Aperiodic Instability Research Articles

PARAMETERS OF THE PERTURBED STATE OF THE DENDRITE TIP IN DEEPLY SUPERCOOLED NICKEL AND COPPER MELTS

The object of study is the morphological stability of the tip of a free dendrite in a supercooled melt of a pure substance. Areas of deep supercooling are considered: for nickel DT > 166 K, for copper – DT > 180 K. A distinctive feature of the processes being studied is the presence of two propagation velocities of small disturbances (velocities of “sound”). The dependences of these rates on the supercooling of the melt were determined. The periodic and coordinate-aperiodic modes of perturbation of the growth line have been studied in detail. For these stable regimes, the possibility of observing the same speed of the disturbance wave in two processes, differing from each other in the size of the spatial inhomogeneity of the background in front of the wave and the characteristic wave attenuation times, was discovered. It is shown that aperiodic instability appears if, after the passage of the wave front, the width of the growth line inhomogeneity zone decreases. The resonant excitation mode of the dendrite tip demonstrates important differences between the properties of the nickel and copper melts. First of all, this relates to the temperature dependences of the resonant frequency and the speed of a standing wave formed in the vicinity of the vertex. Numerical calculations are presented and graphic information is presented illustrating the patterns of growth of nickel and copper dendrites.

Transient DC-link voltage oscillation stability assessment of VSC-HVDC systems using Lyapunov direct method

Lyapunov direct method is utilized in this paper to reveal the transient voltage oscillation stability mechanism for VSC-HVDC systems. Firstly, a reduced analytical nonlinear model for transient voltage oscillation stability assessment is proposed, which is a Liénard system. Based on the proposed model, a novel Lyapunov function is constructed and the conservative stability boundary is depicted, which reveals that the transient voltage oscillation can be well damped when the operating points are within the domain of asymptotic stability. In addition, it is found that there exists one limit cycle for VSC-HVDC systems. Once any system operation point exceeds the limit cycle, the divergent oscillations are triggered, and the aperiodic instability will eventually appear if the perturbations failed to be cleared in time. Finally, according to the limit cycle theory, one sufficient instability condition is derived and the transient voltage instability risk of the VSC-HVDC systems can be well evaluated.

Influence of Electron Collisions on Electromagnetic Modes of Plasma Produced by Multi-Photon Ionization of an Inert Gas

Collective electromagnetic modes in weakly ionized plasma formed by multiphoton ionization of inert gas atoms, in which the Ramsauer–Townsend effect takes place, are studied. It is shown that at a relatively low energy of photoelectrons of the order of 1 eV, typical for multiphoton ionization, amplification of electromagnetic waves is possible. Amplification is possible both in the case of rare collisions of photoelectrons with neutral atoms and for collision frequencies higher than electron plasma frequency. At photoelectron energies somewhat higher than 1 eV, aperiodic instability can develop with growth rate whose value is comparable to electron plasma frequency. Detailed analytical and numerical analysis of the effect of collisions of photoelectrons with neutral atoms on the dispersion law of electromagnetic wave and the growth rates of instabilities is presented.

The aperiodic firehose instability of counter-beaming electrons in space plasmas

Context.Recent studies have revealed new unstable regimes of the counter-beaming electrons specific to hot and dilute plasmas from astrophysical scenarios: an aperiodic firehose-like instability is induced for highly oblique angles of propagation relative to the magnetic field, resembling the fast growing and aperiodic mode triggered by the temperature anisotropyT∥ > T⊥(where ∥, ⊥ denote directions relative to the magnetic field).Aims.The counter-beaming electron firehose instability is investigated here for space plasma conditions, which include not only a specific plasma parameterization but, in particular, the influence of an embedding background plasma of electrons and ions (protons).Methods.We applied fundamental plasma kinetic theory to prescribe the unstable regimes, characterize the wave-number dispersion of the growth rates, and differentiate from the regimes of interplay with other instabilities. We also used numerical particle-in-cell (PIC) simulations to confirm the instability of these aperiodic modes, and their effects on the relaxation of counter-beaming electrons.Results.Linear theory predicts a systematic inhibition of the (counter-)beaming electron firehose instability (BEFI) by reduction of the growth rates and the range of unstable wave-number with increasing relative density of the background electrons. To obtain finite and reasonably high values of the growth rate, the (relative) beam speed does not need to be very high (just comparable to the thermal speed), but the (counter-)beams must be dense enough, with a relative density of at least 15%–20% of the total density. Quantified in terms of the beam speed and the beta parameter, the plasma parametric conditions favorable to this instability are also markedly reduced under the influence of background electrons. Numerical simulations confirm not only that BEFI can be excited in the presence of background electrons, but also the inhibiting effect of this population, especially when this latter is cooler. In the regimes of transition to electrostatic (ES) instabilities, BEFI is still robust enough to develop as a secondary instability, after the relaxation of beams under a quick interaction with ES fluctuations.Conclusions.To the features presented in previous studies, we can add that BEFI resembles the properties of solar wind firehose heat-flux instability triggered along the magnetic field by the anti-sunward electron strahl. However, BEFI is driven by a double (counter-beaming) electron strahl, and develops at highly oblique angles, which makes it potentially effective in the regularization and relaxation of the electron counter-beams observed in expanding coronal loops (with closed magnetic field topology) and in interplanetary shocks.

Comparing the Counter-beaming and Temperature Anisotropy Driven Aperiodic Electron Firehose Instabilities in Collisionless Plasma Environments

The electron firehose instabilities are among the most studied kinetic instabilities, especially in the context of space plasmas, whose dynamics is mainly controlled by collisionless wave–particle interactions. This paper undertakes a comparative analysis of the aperiodic electron firehose instabilities excited either by the anisotropic temperature or by the electron counter-beaming populations. Two symmetric counter-beams provide an effective kinetic anisotropy similar to the temperature anisotropy of a single (nondrifting) population, with the temperature along the magnetic field direction larger than that in the perpendicular direction. Therefore, the counter-beaming plasma is susceptible to firehose-like instabilities (FIs), parallel and oblique branches. Here we focus on the oblique beaming FI, which is also aperiodic when the free energy is provided by symmetric counter-beams. Our results show that, for relative small drifts or beaming speeds (U), not exceeding the thermal speed (α), the aperiodic FIs exist in the same interval of wavenumbers and the same range of oblique angles (with respect to the magnetic field direction), but the growth rates of counter-beaming FI (CBFI) are always higher than those of temperature anisotropy FI (TAFI). For U/α > 1, however, another electrostatic two-stream instability is also predicted, which may have growth rates higher than those of CBFI, and may dominate in that case the dynamics.

Electron mirror and cyclotron instabilities for solar wind plasma

ABSTRACT The solar wind plasma is characterized by unequal effective kinetic temperatures defined in perpendicular and parallel directions with respect to the ambient magnetic field. For electrons, the excessive perpendicular temperature anisotropy leads to quasi-parallel electromagnetic electron cyclotron (or whistler) instability and aperiodic electron-mirror instability with oblique wave vectors. The present paper carries out a direct side-by-side comparison of quasi-linear (QL) theory and particle-in-cell (PIC) simulation of combined mirror and cyclotron instabilities acting upon the initially anisotropic electron temperatures, and find that the QL theory satisfactorily encapsulates the non-linear aspect of the combined instability effects. However, a discrepancy between the present study and a previous PIC simulation result is also found, which points to the need for further investigation to resolve such an issue.

Effect of Nonreciprocal Forces on the Stability of Dust Clusters

Results are presented from studies of the stability of the plane dust clusters in the form of a regular polygon with the number of particles from two to five. It is assumed that the particles are placed in the plasma consisting of Maxwellian electrons and a directed flow of cold ions. It is shown that, in such clusters, the oscillatory instabilities can develop along with the aperiodic instabilities. The ranges of plasma parameters are determined, within which the oscillatory instability of the five-particle cluster becomes saturated at the weakly nonlinear stage. As a result, the cluster forms a time crystal, which can be a chiral crystal.

Longitudinal electron waves and instability of collisional plasma formed by multiphoton ionization of gas atoms

Longitudinal collective modes in plasma produced by multiphoton ionization of inert gas atoms are studied. The high-frequency and the low-frequency modes in Xe plasma are considered in detail. It is shown that due to the Ramsauer–Townsend effect, photoelectron collisions with neutral atoms lead to a significant increase in decrement of high-frequency mode in the long-wavelength region where this mode frequency is close to the electron Langmuir one. In the region of wave numbers larger than the ratio of electron Langmuir frequency to photoelectrons average velocity, the dispersion law of high-frequency mode is close to the dispersion law of electron acoustic wave, the phase and the group velocities of which are close to photoelectrons' average velocity. In this case, the acoustic wave is weakly damped even for photoelectrons' collision frequencies comparable to electron Langmuir frequency. There is a low-frequency mode along with the high-frequency one. In the region of relatively small wave numbers, this mode describes aperiodic instability with the growth rate not exceeding half of the electron Langmuir frequency. The instability is caused by the Ramsauer–Townsend effect. As the wave number increases, the low-frequency mode transforms into a longitudinal wave, the amplitude of which increases with time. In the region of wave numbers greater than the ratio of photoelectron average velocity to electron Langmuir frequency, the low-frequency wave is strongly damped due to photoelectron collisions. Influence of the spread of photoelectrons in energy on the low-frequency mode is relatively small. In contrast, a finite width of photoelectron distribution over energy leads to significant collisionless damping of high-frequency wave in the short-wavelength region.

Nonlinear Dynamics of a Linear Dust Particle Chain

The nonlinear stage of development of the dust particle chain instabilities is studied. It is assumed that dust particles interact with the plasma consisting of Maxwellian electrons and a directed flow of cold ions. The truncated equations are derived describing the nonlinear dynamics of the standing wave in the range of parameters close to the threshold for the development of the instability of coupled waves. It is shown that, in a narrow range of the ion flow Mach numbers, the instability of coupled waves becomes saturated in the weakly nonlinear stage of its development. In the remaining cases, the instability development becomes explosive. The nonlinear dynamics is also considered of the aperiodic period-doubling instability, which always becomes saturated in the weakly nonlinear stage of its development.

Voltage stability assessment accounting for current-limited converters

This paper investigates how current-limited converters influence system stability. An improved approach for assessing voltage stability is introduced, which determines the maximum deliverable power to a load by accounting for changes in the Thévenin voltages. The new approach is able to detect voltage instability well before the traditional approach based on Thévenin impedance matching. A new stability boundary is discovered that describes the aperiodic small signal stability boundary for current-limited converters. The improved approach was modified to account for current-limited converters. The detection of voltage and rotor angle instability during current limitation were demonstrated on a seven bus system, where test cases were performed. The test cases showed that voltage instability can lead to aperiodic small signal instability, when the converter has reached its current limit and loss of synchronism in the unstable region during current-limitation causes the system voltages to collapse.

A firehose-like aperiodic instability of counter-beaming electron plasmas

Depending on the physical conditions involved, beam plasma systems may reveal new unstable regimes triggered by wave instabilities of different natures. We show through linear theory and numerical simulations the existence of an aperiodic electromagnetic instability which solely develops and controls the stability of two symmetric plasma populations counter-moving along the regular magnetic field with a relative drift, vd, small enough to not exceed the particle thermal speed, αe. Emerging at highly oblique angles this mode resembles properties of the aperiodic firehose instability driven by temperature anisotropy. The high growth rates achieved with increasing the relative drift or/and decreasing the plasma beta parameter lead to significant saturation levels of the fluctuating magnetic field power, which explain the relatively fast relaxation of electrons. For this instability can coexist with the electrostatic two-stream instability, dominating the long-term dynamics of the plasma as soon as vd has relaxed to values smaller than the thermal speed.

Stability of a Planar Plasma Crystal

The stability of a planar plasma crystal in an external confining force field is investigated. Particles are assumed to be located in the plasma with Maxwellian electrons and with a directed flow of cold ions. It is shown that, together with the coupled wave instability, four more types of aperiodic instabilities arise, which lead to the formation of different structures. A region of the crystal stability in the space of external parameters is constructed.

Stability of a Linear Plasma Crystal

The stability of a linear chain of dust particles in an external confining force field is studied. It is assumed that the particles are located in a plasma with Maxwellian electrons with a directed flow of cold ions. It is shown that the aperiodic instability of doubling the chain period can develop in a subsonic flow together with the instability of coupled waves. The region of the crystal stability in the space of external parameters is constructed.

Collective modes of plasma formed by multiphoton ionization of rarefied gas

High-frequency collective modes in plasma with strongly anisotropic velocity distribution of photoelectrons formed by multiphoton or above-threshold ionization of gas atoms are studied. In the case of multiphoton ionization, along with the usual electromagnetic wave, there are two additional modes. In the region of large wavelengths, the higher-frequency mode is similar to the electron Langmuir wave. Its group velocity is mainly determined by the average photoelectron velocity, and Cherenkov damping is due to small velocity dispersion of photoelectron distribution. In the region of short waves, but with a small Cherenkov damping, the group and phase velocities of this wave are close to the average electron velocity. The second mode, which has lower frequency, in the region of wavelengths smaller than the ratio of average electron velocity to the plasma frequency, corresponds to quasi-potential wave. Its dispersion law is close to the linear one. In contrast, in the region of large wavelengths, this mode corresponds to aperiodic instability, the maximum growth rate of which is comparable to the plasma frequency. The distribution of photoelectrons formed during above-threshold ionization is characterized by the large number of energy peaks, which is accompanied by increasing in the number of collective modes. In particular, in plasma with photoelectron distribution which has two energy peaks, in addition to the electromagnetic mode four extra modes are possible. In the shortwave region, all four modes correspond to the waves that are damped due to Cherenkov interaction with photoelectrons. Two of these modes in the region of relatively long wavelengths are unstable. One of these unstable modes corresponds to quasi-potential wave whose amplitude aperiodically increases with time. The reason for the instabilities is the presence of counter streams of photoelectrons.

Convolutional neural network-based power system transient stability assessment and instability mode prediction

Online transient stability assessment (TSA) is vital for power system control as it provides the basis for operators to decide emergency control actions. But none of previous TSA research has taken into consideration the difference between two instability modes (aperiodic instability and oscillatory instability), which may threaten secure operation of power system. To address this problem, a TSA and instability mode prediction method based on convolutional neural network is proposed. The method takes the bus voltage phasor sampled by phasor measurement units (PMUs) during a short observation window after disturbance as input, and outputs the prediction result promptly: stable, aperiodic unstable or oscillatory unstable. The end-to-end model automatically extracts needed features from the raw measurement data, thus freeing itself from reliance on expertise. At the offline training stage, stochastic gradient descent with warm restart (SGDR) optimization algorithm is employed so that the model tends to converge to 'flat' and 'wide' minima with better generalization ability. Case studies conducted on New England 39-bus system and Western Electricity Coordinating Council (WECC) 179-bus system demonstrate superior accuracy, adaptability and scalability of the proposed method compared with conventional machine learning methods. Furthermore, the proposed model is empirically proven to be robust to PMU noise and loss.

Simulation studies of temperature anisotropy driven pair-Alfvén and aperiodic instabilities in magnetized pair plasma

We compare with one-dimensional particle-in-cell simulations the aperiodically growing instabilities driven by a bi-Maxwellian velocity distribution in unmagnetized electron plasma (Weibel instability) and in pair plasma. The simulation box is aligned with the cool direction. The waves in both simulations evolve towards a circularly polarized non-propagating magnetic structure. Its current and magnetic field are aligned and the structure is in a force-free state. We examine how a background magnetic field B0, which is parallel to the simulation direction, affects the waves in the pair plasma. A weak B0 cannot inhibit the growth of the aperiodically growing instability but it prevents it from reaching the force-free stable state. The mode collapses and seeds a pair Alfvén waves. An intermediate B0 couples the thermal anisotropy to the pair Alfvén mode and propagating magnetowaves grow. The phase speed of the pair of Alfvén waves is increased by the thermal anisotropy. Its growth is suppressed when B0 is set to the value that stabilizes the mirror mode.

Analysis of similarity criteria for experimental models and equipment of nuclear plant safety systems

A criterial method is proposed for analyzing the adequacy of real pipeline systems with pumps of nuclear power plants and experimental installations. The method is based on an analysis of the identity of the determining criteria for the similarity of hydrodynamic processes in real and experimental conditions. The criteria for similarity of real and experimental conditions and conditions of water hammer for pipeline systems with pumps of nuclear power plants in transient and operating modes are determined. Water hammers in transient regimes are a consequence of aperiodic hydrodynamic instability of the flow; and in operating conditions - a consequence of oscillatory hydrodynamic instability. The determining factor of hydrodynamic oscillatory instability is the inertia of the pressure-supply characteristic of pumps. On the basis of the proposed method, an example of the practical application of the similarity criteria obtained for real active safety systems and an experimental plant A.V. Korolev is presented. It is shown that the necessary conditions for identicality of similarity criteria are not met and extrapolation of the results of known experiments to real conditions of active safety systems of nuclear installations with WWER reactors is not justified.

Water Hammers in Transonic Modes of Steam-Liquid Flows in NPP Equipment

The analysis of well-known studies in modelling conditions for water hammers in equipment and components of pipeline systems has revealed that definition of conditions and parameters of water hammers in the transonic modes of single- and two-phase flows (at a speed of propagation of acoustic disturbances) is the least studied problem.
 The original method is proposed for determining the conditions and parameters of water hammers in transonic flow modes subject to the transition of the kinetic energy of the flow stagnation into the energy of the water hammer pulse.
 It was found that the simulated hydrodynamic loads in transonic modes can significantly exceed the corresponding known recommendations of N. Zhukovsky.
 The proposed method of equations computer modelling served to determine the criteria range for water hammers due to aperiodic thermohydrodynamic instability in transonic flow modes.

Particle-in-cell Simulations of Firehose Instability Driven by Bi-Kappa Electrons

Abstract We report the first results from particle-in-cell simulations of the fast-growing aperiodic electron firehose instability driven by the anisotropic bi-Kappa distributed electrons. Such electrons characterize space plasmas, e.g., solar wind and planetary magnetospheres. Predictions made by the linear theory for full wave-frequency and wave-vector spectra of instabilities are confirmed by the simulations showing that only the aperiodic branch develops at oblique angles with respect to the magnetic field direction. Angles corresponding to the peak magnetic field fluctuating power spectrum increase with the increase in the anisotropy and with the decrease in the inverse power-law index κ. The instability saturation and later nonlinear evolutions are also dominated by the oblique fluctuations, which are enhanced by the suprathermals and trigger a faster relaxation of the anisotropic electrons. Diffusion in velocity space is stimulated by the growing fluctuations, which scatter the electrons, starting with the more energetic suprathermal populations, as appears already before the saturation. After saturation the fluctuating magnetic field power shows decay patterns in the wave-vector space and a shift toward lower angles of propagation.

Nonlinear structures of lower-hybrid waves driven by the ion beam

The lower-hybrid waves can be driven unstable by the transverse ion beam in a partially magnetized plasma of a finite length. This instability mechanism, which relies on the presence of fixed potential boundary conditions, is of particular relevance to axially propagating modes in a Hall effect thruster. The linear and nonlinear regimes of this instability are studied here with numerical simulations. In the linear regime, our results agree with analytical and numerical eigenvalue analysis conducted by Kapulkin and Behar [IEEE Trans. Plasma Sci. 43, 64 (2015)]. It is shown that in nonlinear regimes, the mode saturation results in coherent nonlinear structures. For the aperiodic instability [with Re(ω)=0—odd Pierce zones], the unstable eigen-function saturates into new stationary nonlinear equilibrium. In the case of oscillatory instability [Re(ω)≠0—even Pierce zones], the instability results in the nonlinear oscillating standing wave. It is also shown that finite Larmor radius effects stabilize instability for parameters corresponding to a large number of Pierce zones, and therefore, only few first zones remain relevant.