To understand the turbulent generation of large-scale magnetic fields and to advance beyond purely kinematic approaches to the dynamo effect like that introduced by Steenbeck, Krause & Radler (1966)’ a new nonlinear theory is developed for three-dimensional, homogeneous, isotropic, incompressible MHD turbulence with helicity, i.e. not statistically invariant under plane reflexions. For this, techniques introduced for ordinary turbulence in recent years by Kraichnan (1971 a)’ Orszag (1970, 1976) and others are generalized to MHD; in particular we make use of the eddy-damped quasi-normal Markovian approximation. The resulting closed equations for the evolution of the kinetic and magnetic energy and helicity spectra are studied both theoretically and numerically in situations with high Reynolds number and unit magnetic Prandtl number.Interactions between widely separated scales are much more important than for non-magnetic turbulence. Large-scale magnetic energy brings to equipartition small-scale kinetic and magnetic excitation (energy or helicity) by the ‘Alfvén effect’; the small-scale ‘residual’ helicity, which is the difference between a purely kinetic and a purely magnetic helical term, induces growth of large-scale magnetic energy and helicity by the ‘helicity effect’. In the absence of helicity an inertial range occurs with a cascade of energy to small scales; to lowest order it is a −3/2 power law with equipartition of kinetic and magnetic energy spectra as in Kraichnan (1965) but there are −2 corrections (and possibly higher ones) leading to a slight excess of magnetic energy. When kinetic energy is continuously injected, an initial seed of magnetic field will grow to approximate equipartition, at least in the small scales. If in addition kinetic helicity is injected, an inverse cascade of magnetic helicity is obtained leading to the appearance of magnetic energy and helicity in ever-increasing scales (in fact, limited by the size of the system). This inverse cascade, predicted by Frischet al.(1975), results from a competition between the helicity and Alféh effects and yields an inertial range with approximately — 1 and — 2 power laws for magnetic energy and helicity. When kinetic helicity is injected at the scale linjand the rate$\tilde{\epsilon}^V$(per unit mass), the time of build-up of magnetic energy with scaleL[Gt ] linjis$t \approx L(|\tilde{\epsilon}^V|l^2_{\rm inj})^{-1/3}.$

Abstract. We derive a weak turbulence formalism for incompressible magnetohydrodynamics. Three-wave interactions lead to a system of kinetic equations for the spectral densities of energy and helicity. The kinetic equations conserve energy in all wavevector planes normal to the applied magnetic field B 0ê . Numerically and analytically, we find energy spectra E ± ∼ k n± ⊥ , such that n + + n − = −4, where E ± are the spectra of the Elsässer variables z ± = v ± b in the two-dimensional case (k = 0). The constants of the spectra are computed exactly and found to depend on the amount of correlation between the velocity and the magnetic field. Comparison with several numerical simulations and models is also made.

Some of the consequences of the conservation of magnetic helicity a . bd3r (a = vector potential of magnetic field b) s for incompressible three-dimensional turbulent MHD flows are investigated. Absolute equilibrium spectra for inviscid infinitely conducting flows truncated at lower and upper wavenumbers k,,, and k , , , are obtained. When the total magnetic helicity approaches an upper limit given by the total energy (kinetic plus magnetic) divided by the spectra of magnetic energy and helicity are strongly peaked near kmin; in addition, when the cross-correlations between the velocity and magnetic fields are small, the magnetic energy density near kmin greatly exceeds the kinetic energy density. Several arguments are presented in favour of the existence of inverse cascades of magnetic helicity towards small wavenumbers leading to the generation of large-scale magnetic energy. 49(3)

Thus, the observation and identification of the trapped-ion instability has been seen in many ways. These are as follows: the dependence of the wave amplitude on collisionality was in the range and in the manner predicted for the trappedion instability; the instability existed only on the density gradient and it existed only when and where there were trapped particles; and the observed frequency of the trapped-ion instability was at the predicted frequency (^Sco^*) and showed the proper dependence on trapped fraction. Although other experiments have operated in the proper collisionality range for the trapped-ion instability 10 ' 11 they were unable to satisfy requirement (1), oo r «oj bi . This experiment satisfied all of the requirements and provides the first positive identification of the dissipative trapped-ion instability.The stretching of magnetic field lines by turbulent motions in a conducting fluid is one of the most frequently invoked mechanisms for the generation of the magnetic fields of the earth, the sun, stars, and galaxies. 1 It may also lead to undesirable magnetic fields in the liquid sodium cooling system of large breeder reactors. 2 ' 3 When the magnetic Reynolds number R M exceeds a critical value R C M 9 the stretching is sufficiently 1 B. B. Kadomtsev and O. P. Pogutse, Zh. Eksp. Teor.Direct numerical simulations of three-dimensional magnetohydrodynamic turbulence with kinetic and magnetic Reynolds numbers up to 100 are presented. Spatially intermittent magnetic fields are observed in a flow with nonhelical driving. Small-scale helical driving produces strong large-scale nearly force-free magnetic fields.

Abstract. We derive two symmetric global scaling laws for third-order structure functions of magnetized fluids under the assumptions of full isotropy, homogeneity and incompressibility. The compatibility with previous la•vs involving both structure and correlation functions of only the longitudinal components of the fields is demonstrated. These new laws provide a better set of functions with which one can determine intermittency scaling of MHD turbulence, as in the Solar Wind.

A derivation in variable dimension of the scaling laws for mixed third-order longitudinal structure and correlation functions for incompressible magnetized flows is given for arbitrary correlation between the velocity and magnetic field with full isotropy, homogeneity, and incompressibility assumed. When close to equipartition between kinetic and magnetic energy, the scaling relations involve only structure functions in a manner similar to the '' 4 5 law'' of Kolmogorov.

We present a three-pronged numerical approach to the dynamo problem at low magnetic Prandtl numbers PM . The difficulty of resolving a large range of scales is circumvented by combining Direct Numerical Simulations, a Lagrangian-averaged model, and Large-Eddy Simulations (LES). 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 PM = 1 down to PM = 10 −2 ; (ii) the critical magnetic Reynolds number increases sharply with P −1 M as turbulence sets in and then saturates; (iii) in the linear growth phase, the most unstable magnetic modes move to small scales as PM is decreased and a Kazantsev k 3/2 spectrum develops; then the dynamo grows at large scales and modifies the turbulent velocity fluctuations.PACS numbers: 47.27.eq,47.65.+a91.25wThe generation of magnetic fields in celestial bodies occurs in media for which the viscosity ν and the magnetic diffusivity η are vastly different. For example, in the interstellar medium the magnetic Prandtl number P M = ν/η has been estimated to be as large as 10 14 , whereas in stars such as the Sun and for planets such as the Earth, it can be very low (P M < 10 −5 , the value for the Earth's iron core). Similarly in liquid breeder reactors and in laboratory experiments in liquid metals, P M ≪ 1. At the same time, the Reynolds number R V = U L/ν (U is the r.m.s. velocity, L is the integral scale of the flow) is very large, and the flow is highly complex and turbulent, with prevailing non-linear effects rendering the problem difficult to address. If in the smallest scales of astrophysical objects plasma effects may prevail, the large scales are adequately described by the equations of magnetohydrodynamics (MHD),together with ∇ · v = 0, ∇ · B = 0, and assuming a constant mass density. Here, v is the velocity field normalized to the r.m.s. fluid flow speed, and B the magnetic field converted to velocity units by means of an equivalent Alfvén speed. P is the pressure and j = ∇ × B the current density. F is a forcing term, responsible for the generation of the flow (buoyancy and Coriolis in planets, mechanical drive in experiments). Several mechanisms have been studied for dynamo action, both analytically and numerically, involving in particular the role of helicity [1] (i.e. the correlation between velocity and its curl, the vorticity) for dynamo growth at scales larger than that of the velocity, and the role of chaotic fields for small-scale growth of magnetic excitation (for a recent review, see [2]). Granted that the stretching and folding of magnetic field lines by velocity gradients overcome dissipation, dynamo action takes place above a critical magnetic Reynolds number R c M ,Dynamo experiments engineering constrained helical flows of liquid sodium have been successful [3]. However, these experimental setups do not allow for a complete investigation of the dynamical regime, and many groups have searched to implement unconstrain...

Weak turbulence of shear-Alfvén waves is considered in the limit of strongly anisotropic pulsations that are elongated along the external magnetic field. The kinetic equation thus derived agrees with the Galtier et al. formulation of the full three-dimensional helical case when taking the proper limit. This new approach allows for significant simplification, and, as a result, the applicability conditions for the weak turbulence theory are now more transparent. It thus provides an attractive theoretical framework for describing anisotropic MHD turbulence in astrophysical contexts where a strong magnetic field is present and for which shear-Alfvén waves are important.