The role of the different helical components of the magnetic and velocity fields in the inverse spectral transfer of magnetic helicity is investigated through Fourier shell-to-shell transfer analysis. Both magnetic helicity and energetic transfer analysis are performed on chosen data from direct numerical simulations of homogeneous isothermal compressible magnetohydrodynamic turbulence, subject to both a large-scale mechanical forcing and a small-scale helical electromotive driving. The root mean square Mach number of the hydrodynamic turbulent steady-state taken as initial condition varies from 0.1 to about 11. Three physical phenomena can be distinguished in the general picture of the spectral transfer of magnetic helicity towards larger spatial scales: local inverse transfer, non-local inverse transfer and local direct transfer. A shell decomposition allows to associate these three phenomena with clearly distinct velocity scales while the helical decomposition allows to establish the role of the different helical components and the compressive part of the velocity field on the different transfer processes. The locality and relative strength of the different helical contributions are mainly determined by the triad helical geometric factor.
The inverse transfer of magnetic helicity is investigated through direct numerical simulations of large-scale-mechanically-driven turbulent flows in the isothermal ideal magnetohydrodynamics (MHD) framework. The mechanical forcing is either purely solenoidal or purely compressive and the turbulent steady-states considered exhibit root mean square (RMS) Mach numbers 0.1 $\lesssim$ M $\lesssim$ 11. A continuous small-scale electromotive forcing injects magnetic helical fluctuations, which lead to the build-up of ever larger magnetic structures. Spectral scaling exponents are observed which, for …
Understanding the in situ amplification of large scale magnetic fields in turbulent astrophysical rotators has been a core subject of dynamo theory. When turbulent velocities are helical, large scale dynamos that substantially amplify fields on scales that exceed the turbulent forcing scale arise, but the minimum sufficient fractional kinetic helicity f_h,C has not been previously well quantified. Using direct numerical simulations for a simple helical dynamo, we show that f_h,C decreases as the ratio of forcing to large scale wave numbers k_F/k_min increases. From the condition that a large s…
Kinetic helicity (hereafter helicity) is defined by the correlation between the velocity and the flow-aligned vorticity. Helicity, as well as energy, is an inviscid invariant of the hydrodynamic equations. In contrast to energy, a measure of the turbulent intensity, turbulent helicity, representing right- and left-handed twist associated with a fluctuating motion, provides a measure of the structural or topological property of the fluctuation. The helicity effect on the turbulent transport can be analytically obtained in the framework of the multiple-scale renormalized perturbation expansion t…
The distributed chaos driven by Levich-Tsinober (helicity) integral: $I=\int \langle h({\bf x},t)~h({\bf x}+{\bf r}, t)\rangle d{\bf r}$ has been studied. It is shown that the helical distributed chaos can be considered as basis for complex turbulent flows with interplay between large-scale coherent structures and small-scale turbulence, such as Cuette-Taylor flow, wake behind cylinder and turbulent flow in the Large Plasma Device (LAPD) with inserted limiters. In the last case appearance of the helical distributed chaos, caused by the limiters, results in improvement of radial particle confin…
The presence of large scale magnetic fields in nature is often attributed to the inverse cascade of magnetic helicity driven by turbulent helical dynamos. In this work we show that in turbulent helical dynamos, the inverse flux of magnetic helicity towards the large scales $Π_{\mathcal{H}}$ is bounded by $|Π_{\mathcal{H}}|\le c εk_η^{-1}$, where $ε$ is the energy injection rate, $k_η$ is the Kolmogorov magnetic dissipation wavenumber and $c$ an order one constant. Assuming the classical isotropic turbulence scaling, the inverse flux of magnetic helicity $Π_{\mathcal{H}}$ decreases at least as …
Helicity, a measure of the breakage of reflectional symmetry representing the topology of turbulent flows, contributes in a crucial way to their dynamics and to their fundamental statistical properties. We review several of their main features, both new and old, as the discovery of bi-directional cascades or the role of helical vortices in the enhancement of large-scale magnetic fields in the dynamo problem. The dynamical contribution in magnetohydrodynamic (MHD) of the cross-correlation between velocity and induction is discussed as well. We consider next how turbulent transport is affected b…
We derive exact scaling laws for a three-dimensional incompressible helical two-fluid plasma, without the assumption of isotropy. For each ideal invariant of the two-fluid model, i.e. the total energy, the electron helicity and the proton helicity, we derive simple scaling laws in terms of two-point increments correlation functions expressed in terms of the velocity field of each species and the magnetic field. These variables are appropriate for comparison with \textit{in-situ} measurements in the solar wind at different spatial ranges and data from numerical simulations. Finally, with the ex…
The excitation and further sustenance of large-scale magnetic fields in rotating astrophysical systems, including planets, stars and galaxies, is generally thought to involve a fluid magnetic dynamo effect driven by helical magnetohydrodynamic turbulence. While this scenario is appealing on general grounds, it however currently remains largely unconstrained, notably because a fundamental understanding of the nonlinear asymptotic behaviour of large-scale fluid magnetism in the astrophysically-relevant but treacherous regime of large magnetic Reynolds number $Rm$ is still lacking. We explore thi…
We present calculations of the relaxation of magnetic field structures that have the shape of particular knots and links. A set of helical magnetic flux configurations is considered, which we call $n$-foil knots of which the trefoil knot is the most primitive member. We also consider two nonhelical knots; namely, the Borromean rings as well as a single interlocked flux rope that also serves as the logo of the Inter-University Centre for Astronomy and Astrophysics in Pune, India. The field decay characteristics of both configurations is investigated and compared with previous calculations of he…
We show that oppositely directed fluxes of energy and magnetic helicity coexist in the inertial range in fully developed magnetohydrodynamic (MHD) turbulence with small-scale sources of magnetic helicity. Using a helical shell model of MHD turbulence, we study the high Reynolds number magnetohydrodynamic turbulence for helicity injection at a scale that is much smaller than the scale of energy injection. In a short range of scales larger than the forcing scale of magnetic helicity, a bottleneck-like effect appears, which results in a local reduction of the spectral slope. The slope changes in …
In our conventional understanding, large-scale magnetic fields are thought to originate from an inverse cascade in the presence of magnetic helicity, differential rotation, or a magneto-rotational instability. However, as recent simulations have given strong indications that an inverse cascade (transfer) may occur even in the absence of magnetic helicity, the physical origin of this inverse cascade is still not fully understood. We here present two simulations of freely decaying helical \& non-helical magnetohydrodynamic (MHD) turbulence. We verified the inverse transfer of helical and non-hel…
Models of large scale (magnetohydrodynamic) dynamos (LSD) which couple large scale field growth to total magnetic helicity evolution best predict the saturation of LSDs seen in simulations. For the simplest so called "α2" LSDs in periodic boxes, the electromotive force driving LSD growth depends on the difference between the time-integrated kinetic and current helicity associated with fluctuations. When the system is helically kinetically forced (KF), the growth of the large scale helical field is accompanied by growth of small scale magnetic (and current) helicity which ultimately quench the …
Progress toward understanding principles of nonlinear growth and saturation of large scale magnetic fields has emerged from comparison of theoretical models that incorporate the evolution of magnetic helicity with numerical simulations for problems that are more idealized than expected in astrophysical circumstances, but still fully non-linear. We carry out a new comparison of this sort for the magnetic field growth from forced isotropic helical turbulence in a periodic box. Previous comparisons be- tween analytic theory and simulations of this problem have shown that a two-scale model compare…
A non-linear, time-dependent, magnetically driven dynamo theory which shows how magnetically dominated configurations can relax to become helical on the largest scale available is presented. Coupled time-dependent differential equations for large scale magnetic helicity, small scale magnetic helicity, velocity, and the electromotive force are solved. The magnetic helicity on small scales relaxes to drive significant large scale helical field growth on dynamical (Alfvén crossing) time scales, independent of the magnitude of finite microphysical transport coefficients, after which the growing ki…
In this paper a relaxation theory, proposed several years ago for plasmas where a single dominant mode is present, is revisited. The solutions of the related eigenvalue problem are numerically calculated and discussed. Although these solutions are very rich and can reproduce well the magnetic fields measured in experiments, there is no manner within the theory to determine the dominant helicity, which is a free parameter in the model. To find the preferred helicity in the system, we propose to minimize the distance of the relaxed state from another state which is constructed as a two region ge…
A recent study on axisymmetric ideal magnetohydrodynamic equilibria with incompressible flows [H. Tasso and G. N. Throumoulopoulos, Phys. Plasmas {\bf 5}, 2378 (1998)] is extended to the generic case of helically symmetric equilibria with incompressible flows. It is shown that the equilibrium states of the system under consideration are governed by an elliptic partial differential equation for the helical magnetic flux function $ψ$ containing five surface quantities along with a relation for the pressure. The above mentioned equation can be transformed to one possessing differential part ident…
The free decay of MHD turbulence at large Reynolds numbers is studied numerically using a shell model. We study the statistical properties based on representative sample of realisations (128 realisations for each type of initial conditions) over the period of $10^5$ large-scale turnover times. The performed simulations show that the force-free non-helical MHD turbulence can demonstrate two different scenarios of evolution in spite of similar initial conditions. Within the first scenario, the cross-helicity accumulation is so fast that the energy cascade vanishes before significant magnetic ene…
The buildup of small-scale magnetic helicity which accompanies the oppositely signed growth on large scales is central to conventional dynamical quenching theories of mean-field dynamos. However, the conventional formalism presumes isotropic turbulence and thereby excludes part of the magnetic Lorentz back-reaction. This renders it insufficient to predict the full quenching for general anisotropic flows. To overcome this deficiency, we derive a new generalized quenching formalism that includes the full back-reacting Lorentz force, and a new "selective-damping-$τ$" closure which conserves magne…
Recent MHD dynamo simulations for magnetic Prandtl number $>1$ demonstrate that when MHD turbulence is forced with sufficient kinetic helicity, the saturated magnetic energy spectrum evolves from having a single peak below the forcing scale to become doubly peaked with one peak at the system (=largest) scale and one at the forcing scale. The system scale field growth is well modeled by a recent nonlinear two-scale nonlinear helical dynamo theory in which the system and forcing scales carry magnetic helicity of opposite sign. But a two-scale theory cannot model the shift of the small-scale peak…
The extent to which large scale magnetic fields are susceptible to turbulent diffusion is important for interpreting the need for in situ large scale dynamos in astrophysics and for observationally inferring field strengths compared to kinetic energy. By solving coupled equations for magnetic energy and magnetic helicity in a system initiated with isotropic turbulence and an arbitrarily helical large scale field, we quantify the decay rate of the latter for a bounded or periodic system. The energy associated with the non-helical magnetic field rapidly decays by turbulent diffusion, but the dec…
We investigate analytically the amplification of a weak magnetic field in a homogeneous and isotropic turbulent flow lacking reflectional symmetry (helical turbulence). We propose that the spectral distributions of magnetic energy and magnetic helicity can be found as eigenmodes of a self-adjoint, Schrödinger-type system of evolution equations. We argue that large-scale and small-scale magnetic fluctuations cannot be effectively separated, and that the conventional alpha-model is, in general, not an adequate description of the large-scale dynamo mechanism. As a consequence, the correct numeric…
To investigate the effect of energy and helicity on the growth of magnetic field, helical kinetic forcing was applied to the magnetohydrodynamic(MHD) system that had a specific distribution of energy and helicity as initial conditions. Simulation results show the saturation of a system is not influenced by the initial conditions, but the growth rate of large scale magnetic field is proportionally dependent on the initial large scale magnetic energy and helicity. It is already known that the helical component of small scale magnetic field(i.e., current helicity $<{\bf j}\cdot {\bf b}>$) quenche…
A novel plasma state has been found in the presence of a uniform applied axial magnetic field in periodic cylindrical geometry. This state is driven electrostatically by helical electrodes, providing a driving field that depends on radius and $mθ-nζ$, where $θ$ is the poloidal angle and $ζ=z/R$ is the toroidal angle. We focus on $m=n=1$. The radial magnetic field at the wall is taken to be zero. With weak driving, the resulting distortion is very small, but for stronger driving the mean field of the state has field line safety factor $q_0(r)$ just above the pitch of the electrodes $m/n=1$ exce…
Most large scale dynamo research for astrophysical rotators focuses on interior flow driven helical dynamos (FDHDs), but larger scale coronal fields most directly influence observations. It is thus important to understand the relationship between coronal and interior fields. Coronal field relaxation is actually a type of magnetically dominated helical dynamo (MDHD). MDHDs also occur in fusion plasma devices where they drive a system toward its relaxed state in response to magnetic helicity injection that otherwise drives the system away from this state. Global scale fields of astrophysical rot…
The alpha effect is known to be an indispensable energy source of the poloidal magnetic field in the sun or planet. However, the alpha effect is quenched as the magnetic field grows due to the conservation of magnetic helicity. With these conventional understanding, what indeed generates and sustains the observed poloidal magnetic field remains a mystery. To solve this contradiction between theory and real nature, we derived a semi-analytic representation of alpha and beta using large scale magnetic helicity and energy. Applying the simulation data to alpha and beta, we found that the negative…
The term ``dynamo'' means different things to the laboratory fusion plasma and astrophysical plasma communities. To alleviate the resulting confusion and to facilitate interdisciplinary progress, we pinpoint conceptual differences and similarities between laboratory plasma dynamos and astrophysical dynamos. We can divide dynamos into three types: 1. magnetically dominated helical dynamos which sustain a large scale magnetic field against resistive decay and drive the magnetic geometry toward the lowest energy state, 2. flow-driven helical dynamos which amplify or sustain large scale magnetic f…
Understanding large scale magnetic field growth in turbulent plasmas in the magnetohydrodynamic limit is a goal of magnetic dynamo theory. In particular, assessing how well large scale helical field growth and saturation in simulations matches that predicted by existing theories is important for progress. Using numerical simulations of isotropically forced turbulence without large scale shear with the implications, we focus on several aspects of this comparison that have not been previously tested: (1) Leading mean field dynamo theories which break the field into large and small scales predict…
