Session CO6: Turbulence and Transport

Magnetic Reconnection in MHD and Kinetic Turbulence

Recent works have revisited the current understanding of Alfv\'enic turbulence to account for the role of magnetic reconnection [Loureiro17a, Mallett17, Boldyrev17]. Theoretical arguments suggest that reconnection inevitably becomes important in the inertial range, at the scale where it becomes faster than the the eddy turnover time. This leads to a transition to a new sub-inertial interval, suggesting a route to energy dissipation that is fundamentally different from that envisioned in the usual Kolmogorov-like phenomenology. These concepts can be extended to collisionless plasmas, where reconnection is enabled by electron inertia rather than resistivity [Loureiro17b]. Although several different cases must then be considered, a common result is that the energy spectrum exhibits a scaling with the perpendicular wave number that scales between $k_\perp^{-8/3}$ and $k_\perp^{-3}$, in favourable agreement with many numerical results and observations. References: [Loureiro17a] N.F. Loureiro and S. Boldyrev, Phys. Rev. Lett. (2017) [Mallet17] A. Mallet, A. A. Schekochihin and B.D.G. Chandran, Mon. Not. R. Astron. Soc. (2017) [Boldyrev17] S. Boldyrev and N.F. Loureiro, Astrophys. J. {\it accepted} (2017) [Loureiro17b] N.F. Loureiro and S. Boldyrev, {\it in preparation} (2017)   

Nature of Kinetic Scale Turbulence in the Earthʼs Magnetosheath

We present measurements from the Magnetospheric Multi-Scale (MMS) mission, together with corresponding theoretical results, to investigate turbulence at kinetic scales in the Earth’s magnetosheath, the region downstream of the bow shock. In some respects, this turbulence is similar to that in the upstream solar wind, but one key difference is that whereas in the solar wind the ion and electron temperatures are typically comparable, $T_i \sim T_e$, in the magnetosheath, the ions are typically much hotter $T_i \gg T_e$ as a result of processing by the bow shock. Together with $\beta_i\sim 1$, this leads to a new type of turbulence close to electron scales. This turbulence is characterized by an increased magnetic compressibility, following a mode we term the inertial kinetic Alfvén wave, and a steeper spectrum of magnetic fluctuations, consistent with the scaling $k_\perp^{-11/3}$ that we obtain from a set of nonlinear equations. This new regime of plasma turbulence may also be relevant for other astrophysical environments with $T_i \gg T_e$, such as the solar corona, hot accretion flows, and regions downstream of collisionless shocks.   

Reassessing Solar Wind Stability using Nyquist's Method

In nearly-collisionless plasmas, such as the solar wind, non-local thermodynamic equilibrium structures, including temperature anisotropies, beam populations with relative drifts, and agyrotropic features, are frequently observed to persist. These features can act as sources of free energy which may drive instabilities that move the plasma closer to LTE. Analysis techniques applied to solar wind observations for the presence of such instabilities typically consider only a single source of free energy, such the temperature anisotropy of the proton population. We have developed an efficient algorithm for general determination of linear stability considering all sources of free energy using Nyquist's Method. By applying this method to the dispersion relation associated with a particular solar wind observation, we rapidly determine if the plasma is linearly unstable, and if so, how many normal modes are driven. Our technique is verified against well-characterized theoretical and observational cases from the literature, and applied to in situ observations from the Wind spacecraft to determine how additional sources of free energy affect the plasma's stability and may govern the solar wind's evolution.   

Three-Dimensional Hybrid-Kinetic Simulations of Alfvénic Turbulence in the Solar Wind

The interplanetary medium hosts a solar wind, which contains a broadband turbulent spectrum of large-amplitude Alfv\'{e}n waves. In this talk, we present results from hybrid-kinetic simulations of this turbulent and essentially collisionless system. We confirm power-law indices obtained in previous analytical and numerical (e.g., gyrokinetic) studies, and carefully explore the location of the spectral break and physics occurring at the ion-Larmor scale. In the low-beta regime, we find evidence of perpendicular ion heating, which we interpret as stochastic heating arising from interactions between ions and strong fluctuations at wavelengths comparable to the ion-Larmor scale. We explore the dependence of ion heating on plasma beta. Finally, we discuss the interpretation of spacecraft measurements of this turbulence by testing the Taylor hypothesis with synthetic spacecraft measurements of our simulation data.   

Relativistic MHD Turbulence with Synchrotron and Inverse-Compton Radiation Cooling

This work investigates the energetic aspects and observational appearance of driven relativistic MHD turbulence in an optically thin, relativistically hot plasma subject to strong synchrotron and synchrotron-self-Compton (SSC) radiative cooling. Steady-state balance between turbulent heating and radiative cooling is shown to lead, essentially independent of turbulent driving's strength, to a characteristic electron temperature of $T_e/m_e c^2 \sim \tau_T^{-1/2}$, where $\tau_T \ll 1$ is the system’s Thomson optical depth. Furthermore, the SSC cooling power becomes automatically comparable to the synchrotron power. Under certain conditions, a few higher-order inverse-Compton components also become comparable to the synchrotron and SSC losses, and so the broad-band radiation spectrum of the system consists of several distinct peaks with gradually decreasing luminosity, separated by a factor of $\tau_T^{-1} \gg 1$ from each other. The number of these spectral components is governed by synchrotron self-absorption and Klein-Nishina effects. These findings have important implications for several classes of high-energy astrophysical systems including pulsar wind nebulae and black-hole-driven accretion flows, jets, and radio-lobes.   

Kinetic simulations of turbulence in relativistic plasmas

We investigate driven turbulence in collisionless, magnetized, relativistic pair plasma by applying particle-in-cell simulations with up to $1024^3$ cells and 200 billion particles. The results agree with predictions from magnetohydrodynamic turbulence phenomenology at inertial-range scales, including a power-law magnetic energy spectrum with index near -5/3, scale-dependent anisotropy of fluctuations described by critical balance, log-normal distributions for particle density and internal energy (related by a 4/3 adiabatic index), and the presence of intermittency. We also show that the magnetic energy spectrum steepens (to index near -4) at sub-Larmor scales, possibly indicating a kinetic cascade. We demonstrate efficient nonthermal particle acceleration that leads to a power-law particle energy distribution, which hardens with increasing magnetization (becoming shallower than -2 for sufficiently high magnetization) and softens with increasing system size. We discuss the mechanisms of particle acceleration and propose an empirical formula for the distribution index. Our results imply that turbulence can be a viable source of energetic particles in high-energy astrophysical systems, such as pulsar wind nebulae, if scalings asymptotically become insensitive to the system size.   

Onset of magnetic turbulence in non-relativistic collisionless shocks

Collisionless shocks are ubiquitous in astrophysical environments. In relativistic weakly magnetized environments, the Weibel or current filamentation instability is believed to be the dominant mechanism for magnetic field amplification and shock formation. Using 3D particle-in-cell simulations and analytic theory, we show that in the non-relativistic regime, the shock formation process is more complex. It first involves the B-field amplification by the Weibel instability (linear regime) and later the competition between filament merging and kink-like deformation of current filaments (longitudinal instability). The kink-instability dominates the slow down of the flows, shock formation, and onset of magnetic turbulence. We will discuss the implication of these results for particle acceleration and the ability of laser-driven counter-streaming plasma experiments to probe this microphysics.   

Numerical design of a magnetized turbulence experiment at the National Ignition Facility

The origin and amplification of magnetic fields remains an active astrophysical research topic. We discuss design (using three-dimensional FLASH simulations) of a magnetized turbulence experiment at the National Ignition Facility (NIF). NIF lasers drive together two counter-propagating plasma flows to form a hot, turbulent plasma at the center. In the simulations, plasma temperatures are high enough to reach super-critical values of magnetic Reynolds number (Rm). Biermann battery seed magnetic fields (generated during laser-target interaction) are advected into the turbulent region and amplified by fluctuation dynamo in the above-unity Prandtl number regime. Plasma diagnostics are modeled with FLASH for planning and direct comparison with NIF experimental data.   

On the cascade reversal at the electron skin depth

There exist a wide class of systems that exhibit non-ideal effects such as Hall drift and electron inertia. The latter plays role on characteristic length scales smaller than the electron skin depth. To gain relevant understanding it is necessary to work with models such as extended MHD (XMHD) that capture these microscopic effects. XMHD is endowed with topological invariants – two helicities emerging from the Hamiltonian structure and useful for the Hamiltonian Energy-Casimir method [1]. In MHD turbulence the inverse cascade of magnetic helicity is often invoked to explain dynamo action. However, we predict [2] analytically that the phenomenon is suppressed at the electron skin depth, i.e. it appears that the cascade reverses direction. The ongoing investigations focus on a simplified 2D case, which is more amenable to numerical analysis. The analytical queries reveal similar behavior to 3D cascade reversal so we are confident that our 2D case study should be representative. \bibitem{Lingam} [1]\quad M.~Lingam, G.~Miloshevich and P.J.~Morrison, \newblock Phys. Lett. A, 380, 2400 (2016) \bibitem{Miloshevich2} [2]\quad G.~Miloshevich, M.~Lingam and P.J.~Morrison, \newblock New J. Phys. 19 (1), 015007, (2017)   

Heat Transport in Interacting Magnetized Electron Temperature Filaments

Results are presented from basic heat transport experiments and numerical simulations of multiple magnetized electron temperature filaments in close proximity. This arrangement samples cross-field transport from nonlinear drift-Alfven waves and large scale convective cells. Experiments are performed in the Large Plasma Device (LAPD) at UCLA. The setup consists of three biased CeB$_{\mathrm{6}}$ crystal cathodes that inject low energy electrons (below ionization energy) along a strong magnetic field into a pre-existing large and cold plasma forming 3 electron temperature filaments embedded in a colder plasma, and far from the machine walls. A triangular spatial pattern is chosen for the thermal sources and multiple axial and transverse probe measurements allow for determination of the cross-field mode patterns and axial filament length. We have characterized the spontaneous thermal waves and drift-Alfven waves that develop on an individual filament when a single source is activated. When the 3 sources are activated, and in close proximity, a complex wave pattern emerges due to interference of the various wave modes leading to enhanced cross-field transport and chaotic mixing. Steep thermal gradients develop in a periphery region of the filaments where higher azimuthal wavenumber drift-Alfven modes are excited. Detailed spectral analysis and comparison with nonlinear fluid and gyrokinetic simulations will be reported.   

On the universality of power laws for tokamak plasma predictions

Significant deviations from well-established power laws for the thermal energy confinement time, obtained from extensive databases analysis, have been recently reported in dedicated power scans. The validity and universality of power laws as tools for predicting plasma performance is analyzed in the framework of a simplified modeling for the heat transport which is however able to account for the interplay between turbulence and collinear effects with the input power which are known to reduce turbulence, such as fast ion pressure gradients or electromagnetic effects. Whereas at low power usual scaling laws are recovered with little influence of other plasma parameters, at high power it is shown how the exponents obtained are extremely sensitive to the heating deposition, the q profile or even the number and sampling of the points considered. In particular circumstances, even a minimum of the thermal energy confinement time with the input power can be obtained, which means that the approach of the energy confinement time as a power law is intrinsically invalid. Therefore, predictions of future plasmas performance using such approach, mainly at high $\beta $, can lead to significant deviations from reality and provide misleading results.   

Validation of Energetic Particle Transport in DIII- D Tokamak

First-principle global Gyrokinetic Toroidal Code (GTC) is employed to simulate the turbulent transport in fusion plasmas with realistic equilibrium and profiles of DIII-D discharges. In the linear simulations, ion temperature gradient (ITG) mode and trapped electron mode (TEM) are found dominant exactly as experimentally observed in two shots with low plasma temperature and high temperature, respectively. In the nonlinear simulations, electrostatic fluctuation intensity, energetic particle (EP) diffusivity and the perturbations in its density and temperature are analyzed in detail for both the low-temperature ITG and high-temperature TEM cases. For these two cases, energetic particle's diffusivity and density perturbation are almost on the same level in radial direction. This is in reasonable agreement with experimental results that no measured change of energetic particle transport is observed when dominant instability changes from low-temperature ITG to high-temperature TEM. The underlying mechanism responsible for these EP transport by background microturbulence is that the electrostatic fluctuation intensity spectrum in terms of perpendicular wavenumber are similar in nonlinearly steady stage for both low-temperature ITG and high-temperature TEM cases.   

Role of poloidal flows on the particle confinement time in a simple toroidal device : an experimental study

In magnetized toroidal devices without rotational transform also known as Simple Magnetized Torus (SMT). The device BETA at the IPR is one such SMT with a major radius of 45 cm, minor radius of 15 cm and a maximum toroidal field of 0.1 Tesla. Understanding confinement in such helical configurations is an important problem both for fundamental plasma physics and for Tokamak edge physics. In a recent series of experiments it was demonstrated experimentally that the mean plasma profiles, fluctuation, flow and turbulence depend crucially on the parallel connection length, which was controlled by external vertical field. In the present work, we report our experimental findings, wherein we measure the particle confinement time for hot cathode discharge and ECRH discharge, with variation in parallel connection length. As ECRH plasma don't have mean electric field and hence the poloidal rotation of plasma is absent. However, in hot cathode discharge, there exist strong poloidal flows due to mean electric field. An experimental comparison of these along with theoretical model with variation in connection length will be presented. We also present experimental measurements of variation of plasma confinement time with mass as well as the ratio of vertical field to toroidal magnetic field.