Session TO6: Basic Plasma Physics: Simulations, Turbulence and Transport

Stability of nonlinear Vlasov equilibria through spectral deformation and Fourier-Hermite expansion

We study the stability of nonlinear Vlasov-Poisson equilibria through projection of the dynamics to a finite dimensional Fourier-Hermite basis (in the space and velocity variables, respectively), which reduces the problem to an eigenproblem. Use of the method of spectral deformation enhances the rate of convergence of the method. We benchmark the method against linear (spatially homogeneous) equilibria, such as the bump-on-tail configuration and demonstrate its exponential rate of convergence to the eigenvalues obtained by direct solution of the dispersion relation. We then proceed with the study of a nonlinear (spatially inhomogeneous) problem, namely that of periodic Bernstein-Greene-Kruskal waves with multiple phase space depressions. Our results for the growth rate of perturbations agree with the numerical simulations of Ghizzo et al. [Phys. Fluids 31, pp. 72--82 (1988)]. We discuss possible applications to the stability of electrostatic waves in connection to stimulated Raman Scattering saturation.   

Damping of spurious numerical reflections off of coarse-fine adaptive mesh refinement grid boundaries

Adaptive mesh refinement (AMR) is an efficient technique for solving systems of partial differential equations numerically. The underlying algorithm determines where and when a base spatial and temporal grid must be resolved further in order to achieve the desired precision and accuracy in the numerical solution. However, propagating wave solutions prove problematic for AMR. In systems with low degrees of dissipation (e.g. the Maxwell-Vlasov system) a wave traveling from a finely resolved region into a coarsely resolved region encounters a numerical impedance mismatch, resulting in spurious reflections off of the coarse-fine grid boundary. These reflected waves then become trapped inside the fine region. Here, we present a scheme for damping these spurious reflections. We demonstrate its application to the scalar wave equation and an implementation for Maxwell's Equations. We also discuss a possible extension to the Maxwell-Vlasov system.   

Towards a stabilized finite element method for the MHD equations

In MHD flows with large Hartmann and/or Reynolds numbers the Galerkin finite element method does not perform well. It can be shown that in these limits this method looses stability and leads to solutions with spurious oscillations. In order to overcome this problem, we are developing a stabilized finite element method that is derived from a variational multiscale concept. This method introduces a model term to the Galerkin method that emulates the effect of the fine scales of the solution that are not captured by the grid. In doing so, these model terms add stability to the numerical method. In the case of turbulent MHD flows these terms can be interpreted as turbulence models that represent the effect of the fluctuating subgrid scales. In this presentation we will develop the stabilized finite element formulation and assess its performance with test problems.   

Experimental Study of Particle Transport with SMBI and ECRH on HL-2A Tokamak

A spontaneous particle transport barrier has been observed for the first time in the ohmic plasma in HL-2A tokamak. This phenomenon is identified using three different methods. In the barrier region, the turbulence level has been significantly reduced and a drastic change of the turbulence poloidal rotation has been observed. Particle diffusivity and the convective velocity have been separately determined. The formation of the particle transport barrier coincides with the TEM/ITG transition via collisionality. ECRH modulation experiments have also been performed in HL-2A for particle transport investigation. Density pump-out (negative density perturbation) in the central region has been observed as in other tokamaks. Simultaneously a positive density perturbation due to the out-gassing in the peripheral region has been observed. An outward convection has been observed during pump-out transient phase.   

Sensitivity of the Turbulence Kappa Constant to Molecular and Magnetic Field Parameters in Glow Discharge Plasmas

Turbulent parameters in glow discharge plasma have been shown to be influenced by the axial magnetic fields. Specifically, critical turbulent energy is directly related to the changes in these magnetic fields. There is also a possible relationship between the masses of certain noble gases and critical turbulent energy. Using kappa, the universal turbulence constant, as a framework, we will report on the relationship between atomic mass, evolving magnetic field, and critical turbulent energy. We will also address the implications from these results for new turbulent physics.   

Turbulent Signatures in the Optical Spectra of Self-Induced Stark Lines in Hypersonic Argon and Krypton Plasma

Recent experimental evidence suggests that turbulence is influenced by external electromagnetic fields. Localized magnetic fields might also distort turbulent systems. High-speed optical spectral scans in the arc driven shock tube confirm the presence of self-induced Stark Effect lines in argon and krypton plasmas. Analyses of the plasma turbulence in these lines indicates a sensitivity of the spectral index, the characteristic frequency, and turbulent energy to local field strength. Comparison of data in both the primary and reflected shock regions shows consistent behavior of the turbulent parameters as a function of field strength. In addition, the system complexity versus magnetic field also displays a constant behavior with increasing magnetic field. We discuss these results in the context of new turbulent astrophysics and fusion science.   

Evidence of Self-Induced Stark Lines in Turbulent Hypersonic Argon Plasmas

Recent experimental evidence suggests that turbulence is influenced by external electromagnetic fields. Localized magnetic fields might also distort turbulent systems. Using a high-speed spectrograph with an echelle grating and a dual order prism attached to a CCD, we confirm the existence of localized self-induced stark effect lines in argon plasmas produced by the arc-driven shock tube. These Stark lines are treated as a byproduct of a self-induced magnetic field. This diagnostic identifying the lines performs high-speed spatial scans of 160nm in range of up to 20 microseconds allowing for more defined results for analysis. In this talk the diagnostic of the system will be presented.   

Singularities and Reconnection in MHD Turbulence

Observations of reconnection in plasmas indicates that it is typically fast, i.e. at a speed which is a significant fraction of the Alfven speed. Recent theoretical and numerical work has provided support for the hypothesis that in a turbulent medium it occurs at the turbulent velocity. We will discuss the nature of the singularities necessary for fast reconnection, and its speed as a function of scale. Simulations of fast reconnection in three dimensional turbulence provide evidence that the process is mediated by localized current sheets.   

Turbulent Parameter Studies in the Madison Symmetric Torus RFP with High Bandwidth Resolution

Anomalous ion heating is driven by magnetic field fluctuations, but the detailed physical mechanism is unknown. To help us understand how turbulence plays a role in ion heating, we study the standard turbulent parameters, i.e., Spectral Index, Characteristic Frequency, and Chaotic Dimension during the sawtooth crash at the Madison Symmetric Torus (MST). Magnetic field fluctuations have been measured in the 15 -- 50 MHz range using a high bandwidth oscilloscope. During sawtooth crashes we have seen increases in magnetic field turbulent energy occurring at different times and different frequency ranges within the power spectrum. This allows us to look at the standard turbulent parameters during a sawtooth with fine time resolution. Knowing the changes in these parameters may help us to understand turbulence and it's relevancy to anomalous ion heating.   

A Statistical Analysis of Current Sheets in Turbulent MHD Simulations

The statistics of current sheets (CSs) in turbulent reduced-MHD simulations is analyzed in order to assess the importance of magnetic reconnection in the overall energy dissipation and to determine the dissipation intermittency in resistive MHD turbulence. An algorithm is developed for identifying CSs in 2D and 3D and for characterizing them quantitatively in terms of their energy dissipation, peak current density, length, and width. Statistical distributions of these quantities are found to have power-law tails. Furthermore, it is found that most CSs do not contain magnetic X-points and, vice versa, many X-points lie outside CSs. However, most of the strongest CSs do contain X-points and hence presumably are associated with reconnection. Their properties are compared with the Sweet-Parker theory.   

Study of weak Alfvenic turbulence

We report a study of weak incompressible magnetohydrodynamic turbulence in the presence of a strong guide magnetic field. Such turbulence consists of weakly interacting Alfven waves propagating in opposite directions along the guide field. We consider both balanced and imbalanced turbulence. The imbalanced case is the case when the energies of counter-propagating Alfven waves are unequal. In this case we discuss the role of the so-called ``condensate,'' that is, the nonlinear magnetic fluctuations at $k_\|=0$ on the spectrum and structure of turbulence.   

On Lagrangian intermittency in drift-wave

The Lagrangian velocity statistics of dissipative drift-wave turbulence are investigated by means of direct numerical simulation in the context of the Hasegawa-Wakatani model. For large values of the adiabaticity corresponding to small collisionality, the probability density function of the Lagrangian acceleration shows exponential tails, as opposed to the stretched exponential or algebraic tails, generally observed for the highly intermittent acceleration of Navier-Stokes turbulence. This exponential distribution is shown to be a robust feature independent of the Reynolds number. For small adiabaticity, algebraic tails are observed, suggesting the strong influence of point-vortex-like dynamics on the acceleration. A causal connection is found between the shape of the probability density function and the auto-correlation of the norm of the acceleration.   

Full f gyrokinetic turbulence simulations including polarization drift

Elmfire is a global gyrokinetic full f electrostatic particle-in-cell (PIC) code designed for first principle transport simulations of tokamak plasmas including both kinetic ions and electrons. It is based on a gyrokinetic model which includes the polarization drift implicitly in the guiding center equations. The derivation of the equations of motion, the Poisson equation as well as the energy, momentum, and angular momentum conserving rules will be presented.The code has successfully passed neoclassical and code benchmarks and conservation rules have proven to be satisfied. Experimental validation of poloidal velocity is performed by means of a synthetic Doppler reflectometry diagnostic. The experimental FT-2 Doppler reflectometer power spectrum shows good agreements with the synthetic diagnostic in both the Doppler shift as well as the width of the power spectrum, indicating comparable rotation and spreading of the turbulence at several radial positions.