic fields that have been produced by the streaming instability in the upstream region of the shock or by other kinetic instabilities at the shock may be efficiently damped, so the region of enhanced magnetic field strength would typically have a thickness of the order ld = 1016-1017?cm. The nonthermal X-ray filaments observed in young SNRs are thus possibly limited by the magnetic field and not by the energy losses of the radiating electrons. Therefore, the thickness of the filaments would not be a measure of the magnetic field strength, and claims of efficient cosmic-ray acceleration on account of a runaway streaming instability would appear premature.

Runaway “Fingerlike” Instability of Magnetic Walls in Ultrathin Layers

We show that smooth domain walls in ultrathin ferromagnetic films can develop jaggedness even in the absence of random defects when confronted with a sufficiently large tilt between the uniaxial anisotropy direction and the external field. From the Kerr imaging of 0.7 nm thin Co films and from numerical simulations we report a previously unseen runaway fingerlike instability in a magnetic wall that begins on nanoscales but grows to macroscopic lengths for sufficiently large tilt angles. A threshold for the instability is controlled by the ferromagnet's parameters and the applied field.

The runaway instability of thick discs around black holes - II. Non-constant angular momentum discs

We present results from a comprehensive number of relativistic, time-dependent, axisymmetric simulations of the runaway instability of non-constant angular momentum thick discs around black holes. This second paper in the series extends earlier results where only constant angular momentum discs were considered. All relevant aspects of the theory of stationary thick discs around rotating black holes, necessary to build the equilibrium initial data used in our simulations, are presented in great detail. The angular momentum of the evolved discs is assumed to increase outwards with the radial distance according to a power law, l=Krα, where K > 0 corresponds to prograde discs (with respect to the black hole rotation) and K < 0 to retrograde discs. The main simplifying assumptions of our approach are not to include magnetic fields or self-gravity in the discs (test-fluid approximation). Furthermore, the dynamics of the space–time is accounted for by computing the transfer of mass and angular momentum from the disc to the black hole through the event horizon. In this approximation the evolution of the central black hole, which initially is non-rotating, is assumed to follow a sequence of Kerr black holes of increasing mass and spin. All discs we build slightly overflow the potential barrier at the cusp, departing from equilibrium, so that accretion is possible. In agreement with previous results based on stationary models we find that by allowing the mass and the spin of the black hole to grow, constant angular momentum discs rapidly become unstable on a dynamical time-scale (a few orbital periods). The comparison with the results of our first paper shows that the effect of the angular momentum transfer from the tori to the black hole is to make constant angular momentum discs less unstable, increasing the time-scale for the runaway instability to grow. However, we find that non-constant angular momentum discs are dramatically stabilized for very small values of the angular momentum slope α, much smaller than the Keplerian value α= 1/2. Our fully relativistic and time-dependent simulations thus confirm the predictions of stationary studies concerning the stabilizing effect of non-constant angular momentum distributions. For the various disc-to-hole mass ratios considered, we systematically find that the critical values of α below which the runaway instability can exist are slightly smaller than those reported previously in the literature based on stationary studies.

Fluidisation in artesian flow conditions: Hydromechanically unstable granular media

The present analysis focuses on fluidisation and erosion processes involving hydromechanically unstable granular materials in artesian flow conditions, as these phenomena were documented in column tests with gap-graded soils by Skempton &amp; Brogan. It is shown that the observed abnormal decrease in hydraulic resistivity can be attributed to fluidisation of the fines fraction of the soil, which eventually leads to unplugging of the pore space and segregation piping erosion in the form of a runaway instability. For the description of the erosion process a continuum theory for three-phase media consisting of stationary grains, transported grains and pore fluid is presented. The governing mass balance and momentum balance equations, and the constitutive law for particle erosion are formulated and discussed in the light of the experimental evidence.

Fluidisation in artesian flow conditions: Hydromechanically unstable granular media

The present analysis focuses on fluidisation and erosion processes involving hydromechanically unstable granular materials in artesian flow conditions, as these phenomena were documented in column tests with gap-graded soils by Skempton & Brogan. It is shown that the observed abnormal decrease in hydraulic resistivity can be attributed to fluidisation of the fines fraction of the soil, which eventually leads to unplugging of the pore space and segregation piping erosion in the form of a runaway instability. For the description of the erosion process a continuum theory for three-phase media consisting of stationary grains, transported grains and pore fluid is presented. The governing mass balance and momentum balance equations, and the constitutive law for particle erosion are formulated and discussed in the light of the experimental evidence.

Dynamics of thick discs around Schwarzschild-de Sitter black holes

We consider the effects of a cosmological constant on the dynamics of constant angular momentum discs orbiting Schwarzschild-de Sitter black holes. The motivation behind this study is to investigate whether the presence of a radial force contrasting the black hole's gravitational attraction can influence the occurrence of the runaway instability, a robust feature of the dynamics of constant angular momentum tori in Schwarzschild and Kerr spacetimes. In addition to the inner cusp near the black hole horizon through which matter can accrete onto the black hole, in fact, a positive cosmological constant introduces also an outer cusp through which matter can leave the torus without accreting onto the black hole. To assess the impact of this outflow on the development of the instability we have performed time-dependent and axisymmetric hydrodynamical simulations of equilibrium initial configurations in a sequence of background spacetimes of Schwarzschild-de Sitter black holes with increasing masses. The simulations have been performed with an unrealistic value for the cosmological constant which, however, yields sufficiently small discs to be resolved accurately on numerical grids and thus provides a first qualitative picture of the dynamics. The calculations, carried out for a wide range of initial conditions, show that the mass-loss from the outer cusp can have a considerable impact on the instability, with the latter being rapidly suppressed if the outflow is large enough.

Oscillations of vertically integrated relativistic tori - I. Axisymmetric modes in a Schwarzschild space-time

This is the first of a series of papers investigating the oscillation properties of relativistic, non-self-gravitating tori orbiting around a black hole. In this initial paper we consider the axisymmetric oscillation modes of a torus constructed in a Schwarzschild space-time. To simplify the treatment and make it as analytical as possible, we build our tori with vertically integrated and vertically averaged quantities, thus transforming the eigenvalue problem into a set of coupled ordinary differential equations. The tori are also modelled with a number of different non-Keplerian distributions of specific angular momentum, and we discuss how the oscillation properties change when different distributions of angular momentum are considered. Our investigation progresses by steps. We first consider a local analysis in Newtonian gravity and determine the properties of acoustic wave propagation within these objects, as well as the relations between acoustic and epicyclic oscillations. Next, we extend the local analysis to a general relativistic framework. Finally, we perform a global analysis and determine both the eigenfunctions and the eigenfrequencies of the axisymmetric oscillations corresponding to the p modes of relativistic tori. These behave as sound waves globally trapped in the torus and possess eigenfrequencies appearing in the simple sequence 2:3:4:..., independently of the distribution of angular momentum considered. The properties of the modes investigated here are in good agreement with those observed in recent numerical simulations, and could have a number of different applications. In X-ray binary systems containing a black hole candidate, for instance, p-mode oscillations could be used to explain the harmonic relations in the high-frequency quasi-periodic oscillations observed. In systems comprising a massive torus orbiting a black hole, on the other hand, p-mode oscillations could be used to explain the development or the suppression of the runaway instability.

Runaway effects at the plasma boundary in ISTTOK

Experimental results on minor and major disruption events in discharges with runaway electrons in the small tokamak ISTTOK and corresponding numerical analysis are presented. Using the experimental data from the soft X-ray diagnostic the image of the plasma column in the presence of runaway electron instability and disruptions was reconstructed. The most probable zones of the interaction of energetic electrons with the plasma surrounding surfaces were detected as spots of the soft X-ray emission on the top and bottom parts of the plasma column during the development of the disruptions. Numerical analysis of the runaway instability allowed determining the runaway electrons characteristics, such as energy ( W eRA⩽30 keV) and density ( n RA∼(0.001–0.01) n e). On the basis of this analysis the level of electrostatic turbulence due to the instability was estimated.