Growth Rate Of Instability Research Articles

Breaking of Internal Waves Parametrically Excited by Ageostrophic Anticyclonic Instability

Abstract A gradient-wind balanced flow with an elliptic streamline parametrically excites internal inertia-gravity waves through ageostrophic anticyclonic instability (AAI). This study numerically investigates the breaking of internal waves and the following turbulence generation resulting from the AAI. In our simulation, we periodically distort the calculation domain following the streamlines of an elliptic vortex and integrate the equations of motion using a Fourier spectral method. This technique enables us to exclude the overall structure of the large-scale vortex from the computation and concentrate on resolving the small-scale waves and turbulence. From a series of experiments, we identify two different scenarios of wave breaking conditioned on the magnitude of the instability growth rate scaled by the buoyancy frequency λ/N. First, when , the primary wave amplitude excited by AAI quickly goes far beyond the overturning threshold and directly breaks. The resulting state is thus strongly nonlinear turbulence. Second, if , weak wave–wave interactions begin to redistribute energy across frequency space before the primary wave reaches a breaking limit. Then, after a sufficiently long time, the system approaches a Garrett–Munk-like stationary spectrum, in which wave breaking occurs at finer vertical scales. Throughout the experimental conditions, the growth and decay time scales of the primary wave energy are well correlated. However, since the primary wave amplitude reaches a prescribed limit in one scenario but not in the other, the energy dissipation rates exhibit two types of scaling properties. This scaling classification has similarities and differences with D’Asaro and Lien’s wave–turbulence transition model. Significance Statement Due to the gradients in buoyancy and pressure, density-stratified seawater supports oscillatory vertical motion called internal waves. When waves significantly skew a density isosurface, dense water lifts over lighter water resulting in gravitational instability and high energy dissipation. In this wave-breaking process, seawater is vertically mixed, transporting heat and nutrients essential to maintain Earth’s climate and ecosystems. This study investigates the generation and breaking of ocean internal waves in a novel numerical simulation setup; we temporally distort the model shape to emulate the wave excitation forced by a larger-size horizontal eddy, a ubiquitous situation at O(1–10) km scales in the upper ocean. The simulation results exhibit two unique wave-breaking scenarios with distinct scaling features in turbulence energy dissipation rates.

Modulation of electromagnetic waves in a relativistic degenerate plasma at finite temperature

We study the modulational instability (MI) of a linearly polarized electromagnetic (EM) wave envelope in an intermediate regime of relativistic degenerate plasmas at a finite temperature (T≠0) where the thermal energy (KBT) and the rest-mass energy (mec2) of electrons do not differ significantly, i.e., βe≡KBT/mec2≲ (or ≳) 1, but the Fermi energy (KBTF) and the chemical potential energy (μe) of electrons are still a bit higher than the thermal energy, i.e., TF>T and ξe=μe/KBT≳1. Starting from a set of relativistic fluid equations for degenerate electrons at finite temperature, coupled to the EM wave equation and using the multiple scale perturbation expansion scheme, a one-dimensional nonlinear Schödinger (NLS) equation is derived, which describes the evolution of slowly varying amplitudes of EM wave envelopes. Then, we study the MI of the latter in two different regimes, namely, βe<1 and βe>1. Like unmagnetized classical cold plasmas, the modulated EM envelope is always unstable in the region βe>4. However, for βe≲1 and 1<βe<4, the wave can be stable or unstable depending on the values of the EM wave frequency, ω, and the parameter ξe. We also obtain the instability growth rate for the modulated wave and find a significant reduction by increasing the values of either βe or ξe. Finally, we present the profiles of the traveling EM waves in the form of bright (envelope pulses) and dark (voids) solitons, as well as the profiles (other than traveling waves) of the Kuznetsov–Ma breather, the Akhmediev breather, and the Peregrine solitons as EM rogue (freak) waves, and discuss their characteristics in the regimes of βe≲1 and βe>1.

Envelope solitons in weakly dissipative dusty plasma

A hydrodynamic model is applied to characterize the linear and nonlinear characteristics of collisional dust acoustic waves of degenerate inertialess ions and electrons. The dispersion properties of dust acoustic waves are derived, inertia provided by dust particles, and restoring force is due to electrons and ions. In nonlinear analysis, we follow the reductive perturbation technique to derive the dissipative nonlinear Schrödinger equation. The modulated growth rate of instability, the envelope, and rogue waves are investigated numerically as well as analytically. This paper will provide an important contribution to understanding the linear and nonlinear properties of electrostatic excitations in degenerate dusty plasma, which are relevant to the DUSTY DAZ WDs.

Effect of electromigration on onset of morphological instability of a nanowire

Solid cylindrical nanowires are vulnerable to a Rayleigh–Plateau-type morphological instability. The instability results in a wire breakup, followed by formation of a chain array of spherical nanoparticles. In this paper, a base model of a morphological instability of a nanowire on a substrate in the applied electric field directed along a nanowire axis is considered. Exact analytical solution is obtained for $$90^\circ $$ contact angle and, assuming axisymmetric perturbations, for a free-standing wire. The latter solution extends the 1965 result by Nichols and Mullins without electromigration effect (Nichols and Mullins in Surface-(Interface-) and volume-diffusion contributions to morphological changes driven by capillarity. Trans Metall Soc AIME 233:1840–1848, 1965). For general contact angles the neutral stability is determined numerically. It is shown that a stronger applied electric field (a stronger current) results in a larger instability growth rate and a decrease of the most dangerous unstable wavelength; in experiment, the latter is expected to yield more dense chain array of nanoparticles. Also it is noted that a wire crystallographic orientation on a substrate has larger impact on stability in a stronger electric field and that a simple switching of the polarity of electrical contacts, i.e. the reversal of the direction of the applied electric field, may suppress the instability development and thus a wire breakup would be prevented. A critical value of the electric field that is required for such wire stabilization is obtained.

Influence of free-stream turbulence on the boundary layer stability of a wind turbine airfoil and near wake

Free-stream turbulence (FST) alters the boundary layer of wind turbine blades, changing the hydrodynamic stability and near wake. Large-eddy simulations (LES) of a blade section with a laminar separation bubble for several turbulence intensities (TI) and a Reynolds number of 105 are performed. The effects of boundary-layer streaks generated by FST on Tollmien-Schlichting (TS) and Kelvin-Helmholtz (KH) instabilities are analyzed with a model based on the parabolized stability equations (PSE). Two competing effects on flow stability are identified. The spanwise-averaged mean-flow distortion stabilizes primary TS/KH modes for increasing TI. However, this contribution seems dominant only for TI ≥ 8.6%. For lower TI, the spanwise-oscillating distortion caused by streaks destabilizes the flow, and the growth rates of secondary modal instabilities increase with the streak amplitude. The destabilization occurs mainly at spanwise locations with negative streaks since the inflection point shifts away from the wall, enhancing inviscid instabilities. Inflection points in the spanwise direction formed by the streaks also contribute to the destabilization. The modal structures from PSE and LES agree. Finally, the trailing-edge near-wake coherent structures are more energetic for TI ≥ 8.6% due to the partial stabilization of modal instabilities, delaying the turbulent breakdown.

Suppression of stimulated Raman scattering by angularly incoherent light, towards a laser system of incoherence in all dimensions of time, space, and angle

Laser–plasma instability (LPI) is one of the main obstacles to achieving predictable and reproducible fusion at high gain through laser-driven inertial confinement fusion (ICF). In this paper, for the first time, we show analytically and confirm with three-dimensional particle-in-cell simulations that angular incoherence provides suppression of the instability growth rate that is additional to and much stronger than that provided by the well-known temporal and spatial incoherence usually used in ICF studies. For the model used in our calculations, the maximum field ratio between the stimulated Raman scattering and the driving pulses drops from 0.2 for a Laguerre–Gaussian pulse with a single nonzero topological charge to 0.05 for a super light spring with an angular momentum spread and random relative phases. In particular, angular incoherence does not introduce extra undesirable hot electrons. This provides a novel method for suppressing LPI by using light with an angular momentum spread and paves the way towards a low-LPI laser system for inertial fusion energy with a super light spring of incoherence in all dimensions of time, space, and angle, and may open the door to the use of longer-wavelength lasers for inertial fusion energy.

Rogue wave solutions over double-periodic wave background of a fifth-order nonlinear Schrödinger equation with quintic terms

Studies on rogue waves (RWs) over constant and periodic wave background are of contemporary interest in several areas of physics. These RWs arise not only on such backgrounds but also appear on double-periodic wave background. In this paper, we derive RW solutions over a double-periodic wave background of a fifth-order nonlinear Schrödinger equation. We create the double-periodic wave background with elliptic functions (in combinations of cn, sn and dn) as seed solutions in the first iteration of Darboux transformation. We then calculate the growth rate of instability for these double-periodic solutions under different values of elliptic modulus parameter. On the top of these background waves, we generate RWs with the help of second independent solution to the eigenvalue problem. Further, we analyze the differences that occur in the appearance of RWs with reference to the lower-order and higher-order dispersions terms. In addition to the above, we examine the derived solutions in detail for certain system and elliptic modulus parameter values and highlight some interesting features that we obtain from our studies.

Twisted dust-acoustic waves in a self-gravitating dusty plasma with nonextensive q-distributed electrons and ions

We have investigated the twisted dust-acoustic waves (TDAWs) in an electrostatic self-gravitating dusty plasma whose electrons and ions are modelled by nonextensive q-distribution function while massive dust particles are Maxwellian distributed. A well-known kinetic theory is employed for this purpose where perturbed distribution function, electrostatic and gravitational potentials are expressed with Laguerre–Gauss functions. The governing equations of kinetic theory are solved together under paraxial approximations. The dispersion relations and instability growth rates are obtained for two situations; a) super-extensivity (q < 1) and b) sub-extensivity (q > 1). Significant modifications concerning the wave frequencies and growth rates are presented with respect to self-gravitation parameter, twist parameter, nonextensive parameter and streaming speed. It is observed that wave frequency and growth rate of TDAWs reduces in the presence of self-gravitating effects. Furthermore, the growth rates exhibit a significant enhancement in amplitude with the increase in twist parameter, q-parameter and streaming speed. Our present results may have applications in interstellar dust clouds and in the dusty plasma environments of Halley’s Comet.

Cosmic ray-driven magnetohydrodynamic waves in magnetized self-gravitating dusty molecular clouds

ABSTRACT The impact of galactic cosmic rays (CRs) in terms of CR pressure and parallel CR diffusion has been investigated on the low-frequency magnetohydrodynamic (MHD) waves and linear gravitational instability in the typical dusty plasma environment of molecular clouds (MCs). The dusty fluid model is formulated by combining the equations of the magnetized electrons/ions and dust particles, including the CR effects. The interactions between CR fluid and gravitating magnetized dusty plasma have been studied with the help of modified dispersion properties of the MHD waves and instabilities using the hydrodynamic fluid–fluid (CR–plasma) approach. CR diffusion affects the coupling of CR pressure-driven mode with dust-Alfvén MHD mode and causes damping in the MHD waves. It persists in its effect along the direction of the magnetic field and is diminished across the magnetic field. The phase-speed diagram shows that for super-Alfvénic wave, the slow mode becomes the intermediate Alfvén mode. The fundamental Jeans instability criterion remains unaffected due to CR effects, but in the absence of CR diffusion, the effects of dust-acoustic speed and CR pressure-driven wave speed are observed in the instability criterion. It is found that CR pressure stabilizes while CR diffusion destabilizes the growth rates of Jeans instability and significantly affects the gravitational collapse of dusty MCs. The charged dust grains play a dominant role in the sub-Alfvénic and super-Alfvénic MHD waves and the collapse of MCs, triggering gravitational instability. The consequences have been discussed to understand the gravitational instability in the dense photodissociation regions of dusty MCs.

Acoustic-gravity waves in quasi-isothermal atmospheres with a random vertical temperature profile

We study acoustic-gravity waves in a quasi-isothermal atmosphere in the presence of a weak random addition to the vertical temperature profile, which simulates the real atmosphere of the Earth at altitudes greater than ∼200 km. The resulting stochastic equation is closed in the Bourret approximation. The poles of the obtained mean Green’s function determine the generalized dispersion relation for acoustic-gravity waves. Two particular cases are considered: random inhomogeneities in the form of white noise (δ-correlated in space) and the opposite case of a δ-shaped noise spectrum. In both cases, instability of acoustic-gravity waves is predicted and the corresponding instability growth rates are determined.

Connecting small-scale to large-scale structures of fast neutrino-flavor conversion

We present a systematic study of fast neutrino-flavor conversion (FFC) with both small-scale and large-scale numerical simulations in spherical symmetry. We find that FFCs can, in general, reach a quasisteady state, and these features in the nonlinear phase are not characterized by the growth rate of FFC instability but rather angular structures of the electron neutrino lepton number (ELN) and the heavy one. Our result suggests that neutrinos can almost reach a flavor equipartition even in cases with low growth rate of instability (e.g., shallow ELN crossing) and narrow angular regions (in momentum space) where flavor conversions occur vigorously. This shows that ELN and heavy-neutrino lepton number angular distributions cannot provide a sufficient information to determine total amount of flavor conversion in neutrinos and antineutrinos of all flavors. Based on the results of our numerical simulations, we provide a new approximate scheme of FFC that is designed so that one can easily incorporate effects of FFCs in existing classical neutrino transport codes for the study of core-collapse supernova and binary neutron star merger. The scheme has an ability to capture key features of quasisteady state of FFCs without solving quantum kinetic neutrino transport, which will serve to facilitate access to FFCs for core-collapse supernova and binary neutron star merger theorists.

The wave energy density and growth rate for the resonant instability in relativistic plasmas

ABSTRACT The wave instability acts in astrophysical plasmas to redistribute energy and momentum in the absence of frequent collisions. There are many different types of waves, and it is important to quantify the wave energy density and growth rate for understanding what types of wave instabilities are possible in different plasma regimes. There are many situations throughout our Universe where plasmas contain a significant fraction of relativistic particles. Theoretical estimates for the wave energy density and growth rate are constrained to either field-aligned propagation angles or non-relativistic considerations. Based on linear theory, we derive the analytic expressions for the energy density and growth rate of an arbitrary resonant wave with an arbitrary propagation angle in relativistic plasmas. For this derivation, we calculate the Hermitian and anti-Hermitian parts of the relativistic-plasma dielectric tensor. We demonstrate that our analytic expression for the wave energy density presents an explicit energy increase in resonant waves in the wavenumber range where the analytic expression for the growth rate is positive (i.e. where a wave instability is driven). For this demonstration, we numerically analyse the loss-cone driven instability, as a specific example, in which the whistler-mode waves scatter relativistic electrons into the loss cone in the radiation belt. Our analytic results further develop the basis for linear theory to better understand the wave instability, and have the potential to combine with quasi-linear theory, which allows to study the time evolution of not only the particle momentum distribution function but also resonant wave properties through an instability.

Multi-instrumental analysis of the day-to-day variability of equatorial plasma bubbles

This paper presents a multi-instrument observational analysis of the equatorial plasma bubbles (EPBs) variation over the American sector during a geomagnetically quiet time period of 07–10 December 2019. The day-to-day variability of EPBs and their underlying drivers are investigated through coordinately utilizing the Global-scale Observations of Limb and Disk (GOLD) ultraviolet images, the Ionospheric Connection Explorer (ICON) in-situ and remote sensing data, the global navigation satellite system (GNSS) total electron content (TEC) observations, as well as ionosonde measurements. The main results are as follows: 1) The postsunset EPBs’ intensity exhibited a large day-to-day variation in the same UT intervals, which was fairly noticeable in the evening of December 07, yet considerably suppressed on December 08 and 09, and then dramatically revived and enhanced on December 10. 2) The postsunset linear Rayleigh-Taylor instability growth rate exhibited a different variation pattern. It had a relatively modest peak value on December 07 and 08, yet a larger peak value on December 09 and 10. There was a 2-h time lag of the growth rate peak time in the evening of December 09 from other nights. This analysis did not show an exact one-to-one relationship between the peak growth rate and the observed EPBs intensity. 3) The EPBs’ day-to-day variation has a better agreement with that of traveling ionospheric disturbances and atmospheric gravity waves signatures, which exhibited relatively strong wavelike perturbations preceding/accompanying the observed EPBs on December 07 and 10 yet relatively weak fluctuations on December 08 and 09. These coordinate observations indicate that the initial wavelike seeding perturbations associated with AGWs, together with the catalyzing factor of the instability growth rate, collectively played important roles to modulate the day-to-day variation of EPBs. A strong seeding perturbation could effectively compensate for a moderate strength of Rayleigh-Taylor instability growth rate and therefore their combined effect could facilitate EPB development. Lacking proper seeding perturbations would make it a more inefficient process for the development of EPBs, especially with a delayed peak value of Rayleigh-Taylor instability growth rate.

Effect of nonlinear saturation of electromagnetic instability on the viscosity of the inertial fusion fuel

One of the interesting topics of recent research is the study of the Weibel electromagnetic instability growth rate in the interaction of high-intensity lasers with the dense plasma of fusion fuel pellets. In this paper, the effect of stresses caused by laser ponderomotive force on the growth rate of Weibel instability in the nonlinear phase is investigated. The growth of the nonlinear phase of Weibel instability growth rate, which is the saturation phase of Weibel instability, in the presence of stress leads to viscosity turbulence. The results show that the coefficient of reduction of fuel viscosity in the presence of the stress flow is about 0.0014 due to the anomalous transfer mechanism caused by the nonlinear growth of the Weibel instability.

Mitigation of the Onset of Hosing in the Linear Regime through Plasma Frequency Detuning.

The hosing instability poses a feasibility risk for plasma-based accelerator concepts. We show that the growth rate for beam hosing in the linear regime (which is relevant for concepts that use a long driver) is a function of the centroid perturbation wavelength. We demonstrate how this property can be used to damp centroid oscillations by detuning the plasma response sufficiently early in the development of the instability. We also develop a new theoretical model for the early evolution of hosing. These findings have implications for the general control of an instability's growth rate.

Stabilization of trapped electron mode through effective diffusion in electron temperature gradient turbulence

Multi-scale gyrokinetic theory and simulations of a toroidal magnetized plasma have revealed the existence of cross-scale interactions of the trapped electron mode (TEM) and the electron temperature gradient (ETG) turbulence. Reduction of the TEM instability growth rate in the ETG turbulence is clearly identified, and is well represented in the form of effective diffusion. A theoretical model based on the stochastic forcing by the ETG turbulence well describes the turbulent diffusion coefficient observed in multi-scale turbulence simulations.

Global linear stability analysis of kinetic trapped ion mode (TIM) in tokamak plasma using the spectral method

Trapped ion modes (TIMs) belong to the family of ion temperature gradient (ITG) modes, which are one of the important ingredients in heat turbulent transport at the ion scale in tokamak plasmas. A global linear analysis of a reduced gyro-bounce kinetic model for trapped particle modes is performed, and a spectral method is proposed to solve the dispersion relation. Importantly, the radial profile of the particle drift velocity is taken into account in the linear analysis by considering the magnetic flux ψ dependency of the equilibrium Hamiltonian in both the quasi-neutrality equation and equilibrium gyro-bounce averaged distribution function . Using this spectral method, linear growth rates of TIM instability in the presence of different temperature profiles and precession frequencies of trapped ions, with an approximated constant Hamiltonian and the exact ψ dependent equilibrium Hamiltonian, are investigated. The growth rate depends on the logarithmic gradient of temperature κ T , density κ n and equilibrium Hamiltonian . With the exact ψ dependent Hamiltonian, the growth rates and potential profiles are modified significantly, compared to the cases with an approximated constant Hamiltonian. All the results from the global linear analysis agree with a semi-Lagrangian based linear Vlasov solver with good accuracy. This spectral method is very fast and requires much less computation resources compared to a linear version of the Vlasov-solver based on a semi-Lagrangian scheme.

Standing accretion shock instability in the collapse of a rotating stellar core

Hydrodynamical instabilities, such as the standing accretion shock instability (SASI), play an essential role in the dynamics of core-collapse supernovae, with observable imprints in the neutrino and gravitational wave signals. Yet, the impact of stellar rotation on the development of SASI is poorly explored. We investigate the conditions favoring the growth of SASI in the presence of rotation through a perturbative analysis. The properties of SASI are compared in two stationary configurations, cylindrical and spherical equatorial, which mainly differ by their advection timescales from the shock to the proto-neutron star surface. Without rotation, the mode $m=1$, corresponding to a one-armed spiral SASI deformation, can be significantly more unstable in the spherical equatorial configuration. In fact, the shorter advection time in the spherical equatorial geometry allows for a larger contribution of the entropic-acoustic coupling from the region of adiabatic compression near the surface of the proto-neutron star. The angular momentum of the collapsing core favors the growth of prograde spiral modes $m=1$ and $m=2$ in both geometries. Although the growth rate of the spiral instability is systematically faster in spherical geometry, its oscillation frequency is remarkably insensitive to the geometry. Such a contrast with nonrotating flows calls for a deeper understanding of the role of advection in the mechanism of spiral SASI. Our findings suggest that the resonant coupling of acoustic waves with their corotation radius may play a major role in the instability mechanism of collapsing cores with rotation. Elucidating this physical mechanism is essential to interpret the signal from future multimessenger supernova observations.

The effect of collisions on the rayleigh-taylor instability in magnetized quantum plasma

Rayleigh-Taylor instability occurs at the interface between light and heavy fluids whenever the heavier fluid is accelerated by the light one. An important issue is the stability conditions of these systems. Various parameters such as density difference between two fluids, density inhomogeneity length, magnetic field, viscosity, collision can affect the stabilization or destabilization of the system. So far, some of these factors have been investigated in the fields of classical and quantum physics. This process has also been studied in both linear and nonlinear states. Here we consider a collisional magnetic inhomogeneous quantum plasma. For the inhomogeneity profile of density as an exponential function, we calculated the second ordinary equation for the disturbed velocity. Since the differential equation does not have an analytical solution, we have calculated the growth rate curve using numerical methods and obtained the disturbed velocity profile in the discontinuity. Then the effects of different parameters such as collision, magnetic field, quantum effects, and density difference of two fluids on the system stabilization are studied. The various branches of the instability growth rate curve and its relationship with the turbulent velocity profile in discontinuity are also discussed.

Vertical control of DIII-D discharges with strong negative triangularity

Through predictive modeling validated by a series of experiments on DIII-D, the vertical stability of low β diverted plasmas with strong negative triangularity (NT) () is assessed. As a result of their unique magnetic geometry, NT plasmas feature larger Shafranov shifts and more elongated inner flux surfaces than positive triangularity counterparts, typically leading to enhanced vertical instability growth rates. However, coupling with the non-conformal vessel DIII-D wall reduces these growth rates to controllable values, providing a path forward for stabilizing strongly NT plasma with a diverted geometry. These discharges are used to validate GSdesign (part of the TokSys code suite) stability calculations in strong NT plasmas on DIII-D, with errors of no more than ∼20% observed between modeled and experimentally measured growth rates. Additions of diagnostic noise and power supply tuning to the TokSys model are needed to accurately capture the time dependence of DIII-D NT discharges, assisting with the design of control schemes specific to the DIII-D poloidal field coils. Finally, implications of these results on a future NT reactor are briefly described.