Helicity, Reconnection, and Dynamo Effects

The inter-relationships between magnetic helicity, magnetic reconnection, and dynamo effects are discussed. In laboratory experiments, where two plasmas are driven to merge, the helicity content of each plasma strongly affects the reconnection rate, as well as the shape of the diffusion region. Conversely, magnetic reconnection events also strongly affect the global helicity, resulting in efficient helicity cancellation (but not dissipation) during counter-helicity reconnection and a finite helicity increase or decrease (but less efficiently than dissipation of magnetic energy) during co-helicity reconnection. Close relationships also exist between magnetic helicity and dynamo effects. The turbulent electromotive force along the mean magnetic field (alpha-effect), due to either electrostatic turbulence or the electron diamagnetic effect, transports mean-field helicity across space without dissipation. This has been supported by direct measurements of helicity flux in a laboratory plasma. When the dynamo effect is driven by electromagnetic turbulence, helicity in the turbulent field is converted to mean-field helicity. In all cases, however, dynamo processes conserve total helicity except for a small battery effect, consistent with the observation that the helicity is approximately conserved during magnetic relaxation.

Two spectral regimes of magnetic field amplification in magnetohydrodynamic (MHD) flows can be distinguished by the scale on which fields are amplified relative to the primary forcing scale of the turbulence. For field amplification at or below the forcing scale, the amplification can be called a “small-scale dynamo.” For amplification at and above the forcing scale the process can be called a “large-scale dynamo.” Non - local (in wave number) effects play a key role in both the growth of the small-scale field in non-helical turbulence and the growth of large and smallscale fields in helical turbulence. Mean field dynamo (MFD) theory represents a simple semi-analytic way to get a handle on large-scale field amplification in MHD turbulence. Helicity has long been known to be important for large scale, flux generating, externally forced MFDs. The extent to which such MFDs operate “slow” or “fast” (dependent or independent on magnetic Reynolds number) has been controversial, but there has been recent progress. Simulations of α2 dynamos in a periodic box dynamo and their quenching can now be largely understood within a simplified dynamical non-linear paradigm in which the MFD growth equation is supplemented by the total magnetic helicity evolution equation. For α2 dynamos, the large-scale field growth is directly related to the large-scale magnetic helicity growth. Magnetic helicity conservation then implies that growth of the large-scale magnetic helicity induces growth of small-scale magnetic (and current) helicity of the opposite sign, which eventually suppresses the α effect driving the MFD growth. Although the α2 MFD then becomes slow in the long time limit, substantial large-scale field growth proceeds in a kinematic, “fast” phase before non-linear asymptotic quenching of the “slow” phase applies. Ultimately, the MFD emerges as a process that transfers magnetic helicity between small and large scales. How these concepts apply to more general dynamos with shear, and open boundary dynamos is a topic of ongoing research. Some unresolved issues are identified. Overall, the following summarizes the most recent progress in mean-field dynamo theory: For a closed turbulent flow, the non-linear mean field dynamo, is first fast and kinematic, then slow and dynamic, and magnetic helicity transfer makes it so.KeywordsMagnetic EnergyMagnetic HelicityMagnetic Reynolds NumberDynamo TheoryForce ScaleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The nonlinear mean-field dynamo due to a shear-current effect in a nonhelical homogeneous turbulence with a mean velocity shear is discussed. The transport of magnetic helicity as a dynamical nonlinearity is taken into account. The shear-current effect is associated with the W × J term in the mean electromotive force, where W is the mean vorticity due to the large-scale shear motions and J is the mean electric current. This effect causes the generation of large-scale magnetic field in a turbulence with large hydrodynamic and magnetic Reynolds numbers. The dynamo action due to the shear-current effect depends on the spatial scaling of the correlation time τ( k ) of the background turbulence, where k is the wave number. For Kolmogorov scaling, τ(k)∝k −2/3, the dynamo instability occurs, while when τ(k) ∝k −2 (small hydrodynamic and magnetic Reynolds numbers) there is no the dynamo action in a sheared nonhelical turbulence. The magnetic helicity flux strongly affects the magnetic field dynamics in the nonlinear stage of the dynamo action. Numerical solutions of the nonlinear mean-field dynamo equations which take into account the shear-current effect, show that if the magnetic helicity flux is not small, the saturated level of the mean magnetic field is of the order of the equipartition field determined by the turbulent kinetic energy. Turbulence with a large-scale velocity shear is a universal feature in astrophysics, and the obtained results can be important for elucidation of origin of the large-scale magnetic fields in astrophysical sheared turbulence.

A large eddy simulation of magnetohydrodynamic (MHD) turbulent channel flow is carried out to investigate the dynamo mechanism. It is shown that the streamwise component of the mean magnetic field is generated and sustained due to the effect of the turbulent electromotive force. The Reynolds-averaged turbulence model for MHD flows is assessed; it is suggested that the cross-helicity dynamo effect contributes to the turbulent electromotive force; that is, the electromotive force parallel to the mean vorticity is generated due to the turbulent cross helicity. To verify the importance of the cross-helicity dynamo, the transport equation for the turbulent electromotive force is evaluated; it is confirmed that the term involving the cross helicity and the mean vorticity is the main production term for the turbulent electromotive force. The transport equations for the turbulent kinetic and magnetic energies are also examined to discuss the dynamo mechanism from the viewpoint of the energy transfer.

The increase of twist helicity by the curl of the Lorentz force in 3‐D time‐dependent reconnection implies a current dynamo effect, which transfers electromagnetic energy into the magnetosphere. Therefore magnetic reconnection is not only a dissipation process (J·E >0) but also a dynamo process (J·E <0), which corresponds to the generation of the field‐aligned current. The dynamo effect is effective if the level of the fluctuations, irregularities and non‐linearity of the plasma in the reconnection region is high. In this case the turbulent plasma with a finite diffusivity can be reorganized to a near force‐ and torque‐free state in the multiple reconnection sites. The current dynamo effect during reconnection gives an explanation for the diversion and disruption of the magnetopause current and the formation of large and small twisted magnetic flux tubes (so called FTEs, mini‐FTEs or impulsive penetration) at the magnetopause. An “overlap‐reconnect‐twist” dynamo process is suggested. The theory of the conversion and approximate conservation of the magnetic helicity during reconnection is used to estimate the average dynamo effect. During magnetic reconnection, the induced electric field consists of the convection electric field (Ec) and the time‐dependent electric field (Ei(X, t)), which correspond to the diffusion (J·Ec > 0) and dynamo processes (<∫J·EidV> <0)respectively.

Context. For a better understanding of the dynamics of the solar corona, it is important to analyse the evolution of the helicity of the magnetic field. Since the helicity cannot be directly determined by observations, we have recently proposed a method to calculate the relative magnetic helicity in a finite volume for a given magnetic field, which however required the flux to be balanced separately on all the sides of the considered volume. Aims. We developed a scheme to obtain the vector potential in a volume without the above restriction at the boundary. We studied the dissipation and escape of relative magnetic helicity from an active region. Methods. In order to allow finite magnetic fluxes through the boundaries, a Coulomb gauge was constructed that allows for global magnetic flux balance. The property of sinusoidal function was used to obtain the vector potentials at the 12 edges of the considered rectangular volume extending above an active region. We tested and verified our method in a theoretical fore-free magnetic field model. Results. We applied the new method to the former calculation data and found a difference of less than 1.2%. We also applied our method to the magnetic field above active region NOAA 11429 obtained by a new photospheric-data-driven magnetohydrodynamics (MHD) model code GOEMHD3. We analysed the magnetic helicity evolution in the solar corona using our new method. We find that the normalized magnetic helicity (H∕Φ2) is equal to −0.038 when fast magnetic reconnection is triggered. This value is comparable to the previous value (−0.029) in the MHD simulations when magnetic reconnection happened and the observed normalized magnetic helicity (−0.036) from the eruption of newly emerging active regions. We find that only 8% of the accumulated magnetic helicity is dissipated after it is injected through the bottom boundary. This is in accordance with the Woltjer conjecture. Only 2% of the magnetic helicity injected from the bottom boundary escapes through the corona. This is consistent with the observation of magnetic clouds, which could take magnetic helicity into the interplanetary space. In the case considered here, several halo coronal mass ejections (CMEs) and two X-class solar flares originate from this active region.

\n Context. The paper is concerned with heating of the solar corona by nanoflares: a superposition of\nsmall transient events in which stored magnetic energy is dissipated by magnetic reconnection.\nIt is proposed that heating occurs in the nonlinear phase of an ideal kink instability, where\nmagnetic reconnection leads to relaxation to a state of minimum magnetic energy.\n Aims. The aim is to investigate the nonlinear aspects of magnetic relaxation on a current loop with zero net axial current.\nThe dynamical processes leading to the establishment of a relaxed state are explored. The efficiency of\nloop heating is investigated. \n Methods. A 3D magnetohydrodynamic numerical code is used to simulate the evolution of coronal\nloops which are initially in ideally unstable equilibrium. The initial states have zero net current.\nThe results are interpreted by comparison both with linear stability analysis\nand with helicity-conserving relaxation theory.\n Results. The disturbance due to the unstable mode is strongly radially confined when the loop carries\nzero net current. Strong current sheets are still formed in the nonlinear phase with dissipation of\nmagnetic energy by fast reconnection. The nonlinear development consists first of\nreconnection in a large scale current sheet, which forms near the quasi-resonant surface of the equilibrium field.\nSubsequently, the current sheet extends and then fragments, leading to multiple\nreconnections and effective relaxation to a constant α field.\n Conclusions. Magnetic reconnection is triggered in the nonlinear phase of kink instability in loops with zero net current.\nInitially, reconnection occurs in a single current sheet, which then fragments into multiple\nreconnection sites, allowing almost full relaxation to the minimum energy state.\nThe loop is heated to high temperatures throughout its volume.\n

This review puts together what we have learned about coronal structures and phenomenology to synthesize a physical picture of the corona as a voluminous, thermally and electrically highly-conducting atmosphere responding dynamically to the injection of magnetic flux from below. The synthesis describes complementary roles played by the magnetic heating of the corona, the different types of flares, and the coronal mass ejections as physical processes by which magnetic flux and helicity make their way from below the photosphere into the corona, and, ultimately, into interplanetary space. In these processes, a physically meaningful interplay among dissipative magnetohydrodynamic turbulence, ideal ordered flows, and magnetic helicity determines how and when the rich variety of relatively long-lived coronal structures, spawned by the emerged magnetic flux, will evolve quasi-steadily or erupt with the impressive energies characteristic of flares and coronal mass ejections. Central to this picture is the suggestion, based on recent theoretical and observational works, that the the emerged flux may take the form of a twisted flux rope residing principally in the corona. Such a flux rope is identified with the low-density cavity at the base of a coronal helmet, often but not always encasing a quiescent prominence. The flux rope may either be bodily transported into the corona from below the photosphere, or reform out of a state of flaring turbulence under some suitable constraint of magnetic-helicity conservation. The appeal of this synthesis is its physical simplicity and the manner it relates a large set of diverse phenomena into a self-consistent whole. The implications of this view point are discussed. The topics covered are: the large-scale corona; helmet streamers; quiescent prominences; coronal mass ejections; flares and heating; magnetic reconnection and magnetic helicity; and, the hydromagnetics of magnetic flux emergence.

By making use of the MHD self-induction equation in general relativity (GR), recently derived by Clarkson and Marklund (2005), it is shown that when Friedmann universe possesses a spatial section whose Riemannian curvature is negative, the magnetic energy bounds computed by Nuñez (2002) also bounds the growth rate of the magnetic field given by the strain matrix of dynamo flow. Since in GR-MHD dynamo equation, the Ricci tensor couples with the universe magnetic field, only through diffusion, and most ages are highly conductive the interest is more theoretical here, and only very specific plasma astrophysical problems can be address such as in laboratory plasmas. Magnetic fields and the negative curvature of some isotropic cosmologies, contribute to enhence the amplification of the magnetic field. Ricci curvature energy is shown to add to strain matrix of the flow, to enhance dynamo action in the universe. Magnetic fluctuations of the Clarkson-Marklund equations for a constant magnetic field seed in highly conductive flat universes, leads to a magnetic contrast of ≈ 2, which is well within observational limits from extragalactic radiosources of ≈ 1.7. In the magnetic helicity fluctuations the magnetic contrast shows that the dynamo effects can be driven by these fluctuations.

Magnetic helicity, an intrinsic property of eruptive helical flux ropes (FRs) forming coronal mass ejections (CMEs), plays an important role in determining CME geoeffectiveness. In the solar atmosphere and heliosphere, helicity remains conserved in a closed volume. Considering this fact as a basis of our study, we perform a quantitative comparison between total magnetic helicity and twisted flux in interplanetary CMEs and those transported to CMEs via magnetic reconnection at low corona. At the source, twisted/poloidal flux (ϕpcme) of CMEs is directly estimated from total reconnection flux, and CME helicity (Hcme) is obtained by combining reconnection flux information with CME physical parameters. At 1 AU, the twisted/poloidal flux (ϕpmc) and helicity (Hmc) of CMEs are obtained from in situ observations. Considering uncertainties steaming from FR length, reconnection flux and CME physical parameter estimations, poloidal flux and helicity of CMEs at 1 AU are found to be highly relevant (ϕpmcϕpcme = 0.4–1.5, HmcHcme = 0.3–1) to low-corona magnetic reconnection at the wake of CMEs. This result remains unchanged despite CME association with pre-existing FRs. We show that a significant reduction in CME helicity during its heliospheric propagation may result from a high rate of FR erosion in the interplanetary medium. Our event analysis confirms that CME’s intrinsic magnetic properties are transported to CME FRs during magnetic reconnection at sheared coronal arcades. A one-to-one correspondence between the chirality of 1-AU CMEs and their pre-eruptive structures complies with the fact that the sense of field line rotations in FRs may remain unchanged during coronal reconnection at the source. By connecting intrinsic magnetic properties of FRs through Sun-Earth medium, this study provides important implications for the origin of geoeffectiveness in CMEs.

The aim of this paper is to look at the magnetic helicity structure of an emerging active region and show that both emergence and flaring signatures are consistent with a same sign for magnetic helicity. We present a multiwavelength analysis of an M1.6 flare occurring in the NOAA active region 10365 on 27 May 2003, in which a large new bipole emerges in a decaying active region. The diverging flow pattern and the “tongue” shape of the magnetic field in the photosphere with elongated polarities are highly suggestive of the emergence of a twisted flux tube. The orientation of these tongues indicates the emergence of a flux tube with a right-hand twist (i.e., positive magnetic helicity). The flare signatures in the chromosphere are ribbons observed in Hα by the MSDP spectrograph in the Meudon solar tower and in 1600 Å by TRACE. These ribbons have a J shape and are shifted along the inversion line. The pattern of these ribbons suggests that the flare was triggered by magnetic reconnection at coronal heights below a twisted flux tube of positive helicity, corresponding to that of the observed emergence. It is the first time that such a consistency between the signatures of the emerging flux through the photosphere and flare ribbons has been clearly identified in observations. Another type of ribbons observed during the flare at the periphery of the active region by the MSDP and SOHO/EIT is related to the existence of a null point, which is found high in the corona in a potential field extrapolation. We discuss the interpretation of these secondary brightenings in terms of the “breakout” model and in terms of plasma compression/heating within large-scale separatrices.

Magnetic reconnection is a fundamental plasma process responsible for the sometimes explosive release of magnetic energy in space and laboratory plasmas. Inside the diffusion regions of magnetic reconnection, the plasma becomes demagnetized and decouples from the magnetic field, enabling the change in magnetic topology necessary to power the energy release over larger scales. Since it was launched in 2015, the Magnetospheric MultiScale (MMS) mission has significantly advanced the understanding of the particle dynamics key to magnetic reconnection by providing high-resolution, in-situ measurements able to resolve ion and electron kinetic scales that have confirmed theoretical predictions, revealed new phenomena, and refined existing models. These breakthroughs are critical for understanding not only space plasmas but also laboratory and astrophysical plasmas where magnetic reconnection occurs. In this talk, we give a brief review and present some recent results of selected topics related to the ion and electron dynamics occurring within the diffusion regions.

In space plasma, various effects of magnetic reconnection and turbulence cause the electron motion to significantly deviate from their Larmor orbits. Collectively these orbits affect the electron velocity distribution function and lead to the appearance of the "non-gyrotropic" elements in the pressure tensor. Quantification of this effect has important applications in space and laboratory plasma, one of which is tracing the electron diffusion region (EDR) of magnetic reconnection in space observations. Three different measures of agyrotropy of pressure tensor have previously been proposed, namely, A∅ e , Dng and Q. The multitude of contradictory measures has caused confusion within the community. We revisit the problem by considering the basic properties an agyrotropy measure should have. We show that A∅ e , Dng and Q are all defined based on the sum of the principle minors (i.e. the rotation invariant I 2) of the pressure tensor. We discuss in detail the problems of I 2-based measures and explain why they may produce ambiguous and biased results. We introduce a new measure AG constructed based on the determinant of the pressure tensor (i.e. the rotation invariant I 3) which does not suffer from the problems of I 2-based measures. We compare AG with other measures in 2 and 3-dimension particle-in-cell magnetic reconnection simulations, and show that AG can effectively trace the EDR of reconnection in both Harris and force-free current sheets. On the other hand, A∅ e does not show prominent peaks in the EDR and part of the separatrix in the force-free reconnection simulations, demonstrating that A∅ e does not measure all the non-gyrotropic effects in this case, and is not suitable for studying magnetic reconnection in more general situations other than Harris sheet reconnection.

We argue that the hypothesis of preservation of shape of dimensionless second- and third-order correlations during decay of incompressible homogeneous magnetohydrodynamic (MHD) turbulence requires, in general, at least two independent similarity length scales. These are associated with the two Elsässer energies. The existence of similarity solutions for the decay of turbulence with varying cross-helicity implies that these length scales cannot remain in proportion, opening the possibility for a wide variety of decay behaviour, in contrast to the simpler classic hydrodynamics case. Although the evolution equations for the second-order correlations lack explicit dependence on either the mean magnetic field or the magnetic helicity, there is inherent implicit dependence on these (and other) quantities through the third-order correlations. The self-similar inertial range, a subclass of the general similarity case, inherits this complexity so that a single universal energy spectral law cannot be anticipated, even though the same pair of third-order laws holds for arbitrary cross-helicity and magnetic helicity. The straightforward notion of universality associated with Kolmogorov theory in hydrodynamics therefore requires careful generalization and reformulation in MHD.

CMPD Final Report Experimental Study of Current-Driven Turbulence During Magnetic Reconnection Miklos Porkolab, PI, Jan Egedal, co-PI, William Fox, graduate student. This is the final report for Grant DE-FC02-04ER54786, MIT Participation in the Center for Multiscale Plasma Dynamics, which was active from 8/1/2004 to 7/31/2010. This Grant supported the thesis work of one MIT graduate student, William Fox, The thesis research consisted of an experimental study of the fluctuations arising during magnetic reconnection in plasmas on the Versatile Toroidal Facility (VTF) at MIT Plasma Science and Fusion Center (PSFC). The thesis was submitted and accepted by the MIT physics Department,. Fox, Experimental Study of Current-Driven Turbulence During Magnetic Reconnection, Ph.D. Thesis, MIT (2009). In the VTF experiment reconnection and current-sheet formation is driven by quickly changing currents in a specially arranged set of internal conductors. Previous work on this device [Egedal, et al, PRL 98, 015003, (2007)] identified a spontaneous reconnection regime. In this work fluctuations were studied using impedance-matched, high-bandwidth Langmuir probes. Strong, broadband fluctuations, with frequencies extending from near the lower-hybrid frequency [fLH = (fcefci)1/2] to the electron cyclotron frequency fce were found to arise during the reconnection events. Based on frequency and wavelength measurements, lower-hybrid waves and Trivelpiece-Gould waves were identified. The lower-hybrid waves are easiest to drive with strong perpendicular drifts or gradients which arise due to the reconnection events; an appealing possibility is strong temperature gradients. The Trivelpiece-Gould modes can result from kinetic, bump-on-tail instability of a runaway electron population energized by the reconnection events. We also observed that the turbulence is often spiky, consisting of discrete positive-potential spikes, which were identified as electron phase-space holes, a class of nonlinear solitary wave known to evolve from a strong beam-on-tail instability. We established that fast electrons were produced by magnetic reconnection. Overall, these instabilities were found to be a consequence of reconnection, specifically the strong energization of electrons, leading to steep gradients in both coordinate- and velocity-space. Estimates (using quasi-linear theory) of the anomalous resistivity due to these modes did not appear large enough to substantially impact the reconnection process. Relevant publications: W. Fox, M. Porkolab, et al, Phys. Rev. Lett. 101, 255003 (2008). W. Fox, M. Porkolab, et al, Phys. Plasmas 17, 072303, (2010).