Session JO5: Waves, Turbulence and Transport

Magnetic stochasticity due to the excitation of subdominant tearing modes

Recent studies have shown that magnetic stochasticity is near-ubiquitous in electromagnetic gyrokinetic simulations scanning the plasma beta. At higher beta values, the associated electron electromagnetic heat flux can become comparable to the transport in the electrostatic channels. This is in spite of the fact that the dominant instabilities are not characterized by tearing parity. In this study we demonstrate that the stochasticity and transport are produced by the nonlinear excitation of subdominant tearing modes. Proper orthogonal decomposition is used to extract mode structures from nonlinear fluctuation data. Using this technique, it is shown that the electron electromagnetic heat transport can be explained as a superposition of an inward heat flux associated with the ITG modes and an outward heat flux associated with the magnetic stochasticity caused by the excitation of subdominant tearing modes. The mechanism for the nonlinear excitation of these tearing modes will also be discussed.   

Convective and diffusive motion in low frequency trapped electron turbulence

Collisionless trapped electron mode (CTEM) is an important instability candidate for burning plasma that leads to electron turbulent transport. Global gyrokinetic particle simulation of CTEM turbulence in toroidal plasmas finds both diffusive and convective electron motion using a Lagrangian analysis of the self-consistent particle orbits. A resonance broadening model fits well the diffusive and convective electron motion. The diffusion component is mainly contributed by the deeply trapped electrons, while the convection component could be caused by either deeply or barely trapped electrons. The kinetic origin of this convective motion is identified to arise from the conservation of the second invariant when trapped electrons lose kinetic energy to the drift wave through toroidal precessional resonance. The relation between the convection velocity and kinetic energy loss of the trapped electron is predicted by analytic theory and verified by simulation quantitatively. The conservation of second invariant is found to act as a powerful constraint in low frequency turbulent transport, which can induce a convective motion by losing/gaining energy. This discovery has extensive applications in many fusion-related scenarios.   

Drift wave-driven chaotic convection in a temperature filament

A numerical model of drift wave-driven plasma convection in a narrow temperature filament is used to study electron temperature transport in the large P\'{e}clet number limit. The model incorporates two drift-waves with different azimuthal mode numbers (m=1 and m=6). Above an amplitude threshold, the nonlinear interaction of the spatially and temporally coherent drift-waves results in chaotic, convection orbits. This deterministic chaos results in temperature transport. Electron heat transport can be modeled well by fractional diffusion and the distributions of convection orbit path lengths are found to be in the Levy stable class. The convection model produces asymmetric, probability density functions (PDFs) of fluctuation amplitudes, and exponential frequency power spectra that have been observed in temperature filament experiments [D. C. Pace \textit{et al.}, Phys. Plasmas \underline {15}, 122304 (2008)]. Exponential k-spectra with two characteristic scales are also observed in the model results.   

Non-Gaussian properties of global particle and momentum fluxes driven by turbulence in a linear plasma

Non-Gaussian statistical properties of the azimuthally averaged momentum and particle fluxes driven by turbulence have been simultaneously observed in an inhomogeneous magnetized linear plasma column for the first time. We identified the distributions of both averaged fluxes as stretched Gaussians, and the transition from point-wise distributions to averaged ones was confirmed. The change in the particle flux precedes that in the momentum flux, demonstrating that the momentum flux is induced by the relaxation of density gradient.   

Cooperative elliptical instability and plasma blob generation

In previous investigations it was found that an $m = 1$ poloidal mode number inside the main plasma column give rise to high-intensity bursts in CSDX. This behavior is also typical for other linear devices, e.g. VINETA and LAPD. Because of the $E\times B$ drift every perturbation in the potential results in a vortex. An $m = 1$ mode in the potential consists of a negative and positive perturbation, which are vortices rotating in opposite directions and therefore an $m = 1$ mode is a counterrotating vortex pair. From fluid mechanics it is known that counter-rotating vortex pairs are subject to the elliptic instability, which is a three-dimensional instability of a two-dimensional flow. This instability can modify the internal structure of the vortex core leading to injection of smaller vortices, which could be a generation mechanism for plasma blobs. Using fast camera measurements first evidence of the existence of the cooperative elliptic instability in magnetized plasmas can be provided.   

Convective cells and blob control in a simple magnetized torus

In view of controlling wall and divertor heat loads in magnetic fusion devices, we investigate the possibility of creating convective cells by means of biased electrodes for turbulence and blob control in the simple magnetized toroidal plasmas of TORPEX. A two-dimensional array of 24 electrodes is installed on a metal limiter to test different biasing schemes. This allows influencing significantly the frequency of the dominant mode as well as radial and vertical velocities of blobs. Detailed measurements along and across the magnetic field provide a rather clear picture of the effect of the biasing. The biased electrodes produce perturbations of the plasma potential and density profiles that are fairly uniform along the magnetic field. Background flows influence the location where potential variations are induced. The magnitude of the achievable potential variations in the plasma is strongly limited by cross-field currents. A quantitative discussion on the origin of these currents is presented.   

Results of Electrode Biasing on Flow and Turbulence Dynamics in a Large Scale Helicon Plasma

Experiments are being conducted in the linear HelCat device, using a helicon source and both concentric ring and grid electrodes to bias the plasma. The goal of these experiments is to affect flow profiles and intrinsic turbulence in a controlled manner. Biasing is found to affect both azimuthal and parallel flows, which exhibit complicated changes. Biasing can also partially or fully suppress intrinsic fluctuations, indicating a change in the dynamics of the system. The parallel flow is downstream in the center of the plasma, but exhibits a return flow at the edge. With positive biasing, the return flow reduces as the fluctuations and associated transport are reduced, seeming to indicate that the return flow may be driven by turbulent radial transport. A linear stability analysis code is being used to further understand the instabilities at work, and a 1D3V PIC\footnote{Supported by Fonds National Suisse de la Recherche Scientifique} code is being used to improve the understanding of the effects of biasing on the plasma potential.   

Suppression of Electron Temperature Gradient Mode by Controlled ExB Velocity Shears in Magnetized Plasmas

A high-frequency ($\sim $5 MHz) instability is observed when an electron temperature gradient (ETG) perpendicular to magnetic field lines is formed in an electron cyclotron resonance (ECR) discharge plasma, which is consistent with an ETG mode. On the other hand, ExB velocity shears can be controlled independently of the ETG by changing the bias voltages of concentrically segmented electron emitters. As the result, it is found that the ETG mode amplitudes decrease with increasing the strength of the ExB velocity shears. In addition, the ETG mode is suppressed more effectively in the presence of an electron density gradient, which suggests that the density-gradient driven mode compensates the temperature-gradient driven mode. In conclusion, our experiment clearly demonstrates the suppression of the ETG mode, which is affected by the ExB velocity shears and the electron density gradient.   

Observation of very low frequency drift wave in ECR produced plasma in the MaPLE device

Plasma is produced by Electron Cyclotron Resonance(ECR) method using $2.45GHz$ microwave in the MaPLE device [R. Pal, S. Biswas et. al., Rev. Sci. Instrum. 81, 73507(2011)] Density fluctuation of the order of 40\% is created by modulating the microwave power at a frequency of $300 Hz$. Floating potential measurement shows the presence of $300 Hz$ frequency along with $600 Hz$ and $900 Hz$ frequencies. Amplitudes of the fluctuations are maximum at radial position $R=6cm$. Density gradient scale length gives the drift wave frequency close to $600 Hz$. Measurement of poloidal propagation confirms it to be a drift wave with mode no $m=2$ and wavelength $\lambda_{\perp}\approx 20cm$. Measured phase velocity in the poloidal direction is $1.3\times10^{4}cm/s$ which is about the electron diamagnetic drift velocity. This $600 Hz$ drift wave probably parametrically couples with $300 Hz$ pump wave and excite $300 Hz$ and $900 Hz$ frequencies. In the region between $R=8cm$ and $R=10 cm$, there is a high radial electric field which suppress both $300 Hz$ and $600 Hz$ fluctuations by $\bf{E \times B}$ flow. Poloidal flow measurement with mach probe also confirms about the presence of $\bf{E \times B}$ flow.   

Design and use of an Els\"{a}sser probe for analysis of Alfv\'{e}n wave fields in a laboratory plasma

We have designed an electric and magnetic field probe which can simultaneously measure both quantities in the directions perpendicular to the applied magnetic field. This new probe allows for the projection of measured wave fields onto modified Els\"{a}sser variables: $z^{\pm }$\textbf{=} $C_{cf }$(\textbf{\textit{E}}\textit{ $\times $ B}$_{0})$/$\vert B_{0}\vert ^{2}\pm \quad \delta B/(\mu _{0}$\textit{$\rho $}$_{0})^{0.5}$. Here the time averaged background field, $B_{0}$, and plasma mass density, \textit{$\rho $}$_{0}$, are measured separately and the correction factor was determined from cold plasma theory to be $1/C_{cf }=\pm $[(1+{\{}$k_{\bot }$\textit{$\delta $}$_{e}${\}}$^{2})$(1-\textit{$\omega $}$^{2}$\textit{/$\Omega $}$^{2})$]$^{0.5}$. Experiments were conducted in singly ionized He plasma at 1810 G in the Large Plasma Device at UCLA. The new probe monitored the propagation of Alfv\'{e}n waves in the $x--z$ plane. Collisionless dispersion of the waves, corresponding to Eq. (1) of Kletzing \textit{et al}. [1], was observed in the field measurements. Simulations of the data confirm these results. Further analysis showed that we are able to measure the Alfv\'{e}n speed ($V_{A} = E/ B)$ from the probe data within 1.5{\%} of that from the time of flight data. Results will be discussed further at confeence.\\[4pt] [1] C. A. Kletzing, D. J. Thuecks, F. Skiff, S. R. Bounds, and S. Vincena, Phys. Rev. Lett. \textbf{104}, 095001(4) (2010).   

Particle-in-Cell Simulations of Two-dimensional Electrostatic Structures

Electrostatic structures have been observed in many regions of space plasmas, including the solar wind, the magnetosphere, the auroral acceleration region. One possible theoretical description of some of these structures is the concept of Bernstein-Greene-Kruskal (BGK) modes, which are exact nonlinear steady-state solutions of the Vlasov-Poisson system of equations in collisionless kinetic theory. Recently we have constructed exact solutions of two-dimensional (2D) BGK modes in a magnetized plasma with finite magnetic field strength in order to gain insights of the ultimate 3D theory [Ng, Bhattacharjee, and Skiff, Phys. Plasmas 13, 055903 (2006)]. Based on the analytic form of these solutions, we have performed Particle-in-Cell (PIC) simulations to study their stability. We have also simulated more general initial conditions, and found that while these are not steady-state solutions, they still keep their overall structures with modulations having frequency of the order of electron cyclotron frequency.   

A new branch of electrostatic fluctuations: the ion-bulk waves

We present the results of kinetic simulations that demonstrate the existence of a novel branch of nonlinear electrostatic waves (dubbed ion-bulk waves) with acoustic type dispersion, excited and sustained by the generation of a population of trapped ions. These waves have phase speed comparable to the ion thermal velocity and are analogous at low frequencies to the so-called electron acoustic waves. During the excitation process, in which an external electric field is used to create the trapped particle population, a secondary instability of the beam-plasma type occurs and brings energy to high wavenumber electric field components. The ion-bulk waves can survive against Landau damping even at low values of the electron to ion temperature ratio, at variance with the ion-acoustic waves. In the long time limit, the electric field waveforms associated with the ion-bulk waves appear as long lived soliton-like structures locked in the phase space trapping vortices. Our results are relevant for the case of the the solar-wind plasmas where the electron to ion temperature ratio is of order unity and a significant level of electrostatic activity is usually recovered from in situ measurements.   

Three-dimensional electromagnetic strong turbulence: I. Scalings, spectra, and field statistics

The first fully three-dimensional (3D) simulations of large-scale electromagnetic strong turbulence (EMST) are performed by numerically solving the electromagnetic Zakharov equations for electron thermal speeds $v_{e}$ with $v_{e}/c \geq 0.025$. The results of these simulations are presented, focusing on scaling behavior, energy density spectra, and field statistics of the Langmuir (longitudinal) and transverse components of the electric fields during steady-state strong turbulence, where multiple wave packets collapse simultaneously and the system is approximately statistically steady in time. It is shown that for $v_{e}/c < 0.17$ strong turbulence is approximately electrostatic and can be explained using the electrostatic two-component model. For $v_{e}/c > 0.17$ the power-law behaviors of the scalings, spectra, and field statistics differ from the electrostatic predictions and results because $v_{e}/c$ is sufficiently high to allow transverse modes to become trapped in density wells. Three-dimensional EMST is shown to have features in common with 2D EMST, such as a two-component structure and trapping of transverse modes.   

Scale Invariance in Madison Symmetric Torus RFP Turbulent Plasmas

Recent studies have shown that turbulence may be a second-order phase transition. Lambda-like profiles of the turbulent parameters have been seen in various types of plasmas, including reversed-field pinch, glow discharge, and laser-induced plasmas. Another signature characteristic of any second-order phase transition is scale invariance. The Hurst exponent characterizes scale invariance by finding negative or positive autocorrelations in a long time series. The Hurst exponent, already found in previous RFP plasmas at RFX, has been found and studied on Madison Symmetric Torus (MST) RFP plasmas. Given the right Hurst exponent, this may show that turbulence is scale invariant, giving more evidence towards turbulence being a second-order phase transition.   

Quantum Macrophysics for New Turbulence Concepts

The classical theory of Ginzburg-Landau second order phase transformations can be applied directly to the transition from laminar to turbulent flow. The generalization of the G-L approach to include turbulence connects the possibility of new insights on turbulence to a large class of second order phase transformations in physical systems. The use of techniques from quantum macrophysics in second order phase transformations affords a list of predictions about behaviors which are unique to the quantum macrophysics prospective.