arXiv subjects

Ethan Vishniac

Publications and source records attributed to Ethan Vishniac.

12 recordsLinked to original sources

arXiv2024

Sub-Alfvenic Turbulence: Magnetic to Kinetic Energy Ratio, Modification of Weak Cascade and Implications for Magnetic Field Strength Measurement

We study the properties of sub-Alfvenic magnetohydrodynamic (MHD) turbulence, i.e., turbulence with Alfven Mach number $M_A=V_L/V_A<1$, where $V_L$ is the velocity at the injection scale and $V_A$ is the Alfven velocity. We demonstrate that weak turbulence can have different regimes depending on whether it is driven by velocity or magnetic fluctuations. If the turbulence is driven by isotropic bulk forces, i.e. velocity-driven, in an incompressible conducting fluid, we predict that the kinetic energy is $M_A^{-2}$ times larger than the energy of magnetic fluctuations. This effect arises from the long parallel wavelength tail of the forcing, which excites modes with $k_\|/k_\perp < M_A$. We also predict that as the turbulent cascade reaches the strong regime the energy of slow modes exceeds the energy of Alfven modes by a factor $M_A^{-1}$. These effects are absent if the turbulence is magnetically driven at the injection scale. We confirm these predictions with numerical simulations. As the assumption of magnetic and kinetic energy equipartition is at the core of the Davis-Chandrasekhar-Fermi (DCF) approach to measuring magnetic field strength in sub-Alfvenic turbulence, we conclude that the DCF technique is not universally applicable. In particular, we suggest that the dynamical excitation of long azimuthal wavelength modes in the galactic disk may compromise the use of the DCF technique. We discuss alternative expressions that can be used to obtain magnetic field strength from observations.

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arXiv2021

Topological theory of physical fields

We study the topology associated with physical vector and scalar fields. A mathematical object, e.g., a ball, can be continuously deformed, without tearing or gluing, to make other topologically equivalent objects, e.g., a cube or a solid disk. If tearing or gluing get involved, i.e., the deformation is not continuous anymore, the initial topology will consequently change giving rise to a topologically distinct object, e.g., a torus. This simple concept in general topology may be employed in the study of physical systems described by fields. Instead of continuously deforming objects, we can take a continuously evolving field, with an appropriately defined topology, such that the topology remains unchanged in time unless the system undergoes an important physical change, e.g., a transition to a different energy state. For instance, a sudden change in the magnetic topology in an energetically relaxing plasma, a process called reconnection, strongly affects the dynamics, e.g., it is involved in launching solar flares and generating large scale magnetic fields in astrophysical objects. In this topological formalism, the magnetic topology in a plasma can spontaneously change due to the presence of dissipative terms in the induction equation which break its time symmetry. We define a topology for the vector field $\bf F$ in the phase space $(\bf x, F)$. As for scalar fields represented by a perfect fluid, e.g., the inhomogeneous inflaton or Higgs fields, the fluid velocity $\bf u$ defines the corresponding topology. The vector field topology in its corresponding phase space $(\bf x, F)$ will be preserved in time if certain conditions including time reversal invariance are satisfied by the field and its governing differential equation.

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arXiv2021

Magnetic topology in fluids

We study the evolution of turbulent magnetic fields from a topological point of view, invoking commonplace mathematical tools from general topology and dynamical systems theory which connect magnetic field evolution to time reversal invariance, entropy increase and the second law of thermodynamics. We show that in fact magnetic topology is well-defined only in the phase space corresponding to a dynamical system governed by the induction equation. Hence the field's topology and stochasticity can be studied in terms of the corresponding phase space trajectories rather than the field lines in real Euclidean space. In fact, our results suggest that magnetic field lines should not be taken too literally because their existence and uniqueness and more importantly continuity in time require strong mathematical conditions, hardly satisfied in astrophysical systems. As for magnetic topology change, it is shown that the phase space topology is preserved in time for a magnetic field which, besides satisfying few continuity conditions, solves a time reversal invariant induction equation. What breaks the time symmetry in the induction equation is the presence of non-ideal plasma effects at small scales such as resistivity, which results from random collisions between diffusing electrons and other particles. The small scale, stochastic disturbances produced thereby are super-linearly amplified by Richardson diffusion in the turbulent cascade, which are eventually manifested as large scale reconnection events, somehow similar to stretching quantum fluctuations during inflation to seed large scale cosmological structures. This suggests that reconnection is rooted in the second law of thermodynamics that dictates entropy increase which in turn breaks the time symmetry.

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arXiv2020

Nanoflare Theory Revisited

Local magnetic reversals are an inseparable part of magnetohydrodynamic (MHD) turbulence whose collective outcome on an arbitrary scale in the inertial range may lead to a global stochastic reconnection event with a rate independent of small scale physics. We show that this picture is intimately related to the nanoflare theory of the solar corona. First, we argue that due to stochastic flux freezing, a generalized version of flux freezing in turbulence, the magnetic field follows the turbulent flow in a statistical sense. Bending and stretching an initially smooth field, therefore, the turbulence generally increases the magnetic spatial complexity. Strong magnetic shears associated with such a highly tangled field can trigger local reversals and field annihilations that convert magnetic energy into kinetic and thermal energy respectively. The former maintains the turbulence, which incidentally continues to entangle the field completing the cycle, while the latter enhances the heat generation in the dissipative range. We support this theoretical picture invoking recent analytical and numerical studies which suggest a correlation between magnetic complexity and magnetic energy dissipation. The amplification of multiple local, in-phase reversals by super-linear Richardson diffusion may initiate a global reconnection at larger scales, however, even in the absence of such a global stochastic reconnection, the small scale reversals will continue to interact with the turbulence. We employ conventional scaling laws of MHD turbulence to illustrate that these local events are indeed efficient in both enhancing the turbulence and generating heat. Finally, using an MHD numerical simulation, we show that the time evolution of the magnetic complexity is statistically correlated with the kinetic energy injection rate and/or magnetic-to-thermal energy conversion rate.

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arXiv2020

Power and spatial complexity in stochastic reconnection

The level of spatial complexity associated with a given vector field on an arbitrary range of scales \iffalse ${\bf F(x}, t)$ can be quantified by a simple, time-dependent function $S(t)={1\over 2}(1-\hat{\bf F}_l.\hat{\bf F}_L)_{rms}$ with ${\bf F}_l$ (${\bf F}_L$) being the average field in a volume of scale $l$ ($L>l$) and the unit vector defined as $\hat{\bf F}={\bf F}/|{\bf F}|$. Thus,\fi can be quantified by a simple, scale-dependent function of time; $0\leq S(t)\leq 1$. Previous work has invoked kinetic and magnetic complexities, associated with velocity and magnetic fields ${\bf u(x}, t)$ and ${\bf B(x}, t)$, to study magnetic reconnection and diffusion in turbulent and magnetized fluids. In this paper, using the coarse-grained momentum equation, we argue that the fluid jets associated with magnetic reconnection events at an arbitrary scale $l$ in the turbulence inertial range are predominantly driven by the Lorentz force ${\bf{N}}_l=({\bf j\times B})_l-{\bf j}_l\times {\bf B}_l$. This force, is induced by the subscale currents and is analogous to the turbulent electromotive force ${\cal E}_l=({\bf u\times B})_l-{\bf u}_l\times {\bf B}_l$ in dynamo theories. Typically, high (low) magnetic complexities during reconnection imply large (small) spatial gradients for the magnetic field, i.e., strong (weak) Lorentz forces ${\bf N}_l$. Reconnection launches jets of fluid, hence the rate of change of kinetic complexity is expected to strongly correlate with the power injected by the Lorentz force ${\bf N}_l$. We test this prediction using an incompressible, homogeneous magnetohydrodynamic (MHD) simulation and associate it with previous results. It follows that the stronger (weaker) the turbulence, the more (less) complex the magnetic field and the stronger (weaker) the reconnection field and thus the ensuing reconnection.

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arXiv2020

Statistical Analysis of Stochastic Magnetic Fields

Previous work has introduced scale-split energy density ψfor a given vector field B in order to quantify the field stochasticity S(t). Application to turbulent magnetic fields leads to the prediction that tangling magnetic field by turbulence increases magnetic stochasticity. An increasing stochasticity in turn leads to disalignments of the coarse-grained fields at smaller scales thus they average to weaker fields at larger scales upon coarse-graining. The field's resistance against tanglement by the turbulence may lead at some point to its sudden slippage through the fluid, decreasing the stochasticity and increasing the energy density. Thus the maxima (minima) of magnetic stochasticity are expected to approximately coincide with the minima (maxima) of energy density, occurrence of which corresponds to slippage of the magnetic field through the fluid. Field-fluid slippage, on the other hand, has been already found to be intimately related to magnetic reconnection. In this paper, we test these theoretical predictions numerically using a homogeneous, incompressible magnetohydrodynamic (MHD) simulation. Apart from expected small scale deviations, possibly due to e.g., intermittency and strong field annihilation, the theoretically predicted global relationship between stochasticity and magnetic energy is observed in different sub-volumes of the simulation box. This may indicate ubiquitous local field-fluid slippage and small scale reconnection events in MHD turbulence. We also show that the maximum magnetic stochasticity, i.e., \partial_t S(t)=0 & \partial^2_t S(t)<0, leads to sudden increases in kinetic stochasticity level which may correspond to fluid jets driven by the reconnecting field lines, i.e., reconnection. This suggests a new mathematical approach to the reconnection problem.

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arXiv2019

Magnetic stochasticity and diffusion

We develop a quantitative relationship between magnetic diffusion and the level of randomness, or stochasticity, of the diffusing magnetic field in a magnetized medium. A general mathematical formulation of magnetic stochasticity in turbulence has been developed in previous work in terms of the ${\cal L}_p$-norm $S_p(t)={1\over 2}|| 1-\hat{\bf B}_l.\hat{\bf B}_L||_p$, $p$th order magnetic stochasticity of the stochastic field ${\bf B}({\bf x}, t)$, based on the coarse-grained fields, ${\bf B}_l$ and ${\bf B}_L$, at different scales, $l\neq L$. For laminar flows, stochasticity level becomes the level of field self-entanglement or spatial complexity. In this paper, we establish a connection between magnetic stochasticity $S_p(t)$ and magnetic diffusion in magnetohydrodynamic (MHD) turbulence and use a homogeneous, incompressible MHD simulation to test this prediction. Our results agree with the well-known fact that magnetic diffusion in turbulent media follows the super-linear Richardson dispersion scheme. This is intimately related to stochastic magnetic reconnection in which super-linear Richardson diffusion broadens the matter outflow width and accelerates the reconnection process.

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arXiv2018

Introduction to Magnetic Reconnection

We review the basic concepts of magnetic reconnection and propose a general framework for the astrophysical reconnection at large scales. Magnetic reconnection is the rearrangement of magnetic field topology. The conventional Sweet-Parker scheme and some of its extensions presume a non-turbulent medium and generally produce very slow reconnection or an unstable configuration. However, the assumption of laminar flow is unrealistic in astrophysics since, even in an initially quiet environment, magnetic reconnection by itself can drive turbulence. The resulting turbulence has the potential to enhance the reconnection rate. This can lead to an unstable feedback loop as reconnection drives turbulence and turbulence drives reconnection. Stochastic reconnection was proposed, and subsequently tested by numerical simulations, for high $β$ plasmas with a magnetic Prandtl number of order unity, $Pr_m\sim 1$. This model predicts reconnection speeds comparable to the large scale turbulent eddy velocity. A recent study of stochastic reconnection for $Pr_m>1$ has shown that the width of the outflow layer and the ejection velocity of matter from the reconnection region seem to be unaffected by viscosity in typical astrophysical systems. However if $Pr_m>1$ viscosity can suppress small scale reconnection events near and below the Kolmogorov or viscous damping scale. This will produce a threshold for the suppression of large scale reconnection by viscosity when $Pr_m$ is larger than the root of the Reynolds number, $Pr_m>\sqrt{Re}$. For $Pr_m>1$ this leads to the spectral index $\sim-4/3$ for length scales between the viscous dissipation scale and eddies larger by roughly $Pr_m^{3/2}$.

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arXiv2003

Radiative Heat Conduction and the Magnetorotational Instability

A photon or neutrino gas--semi-contained by a baryonic species through scattering--comprises a rather peculiar MHD fluid where the magnetic field is truly frozen only to the co-moving volume associated with the mass density. Although radiative diffusion precludes an adiabatic treatment of compressive perturbations, we show that the energy equation may be cast in "quasi-adiabatic" form for exponentially growing non-propagating wave modes. Defining a generalized quasi-adiabatic index leads to a relatively straightforward dispersion relation for non-axisymmetric magnetorotational modes in the horizontal regime when an accretion disk has comparable stress contributions from diffusive and non-diffusive particle species. This analysis is generally applicable to optically thick, neutrino-cooled disks since the pressure contributions from photons, pairs and neutrinos, all have the same temperature dependence whereas only the neutrino component has radiative heat conduction properties on the time and length scales of the instability. We discuss the energy deposition process and the temporal and spatial properties of the ensuing turbulent disk structure on the basis of the derived dispersion relation.

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arXiv2002

MHD Turbulence: Scaling Laws and Astrophysical Implications

Turbulence is the most common state of astrophysical flows. In typical astrophysical fluids, turbulence is accompanied by strong magnetic fields, which has a large impact on the dynamics of the turbulent cascade. Recently, there has been a significant breakthrough on the theory of magnetohydrodynamic (MHD) turbulence. For the first time we have a scaling model that is supported by both observations and numerical simulations. We review recent progress in studies of both incompressible and compressible turbulence. We compare Iroshnikov-Kraichnan and Goldreich-Sridhar models, and discuss scalings of Alfvén, slow, and fast waves. We also discuss the completely new regime of MHD turbulence that happens below the scale at which hydrodynamic turbulent motions are damped by viscosity. In the case of the partially ionized diffuse interstellar gas the viscosity is due to neutrals and truncates the turbulent cascade at $\sim$parsec scales. We show that below this scale magnetic fluctuations with a shallow spectrum persist and discuss the possibility of a resumption of the MHD cascade after ions and neutrals decouple. We discuss the implications of this new insight into MHD turbulence for cosmic ray transport, grain dynamics, etc., and how to test theoretical predictions against observations.

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arXiv2002

New Regime of MHD Turbulence: Cascade Below Viscous Cutoff

In astrophysical situations, e.g. in the interstellar medium (ISM), neutrals can provide viscous damping on scales much larger than the magnetic diffusion scale. Through numerical simulations, we have found that the magnetic field can have a rich structure below the dissipation cutoff scale. This implies that magnetic fields in the ISM can have structures on scales much smaller than parsec scales. Our results show that the magnetic energy contained in a wavenumber band is independent of the wavenumber and magnetic structures are intermittent and extremely anisotropic. We discuss the relation between our results and the formation of the tiny-scale atomic structure (TSAS).

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arXiv2001

Simulations of MHD Turbulence in a Strongly Magnetized Medium

We analyze 3D numerical simulations of driven incompressible magnetohydrodynamic (MHD) turbulence in a periodic box threaded by a moderately strong external magnetic field. We sum over nonlinear interactions within Fourier wavebands and find that the time scale for the energy cascade is consistent with the Goldreich-Sridhar model of strong MHD turbulence. Using higher order longitudinal structure functions we show that the turbulent motions in the plane perpendicular to the local mean magnetic field are similar to ordinary hydrodynamic turbulence while motions parallel to the field are consistent with a scaling correction which arises from the eddy anisotropy. We present the structure tensor describing velocity statistics of Alfvenic and pseudo-Alfvenic turbulence. Finally, we confirm that an imbalance of energy moving up and down magnetic field lines leads to a slow decay of turbulent motions and speculate that this imbalance is common in the interstellar medium where injection of energy is intermittent both in time and space.

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