Helicity Conservation Research Articles

A Check for Consistency between Different Magnetic Helicity Measurements Based on the Helicity Conservation Principle

Magnetic helicity is a useful quantity in characterizing the magnetic systems of solar active regions. The purpose of the present work is to check for consistency between the local correlation tracking (LCT) method used to measure helicity injection through the photosphere, and the linear force-free field (LFFF) method used to determine helicity in the corona, based on the principle of helicity conservation in the solar corona. We have calculated the amount of magnetic helicity injected through the photosphere during the first disk passage of AR 10696 using the LCT method initially described by Chae. We have also measured the coronal magnetic helicity as a function of time using the LFFF method. With a value for the force-free α, the coronal field is constructed from the extrapolation of the Solar and Heliospheric Observatory (SOHO) MDI magnetograms, then compared with the coronal loops in the EUV images taken by the SOHO EIT. The force-free α that best fits the loops is used to calculate the coronal helicity. From a careful comparison of different helicity measurements during each time interval, we have reached the core conclusion that our measurements follow the helicity conservation principle with an uncertainty of ~15% and hence support the consistency between the two different methods with the same amount of uncertainty.

Amplification of mean magnetic field and magnetic helicity production in hot lepton plasma of early universe

We argue that the magnetic helicity conservation is violated at the lepton stage in the evolution of early Universe owing to the parity violation in the Standard Model of electroweak interactions. As a result, a cosmological magnetic field which can be a seed for the galactic dynamo obtains from the beginning a substantial magnetic helicity which has to be taken into account in the magnetic helicity balance at the later stage of galactic dynamo. The particle physics mechanism suggested in our works depends neither on helicity of matter turbulence with plasma vortices resulting in the standard α effect in dynamo theory nor on general rotation. The mechanism can result in a self-exitation of an (almost) uniform cosmological magnetic field.

Rescattering effects of baryon and antibaryon in heavy quarkonium decays

Rescattering effects of baryon and antibaryon in heavy quarkonium decays are investigated by studying their angular distributions. The rescattering amplitudes are phenomenologically evaluated by modeling the intermediate range interaction as a a or pion meson exchange between q (q) over bar quarks. The results show that the rescattering effects play an important role in determination of the angular distribution in heavy quarkonium decays. Especially, for J/psi and psi(2S) decays into Lambda(Lambda) over bar, Sigma(0)(Sigma) over bar (0) and Xi(-)(Xi) over bar (+) the angular distribution parameters could turn to be negative values in the limit of helicity conservation. These results provide us a possible explanation for understanding the negative sign of the angular distribution parameter measured for J/psi -> Sigma(0)(Sigma) over bar (0), namely, it might come from the baryonic SU(3)(F) symmetry breaking by incorporating rescattering effects. (c) 2006 Elsevier B.V. All rights reserved.

Addendum to "Helicity conservation in gauge boson scattering at high energy"

In a previous paper we have established that for any two-body process involving even numbers of transverse vector bosons and gauginos, the dominant asymptotic amplitudes obey helicity conservation (HC); i.e. the sum of the helicities of the two incoming particles equals to the sum of the helicities of the two outgoing ones. This HC has been proved to all orders in MSSM, provided $(s, |t|,|u|)$ are much larger than all masses in the model; but only to leading 1-loop logarithmic order in SM. In the present addendum, the validity of HC is extended to all two-body processes. Renormalizability is crucial for the HC validity, while all known anomalous couplings violate it.

Cosmological magnetic helicity

AbstractWe argue that magnetic helicity conservation is violated at the lepton stage in the evolution of the early Universe. As a result, a cosmological magnetic field which can be a seed for the galactic dynamo obtains a substantial magnetic helicity from the beginning which has to be taken into account on later stages of galactic evolution. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Elastic J/ψ production at HERA

Cross sections for elastic production of J/Psi mesons in photoproduction and electroproduction are measured in electron proton collisions at HERA using an integrated luminosity of 55 pb^{-1}. Results are presented for photon virtualities Q^2 up to 80 GeV^2. The dependence on the photon-proton centre of mass energy W_{gamma p} is analysed in the range 40 < \Wgp < 305 GeV in photoproduction and 40 < \Wgp < 160 GeV in electroproduction. The \Wgp dependences of the cross sections do not change significantly with Q^2 and can be described by models based on perturbative QCD. Within such models, the data show a high sensitivity to the gluon density of the proton in the domain of low Bjorken x and low Q^2. Differential cross sections d\sigma/dt, where t is the squared four-momentum transfer at the proton vertex, are measured in the range |t|<1.2 GeV^2 as functions of \Wgp and Q^2. Effective Pomeron trajectories are determined for photoproduction and electroproduction. The J/Psi production and decay angular distributions are consistent with s-channel helicity conservation. The ratio of the cross sections for longitudinally and transversely polarised photons is measured as a function of Q^2 and is found to be described by perturbative QCD based models.

Conservation laws of turbulence models

The conservation of mass, momentum, energy, helicity, and enstrophy in fluid flow are important because these quantities organize a flow, and characterize change in the flow's structure over time. In turbulent flow, conservation laws remain important in the inertial range of wave numbers, where viscous effects are negligible. It is in the inertial range where energy, helicity (3d), and enstrophy (2d) must be accurately cascaded for a turbulence model to be qualitatively correct. A first and necessary step for an accurate cascade is conservation; however, many turbulent flow simulations are based on turbulence models whose conservation properties are little explored and might be very different from those of the Navier–Stokes equations. We explore conservation laws and approximate conservation laws satisfied by LES turbulence models. For the Leray, Leray deconvolution, Bardina, and Nth order deconvolution models, we give exact or approximate laws for a model mass, momentum, energy, enstrophy and helicity. The possibility of cascades for model quantities is also discussed.

The distribution of current helicity at the solar surface at the beginning of the solar cycle

A fraction of solar active regions are observed to have current helicity of a sign that contradicts the polarity law for magnetic helicity; this law corresponds to the well-known Hale polarity law for sunspots. A significant excess of active regions with the sign of helicity is seen to occur just at the beginning of the cycle. We compare these observations with predictions from a dynamo model based on principles of helicity conservation, discussed by Zhang et al. (2006). This model seems capable of explaining only a fraction of the regions with the wrong sign of the helicity. We attribute the remaining excess to additional current helicity production from the twisting of rising magnetic flux tubes, as suggested by Choudhuri et al. (2004). We estimate the relative contributions of this effect and that connected with the model based on magnetic helicity conservation.

Galactic dynamo and helicity losses through fountain flow

Nonlinear behaviour of galactic dynamos is studied, allowing for magnetic helicity removal by the galactic fountain flow. A suitable advection speed is estimated, and a one-dimensional mean-field dynamo model with dynamic alpha-effect is explored. It is shown that the galactic fountain flow is efficient in removing magnetic helicity from galactic discs. This alleviates the constraint on the galactic mean-field dynamo resulting from magnetic helicity conservation and thereby allows the mean magnetic field to saturate at a strength comparable to equipartition with the turbulent kinetic energy.

Helicity conservation under Reidemeister moves

We discuss a connection between two fields that appear to have little in common: plasma physics and mathematical knot theory. Plasma physicists are interested in studying helicity conservation in magnetic flux ropes and knot theorists commonly consider “Reidemeister moves,” transformations that preserve a property called “knottedness.” To study the tangling, twisting, and untwisting of magnetic flux ropes, it is helpful to know which topological transformations conserve helicity. Although the second and third types of Reidemeister moves applied to a magnetic flux rope clearly conserve the helicity of the flux rope, the first type of Reidemeister move appears to be in conflict with helicity conservation. We show that all three Reidemeister moves conserve helicity in magnetic flux ropes.

Scattering of glue by glue on the light-cone worldsheet: Helicity nonconserving amplitudes

We give the light-cone gauge calculation of the one-loop on-shell scattering amplitudes for gluon-gluon scattering which violate helicity conservation. We regulate infrared divergences by discretizing the ${p}^{+}$ integrations, omitting the terms with ${p}^{+}=0$. Collinear divergences are absent diagram by diagram for the helicity nonconserving amplitudes. We also employ a novel ultraviolet regulator that is natural for the light-cone worldsheet description of planar Feynman diagrams. We show that these regulators give the known answers for the helicity nonconserving one-loop amplitudes, which do not suffer from the usual infrared vagaries of massless particle scattering. For the maximal helicity violating process we elucidate the physics of the remarkable fact that the loop momentum integrand for the on-shell Green function associated with this process, with a suitable momentum routing of the different contributing topologies, is identically zero. We enumerate the counterterms that must be included to give Lorentz covariant results to this order, and we show that they can be described locally in the light-cone worldsheet formulation of the sum of planar diagrams.

Approaching the solar dynamo

The origin of the solar magnetic field remains a stubborn challenge of astrophysics. At the solar surface the magnetic field assumes a complex, hierarchical structure in space and time. Systematic features such as the solar cycle and the butterfly diagram point to the existence of a deep-rooted large-scale predominantly toroidal magnetic field. In this review of solar dynamo theory new developments in our understanding of processes relevant for the solar dynamo are discussed. In recent years there has been significant progress with regard to tachocline physics, magnetic helicity conservation, the α effect, magnetic pumping, and the storage and amplification of the magnetic field. Remaining uncertainties about the nature of the deep-seated magnetic field and the α effect have thus far prevented the formulation of a coherent model for the solar dynamo. It is proposed that further progress is best achieved through a combination of approaches including high-resolution numerical simulations and global mean-field modeling. Along these lines some recent numerical simulations of magnetic pumping and flux expulsion in a magnetic layer are presented. The computations were performed with a new anelastic Cartesian finite-difference MHD code, which is the appropriate tool for studying processes near the base of stellar convection zones with a high spatial resolution. Possible implications for the solar dynamo are discussed.

Factors contributing to the conservation of magnetic helicity

The magnetic helicity is often considered a quasi-invariant in the magnetohydrodynamic evolution of a plasma. While in general this is not the case, this invariance phenomenon occurs in many relevant situations, so that it is interesting to look for physical parameters that may detract from the maximum theoretical decay rate of helicity. The size of the Lorentz force is the main one: based on it, we find that several means of the magnetic energy, the transfer rate between kinetic and magnetic energies, and the variation of the angular momentum tend to slow down the evolution of magnetic helicity.

Non-Current-free Coronal Closure of Subphotospheric MHD Models

We propose a method that allows the matching of two classes of models that have been well developed so far, but largely independently from each other: (1) convection zone (CZ) models, which generally either end up below the photosphere or are matched with an external potential field, and (2) coronal models of eruptive processes and heating, which usually consider the evolution of current-carrying magnetic fields driven by given photospheric changes. In our approach, the thin turbulent photospheric layer between the two large regions is modeled as a resistive layer across which the physical quantities suffer stiff variations. We show that this layer enables the transport of an electric current into the corona through the tangential component of the electric field (continuous across the various interfaces), as well as good conservation of the global magnetic helicity. To illustrate our general approach, we present in detail a model problem in which the rising of an initially twisted flux rope through the CZ is described kinematically while the physics inside the corona is described by a full magnetohydrodynamic model. We show that the evolution leads to the emergence of magnetic flux and electric current into the corona, with the creation of a flux rope that eventually suffers a dynamical transition toward fast expansion.

Variational principle with singular perturbation of hall magnetohydrodynamics

The Hall magnetohydrodynamics (H-MHD) model can describe an intrinsic small scale (ion skin depth ℓi) introduced by the Hall effect. The Hall term appears as a singular perturbation to the conventional magnetohydrodynamics (MHD) model, and hence, the MHD limit (ℓi→0) may be singular. The H-MHD system has three constants of motion, the energy, the magnetic (electron) and ion helicities. The ion helicity is known to be “fragile” with respect to the energy norm of the magnetic and flow fields [Z. Yoshida and S. M. Mahajan, Phys. Rev. Lett. 88, 095001 (2002)]. Under an appropriate ordering of scales, the ion helicity translates as the cross helicity that is a constant of motion of the MHD system. Conservation of the cross helicity is an essential condition to recover the macroscopic MHD picture from the H-MHD framework.

The spheromak confinement device

A general definition of the spheromak is given. The nature of helicity conservation and its importance to the spheromak concept are discussed. The reactor advantages, stability properties, and β limits are covered. Several successful formation schemes and steady state sustainment methods are presented. How they each inject helicity and to what extent they depend on helicity-conserving relaxation is discussed. What helicity conservation tells us about relaxation and what it does not tell us is covered. The major outstanding spheromak issues are presented.

Variational description of multifluid hydrodynamics: Coupling to gauge fields

In this work we extend our previously developed formalism of Newtonian multi-fluid hydrodynamics to allow for coupling between the fluids and the electromagnetic and gravitational field. This is achieved within the convective variational principle by using a standard minimal coupling prescription. In addition to the conservation of total energy and momentum, we derive the conservation of canonical vorticity and helicity, which generalize the corresponding conserved quantities of uncharged fluids. We discuss the application of this formalism to electrically conducting systems, magnetohydrodynamics and superconductivity. The equations of electric conductors derived here are more general than those found in the standard description of such systems, in which the effect of entrainment is overlooked, despite the fact that it will generally be present in any conducting multi-constituent system.

Helicity Conservation in Gauge Boson Scattering at High Energy

We remark that the high energy gauge boson scattering processes involving two-body initial and final states satisfy certain selection rules described as helicity conservation of the gauge boson amplitudes (GBHC). These rules are valid at the Born level, as well as at the level of the leading and subleading 1-loop logarithmic corrections, in both the standard model and the minimal supersymmetric standard model (MSSM). A "fermionic equivalence" theorem is also proved, which suggests that GBHC is valid at all orders in the MSSM at sufficiently high energies, where the mass suppressed contributions are neglected.

A special class in vanishing helicity ideal flows

The derivation of a Lagrangian invariant so-called spirality is reviewed through the Lagrangian coordinates. The value of the spirality is fixed up to a gauge transformation. The helicity conservation follows directly from this invariant. Among all ideal flows with zero helicity in a domain of flow frozen into the fluid motion, a special class is introduced. This special topological class has the possibility to transform its spirality to be identically zero everywhere in the domain. For those simply connected domains of motion, a necessary and a sufficient condition is presented for these zero spirality flows.

The radial distribution of magnetic helicity in the solar convective zone: observations and dynamo theory

We continue our attempt to connect observational data on current helicity in solar active regions with solar dynamo models. In addition to our previous results about temporal and latitudinal distributions of current helicity, we argue that some information concerning the radial profile of the current helicity averaged over time, and latitude can be extracted from the available observations. The main feature of this distribution can be presented as follows. Both shallow and deep active regions demonstrate a clear dominance of one sign of current helicity in a given hemisphere during the whole cycle. Broadly speaking, current helicity has opposite polarities in the Northern and Southern hemispheres, although there are some active regions that violate this polarity rule. The relative number of active regions violating the polarity rule is significantly higher for deeper active regions. A separation of active regions into ‘shallow’, ‘middle’ and ‘deep’ is made by comparing their rotation rate and the helioseismic rotation law. We use a version of Parker’s dynamo model in two spatial dimensions, which employs a nonlinearity based on magnetic helicity conservation arguments. The predictions of this model about the radial distribution of solar current helicity appear to be in remarkable agreement with the available observational data; in particular the relative volume occupied by the current helicity of ‘wrong’ sign grows significantly with the depth.