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Direct measurements of the vector turbulent emf in a driven two-vortex flow of liquid sodium were performed in the Madison Dynamo Experiment [K. Rahbarnia et al., Astrophys. J. 759, 80 (2012)]. The measured turbulent emf is anti-parallel with the mean current and is almost entirely described by an enhanced resistivity, which increases the threshold for a kinematic dynamo. We have demonstrated that this enhanced resistivity can be mitigated by eliminating the largest-scale eddies through the introduction of baffles. By tailoring the flow to reduce large-scale components and control the helical pitch, we have reduced the power required to drive the impellers, doubled the magnetic flux generated by differential rotation, and increased the decay time of externally applied magnetic fields. Despite these improvements, the flows remain sub-critical to the dynamo instability due to the reemergence of turbulent fluctuations at high flow speeds. [ABSTRACT FROM AUTHOR]

The generation of a magnetic field by dynamo action in a Taylor-vortex flow is investigated numerically.We first discuss how the Taylor vortices generate a spatially subharmonic dynamo, for which the axial wavelength of the magnetic field is twice the one of the flow pattern. Then, we investigate the influence of the Reynolds number and the turbulent fluctuations on the structure and the onset of the Taylor-Couette dynamo. Finally, based on the subharmonic nature of this dynamo, we propose new configurations which could be relevant for laboratory experiments. [ABSTRACT FROM AUTHOR]

Experimental results are reported on the magnetohydrodynamic interaction between oscillating flows in adjoining channels of the Karlsruhe dynamo test facility. In the experiment, designed to simulate the Roberts–Busse kinematic dynamo model, a time periodic perturbation has been imposed on the axial channel flows, while the flow rates in the other two helical channel systems were supplied at constant power level. It has been observed that the onset of dynamo action is shifted slightly to lower mean flow rates. A temporal analysis shows distinct correlations between the evolving magnetic field and the different kinds of forced flows in the channels. From the beginning the environmental magnetic field adjusts to fluctuations of the axial channel flow. The fluctuations of the magnetic field increase owing to dynamo action in a transition range and induce quasiperiodic fluctuations on the flow in the helical channels by acting Lorentz forces. In the high supercritical range the fluctuations are dampened. [ABSTRACT FROM AUTHOR]

Action-angle variables corresponding to singular (or improper) eigenmodes are rigorously formulated for the Alfvén and slow (or cusp) continuous spectra of ideal magnetohydrodynamics. The perturbation energy is then transformed into the normal form, namely, the eigenfrequency multiplied by the action variable. It is shown that the Laplace transform approach expedites this action-angle formulation more efficiently than the existing ones devoted to other kinds of continuous spectra. The presence of flow that is either nonparallel to the magnetic field or supersonic at some places brings about singular eigenmodes with negative energy. The Alfvén and slow singular eigenmodes are neutrally stable even in the presence of any external potential fields, but may cause instability when coupled with another singular or nonsingular eigenmode with the opposite sign of energy. [ABSTRACT FROM AUTHOR]

The reversal mechanism of a dipole magnetic field generated by dynamo action in a rotating spherical shell is investigated by a three-dimensional nonlinear magnetohydrodynamic simulation as well as a linear stability analysis. The emphasis of the study is on understanding the relationship between dipole reversal and the symmetry properties of the dynamo solution. As a result, first, it is found that there is a threshold of the magnetic Prandtl number, below which the dipole field is never reversed, and above which the reversal occurs at irregular intervals like the paleomagnetic evolution of the geodynamo. Second, it is shown that the dynamo process responsible for the generation of a dipole field (called “a-dynamo” in this paper) consists only of the antimirror symmetric magnetic field and the mirror symmetric velocity field with respect to the equatorial plane. Third, it is found that the components of the opposite symmetry to the a-dynamo grow only during the polarity reversal events and quickly decay afterwards. This indicates that the dipole field reversal and the loss of equatorial symmetry are tightly connected. In fact, it is clearly demonstrated by numerical analyses that the a-dynamo process is linearly unstable for the perturbation of opposite symmetry when the magnetic Prandtl number exceeds the threshold for dipole reversal. Mode coupling between the longitudinal Fourier components plays a crucial role in creating the instability. Based on the above results, it is proposed that symmetry-breaking instability could be the mechanism for dipole field reversal in the geodynamo process. The energy conversion between components of different symmetry is also analyzed in the quasistable polarity phase and in the polarity reversal phase, respectively. [ABSTRACT FROM AUTHOR]

Turbulent fluctuations in the velocity and magnetic fields of electrically conducting fluids have been experimentally shown to be capable of inducing large-scale magnetic fields. Here, simulations of the Madison Dynamo Experiment are used to qualitatively reproduce these experimental results. Due to the high magnetic Prandtl number of the simulations, Pm=0.08 vs Pm∼10-5 for liquid sodium, the simulations do not identically reproduce the fluctuation levels of the experiment’s magnetic and velocity fields. Nonetheless, the simulations reproduce the qualitative behavior of the fluctuation-induced large-scale magnetic field as a function of applied field magnitude and magnetic Reynolds number. The scaling of the induced dipole moment as a function of Reynolds number is also presented, demonstrating that the nature of the fluctuations in the simulations changes after a critical value of the Reynolds number is crossed, resulting in a change in the direction of the induced dipole moment. Experimental conditions using corotating impellers are presented, demonstrating that the induced dipole moment may be dependent on the shear layer present in the counter-rotating case. Measurements of velocity field fluctuations are examined to determine the possibility of an inhomogeneous turbulent resistivity. [ABSTRACT FROM AUTHOR]

The physics of spheromak plasmas is addressed by time-dependent, three-dimensional, resistive magnetohydrodynamic simulations with the NIMROD code [C. R. Sovinec et al., J. Comput. Phys. 195, 355 (2004)]. Included in some detail are the formation of a spheromak driven electrostatically by a coaxial plasma gun with a flux-conserver geometry and power systems that accurately model the sustained spheromak physics experiment [R. D. Wood et al., Nucl. Fusion 45, 1582 (2005)]. The controlled decay of the spheromak plasma over several milliseconds is also modeled as the programmable current and voltage relax, resulting in simulations of entire experimental pulses. Reconnection phenomena and the effects of current profile evolution on the growth of symmetry-breaking toroidal modes are diagnosed; these in turn affect the quality of magnetic surfaces and the energy confinement. The sensitivity of the simulation results addresses variations in both physical and numerical parameters, including spatial resolution. There are significant points of agreement between the simulations and the observed experimental behavior, e.g., in the evolution of the magnetics and the sensitivity of the energy confinement to the presence of symmetry-breaking magnetic fluctuations. [ABSTRACT FROM AUTHOR]

The turbulent electromotive force in the mean-field equation needs to be modeled to predict a large-scale magnetic field in magnetohydrodynamic turbulence at high Reynolds number. Using a statistical theory for inhomogeneous turbulence, model expressions for transport coefficients appearing in the turbulent electromotive force are derived including the α coefficient and the turbulent diffusivity. In particular, as one of the dynamo effects, the pumping effect is investigated and a model expression for the pumping term is obtained. It is shown that the pumping velocity is closely related to the gradient of the turbulent residual energy, or the difference between the turbulent kinetic and magnetic energies. The production terms in the transport equation for the turbulent electromotive force are also examined and the validity of the model expression is assessed by comparing with earlier results concerning the isotropic α coefficient. The mean magnetic field in a rotating spherical shell is calculated using a turbulence model to demonstrate the pumping effect. [ABSTRACT FROM AUTHOR]

The effect of turbulent fluctuations on the zonal (flux surface averaged) magnetic field in drift-ballooning turbulence is shown to be equivalent to a turbulent anti-resistivity. The flux surface average of the convective nonlinearity in Ohm’s law is proportional to the flux surface average of the current. The coefficient of proportionality can be defined as a turbulent resistivity ηturb. The correlation of the flux surface average of the convective nonlinearity with the negative of the flux surface average of the current is nearly 100%. Because the convective nonlinearity is correlated with the negative of the current, and not the current, the turbulent resistivity is negative. The magnitude of ηturb is virtually identical to the magnitude of the collisional resistivity η, but opposite in sign, so that the total resistivity ηtotal=η+ηturb is nearly zero. The effect of the fluctuations is to balance the effect of collisional resistive diffusion. As a result, while the energy in the zonal flow increases to a large value as the fluctuations grow and saturate, the energy in the zonal magnetic field remains very small. [ABSTRACT FROM AUTHOR]

We study the dynamo threshold of a helical flow made of a mean plus a fluctuating part. Two flow geometries are studied: (i) solid body and (ii) smooth. Two well-known resonant dynamo conditions, elaborated for stationary helical flows in the limit of large magnetic Reynolds numbers, are tested against lower magnetic Reynolds numbers and for fluctuating flows with zero mean. For a flow made of a mean plus a fluctuating part, the dynamo threshold depends on the frequency and the strength of the fluctuation. The resonant dynamo conditions applied on the fluctuating (respectively, mean) part seems to be a good diagnostic to predict the existence of a dynamo threshold when the fluctuation level is high (respectively, low). [ABSTRACT FROM AUTHOR]

Two-dimensional Boussinesq magnetoconvection with idealized stress-free boundary conditions is numerically investigated in order to make clear the difference between chaos and turbulence. It is shown that the long-term behavior of magnetoconvection exhibits spatially coherent and temporally chaotic rolls in marked contrast to highly turbulent fluids. It is also shown that heat transport becomes larger anomalously when the polarity reversal of the magnetic field occurs intermittently in the case of temporally chaotic magnetoconvection. It is found that the Poincaré return map of the relative maximum temperature fluctuation of partial differential equations as a function of the preceding maximum resembles the famous Lorenz plot in narrow rolls of magnetoconvection. The chaotic behavior of narrow rolls for individual parameter values robustly persists up to rolls about one fifth as wide as they are high near the codimension-two bifurcation point. [ABSTRACT FROM AUTHOR]

It is shown that the α2-dynamo of magnetohydrodynamics, the hydrodynamic Squire equation as well as an interpolation model of PT-symmetric quantum mechanics are closely related as spectral problems in Krein spaces. For the α2-dynamo and the PT-symmetric model the strong similarities are demonstrated with the help of a 2×2 operator matrix representation, whereas the Squire equation is reinterpreted as a rescaled and Wick-rotated PT-symmetric problem. Based on recent results on the Squire equation the spectrum of the PT-symmetric interpolation model is analyzed in detail and the Herbst limit is described as spectral singularity. [ABSTRACT FROM AUTHOR]

Here we describe a technique for solving the four-field extended-magnetohydrodynamic (MHD) equations in two dimensions. The introduction of triangular high-order finite elements with continuous first derivatives (C1 continuity) leads to a compact representation compatible with direct inversion of the associated sparse matrices. The split semi-implicit method is introduced and used to integrate the equations in time, yielding unconditional stability for arbitrary time step. The method is applied to the cylindrical tilt mode problem with the result that a nonzero value of the collisionless ion skin depth will increase the growth rate of that mode. The effect of this parameter on the reconnection rate and geometry of a Harris equilibrium and on the Taylor reconnection problem is also demonstrated. This method forms the basis for a generalization to a full extended-MHD description of the plasma with six, eight, or more scalar fields. [ABSTRACT FROM AUTHOR]

The dynamo effect is demonstrated numerically in precession driven flow in a spherical container. Both laminar as well as unstable flows act as dynamos. At low Ekman numbers in unstable flows, the dynamo mechanism relies predominantly on the components of the flow excited by instabilities. All calculations are performed in a frame of reference attached to the boundaries. In this frame, the rotation axis of the fluid executes a periodic motion with a period equal to the rotation period of the boundaries, whereas the magnetic dipole moment undergoes slower variations interrupted by reversals. [ABSTRACT FROM AUTHOR]

A nonlinear, time-dependent, magnetically driven dynamo theory that 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 kinetic helicity slows the growth to a viscously limited pace. This magnetically driven dynamo complements the nonlinear kinetic helicity-driven dynamo; for the latter, the growing magnetic helicity fluctuations suppress, rather than drive, large-scale magnetic helicity growth. A unified set of equations accommodates both types of dynamos. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The Ponomarenko dynamo theory is revisited to take into account time-dependent flows. Our purpose is to investigate how a small departure from a steady flow can modify the onset of dynamo action. We consider a typical helical flow when the velocity components are modulated in time at the same frequency and with a small modulation amplitude of the order ∊. Using ∊ as an expansion parameter we calculated the shift in the critical magnetic Reynolds number and the shift in frequency at dynamo onset. We found that modulation can either lower or enhance the threshold of dynamo action depending on ∊[SUB1], the relative amplitude of modulation of the azimuthal and axial velocity components. More specifically, in-phase modulation with 0.7≤∊[SUB1]≤1 delays the onset of dynamo action, while in a larger range including out-of-phase modulation, -1≤∊[SUB1]<0.7, low-frequency forcing promotes dynamo action. [ABSTRACT FROM AUTHOR]

Mean field dynamo theory is a leading candidate to explain the large scale magnetic fields of galaxies and stars. However, controversy arises over the extent of quenching by the backreaction of the growing field. Here boundary conditions and magnetic helicity flow are shown to play a role in determining whether the mean field dynamo action is fast, as required by astrophysical systems, or resistively limited (slow). Existing work suggesting that mean field dynamos are resistively limited include restrictive approximations such as stationarity and periodic boundary conditions that suppress magnetic helicity flow. Thus even though the backreaction is present, such studies cannot unambiguously reveal whether real astrophysical mean field dynamos are dynamically suppressed when the helicity flow is allowed. If the dynamo is sustained by an outflow of helicity from the system, then a magnetically active corona is expected. Open boundaries alone may not be sufficient for rapid dynamo action and the additional physics of buoyancy and outflows may be required. Possible simulation approaches to test some of the principles are briefly discussed. Some limitations of the"Zeldovich relation" are also addressed. [ABSTRACT FROM AUTHOR]

The dynamo structure in the reversed-field pinch (RFP) is studied through the nonlinear dynamics of a single-helicity mode. Simulation is concentrated upon the physical structure of nonlinear interactions of the plasma flow and magnetic fluctuation. The result indicates that when the initial equilibrium profile is deformed by resistive diffusion, the radial flow is driven near the core of the plasma. As this flow forms a vortex structure and magnetic fluctuation grows radially, the dynamo electric field is helically induced just inside the reversal surface and then the toroidal flux is increased. This dynamo electric field correlates to the nonlinear evolution of the kinetic energy of the m=1 mode, and the increase of the toroidal flux originates in the growth process of the magnetic energy of this mode. Consequently, the RFP configuration can be sustained by the single-helicity evolution of the m=1 mode alone, and the electric field induced by the interactions of the toroidal velocity and the radial magnetic field is the most dominant source on the dynamo action. [ABSTRACT FROM AUTHOR]

The transport of angular momentum in astrophysical disks is one of the major issues in modern astrophysics. Here, recent work [Astrophys. J. 347, 435 ( 1989); 365, 648 (1990) ] will be reviewed that suggests that internal waves, analogous to deep ocean waves, play a critical role in transporting angular momentum in neutral disks and generating a magnetic dynamo in ionized disks. Previously, it was shown that low-frequency, slightly nonaxisymmetric (m = 1 ) waves in thin accretion disks could penetrate to small radii with a unique amplitude because of nonlinear saturation. Here, the ability of these waves to drive an α-Ω dynamo in a disk of thickness H and radius r and keplerian rotational frequency Ω(r) ∞ r[sup -3/2] is examined. The asymmetry in the wave distribution that creates a nonzero helicity follows from the fact that the fundamental waves all have a positive angular momentum flux. As a result, there will be a large-scale magnetic field driven by an α-Ω dynamo. It is also likely that small-scale fields, driven by higher-order wave modes, will contribute significantly to the local value of B[sub r]B[sub φ]. It is argued that the magnetic field saturates when its pressure is comparable to the thermal pressure and a crude model of the nonlinear transfer of power to small-scale turbulence is presented. The dynamo process creates a large-scale, axisymmetric toroidal field with B[sub r] ∼ (H/r)[sup 3/2]B[sub φ]. Smaller-scale waves create small-scale fields with a maximum b[sub r]b[sub φ] ∼ (H/r)&frac65;P. In this model, viscous and thermal instabilities in radiation pressure dominated, and electron scattering regions in accretion disks appear to be substantially suppressed. [ABSTRACT FROM AUTHOR]

A boundary-layer solution to a high magnetic Reynolds number R periodic dynamo model shows that: (1) flux expulsion forces the magnetic field into flux sheets; (2) the principal contribution to the a effect arises from regions of flow stagnation along a flux sheet; and (3) the a effect scales as R[sup -1/2]. Arguments for these effects persisting in turbulent dynamos are given. [ABSTRACT FROM AUTHOR]

Alpha, an important parameter in dynamo theory, is shown to be proportional to either the kinetic, current, magnetic, or velocity helicities of the fluctuating magnetic field and fluctuating velocity field. The particular helicity to which alpha is proportional depends on the assumptions used in deriving the first-order smoothed equations that describe the alpha effect. In two cases, viz., when alpha is proportional to either the magnetic helicity or velocity helicity, alpha can be determined experimentally from two-point measurements of the fluctuating fields in incompressible, homogeneous turbulence with arbitrary rotational symmetry. For the other two possibilities, alpha can be determined if the turbulence is isotropic. [ABSTRACT FROM AUTHOR]

Discusses the analogy between the dynamo equation for the generation of a magnetic field by the motion of an electrically conducting fluid and the equation for the evolution of vorticity of a viscous fluid. Exponential stretching feature of the underlying instability problem; Instability of the growth rate of an infinitesimal perturbation in a metric with derivatives.