Session BM10: Mini-Conference: Magnetized Turbulence I

Transient growth in MHD shear layers

Shear flows are ubiquitous in astrophysical and fusion plasmas and can drive turbulent fluctuations that enhance momentum, heat, and particle transport. Normal-mode linear stability analyses are widely used to identify unstable parameter regimes that might drive such turbulence. However, these analyses are known to be misleading in many fluid and plasma systems, including drift-wave instabilities and the magnetorotational instability. Even in the absence of linear instability, small-amplitude perturbations can grow significantly due to transient, nonmodal growth mechanisms. In some cases, they can even drive turbulence and significant mixing.

Here, we show that nonmodal growth is significant in linearly stable plasma shear flows. We study a simple shear layer with a uniform magnetic field in the MHD limit. When the field is strong enough to suppress the Kelvin-Helmholtz (KH) instability, the same nonmodal effects that drive turbulence in neutral fluids also drive significant linear growth of Alfvenic fluctuations. This growth increases dramatically in domains much larger than the typical KH lengthscale. This demonstrates that modal analyses can be misleading when used to assess stability of plasma shear flows and that simulations in small domains may miss crucial dynamics.   

Role of Tearing Instability in Magnetohydrodynamic Turbulence

Magnetohydrodynamic turbulence regulates the transfer of energy from large to small scales in many astrophysical systems, including the solar atmosphere. We performed three-dimensional magnetohydrodynamic simulations with unprecedentedly large magnetic Reynolds number (at a cost of ~200 million CPU hours) to reveal how rapid reconnection of magnetic field lines changes the classical paradigm of the turbulent energy cascade. By breaking elongated current sheets into chains of small magnetic flux ropes (or plasmoids), magnetic reconnection leads to a new range of energy cascade, where the rate of energy transfer is controlled by the growth rate of the plasmoids. As a consequence, the turbulent energy spectra steepen and attain a spectral index of -2.2 that is accompanied by changes in the anisotropy of turbulence eddies. The omnipresence of plasmoids and their consequences on, e.g., solar coronal heating, can be further explored with current and future satellites/telescopes.

    

Stochastic Parker Field -- Effects of Footpoint motion on the Interplanetary magnetic field

 Shortly after Parker developed the hydrodynamic solar wind model, Leighton considered how the footpoint motion of IMF can modify the original Parker spiral. He assumed a diffusion of the footpoint which contains an intrinsic difficulty in that the resulting field lines can have length unbounded in the limit that the correlation length in the diffusion model tends to zero. We extend the Leighton's diffusion model describing the turbulent mixing of magnetic footpoints on the solar wind source surface by a spherical Ornstein-Uhlenbeck process with a constant drift given by the rotation of the Sun.  Our model contains two parameters: the Lagrangian integral timescale τ_L, and the root-mean-square footpoint velocity V_rms. The Lagrangian velocity and the positions of magnetic footpoints on the solar wind source surface are obtained from the solutions of a set of stochastic differential equations. The spherical diffusion model of Leighton is recovered in the singular Markov limit when the Lagrangian integral timescale tends to zero while keeping the footpoint diffusivity finite. In contrast to the magnetic field lines driven by standard Brownian processes on the solar wind source surface, the interplanetary magnetic field lines are smooth differentiable functions with finite path lengths in our model.  The probability distributions of path length at 1 au are computed numerically and are shown to develop a significant skewness when the width of the distributions increases.   

Laboratory Observations of Residual Energy Generation in Strong Alfvén Wave Interactions

In the MHD inertial range (scales larger than ion-kinetic scales) turbulent fluctuations in the solar wind are often Alfvénic in character, meaning that their magnetic and flow velocity fluctuations are proportional to each other and predominantly perpendicular to the background magnetic field. However, observations of the solar wind have shown that there is a significant difference in the energy in velocity fluctuations and normalized magnetic fluctuations. This difference, called the residual energy, should be zero for linear Alfvén waves, but is consistently observed to be negative in the solar wind, with magnetic fluctuations dominating. This work investigates the energy partition in strong three-wave interactions through an experimental campaign on the LArge Plasma Device (LAPD) in an MHD-like regime. Primary (driven) modes are launched from antennas, and the spectrum of secondary modes generated by the strong three-wave interaction is observed. The primary modes are observed to have no residual energy, while the secondary modes have significant residual energy. These results constitute the first laboratory demonstration that residual energy can indeed be generated by nonlinear mode coupling.

Supported by DE-SC0021291.   

Magnetised turbulence in through pulsed-power-driven magnetic flux-tube merging

Magnetised turbulence is a key driver of many important phenomena in astrophysical plasmas, but studying magnetised turbulence in the laboratory poses two major challenges - accessing high Reynolds numbers on laboratory length scales, and reliably diagnosing the fundamentally three-dimensional nature of the turbulence. 

We present experimental results from a new pulsed-power-driven platform based on flux-tube merging, in which magnetised supersonic carbon flows converge inside a cylindrical wire array to produce a column of turbulent plasma.This column is confined for much longer than the hydrodynamic time scales by continuous inflows of plasma from the wires, and the magnetic fields are dynamically and energetically significant, which is an astrophysically relevant regime.

We characterise this plasma using a suite of spatially and temporally resolved diagnostics, including ultra high speed imaging, laser shadowgraphy, interferometry, Thomson scattering and Faraday rotation imaging. We discuss new diagnostics such as the imaging refractometer which can be used to measure the power spectrum and intermittency of turbulence in these experiments, and a new pulsed-power facility, PUFFIN, at MIT, which will be used to continue these experiments.   

Particle Acceleration in Magnetic Reconnection

How magnetic reconnection efficiently produces a huge number of mildly relativistic energetic particles is an outstanding problem in solar physics and heliophysics. In particular, three major problems in solar particle acceleration have to be addressed: 1) the development of power-law energy spectra for both electrons and ions; 2) the "big number problem" of electrons. Recent observations discovered that the time to accelerate electrons to a power-law energy distribution in solar flares can be shorter than 50 ms while nearly the total number of electrons in the current sheet is accelerated in 1000s. 3) Observations suggest that the acceleration process of ions is related to the electrons'. In this talk, I will present a novel acceleration mechanism in magnetic reconnection. I will show how the velocity shear stored naturally in force-free currents of solar flares can drive an electron Kelvin-Helmholtz instability (EKHI) during magnetic reconnection. The EKHI efficiently accelerates electrons to a power-law energy spectrum with an index comparable to the observations in a few tens of ion gyro-periods (~ 0.1 ms for solar corona plasma). With the proceeding of reconnection, the EKHI induced Alfvenic turbulence can accelerate ions to broken power-law energy spectra. The simulation and theoretical results are well supported by solar x-ray and recent in-site MMS observations.   

Resilient Layered Structures in a Fluctuating Vortex Array

Layered profile structures, or staircases, have been observed in several systems, including drift-wave turbulence near marginality. The simplest type of staircase occurs in passive scalar advection by an array of convection cells, due to the existence of two disparate time scales, the cell turn-over and the diffusion times. To better represent physics of dynamic drift-wave turbulence, we adopt a novel model of a fluctuating vortex array as a basis for a series of numerical experiments. We study staircase persistence and resiliency. By systematically scattering the elements of the vortex array, we show that staircase profiles form and are resilient over a broad range of modest Reynolds numbers. We find that scalar concentration flows around vortices, thus staircase barriers form first and scalar concentration “homogenizes” in vortices later. We also examine the case of active scalar staircase formation. The dynamics of the active scalar are comparable to that of magnetic fields in flux expulsion, where fields are expelled to cell boundaries and stabilize the staircase cells. The active scalar system manifests a novel feedback mechanism that reinforces global staircase structure and self-organization. We show that the spontaneous reinforcement of the cell array structure in the presence of fluctuations occurs only for a narrow range of magnetic field strength. These numerical results can be applied to applications where layered structures occur, such as astrophysical systems and laboratory plasmas.   

On a Plasma sheath with a Small Normal Magnetic Field Separating Regions of Oppositely Directed Magnetic Field

Current sheets form intermittently during plasma turbulence and are a fundamental signature of the turbulence's non-linear character. An understanding of the simple current sheet configurations therefore become an important building block for turbulence theory. The Harris-sheet model [1] provides an exact solution to the kinetic plasma equations for a steady state 1D current sheet geometry separating regions with oppositely directed magnetic field. However, adding just a small normal magnetic field to the Harris configuration yields thermal streaming of particles into and out of the current sheet, fundamentally changing the form of its kinetic description. In contrast to the magnetic moment, the action variable associated with the oscillatory orbit motion perpendicular to the current sheet, is well conserved. This facilitates the development of a new “action kinetic” model, providing a new kinetic solution for 1D current sheets including a normal magnetic field. Considering the case of isotropic ion pressure, the current sheets are supported by electron pressure anisotropy, and the total current across a particular sheet is set by the fire-hose condition based on the electron pressures normalized by the pressure of the asymptotic magnetic field. Analytical approximations are obtained for the numerical solutions expressed in terms of the asymptotic electron temperature anisotropy and the ion temperature.

 [1] E. Harris, On a plasma sheath separating regions of oppositely directed magnetic field, Nuovi Cimento 23, 115+ (1962).   

Shear-flow-driven and reconnection-controlled dynamo

Turbulence tangles magnetic fields, generating strong small-scale currents. Yet large-scale magnetic fields are observed in astrophysics. To understand such and to model transport of energy and momentum, MHD Kelvin-Helmholtz-instability (KHI)-driven, quasi-stationary two- and three-dimensional (3D) turbulence is studied here with a mean flow forced toward its initial profile. The resulting turbulence is analyzed using the large-scale stable and unstable modes of the system.

In 2D, the magnetic field is rapidly folded by the KHI-driven turbulence when stable modes are removed; but when retained, large-scale structures emerge. While in both cases kinetic and magnetic energies cascade to small scales, the cascading energy fluxes are reduced by orders of magnitude due to the stable modes.^1,2,3

In 3D, large-scale magnetic fields are amplified by a KHI-driven dynamo, with the aid of the stable modes. The fields generated have field line reversals. The accompanying current layers then undergo disruption but are regenerated by turbulence. The field-reversal scale is compared against an analytical theory by varying the (magnetic) Reynolds number, which suggests that the KHI-driven dynamo can trigger tearing instability, an effect seen also in reconnection-driven turbulence.   

Kelvin-Helmholtz turbulence in the terrestrial magnetopause.

The Kelvin-Helmholtz (KH) instability in its non-linear phase plays a significant role in transporting solar wind plasma into the Earth's magnetosphere. During northward solar wind magnetic field conditions, the flow shear‐induced reconnection generates turbulence at the magnetopause. Specifically, this 3D vortex-induced reconnection serves as the main driver of plasma transport at the dayside flank. In this work, we will report reconnection signatures of KH waves recorded by Magnetospheric Multiscale (MMS) spacecraft during a geomagnetic storm on 14 April 2022 under northward IMF. During this KH interval, MMS encountered a current sheet near an electron diffusion region, accompanied by intense electron jets. This observation is consistent with strong guide-field asymmetric reconnection across the magnetopause. We compare the wave power spectra for KH turbulence with and without reconnecting current sheets and extend the study to characterize the KH turbulence during both storm and non-storm periods.   

Interactions between Turbulence and Zonal Flows as Self-regulating Saturation Processes in Astrophysical Accretion Disks

The angular momentum transport mechanism in accretion disks is crucial for understanding their behavior. However, the saturation processes in a hydrodynamics disk remains uncertain. The Taylor Identity, which explains non-linear momentum transport from small-scale turbulence to large-scale zonal flow (ZF), presents a potential explanation for the turbulence saturation level. In this study, we derive the Taylor Identity for a compressible disk fluid in the presence of Rossby wave instability (RWI) associated with a pressure and density bump, analytically calculate the momentum transport, and elucidate the turbulence level in the saturation state.

To investigate the physics behind the turbulence level in a saturation state, we propose a self-regulation model. We conduct a 2D compressible hydrodynamic simulation of astrophysical disks containing a pressure bump, exploring momentum/energy transport between turbulence intensity, zonal flow, and free energy evolution during the disk saturation. Our findings indicate that: (1) the evolution of RWI leads to zonal flow generation; (2) the dynamics between turbulence intensity and zonal flow regulates the nonlinear stage; (3) the self-binding pressure bump mechanism dominates the oscillation frequency. These results strongly suggest that the dynamics of turbulence interacting with the zonal governs the nonlinear saturation state in accretion disks.

Future studies will focus on the self-regulated mechanism and its role in magnetized accretion disk, particularly the interaction with magnetorotational instability.