Session GO06: Fundamental Plasmas: Turbulence II

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An overview and recent progress of activities at the Bryn Mawr Plasma Laboratory (BMPL) is presented. The main experiment at the facility, the Bryn Mawr eXperiment (BMX), consists of a 4mF, 2kV pulse-forming network that generates \textasciitilde 180us of stationary broadband fluctuations of magnetic field and plasma using a magnetized coaxial plasma gun source. These self-organized magnetized structures are launched into a 2.7m flux-conserving cylindrical wind tunnel. Single-loop magnetic pickup coils measure fluctuating magnetic field and time-delay estimated velocity. Multipoint measurements of spectra are made from linear arrays of probes along the axial direction of the chamber.   

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The Bryn Mawr Experiment (BMX) is a newly constructed experiment at the Bryn Mawr Plasma Laboratory (BMPL). BMPL is investigating magnetic turbulent generated by injecting helicity with a magnetized coaxial gun source into a flux conserving cylindrical wind-tunnel. This presentation represents the studies of MHD turbulent properties at BMPL. Spatial-temporal correlation analysis of magnetic fluctuations is used to estimate outer and inner scales of the energy-cascade inertial range. With these estimates a magnetic Reynolds number is calculated. The spatial correlation scale is used as the outer scale. The Taylor microscale from Taylor hypothesized temporal correlations is used as the inner scale. Comparisons between Taylor hypothesized temporal correlation properties and spatial correlation properties are also presented.   

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Analysis of recent data obtained from the Bryn Mawr Magnetohydrodynamic Experiment (BMX) housed in the Bryn Mawr Plasma Laboratory (BMPL) is presented. The BMX investigates self-organized structures of magnetic field and plasma generated by a magnetized coaxial plasma gun source. These structures are discharged into a flux-conserving cylindrical wind tunnel after initial confinement within the gun region via a stuffing magnetic flux. Probes arranged along the z-axis of the tunnel measure fluctuations in magnetic field and time-delay estimated velocity as the structure moves through the system. Multipoint spectra measurements as a function of stuffing flux delay and spectral indices as a function of axial position are discussed.   

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The variation of pressure-gradient driven turbulence with plasma $\beta$ (up to $\beta \approx 15\%$) is investigated in linear, magnetized plasma. The magnitude of magnetic fluctuations is observed to increase substantially with increasing $\beta$. More importantly, parallel magnetic fluctuations are observed to dominate at higher $\beta$ values, with $\delta B_\parallel / \delta B_\perp \approx 2$ and $\delta B / B \approx 1\%$. Parallel magnetic fluctuations are strongly correlated with density fluctuations and the two are observed to be out of phase. The relative magnitude of and cross-phase between density and parallel magnetic field fluctuations are consistent with dynamic pressure balance ($P+\frac{B_{\parallel}^2}{2\mu_0} = $ constant). A local theory of modified drift-Alfvén waves, including parallel magnetic fluctuations is qualitatively and quantitatively consistent with the observations.   

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Transport and mixing in turbulent magnetized plasmas driven by unstable shear flows is a challenging nonlinear problem. Linearly stable (damped) eigenmodes, which are often neglected, can be crucial in saturating the instability. In gyrokinetic simulations of turbulence arising from a driven unstable shear flow, unstable and stable modes reach near-equipartition [Fraser et al. PoP (2018)]. When the flow is not driven and there is a flow-aligned magnetic field, faster relaxation in stronger fields can quasilinearly flatten the profile before stable modes have time to affect the evolution. Here, we investigate turbulent saturation in MHD simulations of Kelvin-Helmholtz-unstable flows that are forced to prevent flattening of the mean flow, employing the Dedalus code with a flow-aligned magnetic field. We demonstrate that the stable modes break the hegemony of unstable modes in the nonlinear regime. The role of the magnetic field in determining the amplitudes of stable and unstable modes is quantified. With the nonlinear interaction among the magnetic field and different linear eigenmodes in hand, we pursue reduced models of Reynolds stresses, Maxwell stresses, and the ensuing transport phenomena by including the stable modes at saturation.   

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High-$\beta$ plasmas can be highly magnetized ($\rho/H\ll 1$) at the largest astrophysical scales, e.g., in the intracluster medium of galaxy clusters. If the plasma is furthermore weakly collisional, the transport of momentum and heat is highly anisotropic with respect to the magnetic field direction. Such transport can result in significant parallel heat flux and pressure anisotropy, which trigger kinetic instabilities that back-react on the transport. In this work, we use the particle-in-cell code Tristan-MP to calculate the steady-state heat flux through a stratified, high-$\beta$, collisionless, magnetized plasma. The consequent departures from a Maxwellian distribution function excite the heat-flux-driven whistler instability and the pressure-anisotropy-driven mirror instability. Both instabilities reduce heat transport by scattering and/or trapping particles (e.g., Roberg-Clark et al. 2018; Komarov et al. 2016, 2018). By tracking thousands of particles and simulating across a range of $\beta$ and ion-electron mass ratio, we construct a space- and time-resolved, energy-dependent collision operator which quantitatively describes the effect of the saturated instabilities on particle motion, and therefore on the transport properties of the plasma.   

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In weakly-collisional plasma environments with sufficiently low electron beta, Alfv\'enic turbulence transforms into inertial Alfv\'enic turbulence at scales below the electron skin-depth, $k_\perp d_e > 1$. We argue that, in inertial Alfv\'enic turbulence, both energy and generalized kinetic helicity exhibit direct cascades. We demonstrate that the two cascades are compatible due to the existence of a strong scale-dependence of the phase alignment angle between velocity and magnetic field fluctuations, with the phase alignment angle scaling as $\cos\alpha_k\propto k_{\perp}^{-1}$. As a result of the dual direct cascade, the generalized-helicity spectrum scales as $\propto k^{-5/3}_{\perp}$, implying progressive balancing of the turbulence as the cascade proceeds to smaller scales in the $k_{\perp} d_e \gg 1$ range. Our results may be applicable to a variety of geophysical, space, and astrophysical environments, including the Earth's magnetosheath and ionosphere, solar corona, non-relativistic pair plasmas, as well as to strongly rotating non-ionized fluids.   

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The fundamental difference between incompressible ideal magnetohydrodynamics and the dynamics of a non-conducting fluid is that magnetic fields exert a tension force that opposes their bending; magnetic fields behave like elastic strings threading the fluid. It is natural, therefore, to expect that a magnetic field tangled at small length scales should resist a large-scale shear in an elastic way, much as a ball of tangled elastic strings responds elastically to an impulse. In this talk, I will describe a treatment of magnetoelasticity motivated by the need to understand the large-scale dynamics of the hot, rarified plasma of the intra-cluster medium (ICM). In contrast to previous work, the treatment I present explicitly accounts for intermittency of the Maxwell stress. I will show, via analytical theory and supporting numerical work, that this intermittency necessarily decreases the frequency of `magnetoelastic waves' propagating through a tangled-magnetic-field equilibrium, and results in anomalous viscous damping. I will also present numerical simulations of sporadically-driven MHD turbulence, elucidating the possible role of magnetoelastic waves in facilitating energy transport in the turbulent ICM.   

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The ExB electron drift instability is,observed in many magnetized plasma devices, an important agent in crossfield particle transport. The collisionless electron transport mechanism is analyse, due to presence of a single electrostatic mode generated fromthis instability, by considering a reduced two-degrees-of-freedom Hamiltonian. It helps to simplify the original dynamics complexity. In the presence of this electrostatic wave the magnetized charged particle dynamics becomes chaotic, and for different parameter values it generates Halloween-mask like and other different stochastic webs in the phase-space. A scaling exponent is defined to characterise transport in such phase-space, and find anomalous transport, of super-diffusive type. The trajectories stick to different kinds of islands in phase space, and their different sticking time power-law statistics generate successive regimes of the super-diffusive transport. In the next part we are intending to generate the ExB drift instability self-consistently, in Hall-thruster geometry using a 2D PIC-MCC simulation, and compare the crossfield transport coefficient value with that coming from the simplified model.   

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Density limit phenomenology has been associated with the collapse of edge shear layers at high density. Theoretical work has suggested that the onset of such collapse occurs when adiabaticity $\alpha=k_{\parallel}^{2}V_{th}^{2}/\omega\nu$ drops below $\alpha_{crit}\approx1$. Here, we explored shear flow dynamics in a spatially varying $\alpha\left(x\right)$ profile. $\alpha<\alpha_{crit}$ on the outer boundary, and $\alpha>\alpha_{crit}$ on the inner one. The gradient in $\alpha$ triggers the formation of a barrier shear layer, which separates the regions of isotropic turbulence and zonal flows. The barrier is pinned to the location of $\alpha_{crit}$ and does not propagate. Work on the effect of a spatially profiled neutral drag (reflecting a neutral profile) is ongoing. More generally, we report on some interesting differences between zonal flow phenomena in the conventional doubly periodic box and in channel flows. Specifically: i) Zonal flows are more coherent in the channel flow. ii) A transition curve of $R=\frac{ZF Energy}{Total Kinetic Energy}$ is largely monotonic in for the box. More complex behavior is shown in the case of the channel flow. iii) Time histories are different for the box and channel cases. Work on all the issues discussed above is ongoing.   

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Spectral equations for zonal flow and turbulence energy have been derived for the drift wave turbulence. The spectral equation for the zonal flow energy shows two distinct mechanisms of zonal flow excitation- modulational growth and zonal noise drive. The two are of comparable strength. The zonal noise term scales as spectral Reynolds stress squared times the triad interaction time. The zonal noise is positive definite and is insensitive to the spectral slope. Zonal nonlinear noise generates the zonal flow even when the drift waves are modulationally stable. Noise eliminates the threshold in the linear growth rate of turbulence for zonal flow excitation within the predator prey model. This is consistent with the observation of zonal flows without a critical power in experiments. The zonal intensity increases and turbulence intensity decreases with the strength of zonal noise. A 0D model is advanced to study the effect of zonal noise on L-H transition dynamics. With noise, substantial zonal flows appear much below the threshold for the modulational excitation without noise. This reduces the predicted threshold power for the transition to the H mode. I-phase persist, but with lower onset threshold and reduced oscillations.   

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Zonal flow (ZF) is a poloidally symmetric band like shear flow, a secondary mode driven by drift waves, which regulates turbulence and transport. Here, we report observation of ZF driven by electron temperature gradient (ETG) driven drift wave turbulence in a linear machine. A low frequency (0.2-0.3 kHz) mode is identified as ZF by measuring density and potential fluctuations, and radial, poloidal and axial wave numbers. In radius, maxima of ZF amplitudes tracks the minima of the ETG scale length ($L_{Te}$) on controlled variation of the location of minimum of the later. The theoretical criteria $L_{Te} / L_{n} < 1.5$ for excitation of ETG driven mode is well satisfied in the experiment. Here, $L_{n}$ is the density gradient scale length. Electron density fluctuations has a broadband spectrum above 300 kHz which is close to theoretically predicted frequency of ETG driven mode. Bicoherence analysis shows coupling of ZF with ETG mode. We have found that ZF becomes stronger when collision frequency is decreased. This further proves that ZF is driven by ETG as ETG driven drift is reactive in nature.