Oblique Modes Research Articles

Collisionless kinetic theory of oblique tearing instabilities

The linear dispersion relation for collisionless kinetic tearing instabilities is calculated for the Harris equilibrium. In contrast to the conventional 2D geometry, which considers only modes at the center of the current sheet, modes can span the current sheet in 3D. Modes at each resonant surface have a unique angle with respect to the guide field direction. Both kinetic simulations and numerical eigenmode solutions of the linearized Vlasov-Maxwell equations have recently revealed that standard analytic theories vastly overestimate the growth rate of oblique modes. We find that this stabilization is associated with the density-gradient-driven diamagnetic drift. The analytic theories miss this drift stabilization because the inner tearing layer broadens at oblique angles sufficiently far that the assumption of scale separation between the inner and outer regions of boundary-layer theory breaks down. The dispersion relation obtained by numerically solving a single second order differential equation is found to approximately capture the drift stabilization predicted by solutions of the full integro-differential eigenvalue problem. A simple analytic estimate for the stability criterion is provided.

Prompt Disappearance and Emergence of Radiation Belt Magnetosonic Waves Induced by Solar Wind Dynamic Pressure Variations

AbstractMagnetosonic waves are highly oblique whistler mode emissions transferring energy from the ring current protons to the radiation belt electrons in the inner magnetosphere. Here we present the first report of prompt disappearance and emergence of magnetosonic waves induced by the solar wind dynamic pressure variations. The solar wind dynamic pressure reduction caused the magnetosphere expansion, adiabatically decelerated the ring current protons for the Bernstein mode instability, and produced the prompt disappearance of magnetosonic waves. On the contrary, because of the adiabatic acceleration of the ring current protons by the solar wind dynamic pressure enhancement, magnetosonic waves emerged suddenly. In the absence of impulsive injections of hot protons, magnetosonic waves were observable even only during the time period with the enhanced solar wind dynamic pressure. Our results demonstrate that the solar wind dynamic pressure is an essential parameter for modeling of magnetosonic waves and their effect on the radiation belt electrons.

Performance improvement of water-cooled screw chiller under part load operation conditions by the paralleling throttle mechanism

Currently, water-cooled screw chiller is widely applied in commercial and industrial buildings, and the energy consumption of water chiller even could cover 70% of air-conditioning energy consumption in the most adverse operating conditions. Moreover, a number of chillers are running at a low rate under part-load state. In order to reduce the energy consumption of water-cooled screw chillers under part-load state, the paper presents the paralleling throttle mechanism. Through experimental study, under part-load state, it can be found that the by-pass tube diameter ?16 has the most positive effect on the performance of water-cooled screw chiller in four by-pass tube diameters. The oblique access mode is better than the vertical access mode, while the spiral access mode has little influence on the chiller performance. Because of paralleling throttle using, the exergetic loss of the evaporator and chiller is able to be reduced by 3.4%-15.5% and 0-6.7%, respectively. Meanwhile, the coefficient of performance of chiller can be enhanced by 0.2%-1.6%, and discharge temperature can be reduced by 0.4-2.7?C. In addition, the economic and environmental benefits of the advanced water-cooled screw chiller are more evident than the conventional water-cooled screw chiller's.

Very Oblique Whistler Mode Propagation in the Radiation Belts: Effects of Hot Plasma and Landau Damping

AbstractSatellite observations of a significant population of very oblique chorus waves in the outer radiation belt have fueled considerable interest in the effects of these waves on energetic electron scattering and acceleration. However, corresponding diffusion rates are extremely sensitive to the refractive index N, controlled by hot plasma effects including Landau damping and wave dispersion modifications by suprathermal (15–100 eV) electrons. A combined investigation of wave and electron distribution characteristics obtained from the Van Allen Probes shows that peculiarities of the measured electron distribution significantly reduce Landau damping, allowing wave propagation with high N ∼ 100–200. Further comparing measured refractive indexes with theoretical estimates incorporating hot plasma corrections to the wave dispersion, we provide the first experimental demonstration that suprathermal electrons indeed control the upper limit of the refractive index of highly oblique whistler mode waves. Such results further support the importance of incorporating very oblique waves into radiation belt models.

Kinetic Simulations of the Interruption of Large-Amplitude Shear-Alfvén Waves in a High- β Plasma

Using two-dimensional hybrid-kinetic simulations, we explore the nonlinear "interruption" of standing and traveling shear-Alfvén waves in collisionless plasmas. Interruption involves a self-generated pressure anisotropy removing the restoring force of a linearly polarized Alfvénic perturbation, and occurs for wave amplitudes δB_{⊥}/B_{0}≳β^{-1/2} (where β is the ratio of thermal to magnetic pressure). We use highly elongated domains to obtain maximal scale separation between the wave and the ion gyroscale. For standing waves above the amplitude limit, we find that the large-scale magnetic field of the wave decays rapidly. The dynamics are strongly affected by the excitation of oblique firehose modes, which transition into long-lived parallel fluctuations at the ion gyroscale and cause significant particle scattering. Traveling waves are damped more slowly, but are also influenced by small-scale parallel fluctuations created by the decay of firehose modes. Our results demonstrate that collisionless plasmas cannot support linearly polarized Alfvén waves above δB_{⊥}/B_{0}∼β^{-1/2}. They also provide a vivid illustration of two key aspects of low-collisionality plasma dynamics: (i)the importance of velocity-space instabilities in regulating plasma dynamics at high β, and (ii)how nonlinear collisionless processes can transfer mechanical energy directly from the largest scales into thermal energy and microscale fluctuations, without the need for a scale-by-scale turbulent cascade.

Whistler Mode Waves Below Lower Hybrid Resonance Frequency: Generation and Spectral Features

AbstractEquatorial noise in the frequency range below the lower hybrid resonance frequency, whose structure is shaped by high proton cyclotron harmonics, has been observed by the Cluster spacecraft. We develop a model of this wave phenomenon which assumes (as, in general, has been suggested long ago) that the observed spectrum is excited due to loss cone instability of energetic ions in the equatorial region of the magnetosphere. The wavefield is represented as a sum of constant frequency wave packets which cross a number of cyclotron resonances while propagating in a highly oblique mode along quite specific trajectories. The growth (damping) rate of these wave packets varies both in sign and magnitude along the raypath, making the wave net amplification, but not the growth rate, the main characteristic of the wave generation process. The growth rates and the wave amplitudes along the ray paths, determined by the equations of geometrical optics, have been calculated for a 3‐D set of wave packets with various frequencies, initial L shells, and initial wave normal angles at the equator. It is shown that the dynamical spectrum resulting from the proposed model qualitatively matches observations.

Nonlinear evolution and secondary instability of steady and unsteady Görtler vortices induced by free-stream vortical disturbances

We study the nonlinear development and secondary instability of steady and unsteady Görtler vortices which are excited by free-stream vortical disturbances (FSVD) in a boundary layer over a concave wall. The focus is on low-frequency (long-wavelength) components of FSVD, to which the boundary layer is most receptive. For simplification, FSVD are modelled by a pair of oblique modes with opposite spanwise wavenumbers $\pm k_{3}$, and their intensity is strong enough (but still of low level) that the excitation and evolution of Görtler vortices are nonlinear. For the general case that the Görtler number $G_{\unicode[STIX]{x1D6EC}}$ (based on the spanwise wavelength $\unicode[STIX]{x1D6EC}$ of the disturbances) is $O(1)$, the formation and evolution of Görtler vortices are governed by the nonlinear unsteady boundary-region equations, supplemented by appropriate upstream and far-field boundary conditions, which characterize the impact of FSVD on the boundary layer. This initial-boundary-value problem is solved numerically. FSVD excite steady and unsteady Görtler vortices, which undergo non-modal growth, modal growth and nonlinear saturation for FSVD of moderate intensity. However, for sufficiently strong FSVD the modal stage is bypassed. Nonlinear interactions cause Görtler vortices to saturate, with the saturated amplitude being independent of FSVD intensity when $G_{\unicode[STIX]{x1D6EC}}\neq 0$. The predicted modified mean-flow profiles and structure of Görtler vortices are in excellent agreement with several steady experimental measurements. As the frequency increases, the nonlinearly generated harmonic component $(0,2)$ (which has zero frequency and wavenumber $2k_{3}$) becomes larger, and as a result the Görtler vortices appear almost steady. The secondary instability analysis indicates that Görtler vortices become inviscidly unstable in the presence of FSVD with a high enough intensity. Three types of inviscid unstable modes, referred to as sinuous (odd) modes I, II and varicose (even) modes I, are identified, and their relevance is delineated. The characteristics of dominant unstable modes, including their frequency ranges and eigenfunctions, are in good agreement with experiments. The secondary instability is intermittent when FSVD are unsteady and of low frequency. However, the intermittence diminishes as the frequency increases. The present theoretical framework, which allows for a detailed and integrated description of the key transition processes, from generation, through linear and nonlinear evolution, to the onset of secondary instability, represents a useful step towards predicting the pre-transitional flow and transition itself of the boundary layer over a blade in turbomachinery.

Numerical modeling and experimentation of three dimensional material removal characteristics in fluid jet polishing

Fluid jet polishing is a promising ultra-precision polishing technology which has been successfully used in polishing various kinds of precision components. The characterization of the material removal plays an important role in deterministic ultra-precision polishing process, which not only helps to better understand its material removal characteristics, but is also used to predict the material removal and help to determine the dwell time needed at different positions of the workpiece. During the fluid jet polishing process, both vertical and oblique polishing modes are often used for different purposes. However, currently published researches about the modeling of fluid jet polishing are usually focused on the vertical impinging mode. Relatively few attentions have been paid to model the material removal in oblique impinging mode, whose material removal profile is asymmetric. As a result, this paper attempts to present a universal three dimensional numerical model (U3DNM) which can be used to model the fluid jet polishing process both in vertical and oblique impinging modes. The U3DMN is built based on the computational fluid dynamic modelling method. Four groups of simulations and polishing experiments were also conducted under various conditions so as to test the feasibility and reliability of this model. The results infer that the proposed numerical model is effective and has high robustness under various conditions. The successful development of the U3DNM provides a better understanding of the material removal characteristics which shed some light for better understanding and analysis of material removal for freeform surfaces which possesses continuous variation of curvatures.

Nonlinear spectral singularities and laser output intensity

The mathematical notion of spectral singularity admits a description in terms of purely outgoing solutions of a corresponding linear wave equation. This leads to a nonlinear generalization of this notion for nonlinearities that are confined in space. We examine the nonlinear spectral singularities in arbitrary transverse electric (TE) and transverse magnetic (TM) modes of a mirrorless slab laser that involves a weak Kerr nonlinearity. This provides a computational scheme for the determination of the laser output intensity I for these modes. In particular, we offer an essentially mathematical derivation of the linear-dependence of I on the gain coefficient g and obtain an explicit analytic expression for its slope. This shows that if the real part η of the refractive index of the slab does not exceed 3, there is a lower bound on the incidence angle θ below which lasing in both its TE and TM modes requires η to be shifted by a small amount as g surpasses the threshold gain. Our results suggest that lasing in the oblique TM modes of the slab is forbidden if the incidence (emission) angle of the TM mode exceeds the Brewster’s angle.

Spreading of electron scale magnetic reconnection with a wave number dependent speed due to the propagation of dispersive waves

In this work, we study electron scale spreading of localized magnetic reconnection in the presence of a guide magnetic field, however, without the influence of ions and cross-scale coupling. These fundamental physics studies will help to understand the coupling of the electron scale spreading with the ion scales in real systems. An electron-magnetohydrodynamic (EMHD) model is employed to model the physics at electron scales. Three dimensional EMHD simulations and linear eigen mode analysis are performed for different guide field strengths. The simulations show a wave-like bi-directional spreading of magnetic reconnection at electron scales. The electron scale spreading, however, unlike the ion scale spreading by Alfvén waves, is caused by the uni- and bi-directional propagation of the dispersive flow induced and whistler wave modes, respectively. The dispersive nature of the two wave modes makes the spreading-speed dependent on the wave numbers of the unstable tearing mode, which depend on the thickness of the electron current sheet and the strength of the guide field. A model of the speed of spreading is developed, in which the spreading-speeds parallel and anti-parallel to the guide field are given by linear combinations of the group speeds of the two wave modes. The model prediction of the spreading speeds agrees well with the speeds obtained from the simulation results. For small guide fields, the spreading is asymmetric being faster in the direction of the electron flow. On increasing the guide field, the spreading becomes increasingly symmetric, with the speeds of the order of electron Alfvén speed in the guide magnetic field, due to the dominance of the whistler group speed in determining the speed of the spreading. As a consequence of the asymmetric spreading, the chain of alternate X- and O-points, formed due the growth of oblique tearing modes, extends farther in the direction of electron flow as compared to that in the direction of the guide magnetic field.

Selective enhancement of oblique waves caused by finite amplitude second mode in supersonic boundary layer

Nonlinear interactions of the two-dimensional (2D) second mode with oblique modes are studied numerically in a Mach 6.0 flat-plate boundary layer, focusing on its selective enhancement effect on amplification of different oblique waves. Evolution of oblique modes with various frequencies and spanwise wavenumbers in the presence of 2D second mode is simulated successively, using a modified parabolized stability equation (PSE) method, which is able to simulate interaction of two modes with different frequencies efficiently. Numerical results show that oblique modes in a broad band of frequencies and spanwise wavenumbers can be enhanced by the finite amplitude 2D second mode instability wave. The enhancement effect is accomplished by interaction of the 2D second mode, the oblique mode, and a forced mode with difference frequency. Two types of oblique modes are found to be more amplified, i.e., oblique modes with frequency close to that of the 2D second mode and low-frequency first mode oblique waves. Each of them may correspond to one type of transition routes found in transition experiments. The spanwise wavenumber of the oblique wave preferred by the nonlinear interaction is also determined by numerical simulations.

Linear Stability Prediction of Vortex Structures on High Pressure Turbine Blades

Velocity profiles are extracted from time- and span-averaged direct numerical simulation data, describing the flow over a high-pressure turbine vane linear cascade near engine-scale conditions with reduced inlet disturbance levels. Based on these velocity profiles, local as well as non-local linear stability analysis of the boundary-layer over the suction side of the vane is carried out in order to characterise a linearly unstable region close to the trailing edge. The largest growth rates are found for oblique modes, but those are only slightly more unstable than 2D modes, which describe the locations and frequencies of most unstable modes very well. The frequencies of the most unstable linear modes predict with good accuracy the predominant frequencies found in the direct numerical simulations (DNS) close to the trailing edge.

Quasi‐linear diffusion coefficients for highly oblique whistler mode waves

AbstractQuasi‐linear diffusion coefficients are considered for highly oblique whistler mode waves, which exhibit a singular “resonance cone” in cold plasma theory. The refractive index becomes both very large and rapidly varying as a function of wave parameters, making the diffusion coefficients difficult to calculate and to characterize. Since such waves have been repeatedly observed both outside and inside the plasmasphere, this problem has received renewed attention. Here the diffusion equations are analytically treated in the limit of large refractive index μ. It is shown that a common approximation to the refractive index allows the associated “normalization integral” to be evaluated in closed form and that this can be exploited in the numerical evaluation of the exact expression. The overall diffusion coefficient formulas for large μ are then reduced to a very simple form, and the remaining integral and sum over resonances are approximated analytically. These formulas are typically written for a modeled distribution of wave magnetic field intensity, but this may not be appropriate for highly oblique whistlers, which become quasi‐electrostatic. Thus, the analysis is also presented in terms of wave electric field intensity. The final results depend strongly on the maximum μ (or μ∥) used to model the wave distribution, so realistic determination of these limiting values becomes paramount.

Langmuir wave filamentation in the kinetic regime. I. Filamentation instability of Bernstein-Greene-Kruskal modes in multidimensional Vlasov simulations

A nonlinear Langmuir wave in the kinetic regime kλD≳0.2 may have a filamentation instability, where k is the wavenumber and λD is the Debye length. The nonlinear stage of that instability develops into the filamentation of Langmuir waves which in turn leads to the saturation of the stimulated Raman scattering in laser-plasma interaction experiments. Here, we study the linear stage of the filamentation instability of the particular family (H. A. Rose and D. A. Russell, Phys. Plasmas 8, 4784 (2001)) of Bernstein-Greene-Kruskal (BGK) modes (I. B. Bernstein et al., Phys. Rev. 108, 546 (1957)) that is a bifurcation of the linear Langmuir wave. Performing direct 2 + 2D Vlasov–Poisson simulations of collisionless plasma, we find the growth rates of oblique modes of the electric field as a function of BGK's amplitude, wavenumber, and the angle of the oblique mode's wavevector relative to the BGK's wavevector. Simulation results are compared to theoretical predictions.

Light propagation in ultra-thin gap in 3D photonic crystals

We investigate the propagation of light in an ultra-thin gap in stacked-stripe three-dimensional (3D) photonic crystals operating in the near-infrared wavelength range. We fabricate 3D photonic crystals composed of 32 stacked layers with an artificially introduced gap (∼200nm) in the center of the structure by using a wafer bonding method. In order to study the characteristics of the gap, we introduce oblique waveguides to connect the gap with the upper and lower sides of the photonic crystal. The observation of light output from waveguides that are distant from the waveguide used for incident light demonstrates for the first time that light propagates along the air gap and is distributed to multiple output waveguides. Moreover, we perform calculations that reveal the formation of a propagation mode resulting from introduction of the ultra-thin gap. We analyze the coupling between the propagation mode and the oblique waveguide mode and discuss the characteristics of light distribution via the gap.

Electromagnetic modes and gravitational instability of spin- 1 / 2 $1/2$ magneto degenerate plasma

We have studied self-gravitational instability using the two fluid model in which the important role of spin effect (due to spin quantum force and spin magnetization current) is established in highly magnetized and degenerate astrophysical environment of pulsar magnetosphere. Along with this; low frequency, high frequency modes of magnetosonic and magnetohydrodynamic waves were carried out discovering its utility in highly magnetized and degenerate astrophysical environments. The plasma is considered to be composed of degenerate electrons and non-degenerate ions and the quantum effects are incorporated via spin and diffraction effects along with the thermal effect of ions. The spin and quantum dominance are discussed analytically and numerically using the dispersion relation in parallel, perpendicular and oblique mode of propagation. The present study can be implemented on highly magnetized white dwarfs, neutron stars and pulsar magnetosphere (with strong magnetic field $B_{0} \le 10^{10}~\mbox{T}$ ) and to degenerate laboratory environments.

Acoustics of small rectangular rooms: Analytical and numerical determination of reverberation parameters

A small rectangular room with hard walls has a number of acoustic flaws and the most serious drawback is a long reverberation time. A technique commonly used for improving room acoustics consists in increasing a sound absorption on a ceiling. In this study, the impact of acoustical treatment of a ceiling on reverberant properties of a small rectangular room was examined. Changes in the modal reverberation time due to this treatment were investigated by the analytical method. As was evidenced by calculations, the initial increase in a sound absorption on a ceiling causes a substantial decrease in the modal reverberation time and a treatment efficiency decreases with a further absorption increase. It was found also that for a room with hard walls statistical and wave theories give the same result as the modal reverberation time for oblique modes and the Sabine’s reverberation time are identical. A more detailed information about reverberant properties of a room was provided by the numerical method employing a backward integration of the squared room impulse response. Using this method, global and local reverberation parameters were determined. Numerical simulations discovered a quite good agreement between global and local reverberation time and high differences between global and local early decay time resulting from a nonlinear shape of a decay curve. Therefore, one can conclude that the global decay times characterize reasonably well a reverberation process in a late stage of sound decay but they are not correctly describe this process in an initial stage.

Simulation study of the formation of a non-relativistic pair shock

We examine with a particle-in-cell (PIC) simulation the collision of two equally dense clouds of cold pair plasma. The clouds interpenetrate until instabilities set in, which heat up the plasma and trigger the formation of a pair of shocks. The fastest-growing waves at the collision speed $c/5$, where $c$ is the speed of light in vacuum, and low temperature are the electrostatic two-stream mode and the quasi-electrostatic oblique mode. Both waves grow and saturate via the formation of phase space vortices. The strong electric fields of these nonlinear plasma structures provide an efficient means of heating up and compressing the inflowing upstream leptons. The interaction of the hot leptons, which leak back into the upstream region, with the inflowing cool upstream leptons continuously drives electrostatic waves that mediate the shock. These waves heat up the inflowing upstream leptons primarily along the shock normal, which results in an anisotropic velocity distribution in the post-shock region. This distribution gives rise to the Weibel instability. Our simulation shows that even if the shock is mediated by quasi-electrostatic waves, strong magnetowaves will still develop in its downstream region.

Bulk-like-phonon polaritons in one-dimensional photonic superlattices

We investigate the properties of a one-dimensional photonic superlattice made of alternating layers of air and wurtzite aluminum nitride. The Maxwell equations are solved for any admissible values of the angle of incidence by means of the transfer matrix formalism. The band structure of the frequency spectrum is obtained, as well as the density of states and transmittance associated to both the TM and TE modes. The dispersion relations indicate that for oblique incidence and TM modes there is a component of the electric field oriented along the growth direction of the structure that couples with the longitudinal optical phonon oscillations of the aluminum nitride thus leading to the appearance of longitudinal phonon polaritons in the system.

Nonlinear dynamics of electrons interacting with oblique whistler mode chorus in the magnetosphere

AbstractWe perform test particle simulations for relativistic electrons interacting with a whistler mode chorus packet propagating at oblique angles. By confirming that the energy transport of oblique lower band chorus is nearly along the ambient magnetic field, we apply the gyroaveraging method in calculating equations of motion of electrons. We trace evolution of a delta function of relativistic electrons in a phase space of kinetic energy and equatorial pitch angle and obtain numerical Green's functions of the chorus wave‐particle interactions. Examining the Green's functions in a wide range of kinetic energies, we find that Landau resonance can accelerate MeV electrons efficiently and that higher nth resonances such as n =− 1 and n = 2 also contribute to acceleration of electrons at high equatorial pitch angles (∼70°) and high energies (∼2 MeV). We investigate the rate of energy gain of the cyclotron resonance acceleration and the Landau resonance acceleration and find that the perpendicular component of wave electric field dominates both accelerations for MeV electrons. Furthermore, the proximity between the parallel components of Vp and Vg of oblique whistler mode waves and the nonlinear trapping condition make the interaction time of Landau resonance much longer than that of n = 1 cyclotron resonance, resulting in efficient acceleration of MeV electrons.