Session TP9: Poster Session VII: Basic Plasma Physics: Turbulence, Simulations, Flows, Sheaths, and Shocks; C-Mod Tokamak; Turbulence and Transport; Mini-Conference: Solar Wind Turbulence

Poincare recurrence and intermittent destruction of the Kelvin wave cascade in turbulence

Spacecraft data for solar wind turbulence shows a more sophisticated magnetic energy spectra than the simple k$^{-5/3}$ Kolmogorov spectrum of fluid turbulence. In particular data shows that while the low wave number magnetic energy spectrum follows the Kolmogorov k$^{-5/3}$ cascade, there is a clear break in the spectral exponent with the spectrum having a somewhat steeper power law decay at the kinetic ion scales. A unitary lattice algorithm, based on interleaved unitary collision-stream operators, is implemented to study turbulence of the nonlinear Schrodinger equation. Because of the near perfect parallelization of this unitary algorithm simulations were performed on 5760$^{3}$ grids, yielding multi-scale physics seen in the multi-cascade behavior of the incompressible kinetic energy. Very short Poincare recurrence times have been seen with the intermittent destruction of the Kelvin wave cascade.   

Unitary Mesoscopic Algorithms for 2D Quantum and Classical Turbulence

The nonlinear Schrodinger (NLS) equation plays an important role in physics: from plasma wave and soliton propagation to turbulence in Bose-Einstein condensates. There is much interest in unravelling the differences between 2D and 3D turbulence - in fluids, plasmas and BECs. In fluid turbulence there is a marked difference between: in 2D, there is an inverse cascade of energy and a direct cascade of enstrophy while in 3D only a direct cascade of energy. MHD, the cascades are similar in both 2D and 3D. To examine the effects of dimensionality on quantum turbulence we device an almost perfectly scalable unitary lattice gas algorithm to solve the NLS equation. Unlike classical or plasma turbulence, a vortex in quantum turbulence is a well-defined topological singularity. For various initial conditions we examine the spectra for both 2D and 3D turbulence on grids that scale from quantum to classical scales.   

Entropic Lattice Boltzmann Algorithms for MHD Turbulence

To achieve high resolution simulations of MHD turbulence, one must have highly parallelized algorithms that scale to hundreds of thousands of cores. Direct lattice Boltzmann algorithms are such explicit schemes - but they are typically restricted in the achievable Reynolds numbers due to numerical instabilities. Here we examine entropic generalizations of LB by introducing a scalar distribution for the magnetic field With the magnetic field arising as a first moment we can enforce positive definiteness on the magnetic scalar distribution and hence an entropic representation. This will permit simulations to be performed at arbitrary high magnetic Reynolds number - limited only by the number of cores available. Results will be presented for the Orszag-Tang vortex. Moreover large eddy simulation (LES) closures can be incorporated into LB without destroying the parallelization of the algorithm as macroscopic gradients are local moments in the LB representation. LB does not loose its parallelization when handling arbitrary boundary conditions. A semi-entropic LB scheme (using a vector distribution for \textbf{B}) will also be considered.   

The effect of diamagnetic drifts on the dynamics of turbulent transport

Recently, much progress has been made toward understanding the fundamental dynamics of turbulent transport in the presence of sheared flows. The insights have come from following Lagrangian trajectories using both gyrokinetic simulations of ITG turbulence [1] and fluid models of drift-wave turbulence [2]. In this work, using the same tools, the impact of simple diamagnetic drifts on the dynamics of the transport is investigated using numerical simulations of 2D-turbulence in slab geometry with the BETA code. By itself, a diamagnetic drift velocity can have a significant an impact on the transport dynamics both with and across flow. However when coupled with a sheared flow additional dynamics are observed which could lead to interesting profile control tools if separately controlled. These new dynamics are in part the result of coherent structure formation localized to particular regions of the flows. The transport dynamics and possible uses will be discussed. \\[4pt] [1] R. Sanchez, D.E. Newman, et al PRL 101, 205002 (2008) \\[0pt] [2] D.E. Newman, et al, Proc. of the 35th EPS Conf on Plasma Physics, ECA Vol. 32, p. 1.044 (2008)   

Parallelization in time of numerical simulations of drift-wave turbulence using the parareal algorithm

The simulation of turbulent fusion plasmas is very computationally intensive due to the large disparity of timescales that play a role in the dynamics. It is widely accepted that first principles simulations of ITER-relevant plasmas are currently unfeasible, and will remain so for quite sometime unless some important algorithmic advances are made. Even shorter simulations of a more restricted range of timescales, such as those based on gyrokinetics, are usually limited to tens of thousands of CPUs due to interprocessor communication, not scaling up to the 100,000+ CPUs that current supercomputers offer. In this contribution we test successfully a recently proposed scheme to parallelize in time the integration of systems of PDEs on a drift-wave turbulence code [1]. The lessons learnt from this exercise suggest that an additional parallelization path exists to enable longer simulations, more complete physics models and a better utilization of existing computational resources. \\[4pt] [1] D. Samaddar, D.E. Newman and R. Sanchez, J. Comput. Phys. 229, 6558 (2010)   

Strongly driven drift modes independent of resistivity in finite beta plasmas

We study drift waves (DW) in collinear magnetic field, beta $\sim $ O(1) systems (e.g., FRCs), wherein the sonic and Alfven drift branches are strongly coupled. For isothermal perturbations, we find that finite beta is strongly stabilizing. With temperature perturbations, we find a rapidly growing instability, mediated by the Braginskii thermal force but not requiring resistivity. The growth rate peaks at the drift frequency. This mode has been described by Mikhailovskii but has not been well studied. The nonlocal and nonlinear theory of this mode is investigated. A finite beta 3D 2-fluid code with Hall terms and thermal force has been developed. The linear thermal force DW is confirmed. The code is also used to investigate dispersion characteristics and the ensuing turbulence. The code will also be used to study the interplay between DWs and the plasma thermoelectric effect. The latter effect generates a B x grad[T] current in magnetized plasmas and is of the same order as the plasma resistivity limited current in finite beta plasmas. It is of interest to study how drift wave turbulence would influence the thermoelectric effect and vice-versa.   

On the measurement of Lagrangian correlation functions in drift wave fluctuations

We explore the possibility of measuring Lagrangian correlation functions in drift wave turbulence in a magnetized plasma cylinder. The connection between Lagrangian and Eulerian correlation functions is known to be complex. For example it is possible for the same process to exhibit chaotic Lagrangian trajectories and at the same time to have a completely integrable Eulerian flow. Using laser-induced fluorescence it is possible to realize the measurement of both Eulerian and Lagrangian correlation functions depending on the degree of optical pumping. We explore the effects of optical pumping on the Eulerian limit (weak optical pumping) as well as what can be learned in the limit of strong optical pumping where the signal is best interpreted in the Lagrangian sense (``optical tagging''). Preliminary data are obtained in a singly ionized Argon plasma with density of 10$^{9}$ - 10$^{10}$ cm$^{-3}$ an electron temperature of typically 4 eV and an ion temperature of typically 0.1 eV. LIF data are collected using both diode laser light at 668 nm and dye laser light at 611nm to excite metastable fluorescence lines.   

Tests of Nonlinear Interactions Between Alfv\'{e}n Waves Using Gyrokinetic Simulation

Nonlinear interactions between Alfv\'{e}n waves are the fundamental action responsible for plasma turbulence, governing energy transport across a wide range of scales and in nearly any plasma environment. MHD theory predicts that turbulent transport in magnetized plasmas occurs as the result of nonlinear interactions between Alfv\'{e}n waves propagating oppositely along the mean magnetic field. This theory suggests a mechanism for these interactions and predicts interaction rates and products. These results from MHD theory have influenced the development of Alfv\'{e}nic turbulence theory, but the MHD approximation does not hold in many plasmas of scientific interest, making it difficult to test the theory by experiment. We present results of a study employing gyrokinetic simulations that test the hypotheses of MHD Alfv\'{e}nic turbulence theory. These simulations, performed with the astrophysical gyrokinetics code AstroGK, enable the construction of MHD approximating conditions without relying explicitly on the assumptions of MHD theory.   

Investigation of Instabilities in a Harris Current Sheet Using a Gyrokinetic Electron and Fully Kinetic Ion Particle Simulation

A novel gyrokinetic electron and fully kinetic ion (GeFi) particle simulation model has been developed for the purpose of investigation of collisionless magnetic reconnection. In this model, the rapid electron cyclotron motion is removed, while retaining the finite electron Larmor radii, wave-particle interaction, and off-diagonal components of the electron pressure tensor. In this talk, we (1) present our recent improvement of scheme by adopting the potential formulations for both electrons and ions and (2) show simulations of current-sheet driven instabilities in a Harris sheet using GeFi code. The simulation is carried out for finite guide field and with a realistic mi/me. Code is benchmarked against our eigen-theory of the tearing instability and the results are compared with the asymptotic matching results of Drake and Lee. For the current-sheet driven instability, in addition to the quasi-electrostatic modified two-stream instability/whistler mode on the edge, a new mode is found in the sheet center, which may contribute to the anomalous resistivity in reconnection.   

Statistical Theory for Energy Distribution in Gyrokinetic Turbulence

Recent gyrokinetic simulations reveal that ITG turbulence excites a large number of damped modes in the wavenumber range of the instability. These dissipative structures engage in an equipartition of dissipated power across the modes of a singular value decomposition (SVD). Energy injected by the instability is simultaneously distributed among all modes. Equipartition is enforced by the large multiplicity of couplings among damped modes, the uniformity of coupling strengths from mode to mode, the propensity for ergodization in individual triads, and the relatively large damping rates. Through the concept of turbulent dissipative contact among separate decompositions, we derive the probability distribution function of dissipated power in any mode and the entropy of the system. We study the effect of different basis decompositions on equipartition. Because the system is dissipative but turbulent, energy not lost to dissipation in a turbulent decorrelation time progresses to smaller scales via a wavenumber cascade. At high $k$ the dissipation rate becomes smaller than the turbulent correlation rate, yielding a power law spectrum asymptotically.   

Gyrokinetic Simulations of Edge Pedestal Turbulence

First-principle simulations of edge pedestal micro-instability are performed with the global gyrokinetic turbulence code GEM. The density, temperature and magnetic equilibrium profiles are obtained from both numerical simulation and experiments. The turbulence from simulation results peaks at the position of strongest pressure gradient and the bottom of Er. The dominant linear instability appears to be caused by the strong density gradient. As a result, the H-mode pedestal is linearly more unstable than L-mode. However, the nonlinear steady-state flux level of H-mode is indeed lower than L-mode. The linear instability requires kinetic electrons but is not due to trapped electrons, and it is nearly insensitive to ion and electron temperature gradients. The dominant instability is likely to be electron drift wave. In a systematic study, we find that there are two ``branches,'' low-n and high-n, of the pedestal instability. The electromagnetic effect is destabilizing in the low-n branch and stabilizing in the high-n branch. In a set of simulations with fixed pedestal height but varying pedestal width, the linear growth rate is first lowered then increased as the pedestal width get thinner and thinner, a phenomenon consistent with kinetic ballooning mode (KBM).   

Study of Shear Flow Effect on turbulence by GTC

Shear flow, which can be generated by external field or turbulence of the plasma itself, is by now generally accepted as one of the most important factors to form transport barriers, both at the edge and further into the plasma core, and thus to enhance plasma confinement for ignition. However, the mechanism which leads shear flow to less transport, especially the transport from Alfven turbulence, is not well understood yet. A Gyrokinetic Particle Simulation (GTC) is applied to study such effects. Ion Acoustic wave, Drift wave and Doppler Effect by flow are now recovered from simulation with good agreement with theory. The code will be used to study the nonlinear effect of shear flow on different modes in tokamak geometry.   

Modeling Plasma Turbulence and Flows in LAPD using BOUT++

A Braginskii fluid model of plasma turbulence in the BOUT code has recently been applied to LAPD at UCLA [1]. While these initial simulations with a reduced model and periodic axial boundary conditions have shown good agreement with measurements (e.g. power spectrum, correlation lengths), these simulations have lacked physics essential for modeling self-consistent, quantitatively correct flows. In particular, the model did not contain parallel plasma flow induced by sheath boundary conditions, and the axisymmetric radial electric field was not consistent with experiment. This work addresses these issues by extending the simulation model in the BOUT++ code [2], a more advanced version of BOUT. Specifically, end-plate sheath boundary conditions are added, as well as equations to evolve electron temperature and parallel ion velocity. Finally, various techniques are used to attempt to match the experimental electric potential profile, including fixing an equilibrium profile, fixing the radial boundaries, and adding an angular momentum source. \\[4pt] [1] Popovich et al., http://arxiv.org/abs/1005.2418 (2010).\\[0pt] [2] Dudson et al., \textit{Computer Physics Communications 180} (2009).   

Flows, turbulence, and transport in the Large Plasma Device

We report on measurements of spontaneous flows, turbulence, Reynold's stress and particle flux in the Large Plasma Device (LAPD) at UCLA. Measurements of perpendicular and parallel flow using a six-sided Mach probe reveal a shear-layer flow in the cathode edge region whose peak flow increases with magnetic field and broadly distributed far-edge perpendicular flows that scale inversely with magnetic field. ~The role of boundary effects and turbulent Reynolds stress in establishing the flow profile is investigated. Reynolds stress is measured with a seven tip vorticity probe; characteristics of the turbulence are measured using triple Langmuir probe. ~The connection among shear flow, turbulence and spatial correlation lengths is examined through cross-correlation techniques, which also serves to establish the relationship between these quantities and gradient driven instabilities such as drift-Alfven or Kelvin-Hemholtz. These results are especially useful for comparisons to ongoing fluid simulations using the BOUT and BOUT++ 3D Braginskii fluid codes.   

Electron Temperature Gradient Turbulence: Validation in the Columbia Linear Machine Experiments

The electron temperature gradient (ETG) mode, which is a dominant mechanism for turbulent electron thermal transport in plasmas, is produced and verified by a recent experiment conducted in the Columbia linear machine[1]. They report modes at $\sim 0.3 - 0.5 \;\rm MHz$, with azimuthal wave numbers $m\sim 14-16$ and parallel wave number $k_\parallel \sim 0.003\; \rm cm^{-1}$. We study these results using a gyro-fluid simulation code DTRANS and a gyro-kinetic simulation code GTC[2]. The results show that in the linear phase, the dispersion relation is consistent with kinetic theory for a slab ETG model and the radial structure of the fluctuation agrees with the experiment. We also investigate the saturation of ETG mode using the ${\bf E}\times {\bf B}$ turbulent mixing and coupling to low frequency modes. It turns out that low frequency drift-ion acoustic waves as in [1] interact with high frequency ETG modes to extract energy and saturate the ETG fluctuations. \\[4pt] [1] X. Wei, V. Sokolov, and A. K. Sen, Physics of Plasmas 17, 042108(2010). \\[0pt] [2] I. Holod, W. L. Zhang, Y. Xiao, and Z. Lin, Physics of Plasmas 16, 122307(2009).   

Self-Regulation Dynamics of Drift Wave-Zonal Flow Turbulence in a Linear Magnetized Plasma

The Low-Frequency Zonal Flow is studied experimentally with the Langmuir probe arrays in a linear magnetized plasma device. In a weakly developed drift turbulence, the 3D mode characteristics of $m\simeq{n}\simeq0, k_r\simeq0.16 cm^{-1}$ and a very near-zero mode frequency are obtained through spectrum analysis ,indicating the feature of zonal flow. The three-wave coupling between ZF and AT is shown through bispectrum analysis. Furthermore, the self-regulation dynamics are studied in such a drift wave-zonal flow (DW-ZF) turbulence through changing axial magnetic field, accompanying with the change of turbelence energy. Finally, the shearing effect of the DW by the ZF is also examined.   

Gyrokinetic inverse cascade in the sub-Larmor range: An analysis in the style of Fj{\o}rtoft, 1953

It is known that an inverse cascade of energy occurs in two-dimensional neutral fluid turbulence and also, under certain conditions, in magnetized plasma turbulence. The reason for this phenomenon in both cases is due to the existence of two quadratic invariants that are {\em mutually-constraining} in the sense that the spectral redistribution of one is constrained by the other. The homogeneous gyrokinetic equation has two collisionless quadratic invariants when restricted to two dimensions in position-space. In this letter, we consider the consequences of this fact for scales smaller than the thermal Larmor radius, where turbulent fluctuations exist, with equal importance, in the position and velocity space dependence of the kinetic distribution function. Using a spectral formalism for position and velocity space, we find that the gyrokinetic invariants are mutually constraining with respect to spectral redistribution of energy. We adapt the analysis of Fj{\o}rtoft (1953) to investigate the consequences of this fact. We find that inverse cascade is possible, but differs from the conventional inverse cascade of fluid turbulence in several ways. In certain scenarios, we argue that a dramatic non-local inverse cascade will occur, whereby fluctuations at scales much smaller than the Larmor radius can transfer energy directly to the Larmor scale. In the other extreme, we argue that the inverse cascade can be completely shut down.   

Freely decaying turbulence of two-dimensional electrostatic gyrokinetics

Electrostatic gyrokinetic turbulence in weakly-collisional magnetized plasmas exhibits a turbulent cascade of an entropy invariant to fine scales in phase space [1]. In two dimensions, the existence of an additional independent collisionless invariant causes a concurrent phase-space cascade, where the second invariant {\em inversely} cascades to large scales. In this presentation, we report the detailed characteristics of the freely decaying turbulence in the two-dimensional (2D) electrostatic gyrokinetics. By applying methods from 2D Navier-Stokes turbulence [2], we present a classification in terms of a dimensionless number (an analogue of the Reynolds number that is characteristic to the phase-space turbulence), and derive various decay laws in each region of the classification. We also show clear evidence of the inverse cascade by the diagnostics of the triad interaction in the wave-number space using the AstroGK code [3]. \\[4pt] [1] T. Tatsuno \textit{et al}., Phys.\ Rev.\ Lett.\ \textbf{103}, 015003 (2009).\\[0pt] [2] J. R. Chasnov, Phys.\ Fluids \textbf{9}, 171 (1997).\\[0pt] [3] http://sourceforge.net/projects/gyrokinetics/   

Mode conversion at density irregularities in the LAPD

Mode conversion of electrostatic plasma oscillations to electromagnetic radiation is commonly observed in space plasmas as Type II and III radio bursts. Much theoretical work has addressed the phenomenon, but due to the transient nature and generation location of the bursts, experimental verification via \emph{in situ} observation has proved difficult. The Large Plasma Device (LAPD) provides a reproducible plasma environment that can be tailored for the study of space plasma phenomena. A highly configurable axial magnetic field and flexible diagnostics make the device well suited for the study of plasma instabilities at density gradients. We present preliminary results of mode conversion studies performed at the LAPD. The studies employed an electron beam source configured to drive Langmuir waves towards high density plasma near the cathode discharge. Internal floating potential probes show the expected plasma oscillations ahead of the beam cathode, and external microwave antenna signals reveal a strong band of radiation near the plasma frequency that persists into the low density plasma afterglow.   

Energy Dissipation in 3D ETG-Driven Fluid Turbulence

Recent efforts to characterize the saturation of micro-turbulence indicate that there is significant dissipation by nonlinearly excited damped eigenmodes. In a 2D ETG fluid model, damped modes co-existing at low $k_y$ with unstable modes dissipate energy during and after the transition to the nonlinear state through a strong nonlinear correlation between potential and pressure.\footnote{J.-H. Kim and P.~W. Terry. Submitted to Phys. Plasmas, 2010.} In this work, energy dissipation is numerically investigated in a 3D ETG fluid model in flux-tube geometry. While dissipation by damped modes is expected to be significant, the relative contributions by damped modes to various types of dissipation, including cross correlations and collisions, are not clear in the presence of Landau damping. The characteristics of energy dissipation in the transition to nonlinear state and the nonlinear steady state will be presented with the detailed analysis of energy transfer channels resolved in wavenumber space to distinguish high wave number dissipation, energy dissipation by damped modes and Landau damping.   

Measurement of Radial Electron Thermal Transport due to ETG Modes in a Basic Experiment

Production and identification of electron temperature gradient (ETG) mode have been successfully demonstrated in a basic experiment in Columbia Linear Machine CLM [1]. Using a dc bias heating scheme of the core plasma, we are able to produce sufficiently strong ETG modes in CLM experiments. A unique miniature triple probe was used for local measurement of electron temperature and plasma potential fluctuations. Their cross-correlation yields the local radial electron thermal flux. A preliminary measurement of electron thermal conductivity indicates $\chi_{\bot e}$ is about $\sim 3 m^2/s \sim 10 \chi_{\bot e,GB}$. This result appears to agree with a value of non-local thermal conductivity obtained from a rough theoretical estimation [2]. This research was supported by U.S. Department of Energy Grant No. DE-FG02-98ER-54464. \\[4pt] [1] X. Wei, V. Sokolov and A.K. Sen, Phys. Plasmas, 17, 042108 (2010). \\[0pt] [2] H.L. Berk et al, Nucl. Fusion, 33, 263 (1993).   

Nonlinear Coupling between Zonal Modes and Damped Modes

A simple fluid ITG model is simulated to study nonlinear coupling between zonal modes (ky=0, zero frequency modes) and damped modes. It is observed that the cross correlation terms dominate the energy dynamics, with the unstable modes supplying all the energy and the damped modes removing a significant portion of it. The remainder is removed by high ``k'' dissipation. However, even the dissipation has significant damped mode effects. Phase mixing analysis shows that transfer of energy from the unstable to damped modes via the zonal modes is more efficient compared to direct transfer of energy from unstable to damped modes. This is confirmed in simulations, which show that when zonal flows are included in the dynamics, 1) there is significantly more energy in the ky = 0 fluctuation component, and 2) the energy transfer channel from unstable modes to zonal modes to damped modes captures almost all of the energy injected by the instability. When zonal flows are not included, damped modes still saturate the instability but the transfer from the unstable modes is less efficient and requires a larger fluctuation level.   

Investigation of Chaotic Fluctuations in a Linear Helicon Plasma under Changing Magnetic Field and Radial Electric Field

Experiments conducted in a linear helicon plasma (HelCat) device show evidence of deterministic chaos in edge fluctuations under DC biasing on a set of concentric rings which terminate the plasma column. At low bias or without bias, a low frequency coherent instability is present in the density gradient region, consistent with a resistive drift mode. At higher bias, there is an increase in azimuthal flow and flow shear, and a new instability is observed which could be a Kelvin-Helmholtz instability or interchange mode. Additionally, a parallel forward flow (away from the source) at the plasma center and backward flow at the plasma edge are observed. This return sheared flow may be an inflow due to increased radial fluctuation-induced transport at the plasma edge, and may play a role in the chaotic dynamics. Increasing magnetic field also affects these instabilities and their nonlinear dynamics. Experimental results and two fluid modeling are presented.   

Understanding Flow Profiles in a Large Scale Helicon Plasma With Electrode Biasing

Experiments on flow shear/turbulence interactions are being conducted in the linear HelCat device, using both concentric ring and grid electrodes to bias the plasma. Flow profiles exhibit complicated changes with bias in both the azimuthal and parallel directions. Azimuthal flows are dominated by ``static'' E$_{r }$x B$_{z}$ rotation, but also have a fluctuation-driven (zonal) flow contribution, due to Reynolds stress at the edge. Biasing is found to change the fluctuation dynamics, including fully suppressing fluctuations under some conditions. Strong parallel downstream flow (away from the source) in the plasma center is observed, while a sheared return flow is seen at the edge. Under biasing, the return flow is reduced and eventually reversed. It appears that this return parallel flow may be an inflow driven by increased turbulent radial transport at the plasma edge, rather than a direct effect of biasing currents. As drift wave transport is suppressed, this parallel return inflow reduces. Experimental and initial two-fluid modeling results are presented.   

Development of a drift wave turbulence transport model for a linear plasma device

This work investigates modeling of transport and flow generation in a linear plasma device using a 1-D transport code. Drift wave turbulence models have been analyzed to derive models for the growth rate, nonlinear saturation mechanism, and Reynolds stress parameterization in the transport model. The goal is to model the HELCAT experiment including the use of biased concentric rings as control elements for the radial electric field profile. By varying the bias voltages, the local ExB flow can be modified. The effect will be identical to a source of \textit{ExB} flow in the limit of zero beta (i.e., when diamagnetic flows are negligible). By varying the momentum sources a sheared radial electric field can be generated that can suppress turbulent particle and heat transport. The impact of ion temperature effects, axial flow and plasma boundary conditions are investigated. Comparisons with density and flow profiles from HELCAT experiments will be undertaken.   

Non-Model-Based Optimal Fluctuation Mitigation by E$\times $B Actuation in HELCAT

Turbulence, and turbulence-driven transport are ubiquitous in magnetically confined plasmas, where there is an intimate relationship between turbulence, transport, destabilizing mechanisms like gradients and currents, and stabilizing mechanisms like shear. We investigate active control of fluctuations via manipulation of flow profiles in a magnetized laboratory plasma device (HELCAT). Fluctuations and particle transport are monitored by electrostatic probes, and E$\times $B flow profiles controlled via biased ring electrodes. A non-model-based optimization algorithm is implemented to seek control inputs that minimize a cost function related to the fluctuation amplitude. The algorithm is also able to identify radial poloidal flow profiles associated with low RMS fluctuations. The long-term goal is to develop model-based feedback controllers to regulate the radial poloidal flow profiles around the identified low-fluctuation profiles.   

Clarification of symmetry breaking mechanism in intrinsic rotation of tokamak plasmas

Intrinsic rotation of tokamak plasmas is considered to be generated by non-diffusive stress (i.e. residual stress) induced by asymmetric $k_{\vert \vert } $ turbulence spectrum. To study the symmetry breaking mechanisms in intrinsic rotation, we have performed numerical simulations of intrinsic rotation by ITG turbulence using the gKPSP code, a delta-f global PIC code for tokamak. It is found that not only distortion of turbulence spectrum by $E\times B$ shear but also spatial diffusion of wave momentum driven by turbulence intensity gradient play an important role in the symmetry breaking mechanism, as expected from a theory [1]. It is hard to recognize individual contribution of $E\times B$ shear and turbulence intensity gradient to the residual stress because their evolution is strongly coupled with the prey-predator feature [2]. To clarify their role, a comprehensive analysis including their nonlinear coupling is performed. The key symmetry breaking mechanism is identified for various physics situations. \\[4pt] [1] P.H. Diamond, et al., Phys. of Plasmas 15, 012303 (2008). \\[0pt] [2] P.H. Diamond, et al., PRL 72, 2565 (1994).   

On the Efficiency of Intrinsic Rotation Generation in Tokamaks

A theory of the plasma flow generation process efficiency is presented. A measure of the \textit{efficiency} of the plasma to produce mesoscale and mean flow from heat flux is introduced by analogy with engines, using entropy budget due to thermal relaxation and flow generation. The efficiency is defined as the ratio of entropy destruction rate due to flow generation and entropy production rate due to $\nabla T$ relaxation (i.e. related to turbulent heat flux). The efficiencies for two different cases, i.e. for the generation of turbulent driven $E\times B$ shear flow (zonal flow) and for toroidal intrinsic rotation are considered for a stationary state, achieved by balancing entropy production rate and destruction rate order by order in $O(k_\parallel/k_\perp)$ where $k$ is a wave number of a mode. The efficiency of intrinsic toroidal rotation is derived and shown to be $e_{IR}\sim0.01$. The scaling form of the efficiency of intrinsic rotation generation is also derived and shown to be $\rho_*^2(q^2/\hat s^2)(R^2/L_T^2)=\rho_*^2(L_s^2/L_T^2)$, which suggests a machine size scaling and an unfavorable plasma current scaling through the shear length.   

MHD wind tunnel

Preliminary results are presented from a high-velocity, turbulent MHD wind tunnel at the SSX facility. The prototype wind tunnel has dimensions $L = 1~m$ and $R = 0.08~m$. Flow is measured with a cylindrical Mach probe calibrated both with magnetic time-of-flight and ion Doppler spectroscopy. Magnetic structure and turbulence are measured with arrays of magnetic probes. In a typical experiment, a magnetized plasma plume is injected at one end at $v \ge 50~km/s$ then the plasma turbulently evolves down the wind tunnel and relaxes to a final state. We measure a relaxed final state with helical twist corresponding to the injected helicity and with $\lambda R = 3.15$, where the fields are minimum energy solutions to the Taylor state: $\nabla \times {\bf B} = \lambda {\bf B}$. The cylindrical copper boundary is baked and cleaned in a $He$ glow discharge to maintain excellent vacuum conditions. Typical plasma parameters are $T_i = 25~eV, T_e = 10~eV, n_e \le 10^{21}~m^{-3}, B = 0.25~T$. Merging experiments with plasma plumes injected from both ends are planned. Results of the merging studies will be presented if available.   

Noise-driven plasma flow in Hasegawa-Mima equation

The generation of intrinsic flows amid turbulence in hot plasmas is of great importance in the nuclear fusion experiments. Instead of working out plasma dynamics of all scales we concentrate on the evolution of large-scale fluctuations. Influence of the microscopic turbulence on the macroscopic dynamics is modeled as a noise. For pedagogical purposes, spontaneous appearance of the flow is studied with driven Hasegawa-Mima equation (HME) by external noise. If the noise has a parity-nonconserving (PNC) property, it is shown that an advective term associated with a uniform flow is inherently generated in the HME. Thus, the plasma transport appears in the form of both convective (non-diffusive) and enhanced diffusive flux. Numerical simulation of the noise driven HME of coarse scale is performed to confirm the result of the analytical theory and to verify the robustness of the noise-driven flow. The result will be discussed at the presentation.   

A JFNK-based implicit moment algorithm for self-consistent, multi-scale, plasma simulation

Jacobian-Free-Newton-Krylov method (JFNK) is an advanced non-linear algorithm that allows solution to a coupled systems of non-linear equations [1]. In [2] we have put forward a JFNK-based implicit, consistent, time integration algorithm and demonstrated it's ability to efficiently step over electron time scales, while retaining electron kinetic effects on the ion time scale. Here we extend this work by investigating a JFNK- based implicit-moments approach for the purpose of consistent scale-bridging between the fluid description and kinetic description in order to resolve the transition region. Our preliminary results, based on a reformulated Poisson's equation (RPE) [3], allows solution to the Vlasov-Poisson system for varying grid resolutions. In the limit of local coarse grid size (grid spacing large compared to Debye length), the RPE represents an electric field based on the moment system, while in the limit of local grid spacing resolving the Debye length, the RPE represents an electric field based on the standard Poisson equation. The technique allows smooth transition between the two regimes, consistently, in one simulation. [1] D.A. Knoll and D.E. Keyes,J. Comput. Phys., vol. 193 (2004) [2] W.T. Taitano, Masters Thesis, Nuclear Engineering, University of Idaho (2010) [3] R. Belaouar, N.Crouseilles and P. Degond,J. Sci. Comput., vol. 41 (2009)   

A Model for Molecular Hydrogen Ground State Rotational Populations in Kinetic Plasmas

A model has been developed to calculate the ground-state rotational populations of homonuclear diatomic molecules in kinetic gases, including the effects of electron-impact excitation, wall collisions, and gas feed rate. The equations are exact within the accuracy of the cross sections used and of the assumed equilibrating effect of wall collisions. It is found that the inflow of feed gas and equilibrating wall collisions can significantly affect the rotational distribution in competition with non-equilibrating electron-impact effects. The resulting steady-state rotational distributions are generally Boltzmann for N$>$2 with a rotational temperature between the wall and feed gas temperatures. The N=0,1,2 rotational level populations depend sensitively on the relative rates of electron-impact excitation versus wall collision and gas feed rates.   

An energy-conserving nonlinearly converged implicit particle-in-cell (PIC) algorithm

Conventional explicit PIC methods have to resolve short-time and small-scale plasma dynamics, suffering from very stringent temporal and spatial stability constrains. An implicit approach can in principle remove these restrictions and solve for long-time and large-scale dynamics. However, a large system of algebraic equations needs to be solved. In this work, we use a Jacobian-free Newton-Krylov method to invert an electrostatic Vlasov-Amp\`{e}re system. Unlike earlier attempts to implicit PIC, our approach self-consistently couples particles and fields, achieving simultaneous convergence on the full system. We show that the implicit formulation enables an exact total energy conservation principle. We have found that the accuracy of the simulation for a large timestep is crucially dependent on enforcing charge conservation and adequately resolving particle orbits. These are accomplished by particle subcycling and orbit averaging, with the energy conservation preserved. We present results of standard test cases such as Langmuir wave, Landau damping, two-stream instability and ion acoustic wave, compared with those from explicit simulations.   

A fully implicit Hall MHD algorithm based on the ion Ohm's law

Hall MHD is characterized by extreme hyperbolic numerical stiffness stemming from fast dispersive waves. Implicit algorithms are potentially advantageous, but of very difficult efficient implementation due to the condition numbers of associated matrices. Here, we explore the extension of a successful fully implicit, fully nonlinear algorithm for resistive MHD,\footnote{L. Chac\'on, {\em Phys. Plasmas}, {\bf 15} (2008)} based on Jacobian-free Newton-Krylov methods with physics-based preconditioning, to Hall MHD. Traditionally, Hall MHD has been formulated using the electron equation of motion (EOM) to determine the electric field in the plasma (the so-called Ohm's law). However, given that the center-of-mass EOM, the ion EOM, and the electron EOM are linearly dependent, one could equivalently employ the ion EOM as the Ohm's law for a Hall MHD formulation. While, from a physical standpoint, there is no {\em a priori} advantage for using one Ohm's law vs. the other, we argue in this poster that there is an algorithmic one. We will show that, while the electron Ohm's law prevents the extension of the resistive MHD preconditioning strategy to Hall MHD, an ion Ohm's law allows it trivially. Verification and performance numerical results on relevant problems will be presented.   

Particle algorithms as reductions of phase space

Particle-In-Cell (PIC) algorithm for simulation of plasmas has become a basic tool for investigating laser-plasma interactions, MHD phenomena, etc. Historically, there have been two ``branches'' of the PIC algorithm, energy conserving and momentum conserving. The momentum conserving algorithm has been more widely adopted so far, however, energy conserving algorithms (including implicit schemes) are being investigated actively. Many physics phenomena depend crucially on the energy conserving property; for example, wave-particle resonance is sensitive to the energy distribution of particles and thus some numerical artifacts, e.g., grid heating, lead to large variation of the simulation results. In this presentation we revisit the connection between momentum and energy conserving algorithms. We show that they essentially are different reductions from the same initial continuous model. We derive a hierarchy of particle algorithms with properties depending on the approximations made; we show what conditions lead to energy or momentum conservation, or how to derive particle algorithms, which conserve both energy and momentum. We present simulations substantiating the above theory.   

Modeling High-Voltage Breakdown for Single- and Multi-stack Dielectric Insulators

Breakdown from DC through microwave in dielectric-insulator configurations with one or more segments will be investigated using an improved 2D PIC simulation model [1]. The goal of this work is to develop the capability to predict and control the breakdown threshold under a wide range of parameters and geometries. Effects considered include secondary-emission [2], space-and surface-charge, ambient and desorbed gas, and surface-plasma generation for single- and multiple-layer [3] insulators with applied fields from DC to THz frequencies. Comparison between simulation and experiment will be conducted where possible. \\[4pt] [1] Taverniers, S., et al., ICOPS 2009 Proc., 2009.\\[0pt] [2] Vaughan, J.R.M., IEEE TED, Vol. 36, No. 9, 1989, pp.1963-1967.\\[0pt] [3] Leopold, J.G., et al., Proc. 2010 PMHVC.   

An Arbitrary Curvilinear Coordinate PIC Method

We demonstrate the feasibility of a new approach to the PIC method in which a grid generation strategy is coupled to a generalization of the PIC algorithm on the logical domain. Our grid generation strategy conforms to objects of arbitrary shape, eliminating such problems as stair-stepping along curved boundaries, and thus allows us to simulate complicated physical structures very accurately. We then use the mappings from the physical to the logical domain to run our PIC code. We have developed a semi-implicit particle mover for based on a generalization of the leapfrog method to arbitrary (including nonorthogonal) grids. We show our mover is symplectic and thus preserves phase-space area exactly. Extensive testing has shown that it also conserves energy to high accuracy. The electrostatic fields are solved on the logical domain using a preconditioned conjugate gradient method. We show test case results for several standard physics examples on multiple physical domains.   

Kinetic properties of the particle-in-cell simulation of a Lorentz plasma

The phenomenon of numerical thermalization in the standard particle-in-cell (PIC) simulation of Vlasov plasmas has been extensively studied at the early stage of its development [1] and was considered well understood. However, it was recently reported [2] that the well-established scaling law for the thermalization time could be compromised by the presence of an additional stochastic force acting on the particles, which is used to simulate collisional processes in a weakly ionized gas. In the present work, we are interested in the problem of electron-ion collisions in a fully ionized plasma. We investigate the thermal relaxation phenomenon in the PIC simulation of a Lorentz plasma in one dimension [3]. The pitch-angle scattering of the electrons by the stationary ion background is modeled by a Monte-Carlo algorithm. The numerical results obtained indicate that the thermal relaxation time is proportional to $N_{D}$ (the number of particles per Debye length), and not $N_{D}^{2}$ as in the standard PIC simulations. Our results appear to complement those found by the previous study [2]. \\[4pt] [1] C. K. Birdsall and A. B. Langdon, \textit{Plasma Physics via Computer Simulation} (McGraw-Hill, New York, 1985). \\[0pt] [2] M. M. Turner, Phys. of Plasmas \underline {13}, 033506 (2006). \\[0pt] [3] R. Shanny, J. M. Dawson, and J. M. Greene, Phys. of Fluids \underline {10}, 1281 (1967).   

Particle-in-cell Simulations with Charge-Conserving Current Deposition on Graphic Processing Units

We present an implementation of a fully relativistic, electromagnetic PIC code, with charge-conserving current deposition, on graphics processing units (GPUs) with NVIDIA's massively multithreaded computing architecture CUDA. A particle-based computation thread assignment was used in the current deposition scheme and write conflicts among the threads were resolved by a thread racing technique. A parallel particle sorting scheme was also developed and used. The implementation took advantage of fast on-chip shared memory. The 2D implementation achieved a one particle-step process time of 2.28 ns for cold plasma runs and 8.53 ns for extremely relativistic plasma runs on a GTX 280 graphic card, which were respectively 90 and 29 times faster than a single threaded state-of-art CPU code. A comparable speedup was also achieved for the 3D implementation.   

Controlling hot electrons by wave amplification and decay in compressing plasma

Through particle-in-cell simulations, it is demonstrated that a part of the mechanical energy of compressing plasma can be controllably transferred to hot electrons by preseeding the plasma with a Langmuir wave that is compressed together with the medium. Initially, a wave is undamped, so it is amplified under compression due to plasmon conservation. Later, as the phase velocity also changes under compression, Landau damping can be induced at a predetermined instant of time. Then the wave energy is transferred to hot electrons, shaping the particle distribution over a controllable velocity interval, which is wider than that in stationary plasma. For multiple excited modes, the transition between the adiabatic amplification and the damping occurs at different moments; thus, individual modes can deposit their energy independently, each at its own prescribed time.   

A Fully-Implicit, Ion-Electron, Vlasov-Poisson Algorithm

The Jacobian-Free-Newton-Krylov method (JFNK) is an advanced non- linear alogorithm that allows solution to a coupled systems of non-linear equations [1]. We put forth a new JFNK-based implicit plasma simulation algorithm. We have studied this algorithm within the context of a two-species Vlasov-Poisson system where the Vlasov equations are solved in an Eulerian frame [2]. We have investigated the route of non-linear-elimination/kinetic- enslavement to reduce the size of block Jacobian matrix in order to solve the field-kinetic system implicitly. The non-linear- elimination/kinetic-enslavement technique allows reduction in the size of non-linear system but still retains high order temporal accuracy and strong non-linear coupling. Our new algorithm make implicit time-dependent, coupled, field-kinetic systems more attractive. As will be shown, a fully implicit run was able to achieve 22 times speed-up compared to the explicit run for our ion-acoustic-showckwave simulation [2].\\[4pt] [1] D.A. Knoll and D.E. Keyes, {\em J. Comput. Phys.} vol. 193 (2004)\\[0pt] [2] W.T. Taitano, Masters Thesis, Nuclear Engineering, University of Idaho (2010)   

Performance evaluation of relativistic electromagnetic particle in cell algorithms in CPU and GPU

The complexity of the phenomena involved in several relevante plasma physics scenarios, where highly nonlinear and kinetic processes dominate, makes purely theoretical descriptions impossible. Further understanding of these scenarios requires detailed numerical modelling, but fully relativistic particle-in-cell codes such as OSIRIS [1] are computationally intensive. Recently graphics processing units (GPUs), offering peak theoretical performances of $\sim $ 1 TFlop/s for general purpose calculations, have received significant attention as an atractive alternative to CPUs for plasma modeling. In this work we perform a detailed performance evaluation of an electromagnetic fully relativistic particle in cell code in both GPUs and CPUs for production runs, focusing on the relative strengths and weaknesses of both architectures for all major algorithm sections, including particle push, current deposition, field solver, and also diagnostics. \\[4pt] [1] R. A. Fonseca et al., LNCS 2331, 342, (2002)   

Multidimensional effects on relativistic electrons in an oblique shock wave

Particle simulations have revealed [1] that prompt electron acceleration to ultrarelativistic energies can occur in a magnetosonic shock wave propagating obliquely to an external magnetic field with the propagation speed of the shock wave $v_{\rm sh}$ close to $c \cos \theta$, where $\theta$ is the propagation angle of the shock wave. In such a wave, some electrons are reflected near the end of the main pulse of the shock wave, get trapped and are energized in the main pulse region. Once electrons are trapped, they cannot readily escape from the wave because of the electromagnetic fields they themselves produce [2]. Although the extensive studies have examined electron trapping and acceleration by a shock wave, the theory and simulations were one-dimensional. In this study, we investigate multi-dimensional effects using two-dimensional (two spatial coordinates and three velocities), particle simulations. It is found that some electrons can be detrapped from the main pulse because of magnetic fluctuations propagating along the shock front. It is furthermore demonstrated that after detrapping, some electrons can be accelerated to much higher energies because they can enter and exit the shock wave several times as a result of their gyromotions. The generation of magnetic fluctuations due to whistler waves is also discussed. \\[0pt] [1] N. Bessho and Y. Ohsawa, Phys.\ Plasmas {\bf 6} 3076 (1999).\\[0pt] [2] M. Toida and K. Shikii, Phys.\ Plasmas {\bf 16} 112305 (2009).   

Kinetic effects and their role on the properties of magnetized shocks

The formation and generation of shocks is a topic of broad interest in many fields of physics, but the role of the kinetics effects and the properties of the particle distribution across the shock front have not been explored in detail. Using particle-in-cell simulations to study electron-positron magnetized collisionless shocks, generated from a reflecting wall in the presence of an initially perpendicular magnetic field, we explore the features of the particle distribution in the upstream, downstream, and shock transition region. In particular, we identify deviations from a Maxwellian distribution. The impact of these deviations on the shock properties (shock velocity, jump conditions) are also examined analytically. The relevance of these results for astrophysical shocks is also discussed.   

Strong Radiation Driven Shocks in Cassio

In this paper we present results of a sensitivity study for strong shocks in the HED code Cassio. Cassio is an Eularian radiation-hydrodynamics code being developed at Los Alamos to study HED physics. The radiation transport cna be eitehr grey diffusion, multi-group diffusion or IMC. The materials models include three-temperature radiation, electron and ions and wither analytic of tabular EOS. We examine the behavior of strong shocks and explore not only the hydrodynamic convergence behavior but also the effect of other physics modeling choices on shock evolution.   

Ion Collection by a Sphere in a Magnetized Collisional Plasma

Ion collection by dust grains and probes in plasmas with a neutral background are of relevance to both space and terrestrial plasmas. It has recently been shown that moderate charge-exchange collisionality can enhance the ion current to a collecting sphere beyond that given by orbital motion limited (OML) theory. In the collisionless case a background magnetic field reduces ion collection, but how a magnetic field affects the collisional current enhancement remains unknown. The hybrid particle-in-cell (PIC) code sceptic3D is used to study collisional current enhancement in the presence of a magnetic field. Figures are presented showing the dependence of the collected current on both magnetic field strength and collisionality, and illustrative examples are used to provide physical insight into the magnetic field and collisional effects on ion collection. Further, a preview is given of future work on the fully 3D problem of ion collection in drifting magnetized plasmas.   

High Frequency Input Admittance of Continuum Regime Langmuir Probe

Measurement of probe complex input impedance, or admittance, has been suggested as a way to increase the amount of information obtained from Langmuir probes [1]. In this poster, a spherical probe immersed in a weakly ionized homogeneous plasma is considered in the regime in which the probe radius is small compard with the Debye length. When the magnitude of the probe potential exceeds the plasma temperature in volts, the low frequency AC input admittance of the negatively biaed probe is given by the ion conductivity times 4$\pi$ times the probe radius plus the admittance associated with the probe vacuum capacitance. The real part of the input admittance falls rapidly when the drive frequency exceeds the reciprocal of the time it takes ions to diffuse a distance on the order of the probe radius. An analytic solution to this problem found by applying the method of matched asymptotic expansions to the describing differential equation is given. Probe circuit models and boundary conditions are reviewed.\\[4pt] [1] D.N. Walker, R.F. Fernsler, D.D. Blackwell, and W.E. Amatucci, Phys. Plasmas 15, 123506 (2008).   

Analysis of plasma interaction with a rough surface

Over the years, a lot of research has been done in an attempt to understand the physics of plasma-wall interaction, in particular the role of sheath -- a boundary between the hot plasma and surface materials, through which the majority of the interactions are taking place. In relatively recent years it became clear that the quality of the wall's surface tremendously influences the physics of plasma-wall interactions. In particular the wall's roughness is thought of playing an important role in the formation of ``hot spots'', sputtering, erosion, arching, thermionic emissions, which have been experimentally observed for years. Present work investigates the effects of the surface roughness on the plasma-wall interactions. Collisionless plasma immersed in magnetic field is interacting with a non-flat surface, with the roughness parameters H and W varying relative to the thermal ion gyro-radius. Steady-state particle and field profiles are analyzed and the scaling of penetration length is discussed.   

The effect of magnetic flux expansion on plasma sheath/presheath

Significant magnetic flux expansion can help spread the plasma heat load over a greater area of tokamak divertor plate. It also appears in the expander of an axisymmetric magnetic mirror, which for its favorable magnetic curvature, helps stabilize the global interchange modes in the central cell. For a weakly collisional plasma, the flux expansion introduces a mirror force accelerating the electron and ion flows downstream, which likely induces an ambipolar parallel electric field. This is in addition to the conventional presheath electric field which accelerates the ion to satisfy the Bohm criteria near the wall. We perform kinetic simulations in two spatial and three velocity dimensions to understand (1) the role of mirror force in the parallel and perpendicular thermal energy transfer, and (2) the combined role of mirror-acceleration and parallel electric field on the parallel flow acceleration in the presheath and sheath. The detailed sheath/presheath plasma profiles and the ambipolar electric field will be investigated. Worked supported by OFES.   

Sheath dynamics in a fusion plasma with oblique magnetic fields

To understand the plasma/surface interaction, one must know how plasma sheath modifies the characteristics of the upstream plasma as it approaches the wall surface. This is not only important to decipher the wall response to the ion bombardment flux, but also necessary for quantifying inward impurity transport and assessing the fate of dust particulates anticipated in a tokamak reactor. The magnetic field typically intercepts the tokamak wall at an oblique angle. Here we present a systematic, kinetic simulation study on how the inclination angle of the magnetic field affects the sheath plasma and its dynamics in both the high-recycling (collisional) and low-recycling (nearly collisionless) regimes. Specifically we will show its effect on wall potential and plasma potential in the sheath and presheath, the characteristics of the normal-to-the-wall and parallel-to-the-B-field particle and energy flux in the sheath/presheath region. The new findings provide an interesting comparison with the standard Chodura model. The implication on dust motion and survivability in a tokamak reactor will be explained, along with the implied constraint on divertor designs.   

Electron heat transport at the interface between hot and cold plasmas

In high energy density plasma experiments where compression is used to form a central hot target plasma, an interface between the hot but low density and cold but dense plasmas often appears. Evaluation of energy transport, especially electron thermal conduction, across this interface, if it is sufficiently sharp, could be complicated by an electric field localized about the boundary between the plasmas. The field emerges through a mechanism, which is somewhat similar to that of the sheath formation and due to the hot electrons traveling at much greater velocities than their cold counterparts. Such a strong electric field can further modify the distribution function of electrons and therefore their thermal conductivity. To calculate this field we treat hot electrons kinetically, assuming that their mean free path is greater than the interface width. On the other hand, the cold electron bulk is collisional and therefore described by usual fluid equations. By including the sheath-like effects into consideration, we are then able to find a more appropriate expression for the rate of the heat exchange between the hot and cold plasmas.   

Low-temperature control of plasma-assisted nanofiber heating

Three model, sheath, growth, and heat models are coupled to investigate the direct dependencies of the carbon nanofiber growth and heating on the plasma parameters in a low-temperature plasma. Using the models, the effects of variation in the plasma sheath parameters and substrate potential on the plasma heating effects in catalyzed growth of carbon nanofiber have been investigated. Numerical results have shown that variations in some parameters such as the electron temperature, electron number density, and substrate potential, which change the sheath width, mainly affect the growth rate and carbon nanofiber heating at low catalyst temperatures and the other parameters such as gas pressure and the ratio of the hydrocarbon/etching gas density to total gas density, change the carbon nanofiber growth at all temperatures and substantially increases the temperature of catalyst particle, attached to carbon nanofiber end, respect to the temperature at substrate interface with substrate-holding platform. These results are also consistent with the available experimental results of the selectively control of plasma-assisted nanostructure heating and the catalyzed growth of some high-aspect-ratio structures.   

Sheath instability around an electron-emitting object

In this work, we analyze the stability of the electrostatic sheath of an electron emitting object, for sheath profiles characterized by a potential barrier. We show that such profiles can be unstable to the Rayleigh-Taylor instability, driven by the favorable combination of the density gradient (of the emitted electrons) and electric field in the sheath [1]. We present an analytical theory based on a simplified fluid model which elucidates various aspects of the instability. We also present nonlinear results from a kinetic PIC code, showing that this instability is associated with periodic oscillations of the sheath profiles. [1] G.L. Delzanno, G. Lapenta, Sheath stability of an electron emitting, positively charged wall, in preparation (2010).   

Novel Electromagnetic Propulsion System Using High-Density Helicon Plasma

We have been conducting an experimental study on advanced electromagnetic propulsion system using high-density plasma, applying the helicon waves for efficient plasma production and the rotating magnetic field (RMF) for plasma acceleration via Lorentz force induced by a nonlinear azimuthal current [1,2]. Since the proposed scheme is completely electrodeless, the issue of electrodes erosion is absent, hence a very long operation lifetime can be expected. Using the Large Mirror Device (LMD) installed at Kyushu University [3], the electron density and the ion flow velocity are measured by Langmuir and Mach probes, respectively, with and without applying the RMF. The penetration conditions of the RMF into the plasma are estimated by using the magnetic probe. The initial results will be presented in detail.\\[4pt] [1] M. Inomoto, IEEJ Trans. FM. \textbf{128}, 319 (2008).\\[0pt] [2] I. R. Jones, \textit{et al}., J. Plasma Phys. \textbf{26}, 441 (1981).\\[0pt] [3] S. Shinohara, \textit{et al}., Jpn. J. Appl. Phys. \textbf{35}, 4503 (1996).   

Electron Transport Dominated Regimes in Alcator C-Mod

In ohmically heated low density plasmas where $\tau _{E} \quad \propto $ n$_{e}$, the so-called neo-Alcator regime, TRANSP results indicate that $\chi _{i}<< \quad \chi _{e}$, while nonlinear gyrokinetic analysis for the measured profiles predicts the opposite inequality [1]. This regime is of great interest for transport studies since Ti $<$ Te, and the electron and ion transport channels can be separated and studied separately. At the same time, measurements of turbulent fluctuations with Phase Contrast Imaging diagnostic (PCI) indicated reasonable agreement with GYRO predictions at frequencies 80-250 kHz, corresponding to core ITG turbulence. The turbulent spectrum at lower frequencies could not be identified since the PCI technique does not allow separation of the core plasma fluctuations from those at the edge. Here we present measurements and analysis from a more extensive set of plasma regimes than previously. Of particular current interest is the role of electron drift wave turbulence driven by ohmic electron drift, U [2], since in these low density regimes U/C$_{s} \quad \le $ 6, and experimentally we find that the global confinement $\tau _{E}$ $\propto $ C$_{s}$/U where C$_{s}$ = (T$_{e}$/m$_{i})^{1/2}$. [1] L. Lin, Invited talk, APS-DPP, 11, 2009, Atlanta, GA. [2] C.J. Lee, P. Diamond, M. Porkolab, presented at TTF workshop, 2010.   

Experimental study of plasma shaping effect in Alcator C-Mod Ohmic low confinement regime*

Previous studies on TCV tokamak suggest that shaping parameters ($\kappa $, $\delta )$ could play a role in the plasma confinement. This study presents the experimental observations in Alcator C-Mod Ohmic L-mode plasmas at different line averaged densities (0.4$\sim $1.0 n20) as the shaping parameters being scanned. The shape of T$_{e}$, T$_{i,}$ n$_{e}$ profiles measured from Thomson scattering, ECE and X-ray spectroscopy diagnostics are compared to extract the degree of profile similarities in these discharges. Sawtooth activities (intensity, period, inversion radius) are characterized from ECE measurements in various shaping configurations. Spectra of plasma fluctuations are monitored by PCI, O-mode reflectometers and magnetic probes. Local particle and heat transport are calculated from 2 dimensional power balance analysis code TRANSP using experimental measurements and to be compared with global confinement scaling and anomalous transport models (e.g. TGLF). Perturbative transport studies will be explored in the future studies. *Supported by USDoE award DE-FC02-99ER54512   

Developing predictive capability for the H-mode pedestal: Experimental contributions from Alcator C-Mod

Experiments on Alcator C-Mod characterize the edge pedestal in several high confinement regimes, as part of a community experimental and theoretical effort to improve predictive capability for the pedestal. Pedestal structure in both transiently evolving and stationary enhanced D$_\alpha$ H-modes is studied and examined alongside edge fluctuations ({\it e.g.} quasi-coherent modes), allowing us to seek evidence for transport-driven mechanisms limiting pedestal width and gradients. The pedestal structure in H-modes with edge-localized modes (ELMs) is likely to be governed both by transport and by intermittent ELM relaxation. ELMy H-modes are diagnosed and used to test directly models for pedestal height/width, {\it e.g.} EPED. Pedestal profiles, fluctuations and ELM activity in these H-mode regimes are compared to those in I-mode, in which a temperature and a pressure pedestal are maintained in the absence of a particle barrier ({\it i.e.} edge $L_n/L_T\gg 1$), and which can provide additional insight into physics governing pedestal formation and structure.   

GYRO simulations of turbulently driven 'intrinsic rotation' in C-mod plasmas

In some C-Mod plasmas with no externally applied torque, the radial profile of the toroidal rotation speed indicates that ``intrinsic rotation'' is generated in the plasma core. GYRO simulations of L-Mode and I-mode plasmas are used to learn if the turbulent transport of toroidal angular momentum might cause intrinsic rotation by removing angular momentum, thereby spinning up the plasma in the opposite direction. Two of the three plasmas have strong radial gradients in the measured toroidal rotation; the third is a ``control'' case. In GYRO simulations there is an inward flow of momentum when the input has no radial gradient of the toroidal rotation speed. We estimate the gradient that GYRO 'predicts' by varying the input gradient until we bracket the target state of zero momentum flux. The sign of the rotation speed gradient predicted by GYRO agrees with experiment, and the magnitude is generally within a factor of two - GYRO tending to be lower, but not everywhere. For the ``control'' case GYRO predicts an intrinsic rotation gradient a factor of 3-5 smaller than for the other cases.   

Momentum transport calculations on Alcator C-Mod in the L-H mode transition

Intrinsic rotation and momentum transport during the L-H transition has been the topic of great interest over the last few years as a possible means of controlling plasma instabilities. Alcator C-Mod is uniquely situated to study these transitions at ITER like densities and magnetic fields. During the L-H mode transition, rotation measurements have been made from the core to approximately r/a $\sim $0.7, and the location of the source of momentum in the plasma was found to match the location of the largest pressure gradient difference between the L and the H-mode. Further refinements of that research are presented here with time and space dependent diffusive and convective transport values and analysis comparing total pressure gradient to temperature gradient values. Power balance and gyrokinetic code calculation results on these transitions are shown as well.   

Comparison of impurity transport in Alcator C-Mod with fluid models of drift wave turbulence

Using a new theory, we investigate the influence of the impurity density and impurity density gradient on turbulent particle transport. Heavy impurities (argon is the example here) appear to have the strongest influence while light impurities (boron, for example) may simply transport as passive tracers when in the presence of a significant quantity of heavy impurity. The theory describes how collisional and trapped electron drift wave dynamics are modified by impurities and how the turbulence transports the impurities in a background hydrogenic plasma. The collisional regime is described using a Hasegawa-Wakatani system of equations. The trapped electron mode is modeled with a generalized form of the Terry-Horton system of equations. Measured positive and negative impurity gradients can be predicted, but new experiments will be required to verify the implications of the theory.   

In-situ wavelength calibration and temperature control for the C-Mod high-resolution x-ray crystal imaging spectrometer

An x-ray crystal imaging spectrometer with high spectral and spatial resolution is currently being used on Alcator C-Mod to infer time histories of temperature and velocity profiles. An in-situ wavelength calibration using a 1 $\mu$m palladium filter in between the crystal and the detectors of choice is being proposed as a natural wavelength-marker using the transmission changes across the L-II and L-III edges at 3722.9 mA and 3907.1 mA, respectively. Recent results also indicate that the crystal temperature should be kept constant within a fraction of a degree since the thermal expansion of the quartz crystal will change the interplanar ($2d$) spacing and introduce fictitious velocity measurements of several km/s. A detailed temperature scan indicates a thermal expansion coefficient ($\alpha_{\perp}$) of $13.5\times10^{-6}$ $/^{\circ}$C and thus a false Doppler shift of $4.05\cdot\Delta T[^{\circ}$C$]$ km/s.   

Inner-wall Impurity Density Measurements on Alcator C-Mod

Recent findings on Alcator C-Mod imply a poloidal impurity density asymmetry in the pedestal region, inferred from boron ($B^{5+}$) velocity measurements at the inner- and outer-wall combined with neoclassical transport theory. In an effort to confirm these findings, the direct measurement of the boron density was made at the inner-wall pedestal using simultaneous spectroscopic views of boron charge exchange recombination spectroscopy (CXRS) ($B^{4+},\, n=7-6,\,\lambda=494.467nm$) and Balmer-$\alpha$ ($D^{0+},\, n=3-2,\,\lambda=656.6nm$). Since the inner-wall CXRS measurement utilizes a deuterium gas puff as the source of neutrals to induce charge exchange, detailed modeling is required in order to calculate the neutral density profile from the Balmer-$\alpha$ measurement. Additionally, due to the low interaction energies the $B^{5+}+D^{0+}(n=2)\rightarrow B^{*(4+)}+D^{1+}$ is the dominant boron CX process, so a collisional-radiative model is required to calculate the $n=2$ deuterium density from the $n=3$ density derived from the Balmer-$\alpha$ measurement. The radial shape of the resulting boron density profile agrees with the profile predicted by the impurity density asymmetry. Supported by USDoE award DE-FC02-99ER54512.   

Correlation Reflectometry Results and Analysis on Alcator C-Mod

A swept frequency O-mode reflectometry system has been operational on the Alcator C-Mod tokamak since the 2009 campaign. The system has a midplane view of the plasma from the low field side and covers the frequency range of 112GHz-140GHz, corresponding to electron density cutoffs of 1.56-2.43 $[10^{20}m^{-3}]$. In conjunction with two fixed frequency O-mode reflectometry channels at 112GHz and 140GHz, it is possible to determine reflectometry radial decorrelation lengths in the plasma. These lengths can be mapped to the turbulent radial decorrelation lengths with the use of a 2-D synthetic diagnostic code[1]. Results and analysis will be presented for density fluctuations in the radial region inside r/a $\sim$ 0.7. \\[4pt] [1] E.J. Valeo, G.J. Kramer, R. Nazikian, Plasma Phys. Control. Fus. 44 (2002) L1   

Analysis tools for turbulence studies at Alcator C-Mod

A new suite of analysis tools written in IDL is being developed to support experimental investigation of turbulence at Alcator C-Mod. The tools include GUIs for spectral analysis (coherence, cross-phase and bicoherence) and characteristic frequency calculations. A user-friendly interface for the GENRAY code, to facilitate in-between shot ray-tracing analysis, is also being developed. The spectral analysis tool is being used to analyze data from existing edge turbulence diagnostics, such as the O-mode correlation reflectometer and Gas Puff Imaging, during I-mode, ITB and EDA H-mode plasmas. GENRAY and the characteristic frequency tool are being used to study diagnostic accessibility limits set by wave propagation and refraction for X-mode Doppler Backscattering and Correlation Electron Cyclotron Emission (CECE) systems that are being planned for core turbulence studies at Alcator C-Mod.   

Correlation ECE and Doppler Backscattering Diagnostics for Alcator C-Mod

A Correlation Electron Cyclotron Emission (CECE) diagnostic and an X-mode reflectometer system are being developed to measure long wavelength ($k_{\theta}\rho_s$) core electron temperature fluctuations and density fluctuations, respectively, at Alcator C-Mod. These new diagnostics will allow for detailed two-field core turbulence measurements and validation studies. Adjustable optics will allow the reflectometer to be configured as a Doppler backscattering system. Global, nonlinear gyrokinetic turbulence simulations (GYRO) and synthetic diagnostics are used to model the diagnostics' expected responses to turbulence in a variety of operating regimes. The challenges associated with the high frequency systems required for core turbulence studies at C-Mod and the feasibility of combining these complementary diagnostics into a single transmission system will be assessed. Accessibility limits, expected wavenumber sensitivity and waveguide/antennae configurations are discussed.   

Measurements of plasma sheath heat flux in the Alcator C-Mod divertor

Heat flux is one of the most important parameters controlling the lifetime of first-wall components in fusion experiments and reactors. The sheath heat flux coefficient $\left(\gamma\right)$ is a parameter relating heat flux (from a plasma to a material surface) to the electron temperature and ion saturation current. Being such a simple expression for a kinetic process, it is of great interest to plasma edge fluid modelers. Under the assumptions of equal ion and electron temperatures, no secondary electron emission, and no net current to the surface the value of $\gamma$ is approximately 7 [1]. Alcator C-Mod provides a unique opportunity among today's experiments to measure reactor-relevant heat fluxes (100's of MW/m$^2$ parallel to the magnetic field) in reactor-like divertor geometry. Motivated by the DoE 2010 joint milestone to measure heat flux footprints, the lower outer divertor of Alcator has been instrumented with a suite of Langmuir probes, novel surface thermocouples, and calorimeters in tiles purposefully ramped to eliminate shadowing; all within view of an IR camera. Initial results indicate that the experimentally inferred values of $\gamma$ are found to agree with simple theory in the sheath limited regime and diverges to lower values as the density increases.   

Kinetic studies of divertor heat fluxes in Alcator C-Mod

The kinetic XGC0 code [C.S. Chang et al, Phys. Plasmas 11 (2004) 2649] is used to model the H- mode pedestal and SOL regions in Alcator C-Mod discharges. The self-consistent simulations in this study include kinetic neoclassical physics and anomalous transport models along with the ExB flow shear effects. The heat fluxes on the divertor plates are computed and the fluxes to the outer plate are compared with experimental observations. The dynamics of the radial electric field near the separatrix and in the SOL region are computed with the XGC0 code, and the effect of the anomalous transport on the heat fluxes in the SOL region is investigated. In particular, the particle and thermal diffusivities obtained in the analysis mode are compared with predictions from the theory-based anomalous transport models such as MMM95 [G. Bateman et al, Phys. Plasmas 5 (1998) 1793] and DRIBM [T. Rafiq et al, to appear in Phys. Plasmas (2010)]. It is found that there is a notable pinch effect in the inner separatrix region. Possible physical mechanisms for the particle and thermal pinches are discussed.   

MHD activity during the pre-thermal quench phase of gas jet mitigated disruptions on Alcator C-Mod

Using multiple AXUV diode arrays on Alcator C-Mod, radiated energy during gas jet mitigated disruptions has been shown to be toroidally asymmetric, with the ratio of energy on opposite- looking diode arrays ranging from 1.1 to 2.6 [Reinke et al., \emph{Bull. Am. Phys. Soc.} {\bf 54}(15), UO4.00003]. Asymmetry of this magnitude during mitigated disruptions on ITER would lead to melting of the beryllium first wall [M. Sugihara et al., \emph{Nucl. Fus.} {\bf 47}(4), 337--352]. Using a toroidal array of poloidal field pickup coils, there is shown to be a link between the growth rates of low-n MHD modes during the pre- thermal quench (pre-TQ) phase of the mitigated disruption and the radiation asymmetry during the TQ. This is also evidence for the role of MHD activity in triggering the TQ. The implications of this correlation for reducing the radiation asymmetry are discussed.   

Stimulation of MHD Modes in Alcator C-Mod

Active MHD (AMHD) spectroscopy involves stimulating MHD modes by external means to study the modes or diagnose the plasma. In many AMHD experiments, drive frequency is swept across a $100-200$ kHz range in which modes are expected; this allows for robust techniques to detect resonant poles in the presence of direct pickup from the driver. However, there is flexibility in the drive mechanism. At Alcator, we have employed a parametric excitation method, amplitude-modulating the ICRF wave (80 MHz) with envelope signals in the AE frequency range (100's kHz). This builds off the ICRF beat technique used in JET in 1996 and ASDEX Upgrade in 2006, but is unique in its use of a single antenna, improving coherence. An advantage of this approach is its ability to couple to the plasma core. It also has high input power, though efficiency is limited by the Manley-Rowe relations. In initial experiments, we excited weak, stable modes in the toroidal Alfv\'{e}n eigenmode band gap. We plan to explore this and other methods for coupling to various MHD-like modes, especially C-Mod's Quasi Coherent mode.   

Progress on the C-Mod FIR Polarimeter System

A poloidally viewing FIR polarimetry diagnostic is being developed for the Alcator C-Mod Tokamak. The primary diagnostic components are a two-wave FIR laser at 117.73 microns and newly developed detectors whose performance characteristics will be described. Faraday rotation will be used both to refine the q-profile measurement by adding constraints to EFIT , and to study density and magnetic field fluctuations. A three-chord system has been installed, one chord of which is being tested during the FY10 C-Mod campaign. The FIR laser source is affected by both stray magnetic fields and mechanical vibrations present in the experimental cell thereby impacting the measurement. Methods developed to mitigate and correct for these effects will be discussed. Initial Faraday data will be compared with expectations from numerical simulation.   

Detection and application of Doppler and motional Stark features in the DNB emission spectrum in the high magnetic field of the Alcator C-Mod tokamak

The spectral region in the vicinity of the D$_{\alpha }$ line is to be studied with a high resolution spectrometer. This region contains spectral lines emitted by atoms in the diagnostic neutral beam (DNB) and plasma atoms and ions. Spectrally isolated emission serves as a measure of the properties of emitting particles and surrounding medium. In C-Mod, the main obstacle for application of these techniques is that at high magnetic fields (5-8T) the spectral separation due to motional Stark splitting is similar to the spectral Doppler shifts of lines emitted by DNB atoms of energies 50, 25 and 18 keV. This results in partial blending of observed spectral lines and consequent masking of Doppler or Stark effect. High spectral resolution ($\sim $ 1A) and complex spectral fitting technique are needed for isolation of different components. Results of this work will be used in the further development of Beam Emission Spectroscopy (BES) system installed at C-Mod and in support for the current Motional Stark Effect (MSE) diagnostic.   

Status and recent MSE results on Alcator C-Mod

Thermal birefringence within in-vessel lenses has been identified as the cause of a spurious drift in the calibration of the MSE diagnostic on Alcator C-Mod. Significant upgrades have been implemented to reduce thermal gradients in the in-vessel components including a gold-plated radiative heat shield and a unique lens mount to thermally isolate the MSE periscope. Experimental results on the effectiveness of these upgrades are presented. An automated calibration system has been designed and constructed to enable a thorough invessel calibration of MSE during brief up-to-air periods. This system was utilized during the Spring 2010 maintenance period to perform multiple parameter scans, including 2D scans of optical loss across the objective lens and 3D scans (2D position and angle-of-incidence) across the PEMs. Based on these measurements, the optical loss due to vignetting in the MSE optics is estimated at 20\%. An overview of the current MSE system performance, opportunities for improvements and MSE q-profile measurements from recent current drive experiments are presented.   

Design considerations for real-time MSE background subtraction on Alcator C-Mod

MSE measurements of the q-profile in Alcator C-Mod are difficult at high density and in H-mode plasmas due to increased partially-polarized background light in the MSE wavelength range. This background is highly variable both spatially and temporally, making traditional beam-on-beam-off background interpolation insufficient. A real-time background subtraction is proposed: spectral studies [See poster 18, Bespamyatnov] have identified a spectral region free of impurity lines adjacent to the MSE measurement region where the polarized background signal can be measured as a proxy for the MSE background signal. A polychromater design that utilizes multiple tunable narrow bandpass filters to simultaneously measure the MSE signal and partially polarized background is presented. Issues pertaining to design and calibration of this instrument and its relevance to diagnostic challenges on ITER are discussed.   

Analysis of Lower Hybrid Current Drive Modification of Sawtooth in Alcator C-Mod

Experiments were performed in Alcator C-Mod, where the onset time for sawteeth was delayed significantly (up to 0.5 s) relative to ohmically heated plasmas, through the injection of off-axis LH current drive power [1]. The LH driven current density profiles in these experiments are being simulated using a ray tracing code (GENRAY) and Fokker Planck code (CQL3D) [2] in order to ascertain the consistency of the simulated current density profiles with the requirements for sawtooth stabilization. Comparisons of simulated LHRF-generated hard x-ray spectra with experimental measurements will be shown. We will also discuss time dependent simulations of these experiments using an advanced parallel computing framework [3]. \\[4pt] [1] C. E. Kessel \textit{et al}, Bull. of the Am. Phys. Soc. \textbf{53}, Poster PP6.00074 (2008). \\[0pt] [2] R. W. Harvey and M. G. McCoy, Proc. of the IAEA Tech. Comm. Mtg on Sim. and Mod. of Therm. Plasmas, Montreal, Canada (1992). \\[0pt] [3] D. Batchelor \textit{et al}, J. of Phys. Conf. Series \textbf{125}, 012039 (2008).   

Investigation of ion toroidal rotation induced by Lower Hybrid waves in Alcator C-Mod using integrated numerical codes

Ion toroidal rotation in the counter current direction has been measured in C-Mod during lower hybrid (LH) RF power injection. Toroidal momentum input from the LH waves determines the initial increase of the counter current ion toroidal rotation. Due to the fast build up time of the plateau ($<$ 1msec), the electron distribution function is assumed to be in steady state. We calculate the toroidal momentum input of LH wave to electrons by iterating a full wave code (TORIC-LH) with a Fokker Plank code (CQL3D) to obtain a self consistent steady state electron distribution function. On the longer time scale, comparable to the transport time ($\sim$100msec), ion rotation is changing due to the constant momentum transfer from electrons to ions and the radial flux of ion toroidal momentum by Reynolds stress and collisional viscosity. We suggest a way to evaluate the viscosity terms for the low flow level rotation bya modifielectrostatic gyrokinetic code.   

The development of a 4.6 GHz reflectometer in Alcator C-Mod

The development of a 4.6 GHz reflectometer system to detect LH waves in Alcator C-Mod plasmas is presented together with preliminary experimental results. Hard X-ray data of the 2008 Alcator C-Mod campaign indicated an anomalous decrease of photon generation in high density plasmas during LHCD experiments, suggesting LH waves did not propagate inside the plasma separatrix. Calculations and simulations show that the nonlinear interaction between a reflectometer probe beam and LH waves in the region where wave matching conditions are satisfied generates back-scattered, frequency shifted signals. To measure these signals, the high frequency stages of existing 60 GHz and 75 GHz O-mode reflectometer channels were modified, and intermediate frequency and power detecting stages have been added. The ray tracing code, GENRAY, and full wave simulations, e.g., TORIC and LHEAF, will be used to optimize plasma conditions for maximum response of frequency shifted signals. Both 1D and 2D transient analysis using the finite element solver, COMSOL, is also presented. Supported by USDoE award DE-FC02-99ER54512.   

Recent results from lower hybrid current drive experiments on Alcator C-Mod

A novel coupler designed to optimize LHRF power delivered to Alcator C-Mod plasmas is now in operation. New diagnostics have also been added to better understand the conversion of waveguide modes in the grill antenna to slow LH waves, and the penetration and damping of the waves as they pass beyond the separatrix. These include a set of 32 RF probes located near the plasma-grill interface, an X-mode reflectometer for measuring the density profile near the grill, and a two-frequency O-mode reflectometer for detecting LH waves beyond the separatrix via Bragg scattering. The latter, supplemented by X-ray and cyclotron emission profiles, is expected to be helpful in understanding the disparity in measured current drive efficiency at high density relative to predictions from ray-tracing and full-wave simulations. This paper surveys the results obtained with the new coupler, including coupling and current drive efficiency, plasma rotation and comparison with results of simulations.   

High Density Scrape-Off-Layer Absorption of Lower Hybrid Waves on the Alcator C-Mod Tokamak

The goal of the LHCD system on Alcator C-Mod is to investigate current profile control under plasma conditions relevant to burning plasma experiments. Bremsstrahlung from fast electrons in the core plasma drops suddenly at a density below the density limit previously observed on other tokamaks ($\omega/\omega_{LH} \sim 2$). Electric currents in the SOL between the inner and outer divertors increase across the same density range that the core bremsstrahlung emission drops while SOL Lyman-$\alpha$ emissivity profiles shift outward, indicating absorption of LH waves in the SOL. The experimental x-ray data are compared to a ray tracing/Fokker-Planck model including collisional absorption in the SOL, which shows good agreement with the experiment across a wide range of densities. The model identifies possible strategies to circumvent the density limit such as increasing the temperature and decreasing the density in the SOL.   

Absorption of lower hybrid waves in the scrape off layer and possible implications for ITER

The goal of the lower hybrid current drive (LHCD) system on Alcator C-Mod is to investigate current profile control at ITER relevant values of magnetic field, plasma density, and LHCD frequency. Experimental observations of an LHCD density limit show that current drive in C-Mod drops suddenly at a density near the upper range expected in ITER steady-state scenarios. Measurements on C-Mod indicate that the LH power is deposited in the SOL at high density. These data are compared to a model including collisional absorption in the SOL, which shows good agreement across a wide range of densities. These results show that strong absorption of LH waves in the SOL is possible and must be considered in simulations of LHCD at high density. Simulations of LHCD on ITER with several possible SOL profiles will be presented. Supported by USDoE awards DE-FC02-99ER54512 and DE-AC02-09CH11466.   

Full wave modeling of off-axis LHCD using the LHEAF code on Alcator C-Mod

We will present LHEAF full wave simulation results of Alcator C-Mod LHCD experiments. LHEAF is a full wave simulation code for LHCD based on the finite element method, which allows simulations of the hot core plasma, the SOL plasma, and the launcher in a seamless manner. The LHEAF Fokker-Planck module has been upgraded to a 3D Fokker-Planck code to compare code results with Alcator C-Mod experiments. Simulation results of stable LHCD discharges show good agreement with the current profile obtained by an equilibrium reconstruction. On the other hand, the code predicts hollower current profile than observed on the discharges which had n=1,m=2 MHD instabilities, implying that those instabilities limited further broadening of the current profile. We will also discuss interesting wave spectrum broadening observed in code simulations in the multipass regime, which may be difficult to reproduce using a traditional ray tracing technique.   

First Results from Alcator C-Mod SOL Reflectometer

The study of antenna-plasma interactions during RF heating and current drive is greatly influenced by the SOL density profile. A swept-frequency X-mode reflectometer has recently being built for Alcator C-mod to measure the SOL density profiles at top, middle and bottom locations in front of the new Lower Hybrid Launcher and adjacent to one of the two-strap ICRF antennas. The system operates between 100 and 146 GHz and covers a density range of approximately 10$^{16}$to 10$^{20}$m$^{-3}$ at 5-5.4T at sweep rates from 10 $\mu $s to 1 ms. First data from the reflectometer will be presented. SOL density profiles will be shown for different plasma conditions, such as various ICRF and LHRF power, L or H regimes, and different line averaged densities. Comparison between the reflectometer and other density profile diagnostics on Alcator C-Mod will also be presented.   

Quantitative assessment of RF sheath rectification in Alcator C-Mod with emissive, b-dot, and ion sensitive probes

Radio frequency (RF) rectification of the plasma sheath is currently being studied as a possible mechanism that leads to prohibitively high molybdenum levels in the plasma core of RF heated discharges in the Alcator C-Mod tokamak. We installed emissive, ion sensitive, and 3D b-dot probes to quantify the presence of RF sheaths in RF heated Alcator C-Mod plasma discharges on surfaces magnetically connected to the active RF antenna. Two probe sets were mounted on fixed limiter surfaces and one set of probes was mounted on a reciprocating (along the major radius) probe, the Surface Science Station. Preliminary results showed that RF rectification of the plasma sheath correlated with the local plasma density with little to no correlation to the local RF fields. Plasma density scans also revealed a threshold-like appearance of the RF sheaths above a certain plasma density value. The strongest RF sheath potentials were observed on magnetic field lines directly mapped to the active RF antenna.   

CXRS-based diagnostic for fast ion detection in the core of the Alcator C-Mod Tokamak

Charge exchange recombination spectroscopy (CXRS) will be used to measure the spatial and temporal distribution of fast ions within the core plasma. Fast ions are generated in C-Mod by minority absorption of injected waves in the ion cyclotron range of frequencies. Typically, the minority is H in a D plasma or possibly He3 in D. Emission from the fast ions is excited by charge exchange with the neutral atoms in a diagnostic neutral beam. [see W.W. Heidbrink, et al., Plasma Phys. Control. Fusion 47, 1855 (2004)] In the new diagnostic, the spectra are captured with 1 cm spatial resolution into approximately 30 poloidal or toroidal channels, spectrally analyzed with a high throughput spectrograph that is modified to reduce scattered light from edge emission lines, and detected with a camera with 10 ms temporal resolution. The capabilities of the diagnostic are explored through simulation of the spectrum and measurements of the emission background. For C-Mod, the diagnostic is uniquely capable of detecting fast ions in the plasma core and thus contributing to RF physics as well as to fast ion transport. Expected fast ion ``signal-to-noise'' will be presented.   

ICRF Mode Conversion Flow Drive on Alcator C-Mod

ICRF mode conversion flow drive (MCFD) may be a candidate for the external control of plasma rotation in large tokamaks like ITER. Recently, we have carried out a detailed study of MCFD on C-Mod, including its dependence on plasma and RF parameters [1]. The observed change in the toroidal rotation ($\Delta $V) is always in the co-I$_{p}$ direction. The flow drive efficiency depends on the $^{3}$He concentration in D($^{3}$He) plasmas. It is strongly affected by density ($\sim $ 1/n$_{e})$, generally increases with I$_{p}$ and decreases with RF frequency. At +90$^{o}$ and dipole antenna phases, we find that $\Delta $V is proportional to P$_{RF}$ up to the maximum available RF power. The rotation at -90$^{o}$ antenna phase is more complicated. In low density L-mode plasmas, $\Delta $V $\sim $110 km/s has been achieved. Results in H-mode plasmas appear to follow a similar parametric scaling, but the observed $\Delta $V in H-mode has been small because of the high density and unfavorable 1/n$_{e}$ scaling. These results may help extrapolate MCFD to other fusion devices.\\[4pt][1] Y. Lin et al, 23$^{rd}$ IAEA Fusion Energy Conference, 2010, EX-W/4-1.   

ICRF Antenna Optimization for Alcator C-Mod

Two major challenges for ICRF utilization are reducing impurity generation and increasing reliability at high voltages. In Alcator C-Mod, we are designing a rotated 4-strap antenna where we seek to lower E-parallel and improve voltage handling. Simulations were conducted to analyze the effect of antenna orientation on the parallel electric field, which is thought to influence impurity production. In addition, simulations were carried out on antenna box and limiter structures with particular emphasis on parallel electric field reduction through image current modification. Antenna septum and limiter thickness, position, and separation were varied. The effect of slotting antenna limiters and antenna box walls was also investigated. Previous experiments suggest that improved voltage handling may be obtained through the use of refractory metals compared with copper. A test stand has been designed and built to characterize ICRF relevant voltage breakdown as a function of: antenna material, neutral pressure, and magnetic field orientation. Results from simulations and experiments will be presented along with details of the new antenna design.   

Impurities Associated with ICRF on C-Mod

In C-Mod experiments, a boron (B) film is applied to minimize the core molybdenum (Mo) content associated with ion cyclotron range of frequency heating; however, experiments suggested a high B erosion rate. A $\sim $100 $\mu $m boron film has been sprayed onto the Mo tile surfaces with the expectation that 20-30 $\mu $m of the B would be locally eroded during a campaign. Following the campaign, the B coating was found not to be significantly eroded except in locations where peeling and melting occurred. The peeling appears to be the result of poor bonding and the melt damage was localized to the outboard midplane of the plasma limiters. Thus, the high erosion rate reflects degradation of localized spots rather than sputtering of large surface areas. Conditions favoring melting limiter surfaces are discharges with low density and high ICRF power. To cause surface melting, the energy delivered to the tile is a small fraction of the injected energy ($<$1{\%}); however, the precise mechanism responsible is yet to be identified.   

Gyrokinetic simulation of short wavelength residual zonal flows

It is widely recognized that zonal flow plays a crucial role in saturating the level of turbulence. Therefore, estimation of residual (i.e., undamped) zonal flow level is important in predicting turbulence transport. There has been considerable theoretical progress on this topic [1,2,3]. In particular, Wang and Hahm [3] formulated an analytic expression for residual zonal flows which is valid for arbitrary wavelength, taking into account of both neoclassical and classical polarization shielding of both species. This is in broad agreement with the previous gyrokinetic simulation results by Jenko et al. [4]. In this work, we examine various parametric dependences of residual zonal flow level in wide wavelength range using gyrokinetic simulation, and compare with the analytic predictions [3]. [1] M.N. Rosenbluth and F.L. Hinton, Phys. Rev. Lett. \textbf{80}, 724 (1998) [2] Y. Xiao and P.J. Catto, Phys. Plasmas \textbf{13}, 102311 (2006) [3] L. Wang and T.S. Hahm, Phys. Plamsas \textbf{16}, 062309 (2009) [4] F. Jenko, W. Dorland, M. Kotschenreuther, and B.N. Rogers, Phys. Plasmas \textbf{7}, 1904 (2000)   

Experimentally Relevant Benchmarks for Gyrokinetic Codes

Although benchmarking of gyrokinetic codes has been performed in the past, e.g., The Numerical Tokamak, The Cyclone Project, The Plasma Microturbulence Project, and various informal activities, these efforts have typically employed simple plasma models. For example, the Cyclone ``base case'' assumed shifted-circle flux surfaces, no magnetic transport, adiabatic electrons, no collisions nor impurities, $\rho_{i}$ $<< \emph{a}$ ($\rho_{i}$ the ion gyroradius and $\emph{a}$ the minor radius), and no \textbf{E}$\times $\textbf{B }flow shear. This work presents comparisons of linear frequencies and nonlinear fluxes from GYRO and GS2 with none of the above approximations except $\rho_{i}$ $<< \emph{a}$ and no \textbf{E}$\times $\textbf{B }flow shear. The comparisons are performed at two radii of a DIII-D plasma, one in the confinement region ($\emph{r/a}$ = 0.5) and the other closer to the edge ($\emph{r/a}$ = 0.7). Many of the plasma parameters differ by a factor of two between these two locations. Good agreement between GYRO and GS2 is found when neglecting collisions. However, differences are found when including e-i collisions (Lorentz model). The sources of the discrepancy are unknown as of yet. Nevertheless, two collisionless benchmarks have been formulated with considerably different plasma parameters. \\Acknowledgements to J. Candy, E. Belli, and M. Barnes.   

Gyrofluid Simulations of Intrinsic Rotation Generation in Reversed Shear Plasmas with Internal Transport Barriers

It is accepted that the intrinsic rotation is generated via the residual stress, which is non-diffusive components of the turbulent Reynolds stress, without external momentum input. The physics leading to the onset of intrinsic rotation in L- and H- mode plasmas have been elucidated elsewhere. However, the physics responsible for the generation and transport of the intrinsic rotation and its relationship to the formation of internal transport barriers (ITBs) in reversed shear (RS) plasmas have not been explored in detail, which is the main subject in the present work. The revised version of the global gyrofluid code TRB is used for this study. It is found that the large intrinsic rotation ($\sim$10-30\% of the ion sound speed depending on ITB characteristics) is generated near the ITB region and propagates into the core. The intrinsic rotation increases linearly as the temperature gradient at ITB position increases, albeit not indefinitely. Key parameters related to the symmetry breaking, such as turbulent intensity and its gradient, the flux surface averaged parallel wavenumber are evaluated dynamically during the ITB formation. In particular, the role of reversed shear and the q-profile curvature is presented in relation to the symmetry breaking in RS plasmas.   

Hysteresis and Back Transitions in Internal Transport Barriers

Understanding and control of the transport barrier formation and back transition are essential to achieve the optimized plasma operation and performance in tokamak plasmas. Back transition dynamics, in particular, is complicated due to the phenomenon of hysteresis, whereby the barrier state persists when the driving power is lowered below the initial threshold value. Here we report new results from theoretical and computational studies of hysteresis in internal transport barrier (ITB) with reversed magnetic shear. A revised version of the global gyrofluid TRB code has been used to study ITG turbulence. ITB formation, back transition, and hysteresis are manifested during slow ramp-ups/downs of the central heating power. Comparisons are made of the similarity/difference in the characteristics of hysteresis when the control parameter is lowered dynamically. The strength of hysteresis is quantified as functions of ion Nusselt number, q-profile shape and lower order rational q surface. In addition to the computational study, an analytical study of a two-field model of pressure and density dynamics is presented for a reversed shear ITB plasma by extending a previous theory that is applied to the edge pedestal.   

The characteristics of density fluctuations induced by geodesic acoustic modes in the edge of plasmas

The geodesic acoustic mode (GAM) induced density fluctuations were measured by the toroidally and poloidally departed Langmuir triple probe arrays in the edges of HL-2A (Chengdu) and HT-7 (Hefei) tokamaks. Some theoretical predictions about the mode features of GAM density fluctuations are verified in our experiments: the toroidal mode number of GAM density fluctuations is $n=0$; the amplitude is consistent with the theoretical prediction in a factor of 2; the GAM density and potential fluctuations are in anti-phase at the top of plasma cross-section. The nonlinear interactions between GAM and ambient turbulence (AT) are also investigated. The cross phase between envelope of high frequency AT and GAM density fluctuations is nearly $\pi/2$ radians, which supports the conclusions that the envelope modulation of density fluctuations is due to the GAM shear effect.   

Poloidal rotation in strongly magnetized plasmas

Poloidal flows play a critical role in the regulation and stabilization of numerous modes within tokamak devices which are known to have detrimental effects on plasma confinement. In this work, a novel mean field formulation of poloidal rotation is developed, with emphasis on the elucidation of mechanisms through which microturbulence drives poloidal flows. In particular, a kinetic generalization of a Taylor identity appropriate to a strongly magnetized plasma is derived, providing an explicit link between the poloidal Reynolds stress and the transport of potential vorticity. A quasilinear calculation of the flux of potential vorticity is carried out, yielding diffusive, turbulent equipartition and thermo-electric convective components. Self-consistency is enforced via the quasineutrality relation, revealing that for the case of a stationary small amplitude wave population, deviations from neoclassical predictions of poloidal rotation can be closely linked to the growth/damping profiles of the underlying drift wave microturbulence, in accord with expectations from wave energy balance at stationarity. Applications of the above theory to poloidal spin up in the vicinity of a transport barrier will be discussed.   

Inter-species Energy Transfer and Turbulent Heating in CTEM

We reconsider the classic problem of calculating ``turbulent heating'' and the inter-species transfer of energy in drift wave turbulence. The total heating is composed of the parallel quasilinear and nonlinear terms, as well as ion polarization and diamagnetic terms. The parallel quasilinear terms effect a collisionless transfer of energy from electrons to ions with ion Landau damping mediating the resulting heating. The nonlinear contribution describes the ion heating associated with beat wave Landau damping. Ion polarization and diamagnetic terms account for the net Reynolds work of the turbulence on the zonal flow. At steady state, these must balance collisional zonal flow damping, thus driving ion heating through zonal flow friction. This process of energy transfer via zonal flows has not previously been accounted for in analyses of energy transfer. Note that these are at least two ``channels'' for turbulent electron-ion energy transfer, namely one via Landau resonance heating and one via zonal flow frictional heating. Ongoing work is concerned with the ratios of these two heating channels in CTEM, including trapped electron beat heating.   

Current Driven Drift Wave Turbulence

Recent and ongoing analyses [1] have indicated that the ``usual suspects'' for the mechanism of electron thermal transport, such as ITG, ETG, CTEM modes, etc., cannot explain results from modest density, $T_e>T_i$ plasmas in either OH or ECH heating regimes. Interestingly, such plasmas exhibit very large toroidal current drift parameters $v_d/c_s$, thus naturally suggesting revisitation of current driven drift waves. In this work, we examine the linear and nonlinear theory of current driven drift wave turbulence. Special attention is focused on the eigenfunction structure and spectral centroid shift induced by finite current. Note that the spatial asymmetry is a signature of current drive and has implications for flow generation and intrinsic rotation as well. We further explore nonlinear saturation mechanisms. In particular, the implications of spectral asymmetry for zonal flow generation and possible synergy or competition between $\mathbf{E} \times \mathbf{B}$ shear and current-induced shifts, and the effects of electron scattering, both in space and velocity; specifically magnetic shear-induced resonance broadening effects on the electron response and its implication for saturation levels.\\[4pt] [1] L. Lin, M. Porkolab et al., PPCF, 2009   

Boundary Layer- and Streamer Flows in Interchange-unstable plasmas

We describe the interchange instability in the simplest two- dimensional Boussinesq fluid approximation. First, using a closure procedure proposed earlier, we reduce the original two-dimensional system to a system of moment equations for the flow velocity and temperature. In the ideal fluid limit, the time asymptotic analysis of these equation predicts an unstable grow of streamers or zonal flows, depending on the initial conditions. By taking finite viscosity and thermoconductivity into account and returning to the original two-dimensional Boussinesq system, we analyze the emerging flow patterns. The link between streamer- and boundary layer flows in convective cells, which are responsible for transporting heat between the opposite walls, is studied in the limit of low viscosity and thermoconductivity for various Prandtl numbers.   

Isotopic Dependence of Fine Scale Zonal Flows

This work addresses the isotopic dependence of the fine scale zonal flow (ZF) dynamics which are generated from fine scale (shorter than $\rho _i $, but significantly larger than $\rho _e )$ electron drift wave turbulence (DWT) which is related to either collisionless TEM or current driven drift waves (CDDW), or inverse cascade of ETG modes. We find that the fine scale zonal flows in deuterium (D) plasmas can be stronger than those of hydrogen (H) plasmas, and therefore lead to lower turbulence and transport and better confinement. We have analytically calculated the Rosenbluth-Hinton (RH) residual level of zonal flows, taking into account both ion and electron dynamics using bounce-kinetics. Since the average ion gyroradius is different for different ion species for the same temperature, a transition from the ion classical polarization shielding dominated regime to the electron neo-classical shielding dominated regime occurs at different values of $k_r \rho _e $ for different ion species. As a consequence, RH ZFs for D plasmas can be stronger than those for H plasmas for $k_r \rho _e $ around 0.01. Based on this observation, we conclude that a significant isotopic dependence of confinement can result from the fine scale zonal flows generated from fine scale DWT.   

Analysis of interaction mechanism of off-resonant mode in reversed shear plasma

It is known that off-resonant modes around q-minimum position in reversed magnetic shear configuration in tokamak bury the resonant surface gap and essentially change the transport to be smooth over the zero-shear region. Such role of the off-resonant mode has been a problem in reproducing ITB with gyro-fluid simulation. The off-resonant ITG mode in vicinity of q-minimum position was reported to be slab-like one coupled with surrounding toroidal ITG mode. However, how they are coupled in the region where toroidal mode coupling is weak has not been stated. In this study, interaction between off-resonant modes and the other modes is investigated. Radial electric field source was introduced into a gyro-fluid code to examine the ExB flow shear effect flexibly on the interaction related to off-resonant mode. It was confirmed that the ExB flow shear with amplitude in the same order as spontaneous zonal flow provided by the electric field source is insufficient to suppress the off-resonant mode. The analysis of coupling mechanism between off-resonant slab-like ITG mode and toroidal resonant modes is in progress.   

Modeling on toroidal angular momentum transport with turbulent Reynolds stress in tokamak plasmas

Turbulent momentum transport is regarded as an important issue since it could account for the intrinsic toroidal rotation and the inward propagation of momentum in tokamaks. The effects of off-diagonal flux of toroidal angular momentum in tokamak plasmas are investigated by 1.5D core transport simulation using ASTRA. The plasma current and angular momentum transport equations are calculated with evolutions of the density and temperature profiles obtained from experiments. A simple momentum transport model [1] is implemented to take into account shear suppressed momentum diffusion, turbulent pinch, and residual stress terms. The theory based model considering turbulent pinch and residual stress shows better agreements with the measured toroidal velocity profile than the model only considering diffusion term, from which the effects of turbulent Reynolds stress are discussed.\\[4pt] [1] O. D. Gurcan et al., Phys. Plasmas, 17, 032509 (2010)   

Heavy Particle Mode: I-Regime, Magnetic Fluctuations and Toroidal Geometry Effects$*$

The ``signature'' mode excited in the I-Regime [1] involves both density and magnetic field fluctuations. Referring to a plane geometry, the ``heavy particle'' mode [2] that we propose as the candidate to explain the mode features has a longitudinal phase velocity ${\rm{v}}_{thI}^2 \sim {{\omega ^2 } \mathord{\left/ {\vphantom {{\omega ^2 } {k_\parallel ^2 < }}} \right. \kern-\nulldelimiterspace} {k_\parallel ^2 < }}{\rm{v}}_{thi}^2 < {\rm{v}}_{the}^2$ where ${\rm{v}}_{thI}^2 = {{2T_I } \mathord{\left/ {\vphantom {{2T_I } {m_I }}} \right. \kern-\nulldelimiterspace} {m_I }}$ and ${m_{I}}$ is the heavy particle (impurity) mass [3]. The main mode driving factor is the impurity pressure gradient near the edge of the plasma column combined with a significant ion temperature gradient[3]. Thus, the mode can be triggered by a heat pulse emitted from the central region. The theory has predicted correctly the direction (electron diamagnetic velocity) of the mode transverse phase velocity and the resulting transport of impurities toward the edge region of the plasma column. A theoretical formulation [4] based on a toroidal geometry is necessary to include the important effects, on the mode, of the curvature and the gradient of the magnetic field. *Sponsored in part by the U.S. D.O.E. [1] E. Marmar \textit{et al. Bull. Am. Phys. Soc.} {\bf54}, 97 (2009). [2] B. Coppi, H.P. Furth, M.N. Rosenbluth and R.Z. Sagdeev, \textit{Phys. Rev. Lett.} {\bf17}, 377 (1966). [3] B. Coppi and T.C. Zhou, MIT-LNS H.E.P. Report 09/04 (2009). [4] B. Coppi, \textit{Phys. Rev. Lett.} {\bf39}, 939 (1977).   

Heavy Particle Mode as the Signature of the I-Regime*

Key features [1] of the I-Regime investigated by the Alcator C-Mod can be explained by the excitation of a new heavy particle (e.g. impurity) mode [2] at the plasma edge. This mode involves both density and magnetic fluctuations. The impurity is treated as collisional. Considering a plane geometry, the dispersion relation has a unstable root for $\eta_i\equiv (dT_i/dr) n_i/(T_i dn_i/dr)>2/3$ and $dn_I/dr>0$. The marginal stability point is reached for a maximum $d n_I/dr$ such that $\omega^I_{**}=\omega_{IA}=\omega$, where $\omega^I_{**}\equiv c k_y T_I (dn_I/dr)/(Ze B n_I)$ and $\omega_{IA}\equiv(5/3) k^2 T_I/m_I$. The instability condition is $\omega^I_{**}<\omega_{IA}$. $\rm{Re}\, \omega/\omega^I_{**}>0$ indicates that the mode phase velocity($v_{ph}$)is in the electron diamagnetic direction, a feature consistent[3]with the observation that the plasma spontaneous rotation is in the ion diamagnetic direction. This predicted direction of $v_{ph}$ has been confirmed by the experiments. The impurity flux evaluated from the quasi-linear theory is $\langle\hat{n}_I \hat{v}_{Ex}\rangle=n_i\langle\widehat{T}_i \hat{v}_{Ex}\rangle/(Z T_i) \simeq -n_i (dT_i/dr)/(Z T_i k^2 v_{th i} \lambda_i) \left[1-2/(3\eta_i)\right] \cdot\langle |\hat{v}_{Ex}|^2\rangle >0$ for $\eta_i>2/3$, where $\lambda_i$ is the effective main ion mean free path. This shows that both the main ion thermal energy and the impurity are transported outwards. These features are consistent with a mode with frequency $\sim 200\, kHz$ observed in the I- Regime and with the fact that impurities are confined at the edge in this regime. *Sponsored by the DOE. [1] E. Marmar, B. Lipschultz, A. Dominguez, et al., Bull. Am. Phys. Soc. {\bf 54} (2009) 97 [2] B. Coppi, H. Furth, M. Rosenbluth and R. Sagdeev, Phys. Rev. Lett. {\bf{17}} (1966) 377-379 [3] B. Coppi, Nucl. Fusion {\bf{42}} (2002) 1-4   

Interaction of energetic ions with the background microtubulence in a tokamak

Interaction of energetic ions with the background microturbulence induced by pressure gradient driven modes such as ion temperature gradient (ITG) driven mode and trapped electron mode (TEM) is investigated using the global Gyrokinetic Tokamak Simulation (GTS) code [1]. The energetic ions are treated as test-particles, which respond to the perturbed fields, but do not contribute to them. The radial transport of energetic particles is estimated with respect to its characteristic dependence on the ratio of e$\phi/T_E$ in different turbulence regimes. The phase space evolution of the energetic particles is analyzed and its effect on energetic-particle-driven-modes will be discussed. Interactions of these energetic ions with particular (n,m) mode, where n and m being the toroidal and poloidal mode numbers, are studied with focus on the identification of resonant and non-resonant contributions to the energetic particle transport in both ITG and TEM regimes.\\[4pt] [1] W. X. Wang et al., Phys. Plasmas 13, 092505 (2006).   

Non-local transport across zonal shear flows

In the diffusive transport model, the flux is completely determined by the local value of the gradient. Despite the relative success of this approach, there are situations in which the local flux-gradient assumption does not hold. In particular, in the presence of non-local transport, the flux at a point might depend on the gradients throughout the entire domain. Evidence of this type of transport includes perturbative experiments in tokamaks, numerical simulations of turbulent transport, and generalized random walk theoretical models. The goal of this presentation is to study non-local transport in the presence of zonal shear flows. Zonal flows play a key role in the dynamics and transport in magnetically confined plasmas and it is of significant theoretical and practical importance to understand their impact on non-local transport. Our study is based on a simplified 2-dimensional advection non-local diffusion model consisting of a poloidal zonal flow coupled to a radial non-local transport channel. Extending previous work we model non-local transport using truncated fractional derivatives that allow the incorporation of finite size effects. Numerical and analytical results on non-local transport across the zonal flow are presented, along with a numerical study of truncation effects in fluctuation-driven transport.   

Finite Larmor radius effects on chaotic transport in ${\bf E} \times {\bf B}$ zonal flows

Finite Larmor radius (FLR) effects on chaotic test particle transport are studied in the context of Hamiltonian dynamical systems. Based on a marginal stability assumption, the Hamiltonian is modeled as the superposition of a non-monotonic zonal shear flow and regular neutral drift wave modes. FLR effects are incorporated through a gyro-average of the ${\bf E} \times {\bf B}$ Hamiltonian. We provide numerical evidence of the following novel FLR effects on chaotic transport: (i) Bifurcation leading to the creation of additional shearless regions in the zonal flow profile; (ii) Double heteroclinic-homoclinic separatrix reconnection; and (iii) Chaotic transport suppression and transport barrier formation. Of particular interest is the dependence on the Larmor radius of the destruction of shearless transport barriers leading to global transport. To compute this we use indicator points based on the symmetry properties of the Poincare map.   

Local and nonlocal parallel heat transport in general magnetic fields

A novel approach that enables the study of purely parallel transport in magnetized plasmas is proposed. The approach is based on a Lagrangian Green's function method applicable to general magnetic fields (2-D and 3-D from integrable to completely chaotic), and with local or nonlocal parallel heat-flux closures. The approach is free from numerical pollution, and preserves temperature positivity by construction. The method is used to study: (i) local and nonlocal temperature flattening in magnetic islands; (ii) the fractal structure of the devil staircase temperature profile in weakly chaotic fields; and (iii) effective radial transport in fully chaotic 3D fields. For (iii), self-similar evolution of the form $T=(\chi_{\parallel} t)^{-\gamma/2} f(\eta)$ is observed with similarity variable $\eta=(\psi-<\psi>)/(\chi_{\parallel} t^{\gamma/2})$ where $\psi$ is a radial flux function. Different to the well-know local transport case (Rechester-Rosenbluth), it is shown that in the case of non-local parallel transport $f$ is an algebraic decaying, $f \sim \eta^{-3}$, non-Gaussian function, and $\gamma=1$. Recent work on the extension of the method to include perpendicular transport and heat sources is presented. The approach is algorithmically scalable, and second-order accurate in time on the slow-perpendicular-time scale. Numerical examples of relevance to magnetic fusion geometries will be presented.   

Impurity dynamics in plasma turbulence: multiscale analysis, intermittency, and non-diffusive transport

Impurity transport in tokamak plasmas is investigated using a three-dimensional fluid global code. The impurities are treated as an active scalar and the self-consistent interaction between the impurity concentration and the turbulence is studied in detail. A multiscale analysis based on proper orthogonal decomposition methods reveals that the impurity concentration gives rise to strong intermittency in the ${\bf E} \times {\bf B}$ flow and the ion temperature flux. The probability density functions of fluctuations exhibit a transition from Gaussian (for low Z impurities) to exponential (for high Z impurities). Spatio-temporal flux-gradient cross correlation functions are used to characterize the level of non-diffusive, non-local transport in the system.   

Tensor Product Decomposition of Gyrokinetic Microturbulence Data

Gyrokinetic microturbulence simulations generate large amounts of data. Typical simulations involve distribution functions in five or six dimensions plus time, which, for a very modest simulation, would require computer memory on the order of terabytes to store. As a result, data output is usually limited to electromagnetic fields and certain moments of the distribution function for a subset of time points. It would be desirable to develop methods to efficiently represent the gyrokinetic distribution function with the aim of compressing the data and extracting the relevant information. In this presentation we propose the use of tensor product decomposition (TPD) methods to achieve this task. In its simplest version (order-2 tensors) TPD reduces to the singular value decomposition (SVD) of the corresponding matrix. For higher order tensors of interest to gyrokinetic simulations we discuss the use of high order SVD (HOSVD) and generalized low rank approximation of matrices (GLRAM) methods.   

Bifurcation to improved confinement driven by intrinsic rotation

We study the effect of sheared flow on the turbulent transport of energy and momentum employing the gyrokinetic flux tube code GS2. The results show two features, namely, (i) given the value of the heat flux, there is a maximum temperature gradient that is achieved for a finite velocity shear; and (ii) the ratio of turbulent momentum and energy diffusivities is constant for a wide range of flow shear values. Based on this knowledge, we investigate the equilibrium of a tokamak heated by neutral beams. Considering only turbulent transport, bifurcations to enhanced confinement are not possible because for given energy and momentum depositions there is only one solution. If neoclassical transport is included, under specific circumstances there are up to three simultaneous solutions. It is possible to transit to enhanced confinement solutions, but to do so it is necessary to decrease the energy input. We propose a new mechanism that drives bifurcations to enhanced confinement solutions based on new terms in the momentum equation. These new terms are also the drive of intrinsic rotation.   

Edge-core interaction of ITG turbulence in Tokamaks: Is the Tail Wagging the Dog?

A full-f XGC1 gyrokinetic simulation of ITG turbulence, together with the neoclassical dynamics without scale separation, has been performed for the whole-volume plasma in realistic diverted DIII-D geometry. The simulation revealed that the global structure of the turbulence and transport in tokamak plasmas results from a synergy between edge-driven inward propagation of turbulence intensity and the core-driven outward heat transport. The global ion confinement and the ion temperature gradient then self-organize quickly at turbulence propagation time scale. This synergy results in inward-outward pulse scattering leading to spontaneous production of strong internal shear layers in which the turbulent transport is almost suppressed over several radial correlation lengths. Co-existence of the edge turbulence source and the strong internal shear layer leads to radially increasing turbulence intensity and ion thermal transport profiles.   

Benchhmark of NIMROD kinetic electron closures with the NEO code

The need to close the extended magnetohydrodynamic equations to include perturbed bootstrap current physics in response to magnetic island formation has long been recognized. In this work we discuss a numerical solution of the second-order\footnote{J. Ramos, private communication} drift-kinetic equation (DKE) which supplies the bootstrap current closure for the perturbed Ohms Law in simulations of slowly growing, neoclassical tearing modes. Important aspects of this numerical solution include the conservative properties of the adopted Chapman-Enskog like approach as well as the fully implicit solution for the electron DKE which is staggered in time from the advancing fluid equations. The complexity of the analytic formulation and numerical implementation makes verification of this closure paramount. To this end, we compare axisymmetric NIMROD calculations with the results of NEO\footnote{E. A. Belli, J. M. Candy PPCF 50, 095010 (2008).}, which numerically solves the DKE in 2D geometry, and with various analytic formulas.   

Second-order ion drift-kinetic equation

A novel form of ion drift-kinetic equation is presented, well suited to close the fluid description of slow macroscopic dynamics in low-collisionality, magnetically confined plasmas. It features second-order accuracy in the gyroradius expansion, with diamagnetic-scale ordering of frequencies and flow velocities. This second-order drift-kinetic equation is derived in the moving reference frame of the ion macroscopic flow, which facilitates the precise consistency with the complementary fluid system, as well as the rigorous treatment of the electric field. Examples of intended applications are the precursor of the ``sawtooth'' internal disruption and the ``neoclassical tearing mode'' in fusion-relevant tokamak temperature regimes. With these applications to slow excursions from well confined equilibria in mind, the distribution function is assumed to be close to a Maxwellian. The Maxwellian part carries the density, mean flow and temperature in Chapman-Enskog-like fashion. The resulting drift-kinetic equation for the non-Maxwellian perturbation is shown to be automatically consistent with the required condition that the density, random parallel velocity and random kinetic energy moments of such non-Maxwellian part be equal to zero.   

The importance of ion-electron collisions and temperature evolution in ion transport

Ion-electron collisions have been ignored by the small mass- ratio approximation in studies of ion transport processes, including Braginskii's closure theory. However, recent analytical calculations\footnote{J.-Y. Ji and E. D. Held, Phys. Plasmas {\bf 13}, 102103 (2006); {\bf 15}, 102101 (2008)} show that the ion-electron collision terms must be retained whenever the ion temperature is comparable to or higher than the electron temperature. For equal electron and ion temperatures, the ion transport coefficients are moderately modified by the ion-electron collision operator. When the ion temperature is higher than the electron temperature, temperature change terms in the moment equations must also be kept. The ion coefficient formulas from 3 moment (Laguerre polynomial) calculations, precise to less than 0.4\% error from the convergent values, are discussed for the relevant case that includes both the ion-electron collision and temperature change terms.   

Drift Hamiltonian Guiding Center Orbits with Full Electromagnetic Fields in Axisymmetric Geometry

A Hamiltonian/Lagrangian formulation of the guiding center drift orbits is extended to include full perturbed electromagnetic fields in axisymmetric tokamak geometry. Previous work only admitted perturbed fields with finite parallel component of the vector potential.$^1$ A background magnetohydrodynamic equilibrium state with anisotropic pressure is considered which allows a more consistent treatment of energetic particle physics. The contribution of radial equilibrium magnetic field in the covariant representation, usually ignored in most formulations of Hamiltonian drift orbit analysis, is retained. The manipulation of the drift Lagrangian and the imposition of a gauge transformation that relates the radial projection of the perturbed vector potential to its toroidal component constitute very important steps to identify the canonical angular variables and momenta$^{1,2}$ in the Boozer coordinate frame.$^3$ The radial drift motion and the evolution of the parallel gyroradius are subsequently determined. The drift equations are presented in a form amenable to implementation in the VENUS$+\delta f$ code. \\ \begin{footnotesize} \noindent $^1$G.~A.~Cooper {\em et al.},Phys.~Plasmas \textbf{14} (2007) 102506. \newline $^2$S.~Wang, Phys.~Plasmas \textbf{13} (2006) 052506. \newline $^3$A.~H.~Boozer, Phys.~Fluids \textbf{23} (1980) 904. \end{footnotesize}   

Gyrofluid simulations of turbulence in the Trinity transport code

In order to fully understand the effect of turbulence on the evolution of background profiles in fusion devices, the transport code Trinity was developed to tie together these processes that live on disparate temporal and spatial scales. Such an approach leads to potential computational savings on the order of hundreds (Barnes, et al. PoP 2010). In order to increase the computational savings, we have incorporated the use of the recently updated gyrofluid code gryffin into the Trinity framework decreasing computational size by a factor of a hundred or so. We have furthered enhanced savings by running gryffin calculations on GPUs creating a potential 25 times speed up. Such a computational savings allows for the exploration of novel fusion device configurations. We present initial numerical results.   

Momentum balance and radial electric fields in axisymmetric and nonaxisymmetric toroidal plasmas

It is investigated how symmetry properties of toroidal magnetic configurations influence mechanisms of determining the radial electric field such as the momentum balance and the ambipolar particle transport. Both neoclassical and anomalous transport of particles, heat, and momentum in axisymmetric and nonaxisymmetric toroidal systems are taken into account. Generally, in nonaxisymmetric systems, the radial electric field is determined by the neoclassical ambipolarity condition. For axisymmetric systems with up-down symmetry and quasisymmetric systems with stellarator symmetry, it is shown by using a novel parity transformation that the particle fluxes are automatically ambipolar up to $O(\delta^2)$ and the determination of the radial electric field $E_s$ requires solving the $O(\delta^3)$ momentum balance equations, where $\delta$ denotes the ratio of the thermal gyroradius to the characteristic equilibrium scale length. In axisymmetric systems with large ExB flows on the order of the ion thermal velocity $v_{Ti}$, the radial fluxes of particles, heat, and toroidal momentum are dependent on $E_s$ and its radial derivative while the time evolution of the $E_s$ profile is governed by the $O(\delta^2)$ toroidal momentum balance equation.   

Electron turbulence driven non-diffusive transport and intrinsic rotation in tokamaks

Global gyrokinetic simulations have found that meso-scale phenomena and associated nonlocal transport are largely enhanced in the trapped electron mode (TEM) turbulence regime due to strong coherent wave-particle interaction at the trapped electron precession frequency. Robust radial pinches in toroidal flow, heat and particles, which emerge ``in phase'' in collisionless TEM turbulence, are found to play remarkable roles in determining plasma transport. Particularly, toroidal flow perturbations, which are generated locally (in the center of the plasma in the simulation case) by the turbulence, are found to propagate radially. This result amazingly reproduces the experimental phenomenon of radially inward penetration of perturbed flows created by modulated beams in peripheral regions [1], and thus is highly illuminating. The revealed universal, nonlinear flow generation process due to the residual stress produced by the fluctuation intensity and the intensity gradient, acting with the zonal-flow-shear-induced k$_{//}$ symmetry breaking [2,3] offers an ideal mechanism to drive intrinsic rotation via wave-particle momentum exchange [4]. This turbulence driven intrinsic rotation scales close to linearly with plasma gradients and the inverse of the plasma current in various turbulence regimes, reproducing empirical scaling obtained in multiple fusion devices.   

Studies of turbulence and fast ion interactions in TORPEX simple magnetized plasmas

We present high resolution data together with fluid models and numerical simulations, which advance the understanding of electrostatic turbulence and its effect on transport of bulk plasma and fast ions in the TORPEX simple magnetized device. The dominant instabilities are determined by the ratio of the vertical magnetic field to the toroidal field. For B$_{v}$/B$_{T}>$3{\%}, ideal interchange instabilities are observed, which nonlinearly develop radially propagating blobs. The radial blob velocity is limited by cross-field ion polarization currents and by parallel currents to the sheath in the small and large blob size limits, respectively. The effect of the blobs on the particle, heat and toroidal momentum transport are investigated in detail and complemented by data form a fast framing camera coupled to an image intensifier and a movable gas puff system. The effect of turbulence on fast ions is studied using movable fast ion source and detector in the interchange dominated regime. A theory validation project is conducted, based on comparisons of observables that are defined identically in the 2D and 3D simulations and in the data.   

Fast ion dynamics in the basic plasma physics experiment TORPEX

The transport of fast ions in interchange turbulence is examined in TORPEX, a basic plasma physics experiment with the essential elements of the scrape-off layer (SOL). Extensive modeling in two and three dimensions has shown that TORPEX plasma is well-described by a drift-reduced Braginskii fluid simulation (GBS). We follow fast ion trajectories using the full Lorentz force, specified by the GBS fields. A large ensemble of trajectories allows us to create a synthetic diagnostic, giving results that compare favorably with experimental measurements of current density using a fast ion source/detector pair. We also explore the properties of fast ion transport on timescales longer than those accessible to the experiment. We find that the rate of radial dispersion is strongly dependent on the ratio of ion energy to plasma (electron) temperature. The dispersion tends to be subdiffusive for $\rho_i \sim \Lambda$, where $\rho_i$ is the fast ion Larmor radius and $\Lambda$ is the scale length of the turbulence. The effective diffusivity is examined from the perspectives of (1) trajectory dispersion, (2) the flux-gradient Fick's Law relation, (3) velocity correlation, and (4) waiting-time/flight-length distributions.   

Turbulence and Turbulence Suppression in the Helimak

The Helimak is an approximation to the infinite cylindrical slab, but with open field lines of finite length. Radially-segmented isolated end plates allow application of radial electric fields that drive radial currents. Above a threshold in applied voltage (driven current), the fractional turbulent amplitude is greatly reduced, as is the radial turbulent particle transport in the region of applied bias. Stabilization is observed for both positive and negative bias. Concurrent measurements of the ion flow velocity are made by Doppler spectroscopy. The turbulence -- density, potential, and temperature fluctuations and their relations, will be compared with simulations from a fluid model for this geometry. Comparisons of turbulence reduction with changes in radial correlation length and flow shear will be given. Although the radial correlation length is much smaller than the plasma, the turbulent structures have a large spatial scale of short lifetime. The amplitude reduction is associated with shrinkage in size of the most coherent structures.   

Simulations of turbulence reduction by the bias-induced flows in the Helimak

Global fluid simulations of interchange turbulence are presented for the Helimak in which the open field lines are helices on a surface of constant radius. The three-dimensional simulation is based on an electrostatic two-fluid model that evolves the full plasma density, the electric potential, the electron temperature, and the parallel velocities. In the grounded no-bias case, we find that interchange instabilities produce radially elongated ExB velocity eddies and turbulent radial transport in the bad-curvature region. The plasma potential profiles produce the equilibrium radial electric fields and vertical EXB flows. Application of a bias voltage in the radial direction changes the global structures of plasma potential and flow velocity. Both negative and positive bias are studied. The sheared vertical EXB flows induced by the bias limit the radial extent of the turbulent eddies in the bad curvature region, and thus limit the radial cross-field transport.   

Neoclassical Calculations with Momentum Conservation Using the PENTA Code

The PENTA code calculates neoclassical radial and parallel flows of heat and particles, including the effects of collisional momentum conservation, for arbitrary toroidal geometries. As an input, PENTA uses transport coefficients calculated using a pitch angle scattering (PAS) collision operator, for example from the DKES code. In this sense PENTA acts as a momentum correction technique to transport quantities calculated from the PAS transport coefficients, which are often used in stellarator transport analyses. PENTA has recently been upgraded to account for arbitrary ion impurity species, and to include multiple methods of momentum correction for comparison and benchmarking. For non-(quasi)symmetric configurations, the radial electric field is calculated from the nonambipolar particle fluxes. For (quasi)symmetric devices PENTA recaptures intrinsic ambipolarity, demonstrating its applicability to both 2D and 3D geometries. Momentum correction has been shown to have a significant effect on the calculated parallel flows in the HSX stellarator.   

Influence of the Plasma Shape on the Pinch Effect on Axisymmetric Tokamaks

Numerical calculations of Ware-pinch effect in general plasma configuration are considered. Though analytical treatment of Ware-pinch in plasma configurations including ellipticity and triangularity were presented previously, however, applications of these equations to actual tokamaks are very important and not presentations have been done until now using this technique. Curvilinear coordinates described in previous papers are used [1-4]. This work is justly dedicated to fill out this matter and numerical calculations have been carried out for different tokamaks with different geometry parameters. First, the effect of ellipticity is considered and later triangularity influences are also included in our calculations. Graphics results will be presented. \\[4pt] [1] P. Martin, E. Castro and M. Haines, \textit{Phys. Plasmas} 14, 052502 (2007) \\[0pt] [2] P. Martin and M. Haines, \textit{Phys. Plasmas} 5, 410 (1998) \\[0pt] [3] P. Martin \textit{Phys. Plasmas} 7, 2915 (2000) \\[0pt] [4] P. Martin and E. Castro, Proceedings of 35th Plasma Physics Conference, \underline {32} (2008) P- 5.042   

Plasma Shape Effect on Tokamak Electric Fields

This work considers the effects of tokamak plasma shape, mainly ellipticity and triangularity, on the different components of the electric field. The plasma shape parameters influence mainly the poloidal and transversal electric fields, however the effect on the toroidal electric field is also analyzed. Resistive MHD equations are used for this treatment, as well as, new differential equations obtained by applying the curl operator on the original equations. Curvilinear coordinates described in previous papers are used [1]. In our treatment first, the transversal, poloidal and toroidal velocities are obtained as a function of some geometric parameters and values along some radius lines. The electric field determination comes after that. Axisymmetric conditions are used. Though our treatment is general, some simplifications can be obtained when additional up-down geometry symmetry is assumed. Application of our equation to different tokamaks is performed and compared with the results of previous authors. \\[4pt] [1] P. Martin, E. Castro and M. Haines, \textit{Phys. Plasmas}14, 052502 (2007)   

Effect of Superbanana Diffusion on Fusion Reactivity

The Fokker-Planck equation is solved numerically for the energy distribution of the particles in the tail of the distribution function, assuming a loss rate due to superbanana diffusion. Using a simple random-walk estimate, this loss rate is proportional to a positive power (+7/2) of the particle energy. The rate of repopulation by Coulomb scattering is proportional to a negative power (-3/2) of the particle energy, so the most energetic particles in the tail are most strongly depleted by superbanana diffusion. For ion temperatures relevant for fusion in magnetic confinement devices, it is the tail particles which are most needed for fusion, since the peak of the D-T reaction rate is at roughly 100 kev. The numerically computed energy distribution for the tail particles is used to obtain an integrated fusion reactivity, using a standard fit to the D-T reaction cross section. A plot of reactivity vs loss rate shows that the fusion reactivity is quite sensitive to loss by superbanana diffusion.   

Connection formula for banana-drift neoclassical toroidal viscosity

Non-resonant magnetic perturbations can affect plasma rotation in toroidally confined plasmas through their modification to $|B|$. Variations along a field line induce nonambipolar radial transport and produce a global neoclassical toroidal viscous force [NTV]. In this work, a previously calculated WKB-type solution smoothly connecting the low-collisionality ``$1/\nu$'' and ``$\nu-\sqrt{\nu}$'' regimes is extended to include the superbanana plateau [sbp] regime [1]. The sbp effect occurs for particles whose toroidal $\vec{E}\times\vec{B}$ precessional drift vanishes. In this case, the relevant drift kinetic equation exhibits a ``turning point'' and the WKB method fails. We employ the connection formula method of Langer [2] which continuously varies between the previous WKB result and the superbanana regime without difficultly at the turning point. The resultant smoothed NTV is presented in terms of flows along flux surfaces. \\[4pt] [1] K. C. Shaing, S. A. Sabbagh, and M. S. Chu, PPCF \textbf{51}, 035009 (2009), and refs. cited therein. \\[0pt] [2] R. E. Langer, Phys. Rev. \textbf{51}, 669 (1937).   

Physics of zonal flow, density and field excited by finite beta drift waves

The excitation of zonal perturbations by finite beta drift waves can be investigated using the Floquet Theory. When the growth rate for this process is smaller than the drift frequency, the Floquet expansion can be truncated to a four-wave interaction involving the pump drift-wave, the zonal perturbations and the sum and difference drift-wave sidebands. This leads to nine coupled algebraic equations. First, a quadratic dispersion relation derived in our earlier work is discussed. The dispersion relation is recast into a standard form which helps identify the different physical processes responsible for the modulational instability providing a clearer picture of the role of finite beta effects in determining the parametric dependence of the growth rate on the dimensionless parameters. We compare results obtained by numerically solving the nine coupled equations with the simplified dispersion relation and show that in the range of validity of the theory the agreement for the growth rates computed by the two methods is very good.   

New Developments in the Theory of Incompressible MHD Turbulence with ${\mbox{\textit{Pr}}}_m = 1$

For incompressible MHD turbulence, the correlation lengths along directions parallel and perpendicular to the local mean magnetic field may be defined by iso-energy surfaces derived from second order structure functions. The correlation time of the turbulence may be defined in a similar manner by means of a temporal second order structure function. Moreover, there is a natural correspondence between the lengthscales of fluctuations with a given energy and the timescale of fluctuations of the same energy so that each iso-energy surface is associated with a unique pair of parallel and perpendicular correlation lengths \emph{and} a unique correlation time. In the case when the magnetic Prandtl number is unity, ${\mbox{\textit{Pr}}}_m \equiv \nu/\eta=1$, it is shown that the correlation time $\tau$ associated with an iso-energy contour of energy $E$ is equal to the energy cascade time of the turbulence in the sense that $E/\tau \sim \varepsilon$, where $\varepsilon$ is the energy cascade rate. For balanced MHD turbulence, both the Goldreich and Sridhar theory and the Boldyrev theory are shown to have this same property. I conjecture that the same property also holds for imbalanced MHD turbulence, that is, MHD turbulence with nonvanishing cross-helicity. These and other recent developments in the theory of incompressible MHD turbulence with ${\mbox{\textit{Pr}}}_m=1$ are discussed.   

Measurements of the normalized cross-helicity of solar wind turbulence spanning the entire inertial range

MHD turbulence which is spatially homogeneous and stationary in time is characterized in part by its three dimensional energy spectrum (Fourier spectrum) and its cross-helicity spectrum. The ratio of the cross-helicity spectrum divided by the energy spectrum is the normalized cross-helicity spectrum $\sigma_c$ which takes values between $-1$ and $+1$. Solar wind measurements of the energy spectrum, cross-helicity spectrum, and the normalized cross-helicity spectrum (reduced spectra) have been performed almost since the dawn of the space age 50 years ago. However, measurements of the cross-helicity and the normalized cross-helicity spanning the entire inertial range at 1 AU have only recently been performed for the first time using simultaneous 3-second plasma and magnetic field data from the WIND spacecraft. The new measurements extend the frequency range of previous measurements by 1.5 decades (a factor of $\sim 30$). A large study of over 100 different intervals of solar wind data shows that the normalized cross-helicity is approximately constant throughout the inertial range and, moreover, that this result holds over a wide range of solar wind conditions including both high- and low-speed wind. This result has important implications for theories of imbalanced MHD turbulence as I show in an accompanying poster.   

Whistler Turbulence from Particle-in-Cell Simulations

Two-dimensional particle-in-cell simulations of whistler turbulence in magnetized, homogeneous, collisionless plasmas of electrons and protons have been carried out. Enhanced magnetic fluctuation spectra are initially imposed at relatively long wavelengths, and, as in previous such simulations, the temporal evolution shows a forward cascade of magnetic fluctuation energy to shorter wavelengths and preferentially toward wavevectors relatively perpendicular to the background magnetic field ${\bf B}_o$. Two new results are reported here. First, the wavevector anisotropy is very different for each of the three components of the fluctuating magnetic field. Second, the magnetic fluctuation energy spectrum at relatively short wavelengths ($kc/\omega_{pe}\sim$ 1) is steeper than that predicted by EMHD simulations and theories at relatively long wavelengths. This steep spectrum may correspond to recent solar wind observations of magnetic turbulence spectra at short wavelengths.   

Dispersive magnetized waves in the solar wind plasma

We derive a generalized linear dispersion relation of waves in a strongly magnetized, compressible, homogeneous and isotropic quasi-neutral plasma. Starting from a two-fluid model, describing distinguishable electron and ion fluids, we obtain a six-order linear dispersion relation of magnetized waves that contains effects due to electron and ion inertia, finite plasma beta and angular dependence of phase speed. We investigate propagation characteristics of these magnetized waves in a regime where scale lengths are comparable with electron and ion inertial length scales. This regime corresponds essentially to the solar wind plasma, where length scales, comparable with ion cyclotron frequency, lead to dispersive effects. These scales in conjunction with linear waves present a great deal of challenges in understanding the high-frequency, small-scale dynamics of turbulent fluctuations in the solar wind plasma.   

Inhomogeneous two dimensional whistler turbulence

Whistler turbulence is investigated by including electron density perturbation in two dimensional fluid model. We find that electron density couples with the wave magnetic field and leads to to finite compressibility effects in whistler turbulence. Interestingly it is found from our simulations that despite strong compressibility effects, the density fluctuations couple only weakly to the wave magnetic field fluctuations. In a characteristic regime where large-scale whistlers are predominant, the weakly coupled density fluctuations do not modify inertial range energy cascade processes. Consequently, the turbulent energy is dominated by the large-scale eddies and it follows a Kolmogorov-like spectrum, where k is a characteristic wavenumber.   

Interaction of Charged Particles with Collisionless Shock Ensembles

Collisionless shocks are ubiquitous in the solar wind plasma and their interaction with charged particles is an important, long- standing problem. In the de Hoffmann-Teller frame, particle trajectories upstream and downstream are simple, yet the accurate conditions for particle transmission and reflection have been obtained only for the special cases of quasi-perpendicular and quasi-parallel shocks. In the former case the particle magnetic moment is conserved with a good accuracy, which determines the outcome (transmission/reflection) of a particle encounter with the shock. In the general case of an oblique shock, however, the magnetic moment alone is not sufficient and the angle of incidence is essential as well. First, we show that the process of multiple interaction of particles with an individual, infinitely thin collisionless shock may be formulated in terms of an iterated map involving solutions of the spherical triangles. Second, we consider particle interactions with an ensemble of such shocks, which result naturally from wave steepening and are often observed in the solar wind turbulence.   

Gyrokinetic Particle Simulation of Alfven Turbulence

The issue of spectral cascade and plasma heating in Alfvenic turbulence is a major unsolved problem in plasma physics. Gyrokinetic particle simulation is applied in this work to study the cascade and heating in Alfvenic turbulence with fully self-consistent nonlinear kinetic effects. A massively parallel particle-in-cell 3D code with gyrokinetic ions and fluid-kinetic hybrid electrons is used to study spectral cascading and dissipation of Alfvenic turbulence. A magnetic energy spectrum with index of ``-5/3'' in the inertial range has been observed from the gyrokinetic simulation. The code will be used to study energy dissipation in the Alfvenic turbulence on the spatial scale of the order of ion gyro-radius.   

Wandering magnetic field lines, turbulence and laboratory flux ropes

Understanding the dynamics of flux ropes and their mutual interactions offers the key to many important solar phenomena including magnetic reconnection and turbulence. Kink dynamics and bursty driven dissipative reconnection processes may be important for example in the heating of the solar corona, bursty bulk flows, and magnetotail turbulence. Tangled magnetic field lines are ubiquitous, for example on the sun from differential solar rotation, in the corona, and in the magnetotail. We believe isolated X-lines in 3D space can generate jets and bursty bulk flows. Astrophysical weak MHD turbulence and 3D reconnection are likely related. There is little or no laboratory work on possible links between reconnection and turbulence, or the dynamics of intermittent, unsteady reconnection. We take advantage of a unique collaboration between a LANL experiment and theory- computational capabilities at Univ Wisconsin and LANL, to shed light on the link between magnetic reconnection and turbulence.   

On the nature of the electromagnetic fluctuations in the dissipation/dispersion range of solar wind turbulence

We present a study of the nature of the electromagnetic fluctuations in the dissipation/dispersion range of solar wind turbulence, typically up to a few Hz. It has been shown that wavemodes in this range of frequencies become dispersive and are consistent with Kinetic Alfven Waves (KAW). However, strongly Doppler-shifted KAW in the solar wind can show similar properties as slightly doppler-shifted proton whister waves in the s/c frame. We explore here the possibility of distinguishing between both wavemodes. We analyze several low-beta ambient solar wind intervals, using both electric and magnetic field data from Cluster. This analysis is performed in the s/c frame along with theoretical estimates based on the effect of Doppler shift on KAW and compressional proton whistler waves. The dispersive properties of KAW and whistler waves, as well as the E/B ratio, are determined both analytically and numerically in the plasma and the s/c frame. Those estimates are then directly compared to the data in the s/c frame. We propose this technique as an efficient diagnostics for wave-mode identification in the dissipation/dispersion range of solar wind turbulence.