Low-frequency Instability Research Articles

Suppression of drift waves in a linear magnetized plasma column

In magnetically confined fusion plasmas, drift wave driven turbulence can lead to enhanced particle transport from the plasma. Because of this, a significant research emphasis has been placed on the suppression of drift waves in the plasma edge. However, the combination of the toroidal geometry and short plasma lifetimes can make it difficult to fully characterize the properties of these instabilities. Because linear magnetized plasma devices offer a combination of simpler geometry and steady state plasma generation, it is possible to perform detailed studies of many types of plasma instabilities—including drift waves. This paper reports on a recent experiment in which low frequency instabilities (ω ≤ ωci) in the Auburn Linear EXperiment for Instability Studies plasma device were characterized as drift waves and through changes in the parallel current, it is shown that it is possible to suppress these instabilities.

루프-스타(Loop-Star) 기저 함수와 전제 조건(Preconditioner)을 이용한 모멘트법의 계산 효율 향상에 대한 연구

본 논문에서는 전계 적분 방정식 (Electric Field Integral Equation: EFIE)을 사용하는 모멘트 법의 저주파 오차(low frequency breakdown) 문제를 해결하기 위한 방법으로 루프-스타(loop-star) 기저 함수를 사용하였다. 또한, 모멘트 법의 해를 계산하기 위하여 conjugate gradient method(CGM)과 같은 반복법을 적용할 경우 반복 횟수를 줄이기 위한 기법으로 p-Type Multiplicative Schwarz preconditioner(pMUS)를 이용하였다. 헬름홀쯔 정리(Helmholtz theorem)에 기반한 루프-스타(loop-star) 기저 함수와 주파수 정규화 기법을 이용하여 전계 적분 방정식에서 Rao-Wilton-Glisson(RWG) 기저 함수를 사용하였을 때 발생하는 저주파 오차(low frequency instability) 문제를 해결할 수 있다. 하지만, RWG 기저 함수를 비발산(solenoidal) 성분과 비회전성(irroatational) 성분으로 분해함으로써 발생하는 행렬 방정식의 높은 조건 수(condition number)로 인하여 CGM과 같은 반복법을 사용할 경우 해를 계산하기 위하여 많은 반복 횟수가 요구된다. 본 논문에서는 이러한 문제점을 해결하기 위한 방안으로 pMUS 전제 조건 기법을 이용하여 CGM의 반복 횟수를 줄였다. 수치 해석 결과, pMUS와 같은 희소성(sparsity)을 가진 블럭 대각 전제 조건(Block Diagonal Precondtioner: BDP)과 비교하였을 때 pMUS는 BDP보다 빠르게 해를 계산할 수 있다. This paper uses loop-star basis functions to overcome the low frequency breakdown problem in method of moments (MoM) based on electric field integral equation(EFIE). In addition, p-Type Multiplicative Schwarz preconditioner (p-MUS) technique is employed to reduce the number of iterations required for the conjugate gradient method(CGM). Low frequency instability with Rao Wilton Glisson(RWG) basis functions in EFIE can be resolved using loop-start basis functions and frequency normalized techniques. However, loop-star basis functions, consisting of irrotational and solenoidal components of RWG basis functions, require a large number of iterations to calculate a solution through iterative methods, such as conjugate gradient method(CGM), due to high condition number. To circumvent this problem, in this paper, the pMUS preconditioner technique is proposed to reduce the number of iterations in CGM. Simulation results show that pMUS preconditioner is much faster than block diagonal preconditioner(BDP) when the sparsity of pMUS is the same as that of BDP.

Low-Frequency Instabilities in the Interaction of Ion Beam With Magnetized Plasma

The low-frequency instabilities in the interaction between an ion beam and a magnetoactive plasma are investigated taking into account the effects of the dissipation and thermal motion of the charged particles. Furthermore, the effects of magnetic field strength, ion beam velocity, and propagation angle on the resonance frequency and the growth rate of the instabilities are studied. It is shown that, according to the strength of the magnetic field and the ion beam velocity, the increase of the thermal velocity of the charged particles can increase or decrease the resonance frequency in the ion acoustic frequency range.

Dissipative drift instability in dusty plasma

An investigation has been done on the very low-frequency electrostatic drift waves in a collisional dusty plasma. The dust density gradient is taken perpendicular to the magnetic field \documentclass[12pt]{minimal}\begin{document}$\overrightarrow{B_{0}}$\end{document}B0⃗, which causes the drift wave. In this case, low-frequency drift instabilities can be driven by \documentclass[12pt]{minimal}\begin{document}$\overrightarrow{E_{1}}\times \overrightarrow{B_{0}}$\end{document}E1⃗×B0⃗ and diamagnetic drifts, where \documentclass[12pt]{minimal}\begin{document}$\overrightarrow{E_{1}}$\end{document}E1⃗ is the perturbed electric field. Dust charge fluctuation is also taken into consideration for our study. The dust- neutral and ion-neutral collision terms have been included in equations of motion. It is seen that the low-frequency drift instability gets damped in such a system. Both dust charging and collision of plasma particles with the neutrals may be responsible for the damping of the wave. Both analytical and numerical techniques have been used while developing the theory.

Low-Frequency Combustion Instability Induced by the Combustion Time Lag of Liquid Oxidizer in Hybrid Rocket Motors

This paper deals with a theoretical analysis of the low-frequency combustion instability induced by the combustion time lag of liquid oxidizer in small-scale hybrid rocket motors. We obtained the determined linear stability limit using the following parameters: the combustion time delay of liquid oxidizer, the residence time of a combustion chamber, injector pressure, chamber pressure, mass flux exponent, O/F, and the polytropic exponent of mixture gas in a combustion chamber. Kitagawa and Yuasa sometimes observed low-frequency oscillations, such as chugging, in their swirling-oxidizer-flow-type hybrid rocket engine. The obtained theoretical stability limit was compared with these experimental data.

A unified bifurcation control strategy for voltage source inverter

There exist fast scale and slow scale nonlinear dynamic behaviors in the voltage source inverter. Period doubling bifurcation and low-frequency oscillation instability phenomena are investigated. A unified bifurcation control strategy based on frequency-domain transfer function is proposed to suppress the fast-scale and slow-scale instabilities under the guarantee of the inverter's good dynamic and static performance. The stability boundary of the inverter is greatly expanded with the help of the controller. Harmonic balance method and small-signal averaged model are used to verify the effectiveness of the proposed control method when it is used to suppress the period-doubling bifurcation and the low-frequency oscillation, the stability domain border is also derived with the help of the analysis method. Theoretical analysis and simulation results show that the proposed control strategy is correct and feasible.

Dynamic Kalman filtering to separate low-frequency instabilities from turbulent fluctuations: Application to the Large-Eddy Simulation of unsteady turbulent flows

A dynamic method based on Kalman filtering is presented to isolate low-frequency unsteadiness from turbulent fluctuations in the large-eddy simulation (LES) of unsteady turbulent flows. The method can be viewed as an adaptive exponential smoothing, in which the smoothing factor adapts itself dynamically to the local behavior of the flow. Interestingly, the proposed method does not require any empirical tuning. In practice, it is used to estimate a shear-improved Smagorinsky viscosity, in which the low-frequency component of the velocity field is used to estimate a correction term to the Smagorinsky viscosity. The LES of the flow past a circular cylinder at Reynolds number ReD = 4.7 × 104 is examined as a challenging test case. Good comparisons are obtained with the experimental results, indicating the relevance of the shear-improved Smagorinsky model and the efficiency of the Kalman filtering. Finally, the adaptive cut-off of the Kalman filter is investigated, and shown to adapt locally and instantaneously to the complex flow around the cylinder.

Global stabilities, selection of steady cellular growth, and origin of side branches in directional solidification

The present paper investigates the global instability mechanisms of arrayed-cellular growth with asymptotic approach. We find that the system of directional solidification involves two types of global instability mechanisms: the low-frequency instability and the global oscillatory instability, which are profoundly similar to that found in the system of viscous fingering and free dendritic growth. Based on these global instabilities, the neutral mode selection principle for the limiting state of growth is proposed; the origin and essence of side branching on the interface are elucidated with the so-called global trapped wave mechanism, which involves the interfacial wave reflection and amplification along the interface. It is demonstrated that side branching is self-sustaining and can persist without continuously applying the external noise; the effect of the anisotropy of interfacial energy is not essential for the selection of steady cellular growth and for the origin and formation of side branching at the interface. The comparisons of theoretical results are made with the most recent experimental works and the numerical simulations which show very good quantitative agreement.

Electron-rich sheath dynamics. II. Sheath ionization and relaxation instabilities

Instabilities in an electron-rich sheath on a plane electrode in a discharge plasma have been investigated experimentally. The high-frequency sheath-plasma instability near the electron plasma frequency is observed. With increasing dc voltage, the instability exhibits bursty amplitude and frequency jumps. The electrode current shows spikes and jumps, and the plasma potential near the electrode shows large fluctuations below the ion plasma frequency. Sheath-ionization has been identified as the cause for these low frequency instabilities. Electrons energized in the sheath produce ions which reduce the space charge in the sheath and the electric field and the ionization rate. Ions are ejected from the sheath which increases the charge density, electric field, and ionization rate. The positive feedback between these processes leads to a relaxation instability whose time scale is determined by ion inertia and ionization rates. The associated density and potential fluctuations affect the amplitude and frequency of the sheath-plasma instability. When the sheath ionization rate exceeds the ion losses, the sheath expands into an anode plasma or “fireball.” The potential drop across the sheath decreases and the sheath-plasma instability vanishes. The electrode current-voltage characteristics develop a region of negative conductance. For short grid voltage pulses, the ionization effects can be avoided.

Chugging Instability of H2O2 Monopropellant Thrusters with Reactor Aspect Ratio and Pressures

Among the three types of instabilities, the low-frequency instability (chugging instability) was experimentally investigated with respect to the chamber pressure and aspect ratio (L=D) of catalytic reactors in a monopropellant thruster. ThreeH2O2 thrusterswere used, and two parameters were found to be the dominant factors that generated a chugging instability of the order of several tens of hertz. Ahigh chamber pressure and lowL=D values (lowpressure drop across the catalyst bed) were preferable for reducing pressure oscillation inside the reaction chamber. In addition, it was found that these two parameters were not independent but coupled; therefore, the point where chugging instability occurred varied slightly depending on the interaction between these parameters.

Effects of Injector Recess and Chamber Pressure on Combustion Characteristics of Liquid–Liquid Swirl Coaxial Injectors

Combustion characteristics such as combustion performance and combustion stability have been studied experimentally using a small liquid rocket thrust chamber with 19 liquid–liquid swirl coaxial injectors. Data were obtained from static pressure, temperature, and dynamic pressure sensors installed in propellant manifolds and the combustion chamber. While changing the recess length of the injector, characteristic velocity and pressure fluctuation data were collected and analyzed. In addition, chamber pressure was varied between 42 and 54 bar, which covers the sub- and supercritical pressures of oxygen. The results show that the longer recess length generally promotes combustion performance and the spray interaction between injectors in the multielement combustor increases the characteristic velocity. When the chamber pressure is above the critical pressure of oxygen, the recess length scarcely affects the pressure fluctuation. However, when the chamber pressure is below the critical pressure, the shift from external mixing to internal mixing of oxidizer and fuel sheets by the variation of recess length significantly degrades combustion stability and induces strong low-frequency instability. Accordingly, the effects of both recess length and operating chamber pressure must be taken into consideration when designing liquid–liquid swirl coaxial injectors.

Low-frequency electromagnetic instabilities caused by a rotating dust flow

Low-frequency electromagnetic waves propagating obliquely to an external magnetic field in a plasma with an anisotropic dust component are considered. The cold dust is assumed to have considerable longitudinal and transverse velocity components with respect to the magnetic field. A dispersion relation demonstrating that both fast and slow waves can be unstable is derived in the framework of kinetic theory. Mechanisms and consequences of these instabilities are discussed in the context of the problem of plasma transition into a turbulent state behind the shock front of a supernova.

FAST MULTIPOLE BOUNDARY ELEMENT METHOD FOR LOW-FREQUENCY ACOUSTIC PROBLEMS BASED ON A VARIETY OF FORMULATIONS

The fast multipole boundary element method (FMBEM), which is an efficient BEM that uses the fast multipole method (FMM), is known to suffer from instability at low frequencies when the well-known high-frequency diagonal form is employed. In the present paper, various formulations for a low-frequency FMBEM (LF-FMBEM), which is based on the original multipole expansion theory, are discussed; the LF-FMBEM can be used to prevent the low-frequency instability. Concrete computational procedures for singular, hypersingular, Burton-Miller, indirect (dual BEM), and mixed formulations are described in detail. The computational accuracy and efficiency of the LF-FMBEM are validated by performing numerical experiments and carrying out a formal estimation of the efficiency. Moreover, practically appropriate settings for numerical items such as truncation numbers for multipole/local expansion coefficients and the lowest level of the hierarchical cell structure used in the FMM are investigated; the differences in the efficiency of the LF-FMBEM when different types of formulations are used are also discussed.

Global instability and selection of cellular array growth in solidification

The present paper investigates the global instability mechanisms of arrayed-cellular growth with asymptotic approach. We find that the system involves two types of global instability mechanisms: the low frequency (LF) instability and the global oscillatory (GTW) instability. Based on these results, the selection conditions for the limiting steady arrayed cellular and dendritic pattern formation are proposed.

Lean-limit combustion instabilities of a lean premixed prevaporized gas turbine combustor

One type of low-frequency combustion instability was studied in a lean premixed prevaporized (LPP) gas turbine combustor experiment that was operated at elevated pressures using liquid Jet-A fuel. This intense low-frequency (15 Hz) instability is called a “lean-limit” instability, while in other papers it has been called a “cold tone”, an “incipient blowout” instability or an “entropy wave”. High-speed movies identified the physical mechanism. At first the flame enters the shear layer, is locally extinguished and lifts off. The extinguished region fills with unburned reactants. Finally the premixed flame flashes back into the region of unburned reactants, leading to a large pressure rise which triggers the next cycle. The observations are in general agreement with LES computations published by Huang and Yang. Measurements quantify the time lag between the flame luminosity buildup and subsequent pressure rise as well as the correlation between these two quantities and their spectra. The frequency of this “lean-limit” instability is found to be related to the flow velocity, flame velocity, and the combustor length, as is predicted for an entropy wave. A discussion is presented to qualitatively explain the measured frequencies, which increase as the fuel equivalence ratio is raised. The experiment includes the following realistic conditions: Jet-A liquid fuel, preheated air, elevated pressure and realistic sources of instabilities, including a commercial fuel injector/mixer that creates flame–flame interactions between a non-premixed Pilot and premixed Main flame that are necessary for aircraft applications.

Nonlinear Effects Related to the Simultaneous Excitation of Three Instabiities in Magnetized Plasma

AbstractExperimental results are presented on the nonlinear effects related to the simultaneous excitation of three low‐frequency instabilities in the magnetized plasma column of a Q‐machine, namely the potential relaxation instability, the electrostatic ion‐cyclotron instability and the Kelvin‐Helmholtz instability. The influence of electron drift and magnetic field intensity on appearance, dynamics and mutual interaction of these instabilities was investigated (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Magnetohydrodynamic waves in the presence of relative motion between two populations of a plasma system

The paper investigates the role of relative motion between the fluid components of a plasma model, which is simulated by concatenation of two anisotropic magnetohydrodynamic (MHD) fluids, on the propagation of low-frequency waves and instabilities. The gyrotropic pressure of both the MHD components is given by generalized polytropic laws that allow the system to reduce to a variety of states. The linearized analysis is carried out and dispersion relation is derived using the normal mode technique. The dispersion relation, which gives numerous earlier results as special cases, is discussed both analytically as well as numerically for parameters appropriate for the space plasma. It is found that the relative motion between the two components, besides modifying the condition for fire-hose instability, causes the concatenated system to exhibit different kinds of relative ordering of the magnitudes of phase speeds of the various MHD modes in the directions parallel and antiparallel to the magnetic field. The relative motion between the components also influences the phase relationship between density and magnetic field fluctuations for the various compressive modes in the background ambient plasma.

New low-frequency waves and negative mass instability in dusty plasmas

AbstractLow-frequency dusty plasma waves with frequencies much smaller than the frequency of charging collisions of plasma particles with dust particles are considered taking into account elastic and charging collisions of plasma particles with dust and neutrals. The usual dust sound waves with an upper frequency equal to the dust plasma frequency are found to be present only for wavelengths much smaller than the plasma particle effective mean free path due to the effective collision frequency. The effectice collision frequency is found to be inversely proportional to the square root of the product of the charging frequency and the frequency of particle momentum losses, involving processes due to elastic plasma particle–dust collisions and collisions with neutrals. It is shown that when the wavelength of the wave is much larger than the mean free path for effective collisions, the properties of the waves are different from those considered previously. A negative mass instability is found in this domain of frequencies when the effective mean free path of ions is larger than the effective mean free path of electrons. In the absence of neutrals, this appears to be possible only if the temperature of ions exceeds the electron temperature. This can occur in laboratory experiments and space plasmas but not in plasma-etching experiments. In the absence of instability, a new dust oscillation, a dust charging mode, is found, whose frequency is almost constant over a certain range of wave numbers. It is inversely proportional to the dust mass and charging frequency of the dust. A new dust electron sound wave is found for frequencies less than the frequency of the dust charging mode. The velocity of the dust electron sound wave is determined by the electron temperature but not the ion temperature, as for the usual dust sound waves, with the electron temperature substantially exceeding the ion temperature.

Thermal characteristics of the wake shear layers from a slightly heated circular cylinder

In this paper, we investigate the thermal characteristics of wake shear layers generated by a slightly heated circular cylinder. Measurements of the fluctuating temperature were made in the region x/d = 0.6 to x/d = 3 (where x is the downstream distance from the cylinder axis and d is the cylinder diameter) using a single cold-wire probe. The Reynolds number Re was varied in the range 2,600–8,600. For Re = 5,500, simultaneous measurements were made with a rake of 16 cold wires, aligned in the direction of the mean shear, at x/d = 2 and 3. The results indicate that the passive temperature can be an effective marker of various instabilities of the wake shear layers, including the Kelvin–Helmholtz (KH) instability. The temperature data have confirmed the approximate Rem dependence of the KH instability frequency (fKH) with different values of m over different ranges of Re, as reported previously in the literature. However, it is found that this power-law dependence is not exact, and a third-order polynomial dependence appears to fit the data well over the full range of Re. Importantly, it is found that the wake shear-layer instabilities can be grouped into three categories: (1) one with frequencies much smaller than the Benard–Karman-vortex shedding frequency, (2) one associated with the vortex shedding and (3) one related to the KH instability. The low-frequency shear-layer instabilities from both sides of the cylinder are in-phase, in contrast to the anti-phase high-frequency KH instabilities. Finally, the observed streamwise decrease in the mean KH frequency provides strong support for the occurrence of vortex pairing in wake shear layers from a circular cylinder, thus implying that both the wake shear layer and a mixing layer develop in similar fashion.

Electromagnetic Scattering From Dispersive Dielectric Scatterers Using the Finite Difference Delay Modeling Method

A new method for solving the time-domain integral equations of electromagnetic scattering from dispersive dielectric bodies is proposed. The method is based on the finite difference delay modeling scheme, which accomplishes the temporal discretization by substituting a <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</i> -domain finite-difference approximation for the continuous time Laplace domain <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</i> parameter. The inverse <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</i> -transform used for computing the temporal kernels is calculated numerically using the trapezoidal rule and inverse discrete Fourier transform. Arbitrary dispersive models can be simulated without extraneous convolution using the new technique. The normal field equations are augmented to the standard tangential equations to solve the low-frequency instability problem.