Azimuthal Wave Research Articles

A theoretical investigation of the presence of the azimuthal backward waves (ABWs) and their amplification in a magnetized plasma waveguide with two annular rotating energy sources

In this paper, the azimuthal backward waves (ABWs) in a magnetized plasma waveguide are studied. The waveguide is made of the loss-free metallic cylindrical wall and a dielectric annular layer and a magnetized plasma column in it. There are two annular rotating electron beams as the energy sources in the waveguide. The inner annular rotating electron beam (IAREB) is in the plasma region and the outer annular rotating electron beam (OAREB) is on the dielectric layer. The generation of ABWs as a possible consequence of the presence of two annular electron beams is proved by using Poynting’s theorem in the mentioned configuration. Also, it is observed that the width of allowed and forbidden frequencies of ABWs in the considered waveguide can be enhanced and shifted to the higher frequency side by changing the fundamental physical parameters. In addition, the effective factors on the frequency spectrum and growth rate of ABWs such as the geometric dimensions, the dielectric constant of the dielectric layer and electron plasma frequency of the annular electron beams are studied.

Non-classical electron transport in the cathode plume of a Hall effect thruster

An experimental investigation is presented into the wave-driven electron transport in the near-field plume of a hollow cathode operating in a 300 V, 4.5 kW magnetically shielded Hall thruster. Correlational analysis of probe measurements in the cathode plume shows two types of electrostatic waves: ion acoustic turbulence propagating along the applied longitudinal magnetic field at frequencies from 500 to 1250 kHz and coherent, azimuthal anti-drift waves with a fundamental frequency of 95 kHz and mode numbers from m=1−4. A quasilinear analysis is applied to quantify the impact of each wave on the electron transport in the near-field plume. It is found that the ion acoustic modes give rise to an enhanced effective collision frequency in the direction parallel to the applied magnetic field that exceeds the classical collision frequency by two orders of magnitude. The anti-drift waves promote an anisotropic collision frequency that depends on the direction of the electron drift. While the enhanced collision frequency from these waves is comparable to the classical frequency for motion along the applied magnetic field, the effective collision frequency in the azimuthal direction exceeds the classical by three orders of magnitude. These results are discussed in the context of their impact on the steady-state plasma gradients in the near-field cathode plume. Closure models for incorporating the effective collision frequencies from both types of waves into fluid-based codes are derived and shown to agree with the measured wave-driven collision frequencies.

Selective Acceleration of O+ by Drift‐Bounce Resonance in the Earth's Magnetosphere: MMS Observations

AbstractWe studied O+ drift‐bounce resonance using Magnetospheric Multiscale (MMS) data. A case study of an event on 17 February 2016 shows that O+ flux oscillations at ~10–30 keV occurred at MLT ~ 5 hr and L ~ 8–9 during a storm recovery phase. These flux oscillations were accompanied by a toroidal Pc5 wave and a high‐speed solar wind (~550 km/s). The azimuthal wave number (m‐number) of this Pc5 wave was found to be approximately −2. The O+/H+ flux ratio was enhanced at ~10–30 keV corresponding to the O+ flux oscillations without any clear variations of H+ fluxes, indicating the selective acceleration of O+ ions by the drift‐bounce resonance. A search for similar events in the time period from September 2015 to March 2017 yielded 12 events. These events were mainly observed in the dawn to the afternoon region at L ~ 7–12 when the solar wind speed is high, and all of them were simultaneously identified on the ground, indicating low m‐number. Correlation analysis revealed that the O+/H+ energy density ratio has the highest correlation coefficient with peak power of the electric field in the azimuthal component (Ea). This statistical result supports the selective acceleration of O+ due to the N = 2 drift‐bounce resonance.

Experimental study of a free-surface circular liquid sheet using planar laser-induced fluorescence

This work presents an experimental study of various spatiotemporal events leading to the primary atomization of a radially expanding circular liquid sheet. A cylindrical liquid (water) jet orthogonally made to impinge on the horizontally placed cone-disc deflector to produce a thin free-surface circular liquid sheet from the peripheral edge of the deflector disc. High-speed planar laser-induced fluorescence (PLIF) at 6 kHz framing rate was carried out to capture the atomizing liquid sheet in the side and front views at various jet Weber numbers ($${\text{We}}_{{{\text{jet}}}}$$) over a range of 994 < $${\text{We}}_{{{\text{jet}}}}$$ < 8029. The side view PLIF comprising of three fields of view to capture the complete atomization process of expanding liquid sheet in a time-resolved manner starting from capturing radial wave features on liquid sheet down to the sheet breakup, ligament formation, and droplet production. The azimuthal wave features were captured in the front view PLIF experiments. The quantitative information of different spatiotemporal features was extracted from experimental data using rigorous image processing methods. Advanced feature extraction and transient analysis methods like proper orthogonal decomposition (POD) was applied to obtain the dominant flow features associated with sheet dynamics. The POD analysis showed that the most dominant phenomenon in the flow field for $${\text{We}}_{{{\text{jet}}}}$$ < 1500 is found to be the oscillation of the liquid sheet, the radial wave propagation in the radial direction for 1500 ≤ $${\text{We}}_{{{\text{jet}}}}$$ < 2000, and sheet breaks up at the outer edge for $${\text{We}}_{{{\text{jet}}}}$$ ≥ 2000. It is shown that the dominancy of each of these phenomena changes with $${\text{We}}_{{{\text{jet}}}}$$. Statistical analysis-based ligament length and thickness ($$L_{{{\text{lig}}}}$$ and $$t_{{{\text{lig}}}}$$) follow $${\text{We}}_{{{\text{jet}}}}^{ - 0.6}$$ and droplet diameter ($$D_{32}$$ and $$D_{10}$$) follow $${\text{We}}_{{{\text{jet}}}}^{ - 0.33}$$ power law. Further, the direct correlations obtained showed that the droplet diameter is a stronger function of ligament thickness compared to ligament length. Schematic of optics, laser light and camera arrangements for side view PLIF experiments of a circular liquid sheet. Three FOVs adopted for side view PLIF experiments at different radial locations; RA= 280 mm for A = 100 mm × 100 mm, RB = 360 mm for B = 80 mm × 80 mm, and RC = 420 mm for C = 40 mm × 40 mm Direct imaging of azimuthal waves of liquid sheet using front view PLIF experimental technique

Instability of a horizontal water half-cylinder under vertical vibration

We present the results of an experimental investigation on parametrically driven waves in a water half-cylinder on a rigid horizontal plate, which is sinusoidally vibrated in the vertical direction. As the forcing amplitude is raised above a critical value, stationary waves are excited in the water half-cylinder. Parametrically excited subharmonic waves are non-axisymmetricand qualitatively different from the axisymmetric Savart-Plateau-Rayleigh waves in a vertical liquid cylinder or jet. Depending on the driving frequency, stationary waves of different azimuthal wave numbers are excited. A linear theory is also supplemented, which captures the observed dispersion relations quantitatively.

Real Time Inversion and Field Test of LWD Azimuthal Electromagnetic Waves Based on Quasi-Newton Method

In order to determine the formation interface azimuth and distance by using the data measured by LWD azimuthal electromagnetic wave resistivity logging instrument using the quasi-Newton inversion algorithm.The objective was provide a decision-making basis for geosteering,an accurate and reliable inversion method must be used.For the LWD azimuthal electromagnetic wave resistivity logging instrument,an application model of geological guidance has been established and simulated its response characteristics.By studying the quasi-Newton inversion algorithm and process,the Jacobian matrix was obtained with less calculation cost in the inversion process,which greatly speeds up the inversion.At the same time,the correctness and accuracy of this algorithm were verified by using the theoretical inversion model including both single interface and a double interface strata model.The field test of Well Cao-XX in Shengli Oilfield showed that the real-time inversion results were consistent with the imaging display of azimuthal electromagnetic wave resistivity and also with the drilling/completion/logging results in later stages.This inversion method can meet the requirements of real time geo-steering by efficient and accurate calculation of azimuthal electromagnetic wave resistivity.

Ballooning Instability in the Magnetospheric Plasma: Two‐Dimensional Eigenmode Analysis

AbstractThis paper is concerned with the transverse structure of the ballooning instability in a two‐dimensionally inhomogeneous model of the magnetosphere, which takes into account inhomogeneity both across the magnetic shells and along the field lines. According to the previous studies, the ballooning instability can develop at steep fall of the plasma pressure from the Earth. In this paper, the region of negative plasma pressure gradient is assumed to be sharply localized across the magnetic shells. It causes the localization of the unstable perturbation in the same direction. In this region, the perturbation has a resonator‐like structure, where only modes with discrete set of the growth rate values can exist. The azimuthal wave number of the unstable mode must exceed some critical value, which is determined by the width of the localization region.

Смещения предела устойчивости течения при модуляции скорости вращения

The possibilities of the control of stability limit location were experimentally investigated in spherical Couette flow. The inner sphere rotational rate is periodically varied about non-zero average value, the outer sphere is fixed. Instability in the form of travelling azimuthal waves, the same as at stationary rotation, is caused by increasing of average rotational rate. Flow velocity measurements were carried out by laser Doppler anemometer. It was shown, that when modulation frequency become close to eigenfrequency of linear mode, both flow destabilization and stabilization were possible depending on modulation amplitude.

Electromagnetic energy rotation along plasma-dielectric interface caused by azimuthal surface waves in isotropic cylindrical metallic waveguide

Electromagnetic energy rotation around the axis of cylindrical metallic waveguides partially filled by isotropic plasma is studied. Angular phase velocity and angular velocity of energy transfer are analyzed as functions of the plasma waveguide parameters: plasma column radius, plasma particle density, azimuthal wavenumber, dielectric layer width and dielectric constant, and collision frequency. This study generalizes the results obtained earlier in the case of the wave propagation in two-component plasma-metal structures (cylindrical metallic waveguides entirely filled by magnetoactive plasma) to the case of three-component plasma-dielectric-metal structures.

Eastward Propagating Second Harmonic Poloidal Waves Triggered by Temporary Outward Gradient of Proton Phase Space Density: Van Allen Probe A Observation

AbstractTwo wave packets of second harmonic poloidal Pc 4 waves with a wave frequency of ~7 mHz were detected by Van Allen Probe A at a radial distance of ~5.8 RE and magnetic local time of 13 hr near the magnetic equator, where plasmaspheric refilling was in progress. Proton butterfly distributions with energy dispersions were also measured at the same time; the proton fluxes at 10–30 keV oscillated with the same frequency as the Pc 4 waves. Using the ion sounding technique, we find that the Pc 4 waves propagated eastward with an azimuthal wave number (m number) of ~220 and ~260 for each wave packet, respectively. Such eastward propagating high‐m (m &gt; 100) waves were seldom reported in previous studies. The condition of drift‐bounce resonance is well satisfied for the estimated m numbers in both events. Proton phase space density was also examined to understand the wave excitation mechanism. We obtained temporal variations of the energy and radial gradient of the proton phase space density and find that temporal intensification of the radial gradient can generate the two wave packets. The cold electron density around the spacecraft apogee was &gt;100 cm−3 in the present events, and hence the eigenfrequency of the Pc 4 waves became lower. This causes the increase of the m number which satisfies the resonance condition of drift‐bounce resonance for 10–30 keV protons and meets the condition for destabilization due to gyrokinetic effect.

Azimuthal capillary waves on a hollow filament – the discrete and the continuous spectrum

We study the temporal spectrum of linearised, azimuthal, interfacial perturbations imposed on a cylindrical gaseous filament surrounded by immiscible, viscous, quiescent fluid in radially unbounded geometry. Linear stability analysis shows that the base state is stable to azimuthal perturbations of standing wave form. Normal mode analysis leads to a viscous dispersion relation and shows that in addition to the discrete spectrum, the problem also admits a continuous spectrum. For a given azimuthal Fourier mode and Laplace number, the discrete spectrum yields two eigenfunctions which decay exponentially to zero at large radii and thus cannot represent far field perturbations. In addition to these discrete modes, we find an uncountably infinite set of eigenmodes which decay algebraically to zero. The completeness theorem for perturbation vorticity may be expressed as a sum over the discrete modes and an integral over the continuous ones. We validate our normal mode results by solving the linearised, initial value problem (IVP). The initial perturbation is taken to be an interfacial, azimuthal Fourier mode with zero perturbation vorticity. It is shown that the expression for the time dependent amplitude of a capillary standing wave (in the Laplace domain, ) has poles and branch points on the complex plane. We show that the residue at the poles yields the discrete spectrum, while the contribution from either side of the branch cut provides the continuous spectrum contribution. The particular initial condition treated here in the IVP, has projections on the discrete as well as the continuous spectrum eigenmodes and thus both sets are excited initially. Consequently the time evolution of the standing wave amplitude and the perturbation vorticity field have the form of a sum over discrete exponential contributions and an integral over a continuous range of exponential terms. The solution to the IVP leads to explicit analytical expressions for the standing wave amplitude and the vorticity field in the fluid outside the filament. Linearised analytical results are validated using direct numerical simulations (DNS) conducted using a code developed in-house for solving the incompressible, Navier–Stokes equations with an interface. For small perturbation amplitude, analytical predictions show excellent agreement with DNS. Our analysis complements and extends earlier results on the discrete and the continuous spectrum for interfacial viscous, capillary waves on unbounded domain.

On the stability of the Couette–Taylor flow between rotating porous cylinders with radial flow

We study the stability of the Couette-Taylor flow between porous cylinders with radial throughflow. It had been shown earlier that this flow can be unstable with respect to non-axisymmetric (azimuthal or helical) waves provided that the radial Reynolds number, $R$ (constructed using the radial velocity at the inner cylinder and its radius), is high. In this paper, we present a very detailed and, in many respects, novel chart of critical curves in a region of moderate values of $R$, and we show that, starting from values of $R$, as low as $10$, the critical modes inherited from the inviscid instability gradually substitute the classical Taylor vortices. Also, we have looked more closely at the effect of a weak radial flow (relatively low $R$) on the Taylor instability and found that a radial flow directed from the inner cylinder to the outer one is capable of stabilizing the Couette-Taylor flow provided that the gap between the cylinders is wide enough. This observation is in a sharp contrast with the case of relatively narrow gaps for which the opposite effect is well-known.

Numerical study on wide gap Taylor Couette flow with flow transition

This study aims to investigate the possible sources of nonaxisymmetric disturbances and their propagation mechanism in Taylor Couette flow for wide gap problems using a direct numerical simulation with a radius ratio of 0.5 and the Reynolds number (Re) ranging from 60 to 650. Here, attention is focused on the viscous layer (VL) thickness in near-wall regions and its spatial distribution along the axial direction to gain an insight into the origin and propagation of nonaxisymmetric disturbances. The results show that an axisymmetric Taylor-vortex flow occurs when Re is between 68 and 425. Above Re = 425, transition from axisymmetric to nonaxisymmetric flow is observed up to Re = 575 before the emergence of wavy-vortex flow. From the variation of VL thickness with Re, the VL does not experience any significant changes in the flow separation region of the inner wall, as well as jet impingement region of both the inner and outer walls. However, a sudden increase in VL thickness in the flow separation region of the outer wall reveals possible sources of nonaxisymmetric disturbances in the flow separation region of the outer wall. These disturbances develop into the periodic secondary flow as the axisymmetric flow transforms into nonaxisymmetric flow, and this leads to the emergence of the azimuthal wave. The periodic secondary flow contributes to a sudden increase in the natural wavelength and rapid reduction in the strength of two counter-rotating Taylor vortices. This in turn leads to a substantial reduction of torque in the transition flow vis-à-vis axisymmetric Taylor-vortex flow.

Acoustic $\alpha $-disk

It is shown that the turbulent flow of acoustic waves propagating outward from the inner edge of the disk causes the accretion of the matter onto the center. The exponential amplification of waves takes place in the resonance region, $\omega = (n\pm 1)\Omega $. Here $\omega $ is the frequency of the acoustic wave, $n $ is its azimuthal wave number, $\Omega (r) $ is the angular frequency of rotation of the disk. The effect is similar to the inverse Landau damping in a collisionless plasma. Energy comes from the energy of rotation of the disk. That leads to decrease of the disk angular momentum and to accretion of the matter. The value of the accretion rate $dM/dt$ is ${\dot{M}} = \pi rc_{s} \Sigma _{0} (c_{s} / v_{\phi 0})^{2} W $. Here $c_{s} $ is the speed of sound of the disk gas, $v_{\phi 0} $ is the Keplerian rotation velocity, $\Sigma _{0} $ is the surface density of the disk, $W $ is total power of the acoustic turbulence, $W \simeq \int _{0}^{\infty }d \omega \sum_{n\geq 0} | \frac{\Sigma'}{\Sigma _{0}} |^{2} (\omega , n) $, $|\Sigma'|^{2} (\omega , n) $ is the spectral power of turbulence. The presented picture of accretion is consistent with the observed variations of X-ray and optical radiation from objects whose activity is associated with accretion of gas onto them.

Numerical simulation study on the pure solutocapillary flow of a binary mixture with various solutal coefficients of surface tension in an annular pool

Numerical simulations were undertaken to systematically explore the effects of various solutal coefficients of surface tension on the pure solutocapillary flow of a binary mixture in an annular pool. Ethanol/water binary mixture is selected here as the working fluid, and its solutal coefficient of surface tension reduces as the solute concentration rises. It is found that when the solutocapillary Reynolds number is comparatively small, an axisymmetric and steady flow is observed in the annular pool. With the increase of the solutocapillary Reynolds number, a second vortex emerges near the inner cylinder of the annular pool. Meanwhile, the solutocapillary Reynolds number for the appearance of a second rotating vortex is smaller than that with a constant solutal coefficient of surface tension. Basic flow, standing wave, and traveling wave are orderly observed with the increase of the solutocapillary Reynolds number. Various solutal coefficients of surface tension do not alter the formation mechanisms of flow pattern, or the tendencies of wave number and fundamental oscillation frequency along with the solutocapillary Reynolds number. However, the critical conditions of flow bifurcations of a binary mixture with various solutal coefficients of surface tension are always ahead of those with a constant one. Moreover, it obviously affects the amplitude of azimuthal velocity oscillation, wave number, and fundamental oscillation frequency.

2D3V kinetic simulation of Hall effect thruster, including azimuthal waves and diamagnetic effect

Axial-azimuthal (2D3V) full-kinetic PiC+MCC-model was built to simulate dynamics of Hall effect thruster discharge plasma taking into account azimuthal waves and diamagnetic effect. The transition from ignition to the steady-state regime was simulated. Calculation of discharge ignition shows a significant distortion in the shape of the magnetic field caused by high azimuthal-drift current. This effect and intensive ionization lead to the fact that full potential drop localizes in a thin non-magnetized cathode layer. In the steady-state regime, the distortion of the magnetic field is small. Plasma divides into three regions: dense anode plasma where ionization occurs; magnetic layer where ions accelerate and quasineutral cathode-side plasma (plume). The steady-state regime is subject to auto-oscillations at a gas-transit frequency (20 kHz ‘breathing modes’). Also, two types of azimuthal instabilities have been observed: gradient drift instability and electron cyclotron instability. All these instabilities lead to collisionless ‘anomalous’ electron transport across the magnetic field. Kinetic effects also were considered. It was found that the electron distribution function evolves from initial isotropic (Maxwellian) to essentially anisotropic due to electric field heating. Isotropy is partially restored inside anode plasma due to collisions.

About Azimuthal Acceleration of the Electrons by Azimuthal Surface Waves in a Dielectric-Lined Circular Waveguide With Two Thin Annular Rotating Electron Beams

Considering two annular rotating electron beams in a dielectric-lined waveguide, the frequency spectrum of the azimuthal waves and their field profile distribution are investigated. The charged particle acceleration due to the tangential component of the electric field is simulated. The simulation is carried out for important factors, such as the electron energy gain (acceleration gradient) and the deflection angle in two different vacuum regions (the core and clad of the dielectric waveguide). The graphs of the mentioned parameters versus the traveled distance by the electron are presented, and they are compared with each other. It is found that in some cases, the tangential acceleration of the charged particle in the clad of the cylindrical waveguide can be more effective.

The 2‐D Structure of Foreshock‐Driven Field Line Resonances Observed by THEMIS Satellite and Ground‐Based Imager Conjunctions

AbstractRecent studies of Pc5‐band (150–600 s) ultralow frequency waves found that foreshock disturbances can be a driver of dayside compressional waves and field line resonance, which are two typical Pc5 wave modes in the dayside magnetosphere. However, it is difficult to find spatial structure of dayside Pc5 waves using a small number of satellites or ground magnetometers. This study determines 2‐D structure of dayside Pc5 waves and their driver by utilizing coordinated observations by the THEMIS satellites and the all‐sky imager at South Pole during two series of Pc5 waves on 29 June 2008. These Pc5 waves were found to be field line resonances (FLRs) and driven by foreshock disturbances. The ground‐based all‐sky imager at South Pole shows that periodic poleward moving arcs occurred simultaneously with the FLRs near the satellite footprints over ~3° latitude and had the same frequencies as FLRs. This indicates that they are the auroral signature of the FLRs. The azimuthal distribution of the FLRs in the magnetosphere and their north‐south width in the ionosphere were further determined in the 2‐D images. In the first case, the FLRs distribute symmetrically in the prenoon and postnoon regions with out‐of‐phase oscillation as the odd toroidal mode in the equatorial plane. In the second case, the azimuthal wavelengths of the 350–500 s and 300–450 s period waves were ~8.0 and ~5.2 Re in the equatorial plane. It also shows a fine azimuthal structure embedded in the large‐scale arcs, indicating that a high azimuthal wave number (m ~ 140) mode wave coupled with the low‐wave number FLRs.

Quantitative visualization of vortex ring structure during wall impingement subject to background rotation

A single vortex ring subject to background rotation in the process of wall impingement has been experimentally investigated by particle tracking velocimetry (PTV). Two parameter conditions of Reynolds and Rossby numbers were chosen in addition to stationary environment as much strong and competitive Coriolis force emerges in comparison with inertia induced by vortex rings. From horizontal PTV windows set on the rotating experimental frame above the bottom wall, comprehensive influences of Coriolis force on the wall-impinging reaction are visualized as space–time three-dimensional vorticity distributions. Against natural growth of azimuthal waves due to Widnall instability, wall-impinging suppresses the waves and rather re-organizes original primary vortex because of cyclonic swirl coherently induced during impingement. This resists to turbulent collapse of vortex ring during the impingement and self-boosts own life time. We try to explain the mechanism of such an anti-decaying process in the final part, untangling the phenomenon with best read from the space–time correlations among three vorticity components.

Analysis of coherent structures in the near-field region of an isothermal free swirling jet after vortex breakdown

This work is focused on the near-exit region of a round isothermal free swirling jet to characterize the effect of swirl on the flow field and dominant coherent structures. Most of the work in this field investigated jets produced by vane swirl generators, whereas in our case an axial plus tangential swirl generator without a center-body was used. Stereoscopic PIV has been employed to capture the instantaneous flow field for Reynolds number equal to 21,800 and two swirl levels (0 and 1.4). A proper orthogonal decomposition (POD) applied to the instantaneous velocity vector fields allowed to identify the dominant flow structures associated with the precessing vortex core (PVC). The time coefficients of the most energetic first two POD modes were used to reconstruct the phase of the fluctuating motion in the swirling flow. The phase information was used to conditionally average the instantaneous velocity fields and swirl strength maps; this allowed to reconstruct the 3D structure of the PVC from the 2D data. Overlapping phase slots were used to improve the quality of the reconstructed 3D structure. The minima of negative swirling strength revealed the presence of two co-winding helical structures located in the inner and outer shear layers. The helical structures wind opposite to the base flow rotation and disappear at an axial location of approximately x/D=1.5. Detailed analysis of the mean, phase averaged and POD modes velocity fields are also reported to further highlight the flow field features. The third and fourth transverse POD modes evidenced the presence of a m=2 azimuthal wave buried in the dominant m=1 wave; such wave belong to a vortex pair superimposed to the precessing vortex core. Close to the nozzle exit, the analysis of the coherent and random parts of the velocity fluctuations evidenced that the PVC slightly increases the stochastic velocity fluctuations, but the latter resulted to be more isotropic respect to the non-swirling case. Our results put into evidence that the combined application of PIV, POD and phase averaging techniques can provide detailed observations of coherent fluctuations induced by vortex precession. The latter can help to improve the understanding of PVC and VB and to find possible strategies to prevent/control their formation. Finally, they can be of interest to develop numerical models for the simulation of these complex flows.