Vortices In Space Research Articles

The Impact of Turbulence on the Ionosphere and Magnetosphere

An important property associated with turbulence in plasmas and fluids is anomalous transport. Plasma, being a good conductor, can in addition be affected by turbulence causing an anomalous resistivity that can significantly exceed its classical counterpart. While turbulent transport may be adequately described in configuration space, some aspects of the anomalous resistivity are best accounted for in phase space. Kinetic phenomena like electron and ion phase space vortices can thus act as obstacles for the free flow of slow charged particles. Plasma instabilities and large amplitude plasma waves are candidates for contributions to the anomalous resistivity by generating such structures. Langmuir waves can be relevant, but also others, such as upper- as well as lower-hybrid waves in magnetized plasmas. Often these anomalous resistivity effects can be small, but due to the large spatial and temporal scales involved in space plasmas, planetary ionosphere and magnetosphere in particular, even such moderate effects can be important. This mini-review is discussing elements of the description of plasma turbulence with particular attention to wave phenomena that contribute to anomalous resistivity and diffusion. Turbulence effects can have relevance for space weather phenomena as well, where ground based and airborne activities relying on for instance Global Positioning and Global Navigation Satellite Systems are influenced by plasma conditions in geospace.

Excitation of electrostatic solitary waves during neutralization of ion beam pulse by plasma

The possibility of exciting electrostatic solitary waves (ESWs) during the neutralization of ion beam pulses by plasmas is investigated using a two-dimensional (2D) electrostatic particle-in-cell (PIC) code. The simulation results show that if an axial magnetic field is applied, an ESW can be excited when the ion beam enters the plasma. The ESW is caused by the phase space vortex motion of electrons in the potential well formed by the plasma and the ion beam. The ESW is very stable and has a very long lifetime when it propagates in the plasma and the ion beam. The ESW has a 2D space structure, with about 3 cm length and more than twice the width of the ion beam. The splitting of the ESW is observed when it encounters a potential drop. The excitation conditions of the ESW are also discussed.

Saturation of trapped particle instability induced by vortex-merging in electron plasma waves

Phase space vortex merging in electron plasma waves is researched by applying a periodically changing electric field in plasma space with Maxwellian velocity distribution. The pump electric field excites the electron plasma wave with large amplitude and electron phase space vortices are formed. The electron plasma wave can be transited to longer wave modes through vortex merging processes. Excepting the fundamental mode of electron plasma waves, two or more modes appear and grow exponentially before vortex merging. After merging, another mode replaces the initial pumping wave as the strongest wave mode. It is verified that the growth of this new strong mode is related to trapping particle instability. Vortex merging is one of the saturation mechanisms of trapped particle instability.

Geometrical quench and dynamical quantum phase transition in the α−T3 lattice

We investigate quantum quenches and the Loschmidt echo in the two dimensional, three band $\alpha-T_3$ model, a close descendant of the dice lattice. By adding a chemical potential to the central site, the integral of the Berry curvature of the bands in different valleys is continously tunable by the ratio of the hopping integrals between the sublattices. By investigating one and two filled bands, we find that dynamical quantum phase transition (DQPT), i.e. nonanalytical temporal behaviour in the rate function of the return amplitude, occurs for a certain range of parameters, independent of the band filling. By focusing on the effective low energy description of the model, we find that DQPTs happen not only in the time derivative of the rate function, which is a common feature in two dimensional models, but in the rate function itself. This feature is not related to the change of topological properties of the system during the quench, but rather follows from population inversion for all momenta. This is accompanied by the appearance of dynamical vortices in the time-momentum space of the Pancharatnam geometric phase. The positions of the vortices form an infinite vortex ladder, i.e. a macroscopic phase structure, which allows us to identify the dynamical phases that are separated by the DQPT.

Driven electrostatic phase space vortices in a 1D weakly dissipative Vlasov–Poisson system

The effect of collisions on driven electrostatic phase space vortices is analyzed by means of Eulerian simulation for two different collision models. It was demonstrated recently [P. Trivedi and R. Ganesh, Phys. Plasmas 23, 062112 (2016)] that in the absence of collisions, at late times, steady state phase space vortices manifest to form a plateau in the resonant region of the particle velocity distribution function, due to trapping of particles supporting multiextrema giant phase space vortices (PSVs). In the presence of collisions, over long time, this multiextrema plateau are found to smooth out, since collisions drive the velocity distribution toward Maxwellian, irrespective of how weak the collisions are as long as they are non-zero. In these conditions, kinetic processes and collisionality are found to be in competition, and the evolution of the plasma is found, therefore, to be a result of nontrivial combination of these two effects. An attempt has been made by means of numerical simulations to study the effect of weak collisionality on the electrostatic driven phase space vortices with two types of collision operators: (1) Bhatnagar–Gross–Krook (Krook) collision operator, where the colliding particles can be treated as isolated pairs and, (2) Fokker–Planck (FP) type collision operator (Zakharov–Karpman) in one dimension, where many weak collisions lead to particle diffusion in velocity space. It is shown that depending on the collision model used, the nature of smoothing in velocity space of giant PSVs results in qualitatively very different phase space structures. However, irrespective of the collision model used, excess density fractions over 10% are retained.

Manifestation of a topological gapless phase in a two-dimensional chiral symmetric system through Loschmidt echo

Unlike the edge state of a topological insulator where its energy level lives in the bulk energy gap, the edge state of a topological semimetal hides in the bulk spectrum and is difficult to be identified by the energy. We investigate the sensitivity of bulk and edge states of the gapless phase for a topological semimetal to the disordered perturbation via a concrete two-dimensional chiral symmetric lattice model. The topological gapless phase is characterized by two opposite vortices in the momentum space and nonzero winding numbers, which correspond to the edge flatband when the open boundary condition is applied. For this system, numerical results reveal that a distinguishing feature is that the robustness of the edge states against weak disorder and the flatband edge modes remain locked at zero energy in the presence of weak chiral-symmetry-preserving disorder. We employ the Loschmidt echo (LE) for both bulk and edge states to study the dynamic effect of disordered perturbation. We show that, for an initial bulk state, the LE decays exponentially, whereas it converges to a constant for an initial edge state in the presence of weak disorder. Furthermore, the convergent LE can be utilized to identify the positions of vortices as well as the phase diagram. We discuss the realization of such dynamic investigations in a topological photonic system.

The gas flow dynamics in a separator with coaxially arranged pipes

In order to increase the efficiency of gas purification from the particles of up to 20 microns and to increase the service life of bag and electrostatic filters, the authors propose to use a centrifugal separation device with coaxially arranged pipes to be installed before the fine purification devices. The numerical studies of gas dynamics in a separation device were conducted in ANSYS Fluent software package. As a result of conducted numerical studies, it was found that the pressure loss in the centrifugal separation device is not more than 70 Pa at the inlet gas flow rate from 1 to 15 m/s and the width of rectangular hole within the range from 10 to 15 mm. The low pressure losses are caused by the design features; in particular, the resulting vortices in the inter-cylindrical space practically do not contact the wall surfaces of device. The equations of pressure loss depending on the width of rectangular holes and the hydraulic resistance coefficient of separation device depending on the inlet gas flow rate were obtained. The design coefficient of hydraulic resistance of separation device was equal to 0.45.

Numerical Simulation of Swirling Impinging Jet Issuing from a Threaded Hole under Inclined Condition.

There are some inclined jet holes in the cooling structure of the leading edge region of gas turbine blades. In order to improve the cooling effect of traditional round holes, this paper proposes to replace the round holes with threaded holes, and studies the complex flow and heat transfer performance of the swirling impinging jet (SIJ) issuing from the 45° threaded holes in the inclined condition by numerical simulation. The influencing factors include jet inclination angle α (45°–90°), jet-to-plate distance (H/d = 2, 4, 6), and Reynolds number (6000–24,000). The results show that the inclination angle and jet-to-plate distance have a great influence on the size, shape, and position of vortices in the jet space, while the Reynolds number has little effect on the vortices. In the inclined state, the impinging cooling effect of the swirling impinging jet is better than that of the circular impinging jet (CIJ), both heat transfer coefficients will degrade significantly when the inclination angle is 45°. When the inclination angle is greater than 45°, compared with the round hole, the enhanced heat transfer region for the swirling jet is in the region of r/d < 3, while both of the Nusselt numbers in the wall jet region are weak, with a value of just 20. At the same time, with the increasing of the inclination angle (α > 45°), the average Nusselt number on target surface holds a constant value. Under the inclined conditions, the heat transfer coefficient on the target surface for the swirling jet is increased totally with the increasing of the Re, but when the Re is larger than 18,000, the rate of enhanced heat transfer gradually weakens.

Shocks and phase space vortices driven by a density jump between two clouds of electrons and protons

We study with 1D PIC simulations the expansion of a dense plasma into a dilute one for density ratios 2.5 ≤ α ≤ 20. Both are unmagnetized and consist of electrons and protons. Shocks form in all cases. We determine how α affects the speed of the shock, that of the trailing velocity plateau and the proton beam instabilities in its upstream region. The speed of the velocity plateau relative to the upstream plasma increases significantly with α. Faster shocks reflect more upstream protons and fewer protons make it downstream, which slows down the shock in the downstream frame. This slow-down reduces noticably the increase with α of the shock speed in the upstream frame. All simulations demonstrate that an ion acoustic instability develops between the shock-reflected proton beam and the ambient protons. We solve the linear dispersion relation for ion acoustic waves that have wave vectors which are parallel to the beam velocity vector. Upstream conditions, for which their growth rate is largest, lead to the most unstable upstream plasmas also in the simulation. Even though linear theory predicts the growth of sine waves, which reach a small amplitude in the simulations, solitary waves become the dominant ones upstream of the shock. They enforce the formation of new shocks and ion phase space vortices. We discuss the relevance of our findings to laser-plasma experiments.

Formation of Quantum Vortices at the Ionization of an Atom by an Ultrashort Laser Pulse: Two- and Three-Dimensional Cases

We theoretically analyze the quantum vortices - the zeros of electron wave function which are formed through atom ionization by ultrashort laser pulse. In 2D space we consider the case of above-threshold ionization of hydrogen atom and in 3D space the ionization of the atom in the zero-radius-potential approximation. With the help of obtained analytical results we make the assumption that localization of quantum vortices in 3D space can be predicted by analysis of 2D model.

Numerical Schemes and Hybrid Approach for the Simulation of Unsteady Turbulent Flows

The paper presents a brief review of computational approaches for the simulation of turbulent flows and shows that the correct calculation of large-scale vortex structures necessarily requires the use of eddy-resolving methods, while the applied numerical schemes must be stable and accurately describe the spatial evolution of vortices. The dissipative properties and stability of most numerical schemes implemented in the OpenFOAM package are analyzed by solving problems on the decay of the homogeneous isotropic turbulence and scalar transfer. It is established that the considered schemes are not suitable for correctly calculating the propagation and dissipation of vortices in space; therefore, they are refined to eliminate oscillations and maintain an acceptable level of dissipation. An algorithm for combining the URANS and LES methods using zoning of the computational domain is described and implemented. To test the implemented calculation method of unsteady turbulent flows, we simulate the flow around a maneuvering aircraft with an installed airbrake deflection. The flow patterns of the aircraft and its aerodynamic characteristics are obtained and compared with the experimental data.

Rare transitions to thin-layer turbulent condensates

Turbulent flows in a thin layer can develop an inverse energy cascade leading to spectral condensation of energy when the layer height is smaller than a certain threshold. These spectral condensates take the form of large-scale vortices in physical space. Recently, evidence for bistability was found in this system close to the critical height: depending on the initial conditions, the flow is either in a condensate state with most of the energy in the two-dimensional (2-D) large-scale modes, or in a three-dimensional (3-D) flow state with most of the energy in the small-scale modes. This bistable regime is characterised by the statistical properties of random and rare transitions between these two locally stable states. Here, we examine these statistical properties in thin-layer turbulent flows, where the energy is injected by either stochastic or deterministic forcing. To this end, by using a large number of direct numerical simulations (DNS), we measure the decay time $\unicode[STIX]{x1D70F}_{d}$ of the 2-D condensate to 3-D flow state and the build-up time $\unicode[STIX]{x1D70F}_{b}$ of the 2-D condensate. We show that both of these times $\unicode[STIX]{x1D70F}_{d},\unicode[STIX]{x1D70F}_{b}$ follow an exponential distribution with mean values increasing faster than exponentially as the layer height approaches the threshold. We further show that the dynamics of large-scale kinetic energy may be modelled by a stochastic Langevin equation. From time-series analysis of DNS data, we determine the effective potential that shows two minima corresponding to the 2-D and 3-D states when the layer height is close to the threshold.

Aerodynamics of a two-dimensional flapping wing hovering in proximity of ground

The difference in aerodynamic forces of a two-dimensional flapping wing hovering in unbounded flow field and ground effect is studied. The unsteady laminar Navier–Stokes equations are solved by the finite volume method to simulate the flow field around the wing. In the unbounded flow field, the correspondence between the aerodynamic force, pressure distribution on wing, and typical vortex structures is established, and then the high-lift mechanism of the flapping wing is further explained. In the ground effect, based on the lift variation, the dimensionless height H/ C ( H is the height of the wing above ground and C is the chord length of the wing) can be divided into transition and ground effect regimes. In the transition regime ( H/ C &gt; 2.5), the lift decreases with the decreasing height, and the ground indirectly impacts the vortices near wing by changing the shed vortices in space. In the ground effect regime ( H/ C &lt; 2.5), the lift increases with the decreasing height, and the ground directly impacts the vortices near the wing.

Dynamics of the boundary layer created by the explosion of a dense object in an ambient dilute gas triggered by a high power laser

The dynamics of the boundary layer in between two distinct collisionless plasmas created by the interaction between a dense object modeling a cluster and a short laser pulse in the presence of an ambient gas is studied with two dimensional relativistic particle-in-cell simulations, which are found to be described by three successive processes. In the first phase, a collisionless electrostatic shock wave, launched near the cluster expansion front, reflects the ambient gas ions at a contact surface as a moving wall, which allows a particle acceleration with a narrower energy spread. In the second phase, the contact surface disappears and the compressed surface of the ambient gas ions passes over the shock potential, forming an overlapping region between the cluster expansion front and the compressed surface of the ambient gas. Here, another type of nonlinear wave is found to be evolved, leading to a relaxation of the shock structure, while continuing to reflect the ambient gas ions. The nonlinear wave exhibits a bipolar electric field structure that is sustained for a long timescale coupled with slowly evolving ion dynamics, suggesting that a quasistationary kinetic equilibrium dominated by electron vortices in the phase space is established. In the third phase, a rarefaction wave is triggered and evolves at the compressed surface of ambient gas. This is because some of the ambient gas ions tend to pass over the potential of the bipolar electric field. Simultaneously, a staircase structure, i.e., a kind of internal shock, is formed in the cluster due to the deceleration of cluster ions. Such structure formations and successive dynamics accompanied by the transitions from the shock wave phase through the overlapping phase to the rarefaction wave phase are considered to be a unique nature at the boundary layer created by an explosion of a dense plasma object in an ambient dilute plasma.

Response to “Comment on ‘Symmetry in electron and ion dispersion in 1D Vlasov-Poisson plasma’” [Phys. Plasmas 26, 064701 (2019)

Treating electron and ion kinetics on the same physics footing or in a symmetric framework, dispersion relations (ωr, k) for ion and electron modes in a 1D Vlasov-Poisson (VP) plasma were obtained in the limit of weak flattening of the electron and ion distributions. Using this information of (ωr, k), a nonlinear VP solver with a low amplitude, harmonic external forcing has been solved. A possibility of simultaneous excitation of all the electrostatic normal modes was demonstrated in Trivedi et al. [Phys. Plasmas 25, 112102 (2018)]. The main focus of the paper is on the excitation of normal modes by applying a small amplitude external, monochromatic, electric field drive. In order to drive as well as to identify Phase Space Vortices (i.e., Bernstein-Greene-Kruskal/Cnoidal modes, etc.) formed out of the driven nonlinear VP system, assuming local flattening of electron and ion distributions, the real part of the plasma dispersion function for arbitrary ratios of ion to electron masses and temperatures is solved, which is known to be accurate in the low amplitude, harmonic limit, as pointed out by Schamel [Phys. Plasmas 19, 020501 (2012)].

Topological Photonic Media and the Possibility of Toroidal Electromagnetic Wavepackets

This study aims to present a theoretical investigation of a feasible electromagnetic wavepacket with toroidal-type dual vortices. The paper begins with a discussion on geometric phases and angular momenta of electromagnetic vortices in free space and periodic structures, and introduces topological photonic media with a review on topological phenomena of electron systems in solids, such as quantum Hall systems and topological insulators. Representative simulations demonstrate both the characteristics of electromagnetic vortices in a periodic structure and of exotic boundary modes of a topological photonic crystal, on a Y-shaped waveguide configuration. Those boundary modes stem from photonic helical surface modes, i.e., a photonic analog of electronic helical surface states of topological insulators. Then, we discuss the possibility of toroidal electromagnetic wavepackets via topological photonic media, based on the dynamics of an electronic wavepacket around the boundary of a topological insulator and a correspondence relation between electronic helical surface states and photonic helical surface modes. Finally, after introducing a simple algorithm for the construction of wavepacket solutions to Maxwell’s equations with multiple types of vortices, we examine the stability of a toroidal electromagnetic wavepacket against reflection and refraction, and further discuss the transformation laws of its topological properties in the corresponding processes.

Majorana flat band edge modes of topological gapless phase in 2D Kitaev square lattice

We study a Kitaev model on a square lattice, which describes topologically trivial superconductor when gap opens, while supports topological gapless phase when gap closes. The degeneracy points are characterized by two vortices in momentum space, with opposite winding numbers. We show rigorously that the topological gapless phase always hosts a partial Majorana flat band edge modes in a ribbon geometry, although such a single band model has zero Chern number as a topologically trivial superconductor. The flat band disappears when the gapless phase becomes topologically trivial, associating with the mergence of two vortices. Numerical simulation indicates that the flat band is robust against the disorder.

Coherent phase space structures in a 1D electrostatic plasma using particle-in-cell and Vlasov simulations: A comparative study

We present a quantitative comparative study of the formation of coherent phase space structures in one dimension using two widely followed approaches in kinetic simulations of collision-less plasmas, namely, Monte Carlo based Particle-In-Cell (PIC) simulations and phase space grid based Eulerian Vlasov-Poisson simulations. Using a newly developed PIC solver, we demonstrate that, while for linear regimes, there is a ready quantitative agreement between Vlasov-Poisson and PIC solvers, whereas for weakly nonlinear regimes and late time simulations, for comparable field resolutions, Vlasov-Poisson simulation results are found to be relatively noise-free as compared to PIC results with a large number of PIC particles. As an extreme case, we address using high resolution PIC simulations, the formation of giant phase space vortices obtained recently using the Vlasov-Poisson method [P. Trivedi and R. Ganesh, Phys. Plasmas 23, 062112 (2016)] for an infinitesimal amplitude external drive. For identical parameters and numerical resolution, we present a qualitative and quantitative comparison between PIC results of driven giant phase space structures and those of the Vlasov method, for a Maxwellian plasma.

Scale locality of the energy cascade using real space quantities

The classical energy cascade in turbulence as described by Richardson and Kolmogorov is predominantly a conjecture relying on the locality of interactions between scales of turbulence. This picture is generally accepted and assumes that energy and enstrophy transfers occur between neighboring scales of turbulence and that vortex stretching plays a major role in the dynamics of this energy cascade. Direct numerical simulation data for Reλ ranging from 37 to 1131 is used to gather evidence for the cascade by investigating the energy and enstrophy fluxes between scales and the interplay between vorticity at one scale and strain at an adjacent scale. This is achieved by using a bandpass filter to educe the turbulent structures at various length scales, allowing one to determine the fluxes between these scales and to interrogate the role of nonlocal (in physical space) vortex stretching. It is shown that the structures of a length scale L mostly transfer their energy to structures of size 0.3L and that most of the enstrophy flux goes from structures of scale L to 0.3L. Furthermore, vortical structures of a length scale Lω are stretched mostly by straining structures of size 3Lω to 5Lω, and the stretching by eddies of sizes larger than 10Lω is negligible. The stretching is dominated by the most extensive principal strain rate of the straining structures. These observations are found to be independent of Reλ for the range investigated in this study. These results provide strong evidence for the classical view of an energy cascade transferring energy from large to small scales through a hierarchy of steps, each step consisting of the stretching of vortices by somewhat larger structures.

Observation of Polarization Vortices in Momentum Space.

The vortex, a fundamental topological excitation featuring the in-plane winding of a vector field, is important in various areas such as fluid dynamics, liquid crystals, and superconductors. Although commonly existing in nature, vortices were observed exclusively in real space. Here, we experimentally observed momentum-space vortices as the winding of far-field polarization vectors in the first Brillouin zone of periodic plasmonic structures. Using homemade polarization-resolved momentum-space imaging spectroscopy, we mapped out the dispersion, lifetime, and polarization of all radiative states at the visible wavelengths. The momentum-space vortices were experimentally identified by their winding patterns in the polarization-resolved isofrequency contours and their diverging radiative quality factors. Such polarization vortices can exist robustly on any periodic systems of vectorial fields, while they are not captured by the existing topological band theory developed for scalar fields. Our work provides a new way for designing high-Q plasmonic resonances, generating vector beams, and studying topological photonics in the momentum space.