Helicity Conservation Research Articles

Hydrodynamic and kinetic models for spin-1/2 electron-positron quantum plasmas: Annihilation interaction, helicity conservation, and wave dispersion in magnetized plasmas

We discuss the complete theory of spin-1/2 electron-positron quantum plasmas, when electrons and positrons move with velocities mach smaller than the speed of light. We derive a set of two fluid quantum hydrodynamic equations consisting of the continuity, Euler, spin (magnetic moment) evolution equations for each species. We explicitly include the Coulomb, spin-spin, Darwin and annihilation interactions. The annihilation interaction is the main topic of the paper. We consider the contribution of the annihilation interaction in the quantum hydrodynamic equations and in the spectrum of waves in magnetized electron-positron plasmas. We consider the propagation of waves parallel and perpendicular to an external magnetic field. We also consider the oblique propagation of longitudinal waves. We derive the set of quantum kinetic equations for electron-positron plasmas with the Darwin and annihilation interactions. We apply the kinetic theory to the linear wave behavior in absence of external fields. We calculate the contribution of the Darwin and annihilation interactions in the Landau damping of the Langmuir waves. We should mention that the annihilation interaction does not change number of particles in the system. It does not related to annihilation itself, but it exists as a result of interaction of an electron-positron pair via conversion of the pair into virtual photon. A pair of the non-linear Schrodinger equations for the electron-positron plasmas including the Darwin and annihilation interactions is derived. Existence of the conserving helicity in electron-positron quantum plasmas of spinning particles with the Darwin and annihilation interactions is demonstrated. We show that the annihilation interaction plays an important role in the quantum electron-positron plasmas giving the contribution of the same magnitude as the spin-spin interaction.

Conservation of writhe helicity under anti-parallel reconnection.

Reconnection is a fundamental event in many areas of science, from the interaction of vortices in classical and quantum fluids, and magnetic flux tubes in magnetohydrodynamics and plasma physics, to the recombination in polymer physics and DNA biology. By using fundamental results in topological fluid mechanics, the helicity of a flux tube can be calculated in terms of writhe and twist contributions. Here we show that the writhe is conserved under anti-parallel reconnection. Hence, for a pair of interacting flux tubes of equal flux, if the twist of the reconnected tube is the sum of the original twists of the interacting tubes, then helicity is conserved during reconnection. Thus, any deviation from helicity conservation is entirely due to the intrinsic twist inserted or deleted locally at the reconnection site. This result has important implications for helicity and energy considerations in various physical contexts.

Helicity-resolved Raman scattering of MoS₂, MoSe₂, WS₂, and WSe₂ atomic layers.

The two-fold valley degeneracy in two-dimensional (2D) semiconducting transition metal dichalcogenides (TMDCs) (Mo,W)(S,Se)2 is suitable for "valleytronics", the storage and manipulation of information utilizing the valley degree of freedom. The conservation of luminescent photon helicity in these 2D crystal monolayers has been widely regarded as a benchmark indicator for charge carrier valley polarization. Here we perform helicity-resolved Raman scattering of the TMDC atomic layers. In drastic contrast to luminescence, the dominant first-order zone-center Raman bands, including the low energy breathing and shear modes as well as the higher energy optical phonons, are found to either maintain or completely switch the helicity of incident photons. In addition to providing a useful tool for characterization of TMDC atomic layers, these experimental observations shed new light on the connection between photon helicity and valley polarization.

On a chiral analog of the Einstein-de Haas effect

The Einstein-de Haas effect reveals a transfer of angular momentum from microscopic constituents (electrons) to a macroscopic body, but in the case of massless fermions, one could expect the transfer of the chirality of constituents to macroscopic helical motion. For such a picture to be consistent, the macroscopic helicity is to be conserved classically, to echo the conservation of the angular momentum of a rotating body. The helicity conservation would in turn impose constraints on hydrodynamics of chiral liquids (whose constituents are massless fermions). Essentially, the chiral liquids are dissipation-free, on the classical level. Reservations and alternatives to this scenario are discussed.

Flux Ropes as Singularities of the Vector Potential

A flux rope is a domain of concentration of the magnetic field $\textbf{B}$. Insofar as $\textbf{B}$ outside such a domain is considered as vanishingly small, a flux rope can be described as the core of a singularity of the outer vector potential $\textbf{A}$, whose topological invariant is the magnetic flux through the rope. By 'topological' it is meant that $\oint_C\textbf{A}\cdot\mathrm d\textbf{s}$ measures along any loop $C$ surrounding the flux rope the same constant flux $\Phi$. The electric current intensity is another invariant of the theory, but non-topological. We show that, in this theoretical framework, the linear force-free field (LFFF) Lundquist model and the non-linear (NLFFF) Gold-Hoyle model of a flux rope exhibit stable solutions distributed over quantized strata of increasing energies (an infinite number of strata in the first case, only one stratum in the second case); each stratum is made of a continuous set of stable states. The lowest LFFF stratum and the unique NLFFF stratum come numerically close one to the other, and match with a reasonable accuracy the data collected by spacecrafts travelling across magnetic clouds. The other LFFF strata do not match these data at all. It is not possible at this stage to claim which model fits better the magnetic cloud data. We also analyze in some detail the merging of tubes belonging to the same stratum, with conservation of the magnetic helicity, and the transition of a tube from one stratum to another one, which does not conserve magnetic helicity.

Separated response functions in exclusive, forwardπ±electroproduction on deuterium

Background: Measurements of forward exclusive meson production at different squared four-momenta of the exchanged virtual photon, $Q^2$, and at different four-momentum transfer, t, can be used to probe QCD's transition from meson-nucleon degrees of freedom at long distances to quark-gluon degrees of freedom at short scales. Ratios of separated response functions in $\pi^-$ and $\pi^+$ electroproduction are particularly informative. The ratio for transverse photons may allow this transition to be more easily observed, while the ratio for longitudinal photons provides a crucial verification of the assumed pole dominance, needed for reliable extraction of the pion form factor from electroproduction data. Method: Data were acquired with 2.6-5.2 GeV electron beams and the HMS+SOS spectrometers in Jefferson Lab Hall C, at central $Q^2$ values of 0.6, 1.0, 1.6 GeV$^2$ at W=1.95 GeV, and $Q^2$=2.45 GeV$^2$ at W=2.22 GeV. There was significant coverage in $\phi$ and $\epsilon$, which allowed separation of $\sigma_{L,T,LT,TT}$. Results: $\sigma_L$ shows a clear signature of the pion pole, with a sharp rise at small -t. In contrast, $\sigma_T$ is much flatter versus t. The longitudinal/transverse ratios evolve with $Q^2$ and t, and at the highest $Q^2$=2.45 GeV$^2$ show a slight enhancement for $\pi^-$ production compared to $\pi^+$. The $\pi^-/\pi^+$ ratio for transverse photons exhibits only a small $Q^2$-dependence, following a nearly universal curve with t, with a steep transition to a value of about 0.25, consistent with s-channel quark knockout. The $\sigma_{TT}/\sigma_T$ ratio also drops rapidly with $Q^2$, qualitatively consistent with s-channel helicity conservation. The $\pi^-/\pi^+$ ratio for longitudinal photons indicates a small isoscalar contamination at W=1.95 GeV, consistent with what was observed in our earlier determination of the pion form factor at these kinematics.

Spin density matrix elements in exclusive $$\omega $$ ω electroproduction on $$^1$$ 1 H and $$^2$$ 2 H targets at 27.5 GeV beam energy

Spin Density Matrix Elements (SDMEs) describing the angular distribution of exclusive ρ 0 electroproduction and decay are determined in the HERMES experiment with 27.6 GeV beam energy and unpolarized hydrogen and deuterium targets. Eight (fifteen) SDMEs that are related (unrelated) to the longitudinal polarization of the beam are extracted in the kinematic region 1<Q 2<7 GeV2, 3.0<W<6.3 GeV, and −t<0.4 GeV2. Within the given experimental uncertainties, a hierarchy of relative sizes of helicity amplitudes is observed. Kinematic dependences of all SDMEs on Q 2 and t are presented, as well as the longitudinal-to-transverse ρ 0 electroproduction cross-section ratio as a function of Q 2. A small but statistically significant deviation from the hypothesis of s-channel helicity conservation is observed. An indication is seen of a contribution of unnatural-parity-exchange amplitudes; these amplitudes are naturally generated with a quark-exchange mechanism.

Helicity conservation by flow across scales in reconnecting vortex links and knots.

The conjecture that helicity (or knottedness) is a fundamental conserved quantity has a rich history in fluid mechanics, but the nature of this conservation in the presence of dissipation has proven difficult to resolve. Making use of recent advances, we create vortex knots and links in viscous fluids and simulated superfluids and track their geometry through topology-changing reconnections. We find that the reassociation of vortex lines through a reconnection enables the transfer of helicity from links and knots to helical coils. This process is remarkably efficient, owing to the antiparallel orientation spontaneously adopted by the reconnecting vortices. Using a new method for quantifying the spatial helicity spectrum, we find that the reconnection process can be viewed as transferring helicity between scales, rather than dissipating it. We also infer the presence of geometric deformations that convert helical coils into even smaller scale twist, where it may ultimately be dissipated. Our results suggest that helicity conservation plays an important role in fluids and related fields, even in the presence of dissipation.

A note on helicity conservation in Leray models of incompressible flow

We prove conservation of a regularized helicity HL:=∫Ωu⋅wdx for the Leray model (and its variants) of turbulent flow, where w is the solution of a Leray-regularized vorticity equation. The usual definition of helicity is H=∫Ωu⋅(∇×u)dx, which is considered by Navier–Stokes flows, but is not a conserved quantity of the Leray model. However, if u is a Leray solution, then the difference between H and HL is that HL uses a regularized vorticity and H uses the curl of a regularized velocity. The results are extended to show that the standard Crank–Nicolson finite element method for Leray models conserves both discrete energy and discrete regularized helicity.

Biot-Savart helicity versus physical helicity: A topological description of ideal flows

For an isentropic (thus compressible) flow, fluid trajectories are considered as orbits of a family of one parameter, smooth, orientation-preserving, and nonsingular diffeomorphisms on a compact and smooth-boundary domain in the Euclidian 3-space which necessarily preserve a finite measure, later interpreted as the fluid mass. Under such diffeomorphisms the Biot-Savart helicity of the pushforward of a divergence-free and tangent to the boundary vector field is proved to be conserved and since these circumstances present an isentropic flow, the conservation of the “Biot-Savart helicity” is established for such flows. On the other hand, the well known helicity conservation in ideal flows which here we call it “physical helicity” is found to be an independent constant with respect to the Biot-Savart helicity. The difference between these two helicities reflects some topological features of the domain as well as the velocity and vorticity fields which is discussed and is shown for simply connected domains the two helicities coincide. The energy variation of the vorticity field is shown to be formally the same as for the incompressible flow obtained before. For fluid domains consisting of several disjoint solid tori, at each time, the harmonic knot subspace of smooth vector fields on the fluid domain is found to have two independent base sets with a special type of orthogonality between these two bases by which a topological description of the vortex and velocity fields depending on the helicity difference is achieved since this difference is shown to depend only on the harmonic knot parts of velocity, vorticity, and its Biot-Savart vector field. For an ideal magnetohydrodynamics (MHD) flow three independent constant helicities are reviewed while the helicity of magnetic potential is generalized for non-simply connected domains by inserting a special harmonic knot field in the dynamics of the magnetic potential. It is proved that the harmonic knot part of the vorticity in hydrodynamics and the magnetic field in MHD is presented by constant coefficients (fluxes) when expanded in terms of one of the time dependent base functions.

Pulsar scintillations from corrugated reconnection sheets in the interstellar medium

We show that surface waves along interstellar current sheets closely aligned with the line of sight lead to pulsar scintillation properties consistent with those observed. This mechanism naturally produces the length and density scales of the ISM scattering lenses that are required to explain the magnitude and dynamical spectrum of the scintillations. In this picture, the parts of warm ionized interstellar medium that are responsible for the scintillations are relatively quiescent, with scintillation and scattering resulting from weak waves propagating along magnetic domain boundary current sheets, which are both expected from helicity conservation and have been observed in numerical simulations. The model statistically predicts the spacing and amplitudes of inverted parabolic arcs seen in Fourier-transformed dynamical spectra of strongly scintillating pulsars with only 3 parameters. Multi-frequency, multi-epoch low frequency VLBI observations can quantitatively test this picture. If successful, in addition to mapping the ISM, this may open the door to precise nanoarcsecond pulsar astrometry, distance measurements, and emission studies using these 10AU interferometers in the sky.

Ribbons characterize magnetohydrodynamic magnetic fields better than lines: a lesson from dynamo theory

Blackman and Brandenburg argued that magnetic helicity conservation in dynamo theory can in principle be captured by diagrams of mean field dynamos when the magnetic fields are represented by ribbons or tubes, but not by lines. Here, we present such a schematic ribbon diagram for the α2 dynamo that tracks magnetic helicity and provides distinct scales of large-scale magnetic helicity, small-scale magnetic helicity, and kinetic helicity involved in the process. This also motivates our construction of a new ‘2.5 scale’ minimalist generalization of the helicity-evolving equations for the α2 dynamo that separately allows for these three distinct length-scales while keeping only two dynamical equations. We solve these equations and, as in previous studies, find that the large-scale field first grows at a rate independent of the magnetic Reynolds number RM before quenching to an RM-dependent regime. But we also show that the larger the ratio of the wavenumber where the small-scale current helicity resides to that of the forcing scale, the earlier the non-linear dynamo quenching occurs, and the weaker the large-scale field is at the turnoff from linear growth. The harmony between the theory and the schematic diagram exemplifies a general lesson that magnetic fields in magnetohydrodynamic are better visualized as two-dimensional ribbons (or pairs of lines) rather than single lines.

Some improvements in the theory of plasma relaxation

Taylor's relaxation theory is extended to plasmas with mass flow by using the cross helicity as a conserved quantity, similar to the magnetic helicity. Indeed, it is shown that the conservation of the cross helicity in magnetohydrodynamics is the result of the conservation of two magnetic-like helicities in two-fluid plasmas. In addition, the usually ignored toroidal flux is also held to be conserved. We also view plasma relaxation as attaining a maximum entropy state rather than Taylor's minimum energy state, but prove that maximizing the entropy subject to a given amount of energy is equivalent to minimizing the energy subject to a given amount of entropy. The resulting relaxed state is similar to the one discussed by Finn and Antonsen [Phys. Fluids 26, 3540 (1983)], and involves flow parallel to the magnetic field and constant temperature, but non-constant pressure. We show how to construct an asymptotic solution to the relaxed state based on the smallness of the Alfven Mach number of the flow.

Relativistic helicity and link in Minkowski space-time

A relativistic helicity has been formulated in the four-dimensional Minkowski space-time. Whereas the relativistic distortion of space-time violates the conservation of the conventional helicity, the newly defined relativistic helicity conserves in a barotropic fluid or plasma, dictating a fundamental topological constraint. The relation between the helicity and the vortex-line topology has been delineated by analyzing the linking number of vortex filaments which are singular differential forms representing the pure states of Banach algebra. While the dimension of space-time is four, vortex filaments link, because vorticities are primarily 2-forms and the corresponding 2-chains link in four dimension; the relativistic helicity measures the linking number of vortex filaments that are proper-time cross-sections of the vorticity 2-chains. A thermodynamic force yields an additional term in the vorticity, by which the vortex filaments on a reference-time plane are no longer pure states. However, the vortex filaments on a proper-time plane remain to be pure states, if the thermodynamic force is exact (barotropic), thus, the linking number of vortex filaments conserves.

Helicity-flux-driven α effect in laboratory and astrophysical plasmas.

The constraint imposed by magnetic helicity conservation on the α effect is considered for both magnetically and flow dominated self-organizing plasmas. Direct numerical simulations are presented for a dominant contribution to the α effect, which can be cast in the functional form of a total divergence of an averaged helicity flux, called the helicity-flux-driven α (Hα) effect. Direct numerical simulations of the Hα effect are presented for two examples-the magnetically dominated toroidal plasma unstable to tearing modes, and the flow-dominated accretion disk.

Local and nonlocal advected invariants and helicities in magnetohydrodynamics and gas dynamics I: Lie dragging approach

In this paper advected invariants and conservation laws in ideal magnetohydrodynamics (MHD) and gas dynamics are obtained using Lie dragging techniques. There are different classes of invariants that are advected or Lie dragged with the flow. Simple examples are the advection of the entropy S (a 0-form), and the conservation of magnetic flux (an invariant 2-form advected with the flow). The magnetic flux conservation law is equivalent to Faraday's equation. The gauge condition for the magnetic helicity to be advected with the flow is determined. Different variants of the helicity in ideal fluid dynamics and MHD including: fluid helicity, cross helicity and magnetic helicity are investigated. The fluid helicity conservation law and the cross-helicity conservation law in MHD are derived for the case of a barotropic gas. If the magnetic field lies in the constant entropy surface, then the gas pressure can depend on both the entropy and the density. In these cases the conservation laws are local conservation laws. For non-barotropic gases, we obtain nonlocal conservation laws for fluid helicity and cross helicity by using Clebsch variables. These nonlocal conservation laws are the main new results of the paper. Ertel's theorem and potential vorticity, the Hollman invariant, and the Godbillon–Vey invariant for special flows for which the magnetic helicity is zero are also discussed.

Local and nonlocal advected invariants and helicities in magnetohydrodynamics and gas dynamics: II. Noether's theorems and Casimirs

Conservation laws in ideal gas dynamics and magnetohydrodynamics (MHD) associated with fluid relabeling symmetries are derived using Noether's first and second theorems. Lie dragged invariants are discussed in terms of the MHD Casimirs. A nonlocal conservation law for fluid helicity applicable for a non-barotropic fluid involving Clebsch variables is derived using Noether's theorem, in conjunction with a fluid relabeling symmetry and a gauge transformation. A nonlocal cross helicity conservation law involving Clebsch potentials, and the MHD energy conservation law are derived by the same method. An Euler–Poincaré variational approach is also used to derive conservation laws associated with fluid relabeling symmetries using Noether's second theorem.

Helicity conservation hypothesis and pp-elastic scattering

We propose the helicity conservation model for description of polarization effects in the pp-elastic scattering at asymptotic energies. In this model the complete set of experiments will consist of only three observables. The predictions of model are compared with experimental data.

Forward and backward helicity scattering coefficients for systems with discrete rotational symmetry

The forward and backward scattering off linear systems with discrete rotational symmetries R(z)(2π/n) with n ≥ 3 are shown to be restricted by symmetry reasons. Along the symmetry axis, forward scattering can only be helicity preserving and backward scattering can only be helicity flipping. These restrictions do not exist for n < 3. If, in addition to the n ≥ 3 discrete rotational symmetry, the system has duality symmetry (obeys the helicity conservation law), it will exhibit zero backscattering. The results pinpoint the underlying symmetry reasons for some notable scattering properties of R(z)(2π/4) symmetric systems that have been reported in the metamaterials and radar literature. Applications to planar metamaterials and solar cells are briefly discussed.

An inflationary model with small scalar and large tensor nongaussianities

We study a model of inflation where the scalar perturbations are almost gaussian while there is sizable (equilateral) nongaussianity in the tensor sector. In this model, a rolling pseudoscalar gravitationally coupled to the inflaton amplifies the vacuum fluctuations of a vector field. The vector sources both scalar and tensor metric perturbations. Both kinds of perturbations are nongaussian, but, due to helicity conservation, the tensors have a larger amplitude, so that nongaussianity in the scalar perturbations is negligible. Moreover, the tensors produced this way are chiral. We study, in the flat sky approximation, how constraints on tensor nongaussianities affect the detectability of parity violation in the Cosmic Microwave Background. We expect the model to feature interesting patterns on nongaussianities in the polarization spectra of the CMB.