Non-zero Helicity Research Articles

Non-zero helicity extinction in light scattered from achiral (or chiral) small particles located at points of null incident helicity density

Based on a recent unified formulation on dichroism and extinction of helicity on scattering by a small particle, dipolar in the wide sense, magnetodielectric or not, chiral or achiral, we show that such extinction is enhanced not only at resonances of polarizabilities, but also due to interference between left and right circularly polarized components of the incident wave, which contributes with appropriate parameters of the illuminating field, even if the particle is achiral and is placed at points of the incident field at which the local incident helicity density is zero.This phenomenon goes beyond standard circular dichroism (CD), and we analyze it in detail on account of the values of several quantities involved in the process, both of the incident light and the particle. In addition, this interference produces a term in the helicity extinction that remarkably yields information on the real parts of the electric and/or magnetic polarizabilities, which are not provided by CD, and of which the helicity extinction phenomenon may be considered a generalization.

Non-zero helicity of a cyclonic vortex over localized heat source

Experimental and numerical study of the steady-state cyclonic vortex from isolated heat source in a rotating fluid layer is described. The structure of laboratory cyclonic vortex is similar to the typical structure of tropical cyclones from observational data and numerical modelling including secondary flows in the boundary layer. Differential characteristics of the flow were studied by numerical simulation using CFD software FlowVision. It was found that helicity in a described system has non-zero value. Physical interpretation of helicity distribution is provided.

Magnetic fields and chiral asymmetry in the early hot universe

In this paper, we study analytically the process of external generation and subsequent free evolution of the lepton chiral asymmetry and helical magnetic fields in the early hot universe. This process is known to be affected by the Abelian anomaly of the electroweak gauge interactions. As a consequence, chiral asymmetry in the fermion distribution generates magnetic fields of non-zero helicity, and vice versa. We take into account the presence of thermal bath, which serves as a seed for the development of instability in magnetic field in the presence of externally generated lepton chiral asymmetry. The developed helical magnetic field and lepton chiral asymmetry support each other, considerably prolonging their mutual existence, in the process of `inverse cascade' transferring magnetic-field power from small to large spatial scales. For cosmologically interesting initial conditions, the chiral asymmetry and the energy density of helical magnetic field are shown to evolve by scaling laws, effectively depending on a single combined variable. In this case, the late-time asymptotics of the conformal chiral chemical potential reproduces the universal scaling law previously found in the literature for the system under consideration. This regime is terminated at lower temperatures because of scattering of electrons with chirality change, which exponentially washes out chiral asymmetry. We derive an expression for the termination temperature as a function of the chiral asymmetry and energy density of helical magnetic field.

Topological magnetoelectric effects in microwave far-field radiation

Similar to electromagnetism, described by the Maxwell equations, the physics of magnetoelectric (ME) phenomena deals with the fundamental problem of the relationship between electric and magnetic fields. Despite a formal resemblance between the two notions, they concern effects of different natures. In general, ME-coupling effects manifest in numerous macroscopic phenomena in solids with space and time symmetry breakings. Recently, it was shown that the near fields in the proximity of a small ferrite particle with magnetic-dipolar-mode (MDM) oscillations have the space and time symmetry breakings and the topological properties of these fields are different from the topological properties of the free-space electromagnetic fields. Such MDM-originated fields—called magnetoelectric (ME) fields—carry both spin and orbital angular momenta. They are characterized by power-flow vortices and non-zero helicity. In this paper, we report on observation of the topological ME effects in far-field microwave radiation based on a small microwave antenna with a MDM ferrite resonator. We show that the microwave far-field radiation can be manifested with a torsion structure where an angle between the electric and magnetic field vectors varies. We discuss the question on observation of the regions of localized ME energy in far-field microwave radiation.

CMB anisotropies generated by a stochastic background of primordial magnetic fields with non-zero helicity

We consider the impact of a stochastic background of primordial magnetic fields with non-vanishing helicity on CMB anisotropies in temperature and polarization. We compute the exact expressions for the scalar, vector and tensor part of the energy-momentum tensor including the helical contribution, by assuming a power-law dependence for the spectra and a comoving cutoff which mimics the damping due to viscosity. We also compute the parity-odd correlator between the helical and non-helical contribution which generate the TB and EB cross-correlation in the CMB pattern. We finally show the impact of including the helical term on the power spectra of CMB anisotropies up to multipoles with ℓ ∼ \U0001d4aa(103).

INVERSE CASCADE IN IMBALANCED ELECTRON MAGNETOHYDRODYNAMIC TURBULENCE

Electron magnetohydrodynamics (EMHD) provides a fluid-like description of small-scale magnetized plasmas. Balanced EMHD turbulence has been studied for a long time. However, driven imbalanced EMHD turbulence, in which waves moving in one direction (dominant waves) have higher amplitudes than waves moving in the other direction (sub-dominant waves), has not been well studied. In this paper, we numerically study driven three-dimensional imbalanced weak EMHD turbulence. We find the following results. First, in driven imbalanced EMHD turbulence, we clearly observe inverse cascade of magnetic helicity, as well as magnetic energy. This is because magnetic helicity is a conserved quantity and non-zero magnetic helicity is injected into the system in driven imbalanced EMHD turbulence. Second, the magnetic energy spectrum of the dominant waves on scales larger than the energy injection scale does not show a single power-law spectrum, which indicates that the inverse cascade is not a self-similar process. The peak of the spectrum roughly follows a k –3/2 spectrum, which can be explained by a Kolmogorov-type argument for weak turbulence. Third, a small amount of sub-dominant waves is induced by the dominant waves on large scales and the ratio of helicity densities of the dominant and the sub-dominant waves on large scales seems to converge to a certain value.

Unidirectional magnetoelectric-field multiresonant tunneling

Unidirectional multi-resonant tunneling of the magnetoelectric (ME) field excitations through a subwavelength (regarding the scales of regular electromagnetic radiation) vacuum or isotropic-dielectric regions has been observed in two-port microwave structures having a quasi-2D ferrite disk with magnetic dipolar mode (MDM) oscillations. The excitations manifest themselves as Fano-resonance peaks in the scattering-matrix parameters at the stationary states of the MDM spectrum. The ME near-field excitations are quasimagnetostatic fields with non-zero helicity parameter: Topological phase properties of ME fields are determined by edge chiral currents of MDM oscillations. We show that while for a given direction of a bias magnetic field (in other words, for a given direction of time), the ME field excitations are considered as ‘forward’ tunneling processes, in the opposite direction of a bias magnetic field (the opposite direction of time), there are ‘backward’ tunneling processes. Unidirectional ME field resonant tunneling is observed due to the distinguishable topology of the ‘forward’ and ‘backward’ ME field excitations. We establish a close connection between the Fano-resonance unidirectional tunneling and the topology of the ME fields in different microwave structures.

Primordial magnetic helicity constraints from WMAP nine-year data

If a primordial magnetic field in the universe has non-zero helicity, the violation of parity symmetry results in non-zero correlations between cosmic microwave background temperature and B-mode polarization. In this paper we derive approximations to the relevant microwave background power spectra arising from a helical magnetic field. Using the cross-power spectrum between temperature and B-mode polarization from the WMAP nine-year data, we set a 95\% confidence level upper limit on the helicity amplitude to be 10 nG$^2$ Gpc for helicity spectral index $n_H = -1.9$, for a cosmological magnetic field with effective field strength of 3 nG and a power-law index $n_B = -2.9$ near the scale-invariant value. Future microwave background polarization maps with greater sensitivity will be able to detect the helicity of an inflationary magnetic field well below the maximum value allowed by microwave background constraints on the magnetic field amplitude.

Helicity in the Ekman boundary layer

AbstractHelicity, which is defined as the scalar product of velocity and vorticity, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\mathcal{H}} = {\boldsymbol {u}} \boldsymbol {\cdot }\boldsymbol{\omega}$, is an inviscidly conserved quantity in a barotropic fluid. Mean helicity is zero in flows that are parity invariant. System rotation breaks parity invariance and has therefore the potential of giving rise to non-zero mean helicity. In this paper we study the helicity dynamics in the incompressible Ekman boundary layer. Evolution equations for the mean field helicity and the mean turbulent helicity are derived and it is shown that pressure flux injects helicity at a rate $ 2 \varOmega G^2 $ over the total depth of the Ekman layer, where $ G $ is the geostrophic wind far from the wall and $ {\boldsymbol{\Omega}} = \varOmega {\boldsymbol {e}}_y $ is the rotation vector and $ {\boldsymbol {e}}_y $ is the wall-normal unit vector. Thus right-handed/left-handed helicity will be injected if $ \varOmega $ is positive/negative. We also show that in the uppermost part of the boundary layer there is a net helicity injection with opposite sign as compared with the totally integrated injection. Isotropic relations for the helicity dissipation and the helicity spectrum are derived and it is shown that it is sufficient to measure two transverse velocity components and use Taylor’s hypothesis in the mean flow direction in order to measure the isotropic helicity spectrum. We compare the theoretical predictions with a direct numerical simulation of an Ekman boundary layer and confirm that there is a preference for right-handed helicity in the lower part of the Ekman layer and left-handed helicity in the uppermost part when $ \varOmega > 0 $. In the logarithmic range, the helicity dissipation conforms to isotropic relations. On the other hand, spectra show significant departures from isotropic conditions, suggesting that the Reynolds number considered in the study is not sufficiently large for isotropy to be valid in a wide range of scales. Our analytical and numerical results strongly suggest that there is a turbulent helicity cascade of right-handed helicity in the logarithmic range of the atmospheric boundary layer when $\varOmega >0$, consistent with recent measurements by Koprov, Koprov, Ponomarev & Chkhetiani (Dokl. Phys., vol. 50, 2005, pp. 419–422). The isotropic relations which are derived may facilitate future measurements of the helicity spectrum in the atmospheric boundary layer as well as in controlled wind tunnel experiments.

Helicity and flow topology in three-dimensional anisotropic porous media

Flows showing complex topology are ubiquitous in natural systems. However, contrasting evidence exists on the helical nature of flow in porous media and on the occurrence of groundwater whirls. We analyze the topology of steady-state flow fields in porous media, highlighting the importance of considering the three-dimensionality of the flow field to properly capture the complexity of the system dynamics controlling the deformation of material surfaces, which is widely recognized as the main driver of mixing. We use the helicity density as topological measure and investigate the necessary and sufficient conditions to obtain non-zero helicity density for Darcy flow. We show that helical groundwater flow can develop in both homogeneous and heterogeneous porous media, provided that the hydraulic conductivity is anisotropic. In the homogeneous case, the additional condition of non-vanishing mixed second spatial derivatives of hydraulic head is required, while in heterogeneous media, helical flow may occur even when the hydraulic gradient is uniform. We present illustrative examples of complex flow topology in three-dimensional porous media and discuss the computed streamline patterns and their potential implications for mixing processes.

MAGNETIC HELICITY IN THE DISSIPATION RANGE OF STRONG IMBALANCED TURBULENCE

Hybrid numerical simulations of freely decaying two-dimensional turbulence are presented. The background magnetic field is perpendicular to the simulation plane, which eliminates linear kinetic Alfven waves from the system. The net magnetic helicity of the initial fluctuations at large scales is zero. The turbulence is set to be imbalanced in the sense that the net cross-helicity is not zero. As the turbulence evolves, it develops nonzero magnetic helicity at smaller scales, in the proton kinetic range. In the quasi-steady state of evolution, the magnetic helicity spectrum has a peak consistent with the solar wind observations. The peak position depends on the plasma beta and correlates with a sharp decline of the cross-helicity spectrum.

Microwave magnetoelectric fields and their role in the matter-field interaction

We show that in a source-free subwavelength region of microwave fields, there can exist field structures with a local coupling between the time-varying electric and magnetic fields differing from the electric-magnetic coupling in regular-propagating free-space electromagnetic waves. To distinguish such field structures from regular electromagnetic (EM) field structures, we term them as magnetoelectric (ME) fields. We study a structure and conservation laws of microwave ME near fields. We show that there exist sources of microwave ME near fields-the ME particles. These particles are represented by small quasi-two-dimensional ferrite disks with magnetic-dipolar-oscillation spectra. The near fields originating from such particles are characterized by topologically distinctive power-flow vortices, nonzero helicity, and a torsion degree of freedom. The paper consists of two main parts. In the first one, we give a theoretical background of properties of the electric and magnetic fields inside and outside of a ferrite particle with magnetic-dipolar-oscillation spectra resulting in the appearance of microwave ME near fields. In the second main part, we represent numerical and experimental studies of the microwave ME near fields and their interactions with matter. Based on the obtained properties of the ME near fields, we discuss possibilities for effective microwave sensing of natural and artificial chiral structures.

Stochastic particle acceleration by helical turbulence in solar flares

Flaring release of magnetic energy in solar corona is only possible if the magnetic field deviates from a potential one. We show that the linear magnetohydrodynamic (MHD) modes excited on top of the non-potential magnetic field possess a non-zero kinetic helicity. Accordingly, this necessarily results in a noticeable kinetic helicity of the turbulence, composed of these linear modes with various scales and random phases, generated at the flare site by the primary energy release, which may be important for many applications. In particular, a non-zero turbulence helicity has a potentially strong effect on the particle acceleration because the helical component of the turbulence induces a mean regular large-scale (DC) electric field capable of directly accelerating the charged particles in addition to the commonly considered stochastic turbulent electric field. In this paper, we derive the kinetic helicity density of the linear MHD modes excited on top of a twisted large-scale magnetic field, estimate the corresponding turbulence helicity and take its effect on stochastic particle acceleration by the turbulence into consideration; in particular, we compare this induced mean electric field with the electron and estimated effective ion Dreicer fields. We have discovered that this, so far missing but highly important, ingredient of the turbulence at the flare site can be responsible for the thermal-to-non-thermal energy partition in flares by controlling the process of particle extraction from the thermal pool and formation of the seed particle population to be then stochastically accelerated to higher energies. In addition, it is naturally consistent with such puzzling flare manifestations as spatial separation of electron and proton emission sites, electron beam formation, and enrichment of the accelerated particle population by 3He and other rare ions.

Using Fluid Variational Variables to Obtain New Analytic Solutions of Self-Gravitating Flows with Nonzero Helicity

Flow equations being nonlinear are notoriously difficult to solve analytically. In this work we show that, through a three- independent-functions variational formalism for steady barotropic flows, new analytical solutions of the flow equations can be obtained. A family of flows on predetermined toroidal Bernoulli surfaces is constructed. These flows have nonzero helicity and may be maintained by a suitable irrotational force distribution. For a particular density distribution, this force field can be provided approximately by self-gravitation.

MAGNETIC-DIPOLAR-MODE OSCILLATIONS FOR NEAR- AND FAR-FIELD MANIPULATION OF MICROWAVE RADIATION

There has been a surge of interest in the subwavelength conflnement efiects of the electromagnetic flelds. Based on these efiects, one can obtain new behaviors of the near- and far-fleld radiation. It is well known that in optics, the subwavelength conflnement can be obtained due to surface-plasmon (or electrostatic) oscillations in metal structures. This paper is a review of recent studies on the subwavelength conflnement in microwaves due to magnetic-dipolar-mode (MDM) (or magnetostatic (MS)) oscillations in small ferrite samples. MDM oscillations in a mesoscopic ferrite- disk particle are quantized oscillations, which are characterized by energy eigenstates. The fleld structures are distinguished by power- ∞ow vortices and non-zero helicity. Also in vacuum, the near flelds originated from MDM particles are designated by topologically distinctive power-∞ow vortices, non-zero helicity, and a torsion degree of freedom. To difierentiate such fleld structures from regular electromagnetic (EM) fleld structures, we term them as magnetoelectric (ME) flelds. In a pattern of the microwave fleld scattered by a MDM ferrite disk and MDM-disk arrays, one can observe rotating topological-phase dislocations. This opens a perspective for creation of engineered electromagnetic flelds with unique symmetry properties. In the near-fleld applications, we propose novel microwave sensors for material characterization, biology, and nanotechnology. Strong energy concentration and unique topological structures of the near flelds originated from the MDM resonators allow efiective measuring chiral properties of materials in microwaves. Generating

Solar Dynamo and Toroidal Field Instabilities

The possibility of non-axisymmetric (kink) instabilities of a toroidal field seated in the tachocline is much discussed in the literature. In this work, the basic properties of kink and quasi-interchange instabilities, produced by mixed toroidal and poloidal configuration, will be briefly reviewed. In particular, it will be shown that the unstable modes are strongly localized near the Equator and not near the Poles as often claimed in the literature. Based on the results of recent numerical simulations, it is argued that a non-zero helicity can already be produced at a non-linear level. A mean-field solar dynamo is then constructed with a positive α-effect in the overshoot layer localized near the Equator, and a meridional circulation with deep return flow. Finally, the possibility that the solar cycle is driven by an αΩ dynamo generated by the negative subsurface shear in the supergranulation layer will also be discussed.

Helical scenario of tropical cyclone genesis and intensification

A helical scenario of tropical cyclogenesis and further vortex intensification is proposed based on results of direct numerical simulation of atmospheric flows. The main idea of the scenario consists in a specific topology of helical flows which are characterized by the linkage of vortex lines. Velocity fields resulting from a high resolution numerical simulation by the Regional Atmospheric Modeling System (RAMS) are used to calculate helical and integral characteristics during a tropical cyclone formation. It is shown how non-zero mean helicity is generated by moist convective atmospheric turbulence, which implies a new flow topology with linked vortex lines. A possible role of vortical hot towers (VHTs) is discussed in generating the linkage. It is shown that the linkage results in a positive feedback between the horizontal and vertical circulation in the formation of a larger-scale vortex and contributes to the instability of the macro vortex.

A symmetry break in dynamo models

In accordance with the concepts of dynamo theory, largescale magnetic fields of many astrophysical objects are associated with the rotationinduced break of mirror symmetry (1). The rotation of objects and the presence of depth density gradients (∇ρ) turn out to be sufficient for the existence of a correlation between the vertical velocity and the vorticity of small� scale vortices. This correlation results in the nonzero kinetic helicity χ = 〈v · rotv〉, where v is the turbulent velocity and 〈·〉 implies averaging over an ensemble. In the simplest cases, it is considered that, in the same hemisphere, the helicity is of identical sign: in the northern hemisphere, it is negative when the density increases with depth, which is natural for selfgravitat� ing bodies. In the southern hemisphere, the helicity is positive, e.g., χ = -cosϑ (2, 3), where ϑ is the angle with respect to the rotation z axis in the spherical coor� dinate system (r, ϑ, ϕ). The existence of the nonzero helicity χ of the hemispheres significantly simplifies the generation of a largescale magnetic field. At the same time, the helicity is obtained as a result of aver� aging and is subjected to random fluctuations (4), which, in the long run, affects the generation of the magnetic field (5). The source of the fluctuations can be either an insufficient number of vortices over which averaging is performed or the existence of anomalies at the object boundaries, e.g., the appearance of tidal forces in binary stars or the presence of thermal inho� mogeneities at boundaries of the liquid core and the mantle in planets (6). These arguments can lead to the break of antisymmetry χ with respect to the equatorial plane. In the framework of the Parker model for the αω dynamo, we show below that, even for a linear mode, a small nonparity (χ) violation can lead to a sig� nificant symmetry break of the magnetic field in oppo� site hemispheres. We now consider the Parker model often applied to describe processes of the magneticfield generation in various astrophysical objects (1, 7, 8). We below make use of the following equations in a thin spherical shell:

Magnetic field line random walk in non-axisymmetric turbulence

Including a random component of a magnetic field parallel to an ambient field introduces a mean perpendicular motion to the average field line. This effect is normally not discussed because one customarily chooses at the outset to ignore such a field component in discussing random walk and diffusion of field lines. A discussion of the basic effect is given, indicating that any random magnetic field with a non-zero helicity will lead to such a non-zero perpendicular mean motion. Several exact analytic illustrations are given of the effect as well as a simple numerical illustration.

Parametric study of the transition in the wake of oblate spheroids and flat cylinders

An exhaustive parametric study of the transition scenario in the wake of oblate spheroids and flat cylinders placed with their rotation axis parallel to the flow is presented. The flatness of the investigated objects is classified by the aspect ratio χ defined as χ = d/a for spheroids (with d the diameter and a the length of the polar axis) and as χ = d/h) for cylinders (with h the cylinder height). We find a significant qualitative similarity between both configurations. At large aspect ratios (χ > 2.3 for spheroids and χ ≥ 4 for cylinders), the secondary bifurcation giving rise to a periodic state without planar symmetry is subcritical with a hysteresis interval of about two Reynolds number units. For spheroids, the sphere-like scenario is recovered only at aspect ratios very close to one (χ ≥ 1 are considered), while for cylindrical bodies the same holds for χ ≤ 1.7. For intermediate aspect ratios, a domain of states with non-zero net helicity separates states typical for the sphere wake from those of an infinitely flat disk.