Flow helicity in a simplified statistical model of a fast dynamo

The role of kinetic helicity in small-scale fast dynamo action is investigated by employing a simple statistical model for the underlying flow with statistics that are Gaussian distributed, temporally delta-correlated and spatially homogeneous and isotropic. In order to focus on small-scale dynamo action we restrict our attention to flows possessing no net kinetic helicity. With the help of a diagrammatic technique and a numerical calculation we show that the dynamo growth rate is independent of the kinetic helicity as the magnetic Reynolds number R_m → ∞. It is indicated that the latter enhances the growth of the magnetic energy only for finite R_m.     

Magnetic dynamo action at low magnetic Prandtl numbers

Amplification of magnetic field due to kinematic turbulent dynamo action is studied in the regime of small magnetic Prandtl numbers. Such a regime is relevant for planets and stars interiors, as well as for liquid-metal laboratory experiments. A comprehensive analysis based on the Kazantsev-Kraichnan model is reported, which establishes the dynamo threshold and the dynamo growth rates for varying kinetic helicity of turbulent fluctuations. It is proposed that in contrast with the case of large magnetic Prandtl numbers, the kinematic dynamo action at small magnetic Prandtl numbers is significantly affected by kinetic helicity, and it can be made quite efficient with an appropriate choice of the helicity spectrum.     

Investigation of the helicity of magnetic fields on the Sun within the Parker dynamo model

Construction of the butterfly diagrams for the magnetic helicity in several approximations of a Parker dynamo has been carried out. The diagrams are constructed both for the cases of efficient generation of the magnetic field (large dynamo numbers) and for the weak generation (a small dynamo number). The corresponding asymptotic solution to the solar dynamo is used in the first case. The butterfly diagrams for different values of the meridional circulation were studied due to this solution. The butterfly diagrams are constructed and based on the few-mode approximation, which is valid for moderate dynamo numbers. The issue of which butterfly diagram features are common in all these approximations and can be compared with observational data is discussed.     

Numerical study of dynamo action at low magnetic Prandtl numbers

We present a three-pronged numerical approach to the dynamo problem at low magnetic Prandtl numbers P(M). The difficulty of resolving a large range of scales is circumvented by combining direct numerical simulations, a Lagrangian-averaged model and large-eddy simulations. The flow is generated by the Taylor-Green forcing; it combines a well defined structure at large scales and turbulent fluctuations at small scales. Our main findings are (i) dynamos are observed from P(M)=1 down to P(M)=10(-2), (ii) the critical magnetic Reynolds number increases sharply with P(M)(-1) as turbulence sets in and then it saturates, and (iii) in the linear growth phase, unstable magnetic modes move to smaller scales as P(M) is decreased. Then the dynamo grows at large scales and modifies the turbulent velocity fluctuations.     

Kinetic helicity of vortex in Bose-Einstein condensates

Kinetic helicity of vortex in Bose-Einstein condensates is studied and classified by Hopf index, linking number in geometry. A mechanism of generation and annihilation of vortex line is given by method of phase singularity theory. The dynamic behavior of vortex at the critical points is discussed detailly, and three kinds of length approximation relations at the neighborhood of singularity point are given.     

Energy fluxes in helical magnetohydrodynamics and dynamo action

Renormalized viscosity, renormalized resistivity, and various energy fluxes are calculated for helical magnetohydrodynamics using perturbative field theory. The calculation is of firstorder in perturbation. Kinetic and magnetic helicities do not affect the renormalized parameters, but they induce an inverse cascade of magnetic energy. The sources for the large-scale magnetic field have been shown to be (1) energy flux from large-scale velocity field to large-scale magnetic field arising due to non-helical interactions and (2) inverse energy flux of magnetic energy caused by helical interactions. Based on our flux results, a primitive model for galactic dynamo has been constructed. Our calculations yield dynamo time-scale for a typical galaxy to be of the order of 10⁸ years. Our field-theoretic calculations also reveal that the flux of magnetic helicity is backward, consistent with the earlier observations based on absolute equilibrium theory.     

Generation of a magnetic field by dynamo action in a turbulent flow of liquid sodium

We report the observation of dynamo action in the von Kármán sodium experiment, i.e., the generation of a magnetic field by a strongly turbulent swirling flow of liquid sodium. Both mean and fluctuating parts of the field are studied. The dynamo threshold corresponds to a magnetic Reynolds number R(m) approximately 30. A mean magnetic field of the order of 40 G is observed 30% above threshold at the flow lateral boundary. The rms fluctuations are larger than the corresponding mean value for two of the components. The scaling of the mean square magnetic field is compared to a prediction previously made for high Reynolds number flows.     

Production of axions by cosmic magnetic helicity

We investigate the effects of an external magnetic helicity production on the evolution of the cosmic axion field. It is shown that a helicity larger than (few x 10(-15) G)2 Mpc, if produced at temperatures above a few GeV, is in contradiction with the existence of the axion, since it would produce too much of an axion relic abundance.     

Numerical simulation of a turbulent magnetic dynamo

We present numerical simulations of a turbulent magnetic dynamo mimicking closely the Riga-dynamo experiment at Re approximately 3.5x10(6) and 15< or =Rem< or =20. The Reynolds-averaged Navier-Stokes equations for the fluid flow and turbulence field are solved simultaneously with the direct numerical solution of the magnetic field equations. The fully integrated two-way-coupled simulations reproduced all features of the magnetic self-excitation detected by the Riga experiment, with frequencies and amplitudes of the self-generated magnetic field in good agreement with the experimental records, and provided full insight into the unsteady magnetic and velocity fields and the mechanisms of the dynamo action.     

Metric-torsion decay of non-adiabatic chiral helical magnetic fields against chiral dynamo action in bouncing cosmological models

Metric-torsion effects on chiral massless fermions are investigated in the realm of the adiabatic amplification of cosmological magnetic fields (CMFs) in a general relativistic framework and in the framework of Einstein–Cartan (EC) bouncing cosmologies. In GR the chiral effect is proportional to the Hubble factor and the solution of the dynamo equation leads to an adiabatic magnetic field, while in Einstein–Cartan bouncing cosmology we have non-adiabatic magnetic fields where the breaking of adiabaticity is given by a torsion term. Using a EWPT magnetic field of the order of \(B_{\text {seed}}\sim {10^{24}}\) G at 5 pc scale, we obtain a CMF in EC of the order of \(10^{-10}\) G, which is still able to seed a galactic dynamo which amplifies this field up to galactic magnetic fields of four orders of magnitude, which is a mild dynamo. In the case of massive chiral fermions it is shown that torsion actually attenuated the convective dynamo term in the dynamo equation obtained from the QED of an electron–positron pair \(e^{-}e^{+}\). Chiral effects on general relativity may lead to strong magnetic fields of the order of \(\sim {10^{18}}\) G at the early universe resulting from pure metric effects. Strong magnetic fields of the order of \(B_{\text {metric}-\text {torsion}}\sim {10^{8}}\) G may be obtained from very strong seed fields. At 1 Mpc scale of the present universe a galactic dynamo seed of the order of \(10^{-19}\) G is found. It is shown in this paper that chiral dynamo effects in the expanded universe can be obtained if one takes into account the speed of the cosmic plasma.     

Critical magnetic Prandtl number for small-scale dynamo

We report a series of numerical simulations showing that the critical magnetic Reynolds number Rm(c) for the nonhelical small-scale dynamo depends on the Reynolds number Re. Namely, the dynamo is shut down if the magnetic Prandtl number Pr(m)=Rm/Re is less than some critical value Pr(m,c)< approximately 1 even for Rm for which dynamo exists at Pr(m)> or =1. We argue that, in the limit of Re-->infinity, a finite Pr(m,c) may exist. The second possibility is that Pr(m,c)-->0 as Re--> infinity, while Rm(c) tends to a very large constant value inaccessible at current resolutions. If there is a finite Pr(m,c), the dynamo is sustainable only if magnetic fields can exist at scales smaller than the flow scale, i.e., it is always effectively a large-Pr(m) dynamo. If there is a finite Rm(c), our results provide a lower bound: Rm(c) greater, similar 220 for Pr(m)< or =1/8. This is larger than Rm in many planets and in all liquid-metal experiments.     

Experimental observation of spatially localized dynamo magnetic fields

We report the first experimental observation of a spatially localized dynamo magnetic field, a common feature of astrophysical dynamos and convective dynamo simulations. When the two propellers of the von Kármán sodium experiment are driven at frequencies that differ by 15%, the mean magnetic field's energy measured close to the slower disk is nearly 10 times larger than the one close to the faster one. This strong localization of the magnetic field when a symmetry of the forcing is broken is in good agreement with a prediction based on the interaction between a dipolar and a quadrupolar magnetic mode.     

Rigorous bounds on the fast dynamo growth rate involving topological entropy

The fast dynamo growth rate for aC ^k+1 map or flow is bounded above by topological entropy plus a 1/k correction. The proof uses techniques of random maps combined with a result of Yomdin relating curve growth to topological entropy. This upper bound implies the following anti-dynamo theorem: inC systems fast dynamo action is not possible without the presence of chaos. In addition topological entropy is used to construct a lower bound for the fast dynamo growth rate in the caseR _m =.This author is supported by an NSF postdoctoral fellowshipThis author is partially supported by an NSF grant