It is widely known that cosmic magnetic fields, i.e. the fields of planets, stars, and galaxies, are produced by the hydromagnetic dynamo effect in moving electrically conducting fluids. It is less well known that cosmic magnetic fields play also an active role in cosmic structure formation by enabling outward transport of angular momentum in accretion disks via the magnetorotational instability (MRI). Considerable theoretical and computational progress has been made in understanding both processes. In addition to this, the last ten years have seen tremendous efforts in studying both effects in liquid metal experiments. In 1999, magnetic field self-excitation was observed in the large scale liquid sodium facilities in Riga and Karlsruhe. Recently, self-excitation was also obtained in the French "von Karman sodium" (VKS) experiment. An MRI-like mode was found on the background of a turbulent spherical Couette flow at the University of Maryland. Evidence for MRI as the first instability of an hydrodynamically stable flow was obtained in the "Potsdam Rossendorf Magnetic Instability Experiment" (PROMISE). In this review, the history of dynamo and MRI related experiments is delineated, and some directions of future work are discussed.
Recent advances in understanding of magnetohydrodynamic (MHD) turbulence call for substantial revisions in our understanding of cosmic ray transport. In this paper we use gyroresonance recently obtained scaling laws for MHD modes to calculate the scattering frequency for cosmic rays in the ISM. We consider gyroresonance with MHD modes (Alfvenic, slow and fast) and transit-time damping (TTD) by fast modes. We conclude that the gyroresonance with fast modes is the dominant contribution to cosmic ray scattering for the typical interstellar conditions. In contrast to earlier studies, we find that …
Recent advances in understanding of magnetohydrodynamic (MHD) turbulence call for substantial revisions in the picture of cosmic ray transport. In this paper we use recently obtained scaling laws for MHD modes to calculate the scattering frequency for cosmic rays in the ISM. We consider gyroresonance with MHD modes (Alfvenic, slow and fast) and transit-time damping (TTD) by fast modes. We provide calculations of cosmic ray scattering for various phases of interstellar medium with realistic interstellar turbulence driving that is consistent with the velocity dispersions observed in diffuse gas.…
Recent advances in understanding of magnetohydrodynamic (MHD) turbulence call for revisions in the picture of cosmic ray transport. In this paper we use recently obtained scaling laws for MHD modes to obtain the scattering frequency for cosmic rays. Using quasilinear theory we calculate gyroresonance with MHD modes (Alfvénic, slow and fast) and transit-time damping (TTD) by fast modes. We provide calculations of cosmic ray scattering for various phases of interstellar medium with realistic interstellar turbulence driving that is consistent with the velocity dispersions observed in diffuse gas.…
The physical processes involved in diffusion of Galactic cosmic rays in the interstellar medium are addressed. We study the possibility that the nonlinear MHD cascade sets the power-law spectrum of turbulence which scatters charged energetic particles. We find that the dissipation of waves due to the resonant interaction with cosmic ray particles may terminate the Kraichnan-type cascade below wavelengths 10^13 cm. The effect of this wave dissipation has been incorporated in the GALPROP numerical propagation code in order to asses the impact on measurable astrophysical data. The energy-dependen…
Scattering rates for a Goldreich-Sridhar (GS) spectrum of anisotropic, incompressible, magnetohydrodynamic turbulence are calculated in the quasilinear approximation. Because the small-scale fluctuations are constrained to have wave vectors nearly perpendicular to the background magnetic field, scattering is too weak to provide either the mean free paths commonly used in Galactic cosmic-ray propagation models or the mean free paths required for acceleration of cosmic rays at quasi-parallel shocks. Where strong pitch-angle scattering occurs, it is due to fluctuations not described by the GS spe…
Multi-wavelength observations from radio to soft X-ray bands of large-scale galactic spiral structures offer synthesized and comprehensive views of nearby disk galaxies. In the presence of a massive dark-matter halo, the density-wave dynamics on galactic scales involves the stellar disk, the gas disk of interstellar medium (ISM), the magnetic field, and the cosmic-ray gas (CRG). In this paper, we explore the dynamic and electromagnetic interplay between the magnetized ISM disk and CRG disk so that structural and diagnostic features of optical, infrared, and synchrotron radio-continuum emission…
We construct a map of deflections of ultra-high energy cosmic rays by extragalactic magnetic fields using a magneto-hydrodynamical simulation of cosmic structure formation that realistically reproduces the positions of known galaxy clusters in the Local Universe. Large deflection angles occur in cluster regions, which however cover only an insignificant fraction of the sky. More typical deflections of order $\lsim 1^\circ$ are caused by crossings of filaments. For protons with energies $E \geq 4 \times 10^{19} {\rm eV}$, deflections do not exceed a few degrees over most of the sky up to a prop…
In this era of precision cosmology, a detailed physical understanding on the evolution of cosmic baryons is required. Cosmic magnetic fields, though still poorly understood, may represent an important component in the global cosmic energy flow that affects the baryon dynamics. We have developed an Eulerian-based cosmological magnetohydrodynamics code (CosmoMHD) with modern shock capturing schemes to study the formation and evolution of cosmic structures in the presence of magnetic fields. The code solves the ideal MHD equations as well as the non-equilibrium rate equations for multiple species…
The evolution and viscous damping of cosmic magnetic fields in the early universe, is analysed. Using the fact that the fluid, electromagnetic, and shear viscous energy-momentum tensors are all conformally invariant, the evolution is transformed from the expanding universe setting into that in flat spacetime. Particular attention is paid to the evolution of nonlinear Alfven modes. For a small enough magnetic field, which satisfies our observational constraints, these wave modes either oscillate negligibly or, when they do oscillate, become overdamped. Hence they do not suffer Silk damping on g…
We carried out 2.5-dimensional resistive magnetohydrodynamic simulations to study the effects of magnetic diffusivity on magnetically driven mass accretion and jet formation. We found that (1) when the normalized magnetic diffusivity, is small, mass accretion and jet formation take place intermittently; (2) when diffusivity is middle, the system evolves toward a quasi-steady state; and the system evolves toward a quasi-steady state; and (3) when diffusivity is large, the accretion/mass outflow rate decreases with diffusivity and approaches 0. The results of these simulations indicate magnetic …
We study the evolution of magnetic fields in freely decaying magnetohydrodynamic turbulence. By quasi-linearizing the Navier-Stokes equation, we solve analytically the induction equation in quasi-normal approximation. We find that, if the magnetic field is not helical, the magnetic energy and correlation length evolve in time respectively as E_B \propto t^{-2(1+p)/(3+p)} and ξ_B \propto t^{2/(3+p)}, where p is the index of initial power-law spectrum. In the helical case, the magnetic helicity is an almost conserved quantity and forces the magnetic energy and correlation length to scale as E_B …
We perform direct numerical simulations of three-dimensional freely decaying magnetohydrodynamic (MHD) turbulence. For helical magnetic fields an inverse cascade effect is observed in which power is transfered from smaller scales to larger scales. The magnetic field reaches a scaling regime with self-similar evolution, and power law behavior at high wavenumbers. We also find power law decay in the magnetic and kinematic energies, and power law growth in the characteristic length scale of the magnetic field.
We show that local directional alignment of the velocity and magnetic field fluctuations occurs rapidly in magnetohydrodynamics for a variety of parameters. This is observed both in direct numerical simulations and in solar wind data. The phenomenon is due to an alignment between the magnetic field and either pressure gradients or shear-associated kinetic energy gradients. A similar alignment, of velocity and vorticity, occurs in the Navier Stokes fluid case. This may be the most rapid and robust relaxation process in turbulent flows, and leads to a local weakening of the nonlinear terms in th…
We analyze the decay laws of the kinetic and magnetic energies and the evolution of correlation lengths in freely decaying incompressible magnetohydrodynamic (MHD) turbulence. Scale invariance of MHD equations assures that, in the case of constant dissipation parameters ({\it i.e.} kinematic viscosity and resistivity) and null magnetic helicity, the kinetic and magnetic energies decay in time as $E \sim t^{-1}$, and the correlation lengths evolve as $ξ\sim t^{1/2}$. In the helical case, assuming that the magnetic field evolve towards a force-free state, we show that (in the limit of large magn…
The influence of a toroidal magnetic field on the dynamics of Rossby waves in a thin layer of ideal conductive fluid on a rotating sphere is studied in the "shallow water" magnetohydrodynamic approximation for the first time. Dispersion relations for magnetic Rossby waves are derived analytically in Cartesian and spherical coordinates. It is shown that the magnetic field causes the splitting of low order (long wavelength) Rossby waves into two different modes, here denoted fast and slow {\em magnetic Rossby waves}. The high frequency mode (the fast magnetic Rossby mode) corresponds to an ordin…
A novel model of incompressible magnetohydrodynamic turbulence in the presence of a strong external magnetic field is proposed for explanation of recent numerical results. According to the proposed model, in the presence of the strong external magnetic field, incompressible magnetohydrodynamic turbulence becomes nonlocal in the sense that low frequency modes cause decorrelation of interacting high frequency modes from the inertial interval. It is shown that the obtained nonlocal spectrum of the inertial range of incompressible magnetohydrodynamic turbulence represents an anisotropic analogue o…
We derive analytical solutions and dispersion relations of global magnetic Poincaré (magneto-gravity) and magnetic Rossby waves in the approximation of shallow water magnetohydrodynamics. The solutions are obtained in a rotating spherical coordinate system for strongly and weakly stable stratification separately in the presence of toroidal magnetic field. In both cases magnetic Rossby waves split into fast and slow magnetic Rossby modes. In the case of strongly stable stratification (valid in the radiative part of the tachocline) all waves are slightly affected by the layer thickness and the t…
We investigate field-line separation in strong MHD turbulence using direct numerical simulations. We find that in the static-magnetic-field approximation the thermal conductivity in galaxy clusters is reduced by a factor of about 50 relative to the Spitzer thermal conductivity of a non-magnetized plasma. This value is too small for heat conduction to balance radiative cooling in clusters.
We construct magnetohydrodynamic (MHD) similarity rebound shocks joining `quasi-static' asymptotic solutions around the central degenerate core to explore an MHD model for the evolution of random magnetic field in supernova explosions. This provides a theoretical basis for further studying synchrotron diagnostics, MHD shock acceleration of cosmic rays, and the nature of intense magnetic field in compact objects. The magnetic field strength in space approaches a limiting ratio, that is comparable to the ratio of the ejecta mass driven out versus the progenitor mass, during this self-similar reb…
Steep gradients of temperature and density, called cold fronts, are observed by Chandra in a leading edge of subclusters moving through the intracluster medium (ICM). The presence of cold fronts indicates that thermal conduction across the front is suppressed by magnetic fields. We carried out three-dimensional magnetohydrodynamic (MHD) simulations including anisotropic thermal conduction of a subcluster moving through a magnetically turbulent ICM. We found that turbulent magnetic fields are stretched and amplified by shear flows along the interface between the subcluster and the ambient ICM. …
We propose a phenomenological model for incompressible magnetohydrodynamic turbulence. We argue that nonlinear-wave interaction weakens as the energy cascade proceeds to small scales, however, the anisotropy of fluctuations along the large-scale magnetic field increases, which makes turbulence strong at all scales. To explain the weakening of the interaction, we propose that small-scale fluctuations of the velocity and magnetic fields become increasingly dynamically aligned as their scale decreases, so that turbulent eddies become locally anisotropic in the plane perpendicular to the large-sca…
We present results from N-body + magnetohydrodynamical simulations of merging clusters of galaxies. We find that cluster mergers cause various characteristic magnetic field structures because of the strong bulk flows in the intracluster medium. The moving substructures result in cool regions surrounded by the magnetic field. These will be recognized as magnetized cold fronts in the observational point of view. A relatively ordered magnetic field structure is generated just behind the moving substructure. Eddy-like field configurations are also formed by Kelvin-Helmholtz instabilities. These fe…
We study a nonlinear quenching of turbulent magnetic diffusion and effective drift velocity of large-scale magnetic field in a developed two-dimensional MHD turbulence at large magnetic Reynolds numbers. We show that transport of the mean-square magnetic potential strongly changes quenching of turbulent magnetic diffusion. In particularly, the catastrophic quenching of turbulent magnetic diffusion does not occur for the large-scale magnetic fields $B \gg B_{\rm eq} / \sqrt{\rm Rm}$ when a divergence of the flux of the mean-square magnetic potential is not zero, where $B_{\rm eq}$ is the equipa…
We discuss the results of three-dimensional magnetohydrodynamic simulations, using a pseudo-Newtonian potential, of thin disk (h/r ~ 0.1) accretion onto black holes. We find (i) that magnetic stresses persist within the marginally stable orbit, and (ii) that the importance of those stresses for the dynamics of the flow depends upon the strength of magnetic fields in the disk outside the last stable orbit. Strong disk magnetic fields (alpha > 0.1) lead to a gross violation of the zero-torque boundary condition at the last stable orbit, while weaker fields (alpha ~ 0.01) produce results more aki…
We describe a new method to include magnetic fields into smooth particle hydrodynamics. The derivation of the self-gravitating hydrodynamics equations from a variational principle is discussed in some detail. The non-dissipative magnetic field evolution is instantiated by advecting so-called Euler potentials. This approach enforces the crucial $\nabla\cdot\vec{B}=0$-constraint by construction. These recent developments are implemented in our three-dimensional, self-gravitating magnetohydrodynamics code MAGMA. A suite of tests is presented that demonstrates the superiority of this new approach …
The shell-to-shell energy transfer rates for magnetohydrodynamic (MHD) turbulence are computed analytically, which shows local energy transfer rates from velocity to velocity, velocity to magnetic, magnetic to velocity, and magnetic to magnetic fields for nonhelical MHD in the inertial range. It is also found that for kinetic-energy dominated MHD fluid, there is a preferential shell-to-shell energy transfer from kinetic to magnetic energy; the transfer is reversed for magnetic-energy dominated MHD fluid. This property is the reason for the asymptotic value of Alfven ratio to be close to 0.5. T…
Renormalized viscosity, renormalized resistivity, and various energy fluxes are calculated for helical magnetohydrodynamics using perturbative field theory. The calculation is to first-order 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 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 nonhelical interactions, and (2) inverse energy flux of magnetic energy caused by helical intera…
The scaling properties of the second order magnetic structure function D_2^{(B)}(r) and the corresponding magnetic correlation function C_2^{(B)}(r) are derived for two-dimensional magnetohydrodynamic turbulence in the kinematic regime where the ratio of kinetic energy to magnetic energy is much larger than one. In this regime the magnetic flux function $ψ$ can be treated as a passive scalar advected in a two-dimensional turbulent flow. Its structure function $D_2^{(ψ)}(r)$ and the one for the magnetic field D_2^{(B)}(r) are connected by an exact relation. We calculate D_2^{(ψ)}(r) and thus D_…
Energy cascade rates and Kolmogorov's constant for nonhelical steady magnetohydrodynamic turbulence have been calculated by solving the flux equations to the first order in perturbation. For zero cross helicity and space dimension $d=3$, magnetic energy cascades from large length-scales to small length-scales (forward cascade). In addition, there are energy fluxes from large-scale magnetic field to small-scale velocity field, large-scale velocity field to small-scale magnetic field, and large-scale velocity field to large-scale magnetic field. Kolmogorov's constant for magnetohydrodynamics is …
We investigate whether dual strings could be solutions of the magnetohydrodynamics equations in the limit of infinite conductivity. We find that the induction equation is satisfied, and we discuss the Navier-Stokes equation (without viscosity) with the Lorentz force included. We argue that the dual string equations (with a non-universal maximum velocity) should describe the large scale motion of narrow magnetic flux tubes, because of a large reparametrization (gauge) invariance of the magnetic and electric string fields. It is shown that the energy-momentum tensor for the dual string can be re…
We show that the decaying magnetohydrodynamic turbulence leads to a more rapid growth of the correlation length of a primordial magnetic field than that caused by the expansion of the Universe. As an example, we consider the magnetic fields created during the electroweak phase transition. The expansion of the universe alone would yield a correlation length at the present epoch of 1 AU, whereas we find that the correlation length is likely of order 100 AU, and cannot possibly be longer than $10^4$ AU for non-helical fields. If the primordial field is strongly helical, the correlation length can…
We propose a phenomenological theory of strong incompressible magnetohydrodynamic turbulence in the presence of a strong large-scale external magnetic field. We argue that in the inertial range of scales, magnetic-field and velocity-field fluctuations tend to align the directions of their polarizations. However, the perfect alignment cannot be reached, it is precluded by the presence of a constant energy flux over scales. As a consequence, the directions of fluid and magnetic-field fluctuations at each scale $λ$ become effectively aligned within the angle $ϕ_λ\propto λ^{1/4}$, which leads to s…
The dynamic renormalization group (RG) is used to study the large-distance and long-time limits of viscous and resistive incompressible magnetohydrodynamics subject to random forces and currents. The scale-dependent viscosity and magnetic resistivity are derived and used for carrying out RG-improved perturbation theory. This is applied to derive both the asymptotic scaling and the overall proportionality coefficients for both the velocity and magnetic field correlation functions as well as the kinetic and magnetic energy density spectral functions. The Kolmogorov, Iroshnikov-Kraichnan, as well…
