The Adler DD-function for N=1{\cal N}=1 SQCD regularized by higher covariant derivatives in the three-loop approximation

We calculate the Adler $D$-function for ${\cal N}=1$ SQCD in the three-loop approximation using the higher covariant derivative regularization and the NSVZ-like subtraction scheme. The recently formulated all-order relation between the Adler function and the anomalous dimension of the matter superfields defined in terms of the bare coupling constant is first considered and generalized to the case of an arbitrary representation for the chiral matter superfields. The correctness of this all-order relation is explicitly verified at the three-loop level. The special renormalization scheme in which this all-order relation remains valid for the $D$-function and the anomalous dimension defined in terms of the renormalized coupling constant is constructed in the case of using the higher derivative regularization. The analytic expression for the Adler function for ${\cal N}=1$ SQCD is found in this scheme to the order $O(\alpha_s^2)$. The problem of scheme-dependence of the $D$-function and the NSVZ-like equation is briefly discussed.Comment: 25 pages, 2 figures; the version accepted for publication in Nuclear Physics

Turbulent magnetic dynamo excitation at low magnetic Prandtl number

Planetary and stellar dynamos likely result from turbulent motions in magnetofluids with kinematic viscosities that are small compared to their magnetic diffusivities. Laboratory experiments are in progress to produce similar dynamos in liquid metals. This work reviews recent computations of thresholds in critical magnetic Reynolds number above which dynamo amplification can be expected for mechanically-forced turbulence (helical and non-helical, short wavelength and long wavelength) as a function of the magnetic Prandtl number $P_M$. New results for helical forcing are discussed, for which a dynamo is obtained at $P_M=5\times10^{-3}$. The fact that the kinetic turbulent spectrum is much broader in wavenumber space than the magnetic spectrum leads to numerical difficulties which are bridged by a combination of overlapping direct numerical simulations and subgrid models of magnetohydrodynamic turbulence. Typically, the critical magnetic Reynolds number increases steeply as the magnetic Prandtl number decreases, and then reaches an asymptotic plateau at values of at most a few hundred. In the turbulent regime and for magnetic Reynolds numbers large enough, both small and large scale magnetic fields are excited. The interactions between different scales in the flow are also discussed.Comment: 8 pages, 8 figures, to appear in Physics of Plasma

Stochastic Flux-Freezing and Magnetic Dynamo

We argue that magnetic flux-conservation in turbulent plasmas at high magnetic Reynolds numbers neither holds in the conventional sense nor is entirely broken, but instead is valid in a novel statistical sense associated to the "spontaneous stochasticity" of Lagrangian particle tra jectories. The latter phenomenon is due to the explosive separation of particles undergoing turbulent Richardson diffusion, which leads to a breakdown of Laplacian determinism for classical dynamics. We discuss empirical evidence for spontaneous stochasticity, including our own new numerical results. We then use a Lagrangian path-integral approach to establish stochastic flux-freezing for resistive hydromagnetic equations and to argue, based on the properties of Richardson diffusion, that flux-conservation must remain stochastic at infinite magnetic Reynolds number. As an important application of these results we consider the kinematic, fluctuation dynamo in non-helical, incompressible turbulence at unit magnetic Prandtl number. We present results on the Lagrangian dynamo mechanisms by a stochastic particle method which demonstrate a strong similarity between the Pr = 1 and Pr = 0 dynamos. Stochasticity of field-line motion is an essential ingredient of both. We finally consider briefly some consequences for nonlinear MHD turbulence, dynamo and reconnectionComment: 29 pages, 10 figure

Steady state existence of passive vector fields under the Kraichnan model

The steady state existence problem for Kraichnan advected passive vector models is considered for isotropic and anisotropic initial values in arbitrary dimension. The model includes the magnetohydrodynamic (MHD) equations, linear pressure model (LPM) and linearized Navier-Stokes (LNS) equations. In addition to reproducing the previously known results for the MHD and linear pressure model, we obtain the values of the Kraichnan model roughness parameter $\xi$ for which the LNS steady state exists.Comment: Improved text & figures, added references & other correction

Nonlinear magneto-optical resonances at D1 excitation of 85Rb and 87Rb in an extremely thin cell

Nonlinear magneto-optical resonances have been measured in an extremely thin cell (ETC) for the D1 transition of rubidium in an atomic vapor of natural isotopic composition. All hyperfine transitions of both isotopes have been studied for a wide range of laser power densities, laser detunings, and ETC wall separations. Dark resonances in the laser induced fluorescence (LIF) were observed as expected when the ground state total angular momentum F_g was greater than or equal to the excited state total angular momentum F_e. Unlike the case of ordinary cells, the width and contrast of dark resonances formed in the ETC dramatically depended on the detuning of the laser from the exact atomic transition. A theoretical model based on the optical Bloch equations was applied to calculate the shapes of the resonance curves. The model averaged over the contributions from different atomic velocity groups, considered all neighboring hyperfine transitions, took into account the splitting and mixing of magnetic sublevels in an external magnetic field, and included a detailed treatment of the coherence properties of the laser radiation. Such a theoretical approach had successfully described nonlinear magneto-optical resonances in ordinary vapor cells. Although the values of certain model parameters in the ETC differed significantly from the case of ordinary cells, the same physical processes were used to model both cases. However, to describe the resonances in the ETC, key parameters such as the transit relaxation rate and Doppler width had to be modified in accordance with the ETC's unique features. Agreement between the measured and calculated resonance curves was satisfactory for the ETC, though not as good as in the case of ordinary cells.Comment: v2: substantial changes and expanded theoretical model; 13 pages, 10 figures; accepted for publication in Physical Review

The Generation of Magnetic Fields Through Driven Turbulence

We have tested the ability of driven turbulence to generate magnetic field structure from a weak uniform field using three dimensional numerical simulations of incompressible turbulence. We used a pseudo-spectral code with a numerical resolution of up to $144^3$ collocation points. We find that the magnetic fields are amplified through field line stretching at a rate proportional to the difference between the velocity and the magnetic field strength times a constant. Equipartition between the kinetic and magnetic energy densities occurs at a scale somewhat smaller than the kinetic energy peak. Above the equipartition scale the velocity structure is, as expected, nearly isotropic. The magnetic field structure at these scales is uncertain, but the field correlation function is very weak. At the equipartition scale the magnetic fields show only a moderate degree of anisotropy, so that the typical radius of curvature of field lines is comparable to the typical perpendicular scale for field reversal. In other words, there are few field reversals within eddies at the equipartition scale, and no fine-grained series of reversals at smaller scales. At scales below the equipartition scale, both velocity and magnetic structures are anisotropic; the eddies are stretched along the local magnetic field lines, and the magnetic energy dominates the kinetic energy on the same scale by a factor which increases at higher wavenumbers. We do not show a scale-free inertial range, but the power spectra are a function of resolution and/or the imposed viscosity and resistivity. Our results are consistent with the emergence of a scale-free inertial range at higher Reynolds numbers.Comment: 14 pages (8 NEW figures), ApJ, in press (July 20, 2000?