arXiv subjects

Hantao Ji

Publications and source records attributed to Hantao Ji.

63 records · Page 4Linked to original sources

arXiv2006

Helical Magnetorotational Instability in Magnetized Taylor-Couette Flow

Hollerbach and Rudiger have reported a new type of magnetorotational instability (MRI) in magnetized Taylor-Couette flow in the presence of combined axial and azimuthal magnetic fields. The salient advantage of this "helical'' MRI (HMRI) is that marginal instability occurs at arbitrarily low magnetic Reynolds and Lundquist numbers, suggesting that HMRI might be easier to realize than standard MRI (axial field only). We confirm their results, calculate HMRI growth rates, and show that in the resistive limit, HMRI is a weakly destabilized inertial oscillation propagating in a unique direction along the axis. But we report other features of HMRI that make it less attractive for experiments and for resistive astrophysical disks. Growth rates are small and require large axial currents. More fundamentally, instability of highly resistive flow is peculiar to infinitely long or periodic cylinders: finite cylinders with insulating endcaps are shown to be stable in this limit. Also, keplerian rotation profiles are stable in the resistive limit regardless of axial boundary conditions. Nevertheless, the addition of toroidal field lowers thresholds for instability even in finite cylinders.

astro-ph↗

arXiv2006

Laboratory Plasma Dynamos, Astrophysical Dynamos, and Magnetic Helicity Evolution

The term ``dynamo'' means different things to the laboratory fusion plasma and astrophysical plasma communities. To alleviate the resulting confusion and to facilitate interdisciplinary progress, we pinpoint conceptual differences and similarities between laboratory plasma dynamos and astrophysical dynamos. We can divide dynamos into three types: 1. magnetically dominated helical dynamos which sustain a large scale magnetic field against resistive decay and drive the magnetic geometry toward the lowest energy state, 2. flow-driven helical dynamos which amplify or sustain large scale magnetic fields in an otherwise turbulent flow, and 3. flow-driven nonhelical dynamos which amplify fields on scales at or below the driving turbulence. We discuss how all three types occur in astrophysics whereas plasma confinement device dynamos are of the first type. Type 3 dynamos requires no magnetic or kinetic helicity of any kind. Focusing on type 1 and 2 dynamos, we show how different limits of a unified set of equations for magnetic helicity evolution reveal both types. We explicitly describe a steady-state example of a type 1 dynamo, and three examples of type 2 dynamos: (i) closed volume and time dependent; (ii) steady-state with open boundaries; (iii) time dependent with open boundaries.

astro-ph↗

arXiv2006

Simulations of Magnetorotational Instability in a Magnetized Couette Flow

In preparation for an experimental study of magnetorotational instability (MRI) in liquid metal, we present non-ideal two-dimensional magnetohydrodynamic simulations of the nonlinear evolution of MRI in the experimental geometry. The simulations adopt initially uniform vertical magnetic fields, conducting radial boundaries, and periodic vertical boundary conditions. No-slip conditions are imposed at the cylinders. Our linear growth rates compare well with existing local and global linear analyses. The MRI saturates nonlinearly with horizontal magnetic fields comparable to the initial axial field. The rate of angular momentum transport increases modestly but significantly over the initial state. For modest fluid and magnetic Reynolds numbers Re, Rm between 100 and 1000, the final state is laminar reduced mean shear except near the radial boundaries, and with poloidal circulation scaling as the square root of resistivity, in partial agreement with the analysis of Knobloch and Julien. A sequence of simulations at Rm=20 and 100 < Re < 25,600 enables extrapolation to the experimental regime (Rm ~ 20, Re ~ 10^7), albeit with unrealistic boundary conditions. MRI should increase the experimentally measured torque substantially over its initial purely hydrodynamic value.

astro-ph↗

arXiv2004

Numerical and Experimental Investigation of Circulation in Short Cylinders

In preparation for an experimental study of magnetorotational instability (MRI) in liquid metal, we explore Couette flows having height comparable to the gap between cylinders, centrifugally stable rotation, and high Reynolds number. Experiments in water are compared with numerical simulations. Simulations show that endcaps corotating with the outer cylinder drive a strong poloidal circulation that redistributes angular momentum. Predicted azimuthal flow profiles agree well with experimental measurements. Spin-down times scale with Reynolds number as expected for laminar Ekman circulation; extrapolation from two-dimensional simulations at $Re\le 3200$ agrees remarkably well with experiment at $Re\sim 10^6$. This suggests that turbulence does not dominate the effective viscosity. Further detailed numerical studies reveal a strong radially inward flow near both endcaps. After turning vertically along the inner cylinder, these flows converge at the midplane and depart the boundary in a radial jet. To minimize this circulation in the MRI experiment, endcaps consisting of multiple, differentially rotating rings are proposed. Simulations predict that an adequate approximation to the ideal Couette profile can be obtained with a few rings.

physics.flu-dyn↗

arXiv2003

Electromagnetic Fluctuations during Fast Reconnection in a Laboratory Plasma

Clear evidence for a positive correlation is established between the magnitude of magnetic fluctuations in the lower-hybrid frequency range and enhancement of reconnection rates in a well-controlled laboratory plasma. The fluctuations belong to the right-hand polarized whistler wave branch, propagating obliquely to the reconnecting magnetic field, with a phase velocity comparable to the relative drift velocity between electrons and ions. The short coherence length and large variation along the propagation direction indicate their strongly nonlinear nature in three dimensions.

astro-ph↗

arXiv2001

Magnetorotational Instability in a Rotating Liquid Metal Annulus

Although the magnetorotational instability (MRI) has been widely accepted as a powerful accretion mechanism in magnetized accretion disks, it has not been realized in the laboratory. The possibility of studying MRI in a rotating liquid-metal annulus (Couette flow) is explored by local and global stability analysis and magnetohydrodynamic (MHD) simulations. Stability diagrams are drawn in dimensionless parameters, and also in terms of the angular velocities at the inner and outer cylinders. It is shown that MRI can be triggered in a moderately rapidly rotating table-top apparatus, using easy-to-handle metals such as gallium. Practical issues of this proposed experiment are discussed.

astro-ph↗

arXiv2001

The $α$ Dynamo Effects in Laboratory Plasmas

A concise review of observations of the $α$ dynamo effect in laboratory plasmas is given. Unlike many astrophysical systems, the laboratory pinch plasmas are driven magnetically. When the system is overdriven, the resultant instabilities cause magnetic and flow fields to fluctuate, and their correlation induces electromotive forces along the mean magnetic field. This $α$-effect drives mean parallel electric current, which, in turn, modifies the initial background mean magnetic structure towards the stable regime. This drive-and-relax cycle, or the so-called self-organization process, happens in magnetized plasmas in a time scale much shorter than resistive diffusion time, thus it is a fast and unquenched dynamo process. The observed $α$-effect redistributes magnetic helicity (a measure of twistedness and knottedness of magnetic field lines) but conserves its total value. It can be shown that fast and unquenched dynamos are natural consequences of a driven system where fluctuations are statistically either not stationary in time or not homogeneous in space, or both. Implications to astrophysical phenomena will be discussed.

astro-ph↗

arXiv2001

Magnetorotational instability of dissipative Couette flow

Global axisymmetric stability of viscous, resistive, magnetized Couette flow is re-examined, with the emphasis on flows that would be hydrodynamically stable according to Rayleigh's criterion: opposing gradients of angular velocity and specific angular momentum. In this regime, magnetorotational instabilities [MRI] may occur. Previous work has focused on the Rayleigh-unstable regime. To prepare for an experimental study of MRI, which are of intense astrophysical interest, we solve for global linear modes in a wide gap with realistic dissipation coefficients. Exchange of stability appears to occur through marginal modes. Velocity eigenfunctions of marginal modes are nearly singular at conducting boundaries, but magnetic eigenfunctions are smooth and obey a fourth-order differential equation in the inviscid limit. The viscous marginal system is of tenth order; an eighth-order approximation previously used for Rayleigh-unstable modes does not permit MRI. Peak growth rates are insensitive to boundary conditions. They are predicted with surprising accuracy by WKB methods even for the largest-scale mode. We conclude that MRI is achievable under plausible experimental conditions using easy-to-handle liquid metals such as gallium.

astro-ph↗

arXiv2001

Turbulent Dynamos and Magnetic Helicity

It is shown that the turbulent dynamo $α$-effect converts magnetic helicity from the turbulent field to the mean field when the turbulence is electromagnetic while the magnetic helicity of the mean-field is transported across space when the turbulence is electrostatic or due to the electron diamagnetic effect. In all cases, however, the dynamo effect strictly conserves the total helicity except for resistive effects and a small battery effect. Implications for astrophysical situations, especially for the solar dynamo, are discussed.

astro-ph↗