Runaway Instability Research Articles

Thermal and electric field driven rf breakdown precursor formation on metal surfaces

The phenomenon of electric breakdown poses serious challenges to the design of devices that operate in high electric field environments. Experimental evidence points toward breakdown events that are accompanied by elevated temperatures and dark current spikes, which is attributed to high-asperity nanostructure formation that enhances the local electric field and triggers a runaway process. However, the exact mechanistic origin of such nanostructures under typical macroscopic operational conditions of electric field and magnetic-field-mediated heating remains poorly understood. In this work, we simulate the evolution of a copper surface under the combined action of the electric fields and elevated temperatures. Using a mesoscale curvature-driven surface evolution model, we show how a copper surface can undergo a type of dynamical instability that naturally leads to the formation of sharp asperities in realistic experimental conditions. Exploring the combined effect of fields and temperature rise, we identify the critical regimes that allow for the formation of breakdown precursors. The results show that thermoelastic stresses, while not essential, can significantly lower the critical electric field required for runaway surface instability, which is consistent with experimental observations that thermal effects can increase breakdown rates. Published by the American Physical Society 2024

Formation of field-induced breakdown precursors on metallic electrode surfaces

Understanding the underlying factors responsible for higher-than-anticipated local field enhancements required to trigger vacuum breakdown on pristine metal surfaces is crucial for the development of devices capable of withstanding intense operational fields. In this study, we investigate the behavior of nominally flat copper electrode surfaces exposed to electric fields of hundreds of MV/m. Our novel approach considers curvature-driven diffusion processes to elucidate the formation of sharp breakdown precursors. To do so, we develop a mesoscale finite element model that accounts for driving forces arising from both electrostatic and surface-tension-induced contributions to the free energy. Our findings reveal a dual influence: surface tension tends to mitigate local curvature, while the electric field drives mass transport toward regions of high local field density. This phenomenon can trigger the growth of sharper protrusions, ultimately leading to a rapid enhancement of local fields and, consequently, to a runaway growth instability. We delineate supercritical and subcritical regimes across a range of initial surface roughness. Our numerical results are in qualitative agreement with experimentally reported data, indicating the potential practical relevance of field-driven diffusion in the formation of breakdown precursors.

Two-fluid reconnection jets in a gravitationally stratified atmosphere

Context. Density decreases exponentially with height in the gravitationally stratified solar atmosphere, and therefore collisional coupling between the ionized plasma and the neutrals also decreases. Reconnection is a process observed at all heights in the solar atmosphere. Aims. Here, we investigate the role of collisions between ions and neutrals in the reconnection process occurring at various heights in the atmosphere. Methods. We performed simulations of magnetic reconnection induced by a localized resistivity in a gravitationally stratified atmosphere, in which we varied the height of the initial reconnection X-point. We compared a magnetohydrodynamic (MHD) model and two two-fluid configurations: one in which the collisional coupling was calculated from local plasma parameters, and another in which the coupling was decreased so that collisional effects would be enhanced. The latter setup has a more representative solar collisionality regime. Results. Simulations in a stratified atmosphere show similar structures in MHD and two-fluid simulations, with strong coupling. However, when collisional effects are increased to attain representative parameter regimes, we find a nonlinear runaway instability, which separates the plasma-neutral densities across the current sheet (CS). With increased collisional effects, the initial decoupling in velocity heats the neutrals and this sets up a nonlinear feedback loop, according to which neutrals migrate outside the CS, replacing charged particles that accumulate toward the center of the CS. Conclusions. The reconnection rate has a maximum value of around 0.1 for both reconnection heights, and is consistent with the locally enhanced resistivity used in all three models. The early-stage plasmoid formation observed near the end of our simulations is influenced by the outflow from the primary reconnection point, rather than by collisions. We synthesized optically thin emission for both MHD and two-fluid models, which can show a very different evolution when the charged-particle density is used instead of the total density. Our simulations have relevance for observed plasmoid features associated with chromospheric to low-coronal flare events.

Reducing the O(3) model as an effective field theory

We consider the O(3) or ℂP1 nonlinear sigma model as an effective field theory in a derivative expansion, with the most general Lagrangian that obeys O(3), parity and Lorentz symmetry. We work out the complete list of possible operators (terms) in the Lagrangian and eliminate as many as possible using integrations by parts. We further show at the four-derivative level, that the theory can be shown to avoid the Ostrogradsky instability, because the dependence on the d’Alembertian operator or so-called box, can be eliminated by a field redefinition. Going to the six-derivative order in the derivative expansion, we show that this can no longer be done, unless we are willing to sacrifice Lorentz invariance. By doing so, we can eliminate all dependence on double time derivatives and hence the Ostrogradsky instability or ghost, however, we unveil a remaining dynamical instability that takes the form either as a spiral instability or a runaway instability and estimate the critical field norm, at which the instability sets off.

Regularization of the complex Langevin method

The complex Langevin method, a numerical method used to compute the ensemble average with a complex partition function, often suffers from runaway instability. We study the regularization of the complex Langevin method via augmenting the action with a stabilization term. Since the regularization introduces biases to the numerical result, two approaches, named 2R and 3R methods, are introduced to recover the unbiased result. The 2R method supplements the regularization with regression to estimate the unregularized ensemble average, and the 3R method reduces the computational cost by coupling the regularization with a reweighting strategy before regression. Both methods can be generalized to the SU(n) theory and are assessed from several perspectives. Several numerical experiments in the lattice field theory are carried out to show the effectiveness of our approaches.

Ghosts without Runaway Instabilities.

We present a simple class of mechanical models where a canonical degree of freedom interacts with another one with a negative kinetic term, i.e., with a ghost. We prove analytically that the classical motion of the system is completely stable for all initial conditions, notwithstanding that the conserved Hamiltonian is unbounded from below and above. This is fully supported by numerical computations. Systems with negative kinetic terms often appear in modern cosmology, quantum gravity, and high energy physics and are usually deemed as unstable. Our result demonstrates that for mechanical systems this common lore can be too naive and that living with ghosts can be stable.

The onset of gravothermal core collapse in velocity-dependent self-interacting dark matter subhaloes

ABSTRACT It has been proposed that gravothermal collapse due to dark matter self-interactions (i.e. self-interacting dark matter, SIDM) can explain the observed diversity of the Milky Way (MW) satellites’ central dynamical masses. We investigate the process behind this hypothesis using an N-body simulation of a MW-analogue halo with velocity-dependent SIDM (vdSIDM) in which the low-velocity self-scattering cross-section, $\sigma _{\rm T}/m_{\rm x}$, reaches 100 cm2 g−1; we dub this model the vd100 model. We compare the results of this simulation to simulations of the same halo that employ different dark models, including cold dark matter (CDM) and other, less extreme SIDM models. The masses of the vd100 haloes are very similar to their CDM counterparts, but the values of their maximum circular velocities, Vmax, are significantly higher. We determine that these high Vmax subhaloes were objects in the mass range [5 × 106, 1 × 108] M⊙ at z = 1 that undergo gravothermal core collapse. These collapsed haloes have density profiles that are described by single power laws down to the resolution limit of the simulation, and the inner slope of this density profile is approximately −3. Resolving the ever decreasing collapsed region is challenging, and tailored simulations will be required to model the runaway instability accurately at scales <1 kpc.

Effect of random pinning on nonlinear dynamics and dissipation of a vortex driven by a strong microwave current

We report numerical simulations of a trapped elastic vortex driven by a strong ac magnetic field $H(t)=H\sin\omega t$ parallel to the surface of a superconducting film. The surface resistance and the power dissipated by an oscillating vortex perpendicular to the film surface were calculated as functions of $H$ and $\omega$ for different spatial distributions, densities, and strengths of pinning centers, including bulk pinning, surface pinning, and cluster pinning. Our simulations were performed for both the Bardeen-Stephen viscous vortex drag and the Larkin-Ovchinnikov (LO) drag coefficient $\eta(v)$ decreasing with the vortex velocity $v$. The local residual surface resistance $R_i(H)$ calculated for different statistical realizations of the pinning potential exhibits strong mesoscopic fluctuations caused by local depinning jumps of a vortex segment as $H$ increases, but the global surface resistance $\bar{R}_i(H)$ obtained by averaging $R_i(H)$ over different pin configurations increases smoothly with the field amplitude at small $H$ and levels off at higher fields. For strong pinning, the LO decrease of $\eta(v)$ with $v$ can result in a nonmonotonic field dependence of $R_i(H)$ which decreases with $H$ at higher fields, but cause a runaway instability of the vortex in a thick film for weak pinning. It is shown that overheating of a single moving vortex can produce the LO-like velocity dependence of $\eta(v)$, but can mask the decrease of the surface resistance with $H$ at a higher density of trapped vortices.

Numerical simulation of unstable suction transients in unsaturated soils: the role of wetting collapse

AbstractFluid injection is one of the major triggering factors of instability in unsaturated soils. Robust simulation tools are therefore required to examine hydrologic transients in such a class of inelastic materials. In this paper, the governing equations imposing the balance of mass and momentum in deformable unsaturated porous media are inspected from an analytical perspective. Our main goal is to examine the role of volume collapse on the stability of suction transients. Distinct scenarios are considered in terms of material behavior, distinguishing the case of elastoplastic and viscoplastic materials. It shows that in elastoplastic materials the mathematical ill‐posedness of the partial differential equations leads to a diffusive instability of the pore pressure field, signaled by the loss of stress controllability under water injection. By contrast, the introduction of viscosity restores the mathematical well‐posedness and ensures the positive diffusivity. Numerical implications of these findings have been explored through simulations of water injection with a 1D finite element solver. It shows that an increase of the soil hydraulic sensitivity (i.e., a marked deterioration of the yield stress upon suction removal) can deteriorate the diffusive stability and prevent the computation of suction changes across a collapsible soil layer. While the incorporation of minor amounts of viscosity can restore numerical stability by suppressing the constitutive singularity. Such numerical results have been corroborated by the computation of local stability indicators based on controllability theory, which proved to be robust diagnostic tools to identify the culprit of runaway instability emerging from coupled hydro‐mechanical processes.

Stationary models of magnetized viscous tori around a Schwarzschild black hole

We present stationary solutions of magnetized, viscous thick accretion disks around a Schwarzschild black hole. We assume that the tori are not self-gravitating, are endowed with a toroidal magnetic field, and obey a constant angular momentum law. Our study focuses on the role of the black hole curvature in the shear viscosity tensor and in their potential combined effect on the stationary solutions. Those are built in the framework of a causality-preserving, second-order gradient expansion scheme of relativistic hydrodynamics in the Eckart frame description which gives rise to hyperbolic equations of motion. The stationary models are constructed by numerically solving the general relativistic momentum conservation equation using the method of characteristics. We place constraints in the range of validity of the second-order transport coefficients of the theory. Our results reveal that the effects of the shear viscosity and curvature are particularly noticeable only close to the cusp of the disks. The surfaces of constant pressure are affected by viscosity and curvature and the self-intersecting isocontour - the cusp - moves to smaller radii (i.e. towards the black hole horizon) as the effects become more significant. For highly magnetized disks the shift in the cusp location is smaller. Our findings might have implications on the dynamical stability of constant angular momentum tori which, in the inviscid case, are affected by the runaway instability.

Fermi seas from Bose condensates in Chern-Simons matter theories and a bosonic exclusion principle

We generalize previously obtained results for the (all orders in the ’t Hooft coupling) thermal free energy of bosonic and fermionic large N Chern-Simons theories with fundamental matter, to values of the chemical potential larger than quasiparticle thermal masses. Building on an analysis by Geracie, Goykhman and Son, we present a simple explicit formula for the occupation number for a quasiparticle state of any given energy and charge as a function of the temperature and chemical potential. This formula is a generalization to finite ’t Hooft coupling of the famous occupation number formula of Bose-Einstein statistics, and implies an exclusion principle for Chern-Simons coupled bosons: the total number of bosons occupying any particular state cannot exceed the Chern-Simons level. Specializing our results to zero temperature we construct the phase diagrams of these theories as a function of chemical potential and the UV parameters. At large enough chemical potential, all the bosonic theories we study transit into a compressible Bose condensed phase in which the runaway instability of free Bose condensates is stabilized by the bosonic exclusion principle. This novel Bose condensate is dual to — and reproduces the thermodynamics of — the fermionic Fermi sea.

Effect of shape memory alloys on the mechanical properties of metallic glasses: A molecular dynamics study

The strength-plasticity trade-off of metallic glass (MG) has not still been effectively overcome. The introduction of shape memory alloy (SMA) is an effective way to improve the mechanical properties of MG. Here, the deformation behavior of amorphous/SMA Cu64Zr36/B2-CuZr nanomultilayers (ASNMs) under tension loading is investigated by molecular dynamics (MD) simulation method. The results show that the peak stresses and flow stress of the ASNMs are greater than those of the monolithic MG regardless of SMA volume fraction. The martensitic transformation (MT) in the SMA phase limits the propagation of shear bands (SBs), avoids a runaway instability, and simultaneously induces plastic strain strengthening. The results also indicate that the plastic deformation mode of ASNMs changes from the interaction of multiple SBs dominated to finally brittle fracture caused by nano-pores aggregation with the increase of SMA volume fraction. This means that the plasticity and strength of ASNMs can be significantly improved by adjusting the volume fraction of SMA. The fruits stem from this paper may provide a valuable guidance and theory route for the design of high-performance MGs.

On the Stability of Deep‐Seated Landslides. The Cases of Vaiont (Italy) and Shuping (Three Gorges Dam, China)

AbstractDeep‐seated landslides can have catastrophic impacts on human life and infrastructure when they suddenly fail. These events are devastating because of the large volumes of soil and rock masses involved and their often long runout. The present study suggests an energy‐based method to determine when a landslide becomes unstable, giving critical values for measurable variables (velocity and basal temperature) up to which remediation actions can be deployed. This work focuses on large ancient landslides reactivated by dam‐related water table variations that modify landslide stability. The main hypothesis of this work is that most of the deformation of deep‐seated landslides is concentrated on a thin, basal shear band forming the sliding surface. In particular, this assumption allows an approximation of deep‐seated landslides as elastic/rigid blocks sliding over a viscoplastic shear band, featuring weak phases like expansive clays. When the landslide moves, it causes friction in the shear band that raises the temperature of the clays until they become unstable and collapse catastrophically through a thermal runaway instability. The model is applied to the Vaiont landslide in Northern Italy and the Shuping landslide next to the Three Gorges Dam in China. The results of the model reproduce the sliding behavior of both landslides and provide constraints on the critical points of stability.

Primordial black holes as dark matter through Higgs field criticality

We study the dynamics of a spectator Higgs field which stochastically evolves during inflation onto near-critical trajectories on the edge of a runaway instability. We show that its fluctuations do not produce primordial black holes (PBHs) in sufficient abundance to be the dark matter, nor do they produce significant second-order gravitational waves. First we show that the Higgs produces larger fluctuations on CMB scales than on PBH scales, itself a no-go for a viable PBH scenario. Then we track the superhorizon perturbations nonlinearly through reheating using the delta N formalism to show that they are not converted to large curvature fluctuations. Our conclusions hold regardless of any fine-tuning of the Higgs field for both the Standard Model Higgs and for Higgs potentials modified to prevent unbounded runaway.

Supersolid Properties of a Bose-Einstein Condensate in a Ring Resonator.

We investigate the dynamics of a Bose-Einstein condensate interacting with two noninterfering and counterpropagating modes of a ring resonator. Superfluid, supersolid, and dynamic phases are identified experimentally and theoretically. The supersolid phase is obtained for sufficiently equal pump strengths for the two modes. In this regime we observe the emergence of a steady state with crystalline order, which spontaneously breaks the continuous translational symmetry of the system. The supersolidity of this state is demonstrated by the conservation of global phase coherence at the superfluid to supersolid phase transition. Above a critical pump asymmetry the system evolves into a dynamic runaway instability commonly known as collective atomic recoil lasing. We present a phase diagram and characterize the individual phases by comparing theoretical predictions with experimental observations.

Unraveling the Quantum Nature of Atomic Self-Ordering in a Ring Cavity.

Atomic self-ordering to a crystalline phase in optical resonators is a consequence of the intriguing nonlinear dynamics of strongly coupled atom motion and photons. Generally the resulting phase diagrams and atomic states can be largely understood on a mean-field level. However, close to the phase transition point, quantum fluctuations and atom-field entanglement play a key role and initiate the symmetry breaking. Here we propose a modified ring cavity geometry, in which the asymmetry imposed by a tilted pump beam reveals clear signatures of quantum dynamics even in a larger regime around the phase transition point. Quantum fluctuations become visible both in the dynamic and steady-state properties. Most strikingly we can identify a regime where a mean-field approximation predicts a runaway instability, while in the full quantum model the quantum fluctuations of the light field modes stabilize uniform atomic motion. The proposed geometry thus allows to unveil the "quantumness" of atomic self-ordering via experimentally directly accessible quantities.

Deformation nanotwins suppress shear banding during impact test of CrCoNi medium-entropy alloy

We report deformation bands ahead of the crack tip in a CrCoNi alloy under impact loading, and analyze the effects of deformation twinning on strain localization in the form of shear banding. Due to low stacking fault energy, upon high-strain-rate deformation this medium-entropy alloy forms twins with thickness and spacing of only a few nanometers. These nano-twins are embedded dynamically not only ahead of any developing shear band to retard its advance, but also in its interior to work harden. This dual effect helps to suppress runaway shear banding instability that instigates failure and contributes to the energy absorption as recorded in instrumented Charpy tests.

Optimum shear stability at intermittent-to-smooth transition of plastic flow in metallic glasses at cryogenic temperatures

The runaway instability of shear bands leads to catastrophic failure of metallic glasses while the link between the shear banding process and the macroscopic plasticity in a quantitative manner in metallic glasses remains a major challenge.Through a series of compression tests at cryogenic temperatures, we found that the plasticity of the metallic glass can attain a maximum value at a critical temperature at which the transition from serrated flow to non-serrated flow occurs on a Zr-based metallic glass at cryogenic temperatures. The transition point corresponds to the lowest shear-band velocity and the most stable state of plastic shearing during deformation. The results provide an insight for understanding the temperature-dependent plasticity of metallic glasses from shear-band dynamics and may help to design the plasticity/ductility of metallic glasses at cryogenic temperatures.

Optimum Shear Stability at Intermittent-to-Smooth Transition of Plastic Flow in Metallic Glasses at Cryogenic Temperatures

The runaway instability of shear bands leads to catastrophic failure of metallic glasses while the links between the shear banding process and the macroscopic plasticity in a quantitative manner in metallic glasses remains a major challenge.Through a series of compression tests at cryogenic temperatures, we found that the plasticity of the metallic glass can attain a maximum value at a critical temperature at which the transition from serrated flow to non-serrated flow occurs on a Zr-based metallic glass at cryogenic temperatures. The transition point corresponds to the lowest shear-band velocity and the most stable state of plastic shearing during deformation. The results provides an insight for understanding the temperature-dependent plasticity of metallic glasses from shear-band dynamics and may help to design the plasticity/ductility of metallic glasses at cryogenic temperatures.

Simulating the nonlinear interaction of relativistic electrons and tokamak plasma instabilities: Implementation and validation of a fluid model

For the simulation of disruptions in tokamak fusion plasmas, a fluid model describing the evolution of relativistic runaway electrons and their interaction with the background plasma is presented. The overall aim of the model is to self-consistently describe the nonlinear coupled evolution of runaway electrons (REs) and plasma instabilities during disruptions. In this model, the runaway electrons are considered as a separate fluid species in which the initial seed is generated through the Dreicer source, which eventually grows by the avalanche mechanism (further relevant source mechanisms can easily be added). Advection of the runaway electrons is considered primarily along field lines, but also taking into account the E×B drift. The model is implemented in the nonlinear magnetohydrodynamic (MHD) code jorek based on Bezier finite elements, with current coupling to the thermal plasma. Benchmarking of the code with the one-dimensional runaway electron code go is done using an artificial thermal quench on a circular plasma. As a first demonstration, the code is applied to the problem of an axisymmetric cold vertical displacement event in an ITER plasma, revealing significantly different dynamics between cases computed with and without runaway electrons. Though it is not yet feasible to achieve fully realistic runaway electron velocities close to the speed of light in complete simulations of slowly evolving plasma instabilities, the code is demonstrated to be suitable to study various kinds of MHD-RE interactions in MHD-active and disruption relevant plasmas.