Instability Regime Research Articles

Kinetic instability of whistlers in electron beam-plasma systems

The whistlers in space plasmas and in magnetic fusion experiments are destabilized by beams of fast electrons. While the linear regime of instability is analytically tractable, in most practical cases, the instability operates at the saturated level during the stages of observation and measurement. The saturated states, however, involve nonlinear whistlers, which remain best accessible for analysis by kinetic simulations. Results of electromagnetic Vlasov simulations are presented, analyzing an anisotropic electron beam driven whistler instability. The simulations cover the initially unstable regime followed by a saturated or marginally stable regime. Both regimes are separated by an intermediate nonlinear regime during which the electron distribution undergoes a kinetically self-consistent modification. A linearly obtained generalized marginal stability condition is applied to the stabilized state. The condition obtained in its dispersive version shows the β|| at threshold and, in turn, the residual anisotropy, to be a function of the whistler mode number k.

Numerical MHD simulations of solar flares and their associated small-scale structures

ABSTRACT Using numerical simulations, we study the formation and dynamics of solar flares in a local region of the solar atmosphere. The magnetohydrodynamics (MHD) equations describe the dynamic evolution of flares, including space-dependent and anomalous magnetic resistivity and highly anisotropic thermal conduction on a 2.5 D slice. We adopt an initial solar atmospheric model in magnetohydrostatic equilibrium, with a magnetic configuration consisting of a vertical current sheet, which helps trigger the magnetic reconnection process. Specifically, we study three scenarios, two with only resistivity and the third with resistivity plus thermal conduction. The main results of the numerical simulations show differences in the global morphology of the flares, including the post-flare loops and the current sheet in three cases. In particular, localized resistivity produces more substructure around the post-flare loops that could be related to the Ritchmyer–Meshkov Instability (RMI). Furthermore, in the scenario of anomalous resistivity, we identify the formation of a plasmoid and a jet at coronal heights. On the other hand, in the scenario with resistivity plus thermal conduction, the post-flare loops are smooth, and no apparent substructures develop. Besides, in the z-component of the current density for the Res + TC case, we observe the development of multiple magnetic islands generated due to the Tearing instability in the non-linear regime.

Hot Deformation Behavior of Inconel 718 Alloy Using Regression-based Dynamic Material Model and Applications in Ring Rolling Manufacturing

Inconel 718 nickel-based alloy is extensively used in the aerospace industry (e.g., gas turbine engine components) because of its excellent corrosion resistance and high mechanical properties at elevated temperatures. However, there is a certain limit to manufacturing the alloy through plastic deformation due to its high deformation resistance and complicated deformation behaviors. In this study, the hot deformation behavior of Inconel 718 alloy was investigated to establish how processing conditions of flow stress-strain, at strain rates from 0.001 to 10 s<sup>-1</sup>, and temperatures from 850 to 1200<sup>o</sup>C, affected dynamic recrystallization. The regression-based material model was utilized to calculate the strain-rate sensitivity, and subsequently depict the efficiency of the power dissipation and instability criterion of hot deformation. The processing map and instability criterion predicted by the developed 3<sup>rd</sup>-order polynomial regression model corresponded with the experimental results and in particular, showed a better prediction for instability regime compared to the existing discrete derivative approach. Predicting the strain-rate sensitivity values on a continuous scale with regression analysis covered the additional instability region of the high strain rate near 10 s<sup>-1</sup>. The dynamic recrystallization deformation was also characterized by microstructural analysis along with the processing map. Consequently, ring-rolled aviation parts were manufactured with the optimum processing parameters, which conform to the AMS 5663 standard (Aerospace material specifications for Inconel 718).

Weakly nonlinear stability analysis of non-isothermal parallel flow in a vertical porous annulus

The study examines the stability of parallel airflow within a tall vertical coaxial circular annulus filled with a highly permeable porous medium under stable stratification. The linear stability theory predicts that the least unstable mode can be either axisymmetric or non-axisymmetric, depending on the values of the governing parameters. The curvature parameter, defined as the gap between coaxial circular cylinders, contributes to the stabilization of the flow. Depending on various controlling parameter values, the stably stratified non-isothermal annular parallel flow (SNAPF) can manifest three instability modes: thermal-shear, thermal-buoyant, and mixed or interactive. The instability type can change abruptly with Reynolds number, curvature parameter, and media permeability. A finite-amplitude instability analysis is examined using weakly nonlinear stability theory. The analysis demonstrates both subcritical and supercritical bifurcations near the instability boundary. The range of Reynolds numbers for subcritical bifurcation expands when switching from axisymmetric to non-axisymmetric disturbance. Bifurcation transitions between supercritical and subcritical occur due to changes in the least stable azimuthal mode. The study also investigates the equilibrium/threshold amplitude within the supercritical/subcritical instability regime, and it verifies the existence of subcritical/supercritical bifurcation through nonlinear kinetic energy balance. Furthermore, the finite-amplitude analysis anticipates that the lower critical Rayleigh number increases as the Reynolds number, curvature parameter, or media permeability decreases. An increase in the Reynolds number shifts the point of inflection in the velocity profile toward the inner cylinder, which subsequently leads to a reduction in the size of the core vortex region. In the subcritical instability regime, the radius of the primary vortex cell decreased significantly as the Rayleigh number increased. When the curvature is altered, a structural transition occurs in the isotherms from multicellular to unicellular.

Numerical investigation on nonautonomous optical rogue waves and Modulation Instability analysis for a nonautonomous system

In this paper, we report existence of optical rogue waves in the focussing non—autonomous nonlinear Schrödinger equation (NLSE) through numerical studies of modulation instability (MI). The dynamics of non-autonomous rogue waves discussed and its associated modulation instability through linear stability analysis taken place followed by pulse splitting behaviour due to non—autonomous coefficient. We prove that the excitation of rogue waves with certain conditions in the base band modulation instability regime. The above analysis of complex dynamics in terms of MI processes has allowed to experiments to excite the nonlinear superposition of rogue wave solutions using a modulated plane wave optical field injected into optical fiber which offer the evidence for excitation of nonautonomous rogue waves in an inhomogeneous nonlinear medium. It is identified from the results frequency modulation on a wavefield induces modulation instability as a result of rogue waves. We analyze the dependence of parameters coefficient of group velocity dispersion(GVD) and nonlinearity (α(z)) and non—autonomous coefficient (β(z)) and the instability of rogue waves. Our work suggests that the presence of non-autonomous coefficients can have a significant impact on the emergence of extreme events, particularly in relation to their self—steepening nature.

Resistive-wall instability evaluation along the ramp in the SOLEIL II booster

The ultra-low emittance specification of the SOLEIL II storage ring requires a challenging lattice design of the booster that will inject the beam into it. The dimension of the vacuum chamber in the new booster must be reduced compared to that in the present machine. The resistive-wall (RW) instability is then expected to become more important than in the current booster. However, the Amplitude-Dependent Tune Shift (ADTS) is also expected to be stronger due to the strong sextupole magnets necessary for chromatic error correction in the new lattice. It could then be an important effect to fight against this instability. Therefore, evaluating this instability is important to ensure the machine’s feasibility. This work studies the beam dynamics along the ramp in the RW instability regime using the code mbtrack2. The turn-by-turn tracking allows us to see the evolution of the beam thoroughly and understand how RW, synchrotron radiation, and ADTS impact the beam stability.

Dispersion engineering in a Brillouin fiber laser cavity for Kerr frequency comb formation

We conduct numerical and experimental investigations on Kerr comb generation in a nonlinear and non-reciprocal fiber cavity by leveraging both stimulated Brillouin backscattering and cascaded four-wave mixing. By engineering the net cavity dispersion to be either normal or anomalous, we enable the formation of diverse patterns and localized structures in the cavity field. The comb’s properties depend crucially on the mismatch between the frequency spacing of the bichromatic pump and the free spectral range of the Brillouin laser cavity in both cases. Particularly, in the anomalous regime, adjusting this parameter yields coherent, stable frequency combs in the modulation instability regime. This allows control and expansion of the spectral bandwidth up to 2 THz in normal dispersion and to 6 THz under anomalous net dispersion. This versatile and easily reconfigurable method holds potential for applications in high-speed communications and microwave synthesis.

Deciphering the physical basis of the intermediate-scale instability

We study the underlying physics of cosmic ray (CR)-driven instabilities that play a crucial role for CR transport across a wide range of scales, from interstellar to galaxy cluster environments. By examining the linear dispersion relation of CR-driven instabilities in a magnetised electron–ion background plasma, we establish that both the intermediate and gyroscale instabilities have a resonant origin, and show that these resonances can be understood via a simple graphical interpretation. These instabilities destabilise wave modes parallel to the large-scale background magnetic field at significantly distinct scales and with very different phase speeds. Furthermore, we show that approximating the electron–ion background plasma with either magnetohydrodynamics (MHD) or Hall-MHD fails to capture the fastest-growing instability in the linear regime, namely the intermediate-scale instability. This finding highlights the importance of accurately characterising the background plasma for resolving the most unstable wave modes. Finally, we discuss the implications of the different phase speeds of unstable modes on particle–wave scattering. Further work is needed to investigate the relative importance of these two instabilities in the nonlinear, saturated regime and to develop a physical understanding of the effective CR transport coefficients in large-scale CR hydrodynamics theories.

Continuous-wave operation of an electron cyclotron maser formed in a mirror magnetic trap

Among various non-linear regimes of electron cyclotron instabilities that may be driven by a strong electron cyclotron resonance (ECR) heating in open magnetic traps, the continuous generation of a quasi-monochromatic wave, characterized by a smooth release of a free energy from a system, is especially important for applications, e.g., aimed at performance optimization of ECR ion sources. We study an universal model based on the quasilinear description of plasma–wave interactions that explains the condition of a continuous-wave regime of the cyclotron instability observed experimentally including, in particular, a strong dependence on a magnetic configuration.

Efficient computation of coherent multimode instabilities in lasers using a spectral approach

Coherent multimode instabilities are responsible for several phenomena of recent interest in semiconductor lasers, such as the generation of frequency combs and ultrashort pulses. These techonologies have proven disruptive in optical telecommunications and spectroscopy applications. While the standard Maxwell-Bloch equations (MBEs) encompass such complex lasing phenomena, their integration is computationally expensive and offers limited analytical insight. In this paper, we demonstrate an efficient spectral approach to the simulation of multimode instabilities via a quantitative analysis of the instability of single-frequency lasing in ring lasers, referred to as the Lorenz-Haken (LH) instability or the RNGH instability in distinct parameter regimes. Our approach, referred to as CFTD, uses generally non-Hermitian Constant Flux modes to obtain projected Time Domain equations. CFTD provides excellent agreement with finite-difference integration of the MBEs across a wide range of parameters in regimes of non-stationary inversion, including frequency comb formation and spatiotemporal chaos. We also develop a modal linear stability analysis using CFTD to efficiently predict multimode instabilities in lasers. The combination of numerical accuracy, speedup, and semi-analytic insight across a variety of dynamical regimes make the CFTD approach ideal to analyze multimode instabilities in lasers, especially in more complex geometries or coupled laser arrays.

Near-extinction transient behaviors of counterflow nonpremixed flames in a porous spherical burner at very low stretch rate

Near extinction transient behaviors of CH4/N2 versus O2/N2 counterflow nonpremixed flames were investigated by adopting a porous spherical burner with a large radius of curvature to achieve a very low buoyant stretch rate. By varying the oxygen concentrations in the oxidizer stream, four regimes were identified by three limits of sooting, instability, and extinction. The sooting limit was sensitive to flame temperature, and was characterized by two indexes of fuel injection velocity uF and oxygen concentration XO2. When decreasing uF, the sooting limit was different from high stretch flames because of appreciable heat loss toward the burner surface. In the instability regime, periodic holes were observed whose frequency decreased with XO2. Periodic holes were also found to occur with N2 dilution in the fuel stream, which were more regular with larger frequencies compared with the periodic holes in the diluted oxidizer streams. The edge propagation behaviors for periodic holes in diluted fuel streams were analyzed. The statistical average of the propagation speed of advancing edge (hole closing) Se decreased with increasing fuel concentration gradient, and the ratio of Se with the stoichiometric laminar burning velocity SLst of Se/SLst was larger than unity. Also, the stretch rate significantly affected the propagation speed of advancing edge flames. Determination of the propagation speed of the retreating edge (hole opening) had intrinsic difficulty in estimating the transient radial flow velocity, however, the approximated |Se/SLst| was larger than unity and decreased with the fuel mole fraction. Nitrogen dilution in the oxidizer stream was proven to be more effective than in the fuel stream for flame suppression of methane. This study could enrich the understanding of very low-stretch nonpremixed flames in a counterflow burner and provide information regarding low-stretch flame suppression, which may be relevant to microgravity flame behaviors.

Effects of Small Leading-Edge Bluntness on High-Speed Boundary-Layer Instabilities on Flat Plates

A numerical investigation of the effect of small leading-edge bluntness on the linear stability regime in high-speed boundary layers for flat plates was carried out using linear stability theory. While it is known that increasing leading-edge bluntness leads to stabilization of the linear instability, it is not completely understood when leading-edge bluntness effects become relevant; in other words, for which leading-edge radii the primary instability regime is affected for flat plates at higher Mach numbers. For the so-called “sharp” geometries, it is assumed that the influence of the nose radius on stability and transition is negligible. For cones, it is generally accepted that nose radii resulting in Reynolds numbers (based on nose radius) smaller than 1000 can be considered sharp. However, no clear guidelines supported by numerical or experimental data exist to conclusively determine what constitutes a sharp leading edge for a flat plate. In this work, bluntness effects are assessed by considering the influence of the leading-edge radius on the linear stability characteristics for high-speed flat-plate boundary layers. It was found from linear stability calculations that surprisingly small leading-edge radii have significant effects on the critical Reynolds number and spatial amplification rates, thus resulting in substantially reduced maximum -factors.

Дослідження показників якості організації дорожнього руху в умовах міста методом GPS-треків

The choice of rational quality criteria for the organization of road traffic in cities is an urgent task for scientists in the field of road transport, as it directly affects the effectiveness of activities in the field of ensuring the safety and comfort of car traffic in urban conditions. Depending on the goals of the analysis, the complexity of the network, and technical capabilities, the quality of traffic management can be assessed by indicators of the economic efficiency of the transport process, the level of accidents, environmental safety, social attractiveness, etc. The modern level of development of geo-information technologies allows for constant monitoring of the vehicle's speed mode. To obtain characteristics of the quality of traffic organization, experimental studies were conducted on a section of the street-road network of the city of Kharkiv, which corresponds to a typical route of personal transport from a remote sleeping area to the central part of the city.
 As a result of data processing of the GPS track, a histogram of the distribution of instantaneous speed and graphs of the car’s movement in the coordinates “time-distance”, “time-speed”, "distance-speed” were built, which allow you to visually assess the mode of movement along the entire route and determine potential "bottlenecks". Such spatio-temporal characteristics as average technical speed, specific time in motion, specific idle time, as well as energy indicators of the quality of traffic management were also calculated: acceleration noise, speed gradient, energy gradient. After dividing the experimental route into separate kilometer sections, changes in the characteristics of the quality of traffic organization, as it approached the city center, were analyzed. On the first half of the route, when moving along the main street, the instability of the speed regime was observed due to stops and idling in the zone of regulated intersections. The presence of a trend towards a decrease in the average technical speed when approaching the city center is explained by an increase in the loading of VDM within the central business part of the city and, as a result, the appearance of additional traffic delays. As we approached the city center, the specific time in motion increased with a slight increase in the specific idle time, and an increase in the speed gradient was also observed with a slight decrease in the energy gradient.

Modeling parameters for predicting the fire-induced progressive collapse in steel framed buildings

Fire is one of the extreme loading events that a building may experience during its service life and can have severe consequences on the safety of its occupants, first responders, and the structure. Steel framed buildings under severe fires can experience high levels of instability at a local or global level, which in turn can lead to the partial or progressive collapse of the structure. However, in current practice, fire resistance of structures is obtained without due consideration to a number of critical factors, and this is mainly due to the high level of complexity in undertaking advanced analysis of structures under fire exposure. This paper presents a parametric study on a ten-story braced steel framed building subjected to fire exposure wherein six different parameters are evaluated: fire severity, fire spread, load paths, temperature-induced creep, local instability, and analysis regime. Results from validated finite element models are utilized to evaluate the influence of the different parameters and recommend critical parameters to be incorporated in the analysis. Results show that the susceptibility of fire-induced progressive collapse significantly depends on the severity of the fire exposure scenario, including fire intensity, fire spread, and extent of burning. Also, accounting for the full effects of transient creep in fire-induced progressive collapse analysis is needed to obtain conservative failure times under severe to very intense fire exposure. Additionally, results from the parametric study infer that the sectional classification of a steel section based on local instability can alter under fire exposure and this effect is more critical in steel columns located in the higher stories of the building; a nonslender column at ambient conditions can transform to a slender section at elevated temperatures. This can induce temperature-induced local instability in the column and lead to an early onset of instability at member and structural levels.

Eigenstates and temporal dynamics in cavity optomagnonics

Many studies of magnon–photon coupling are performed in the frequency domain for microwave photons. In this work, we present analytical results of eigenfrequency, eigenstates, and temporal dynamics for the coupling between ferromagnetic magnon and visible photon. In contrast to microwave photons, optical photons can be coupled with magnon in a dispersive interaction which produces both level repulsion and attraction by varying the magnon–photon frequency detuning. At resonance, the hybridized states are of linear polarization and circular polarization for level repulsion and level attraction respectively. As the detuning increases, the polarizations of level repulsion remain linear but those of level attraction vary from elliptical to linear polarizations. The temporal dynamics of level repulsion presents the beat-like behavior. The level attraction presents monotonous decay in the weak coupling regime but gives rise to instability in the strong coupling regime due to the magnon amplification. As the detuning is large, both magnon and photon amplitudes present a synchronizing oscillation. Our results are important for exploring the temporal evolution of magnon–photon coupling in the range of optical frequency and designing magnon-based timing devices.

Self-adjointness of sound-proof models for magnetic buoyancy

An ideal magneto-hydrodynamic fluid, whether fully compressible or incompressible, is a Hamiltonian system. This implies that the equations describing perturbations to any static state are self-adjoint, a fact that is useful in obtaining stability criteria. To describe weakly compressible flows, there are a number of “sound-proof” models that eliminate sound waves by making approximations to the governing equations. However, such approximations may violate the Hamiltonian structure of the system. In a recent work, we have introduced a very general sound-proof model and determined conditions under which it closely approximates the linear regime of magneto-buoyancy instability, motivated by conditions in the solar interior. In the present work, we take a complementary approach, by deriving constraints under which the linearised sound-proof system is self-adjoint. We show that there is a unique set of self-adjoint sound-proof equations that conserves the same energy as the fully compressible system.

A new elastic instability in gravity-driven viscoelastic film flow

We examine the linear stability of the gravity-driven flow of a viscoelastic fluid film down an inclined plane. The viscoelastic fluid is modeled using the Oldroyd-B constitutive equation and, therefore, exhibits a constant shear viscosity and a positive first normal stress difference in viscometric shearing flows; the latter class of flows includes the aforesaid film-flow configuration. We show that the film-flow configuration is susceptible to two distinct purely elastic instabilities in the inertialess limit. The first instability owes its origin entirely to the existence of a free surface and has been examined earlier [Shaqfeh et al., “The stability of gravity driven viscoelastic film-flow at low to moderate Reynolds number,” J. Non-Newtonian Fluid Mech. 31, 87–113 (1989)]. The second one is the analog of the centermode instability recently discovered in plane Poiseuille flow [Khalid et al., “Continuous pathway between the elasto-inertial and elastic turbulent states in viscoelastic channel flow,” Phys. Rev. Lett. 127, 134502 (2021)] and owes its origin to the base-state shear; it is an example of a purely elastic instability of shearing flows with rectilinear streamlines. One may draw an analogy of the aforesaid pair of unstable elastic modes with the inertial free-surface and shear-driven instabilities known for the analogous flow configuration of a Newtonian fluid. While surface tension has the expected stabilizing effect on the Newtonian and elastic free-surface modes, its effect on the corresponding shear modes is, surprisingly, more complicated. For both the Newtonian shear mode and the elastic centermode, surface tension plays a dual role, with there being parameter regimes where it acts as a stabilizing and destabilizing influence. While the Newtonian shear mode remains unstable in the limit of vanishing surface tension, the elastic centermode becomes unstable only when the appropriate non-dimensional surface tension parameter exceeds a threshold. In the limit of surface tension being infinitely dominant, the free-surface boundary conditions for the film-flow configuration reduce to the centerline symmetry conditions satisfied by the elastic centermode in plane Poiseuille flow. As a result, the regime of instability of the film-flow centermode becomes identical to that of the original channel-flow centermode. At intermediate values of the surface tension parameter, however, there exist regimes where the film-flow centermode is unstable even when its channel-flow counterpart is stable. We end with a discussion of the added role of inertia on the aforementioned elastic instabilities.

Measurement of the nonlinear parametric instability gain in dispersion oscillating fibers.

We report the observation of the parametric gain band distortion in the nonlinear (depleted) regime of modulation instability in dispersion oscillating fibers. We show that the maximum gain is shifted even outside the boundaries of the linear parametric gain band. Experimental observations are confirmed by numerical simulations.

Effect of stellar rotation on the development of post-shock instabilities during core-collapse supernovae

Context. The growth of hydrodynamical instabilities is key to triggering a core-collapse supernova explosion during the phase of stalled accretion shock, immediately after the birth of a proto-neutron star (PNS). Stellar rotation is known to affect the standing accretion shock instability (SASI) even for small rotation rates, but its effect on the onset of neutrino-driven convection is still poorly known. Aims. We assess the effect of stellar rotation on SASI when neutrino heating is taken into account as well as the effect of rotation on neutrino-driven convection. The interplay of rotation with these two instabilities affects the frequency of the mode m = 2, which can be detected with gravitational waves at the onset of a supernova explosion. Methods. We used a linear stability analysis to study the dynamics of the accreting gas in the equatorial plane between the surface of the PNS and the stationary shock. We explored rotation effects on the relative strength of SASI and convection by considering a large range of specific angular momenta and neutrino luminosities. Results. The nature of the dominant non-axisymmetric instability developing in the equatorial post-shock region depends on both the convection parameter, χ, and the rotation rate. Equatorial convective modes with χ ≳ 5 are hampered by differential rotation. At smaller χ, however, mixed SASI-convective modes with a large angular scale, m = 1, 2, 3, can take advantage of rotation and become dominant for relatively low rotation rates, at which centrifugal effects are small. For rotation rates exceeding ∼30% of the Keplerian rotation at the PNS surface, a new instability regime is characterised by a frequency that, when measured in units of the post-shock velocity and radius, vsh/rsh, is nearly independent of the convection parameter, χ. A strong prograde m = 2 spiral dominates over a large parameter range and is favorable to the production of gravitational waves. In this regime, a simple linear relation exists between the oscillation frequency of the dominant mode and the specific angular momentum of the accreted gas. Conclusions. Three different regimes of post-shock instabilities can be distinguished depending on the rotation rate. For low rotation rates (less than 10% of the Keplerian rotation at the PNS surface), differential rotation has a linear destabilising effect on SASI and a quadratic stabilising or destabilising effect on the purely convective equatorial modes depending on their azimuthal wavenumber. Intermediate rotation rates (10% to 30% of the Keplerian rotation) lead to the emergence of mixed SASI-convection-rotation modes that involve large angular scales. Finally, strong rotation erases the influence of the buoyancy and heating rate on the instability. This independence allows for a reduction in the parameter space, which can be helpful for gravitational wave analysis.

Analytical Solutions to the Chavy-Waddy–Kolokolnikov Model of Bacterial Aggregates in Phototaxis by Three Integration Schemes

In this work, we find analytical solutions to the Chavy-Waddy–Kolokolnikov equation, a continuum approximation for modeling aggregate formation in bacteria moving toward the light, also known as phototaxis. We used three methods to obtain the solutions, the generalized Kudryashov method, the e−R(ξ)-expansion, and exponential function methods, all of them being very efficient for finding traveling wave-like solutions. Findings can be classified into the case where the nonlinear term can be considered a small perturbation of the linear case and the regime of instability and pattern formation. Standing waves and traveling fronts were also found among the physically interesting cases, in addition to recovering stationary spike-like solutions.