Session PP12: Poster Session VI (Mini-Conference: Plasma Energization-Interactions Between Fluid and Kinetic Scales, Turbulence and Transport, Transport, Transients, ITER and Next-Steps)

Energization by Landau Damping in Two- and Three-Dimensional Plasma Turbulence

Plasma turbulence is ubiquitous in space and astrophysics. It plays an important role in particle energization. The processes that determine energy dissipation in turbulence remain highly controversial. This paper attempts to understand the fundamental physics of turbulent dissipation by considering low-beta (ratio of plasma to magnetic pressure) proton-electron plasma in gyrokinetic simulations with a significant mean magnetic field. We find that nonlinear gyrokinetic simulations in both two and three dimensions (2D and 3D) show a velocity space signature qualitatively similar to that of linear Landau damping of waves in a 3D linear simulation. This provides strong evidence that the turbulence energy is transferred to the particles by linear Landau damping, which eventually enables dissipation. We also show that energy in the 2D and 3D systems evolve in qualitatively similar but quantitatively different ways. The reasons why the limitation to 2D quantitatively changes the evolution of energy, but it does not eliminate Landau damping are elucidated. Applications to space plasma systems are discussed.   

Vlasov simulation of 2D Modulational Instability of Ion Acoustic Waves and Prospects for Modeling such instabilities in Laser Propagation Codes

We present 2D+2V Vlasov simulations of Ion Acoustic waves (IAWs) driven by an external traveling-wave potential, $\phi_0(x,t)$, with frequency, $\omega$, and wavenumber, k, obeying the kinetic dispersion relation. Both electrons and ions are treated kinetically. Simulations with $\phi_0(x,t)$, localized transverse to the propagation direction, model IAWs driven in a laser speckle. The waves bow with a positive or negative curvature of the wave fronts that depends on the sign of the nonlinear frequency shift $\Delta \omega_{NL}$, which is in turn determined by the magnitude of $ZT_e /T_i $ where Z is the charge state and $T_{e,i}$ is the electron, ion temperature. These kinetic effects result can cause modulational and self-focusing instabilities that transfer wave energy to kinetic energy. Linear dispersion properties of IAWs are used in laser propagation codes that predict the amount of light reflected by stimulated Brillouin scattering. At high enough amplitudes, the linear dispersion is invalid and these kinetic effects should be incorporated. Including the spatial and time scales of these instabilities is computationally prohibitive. We report progress including kinetic models in laser propagation codes.   

Signatures of Heating via Landau Damping in Nearly Collisionless Plasmas

It is an open scientific question what mechanisms act to convert large scale turbulent fluctuations into particle heating for nearly collisionless plasmas. One potential mechanism is Landau damping, which generates small scale structures in velocity space; once the gradients of these structures become sufficiently large, weak collisions can act to irreversibly heat the plasma. We consider the case of Landau damping for the gyrokinetic system of equations. An analytic expression for the time evolution of the particle velocity distribution function (VDF) is calculated using a Fourier-Laplace transform. This expression is then compared to VDFs generated using the gyrokinetic code AstroGK. From these expressions and simulations, we construct a set of signatures using VDFs which serve to identify the presence of Landau damping in the solar wind and other turbulent, nearly collisionless plasmas.   

Drift and suppression of x-lines in asymmetric magnetic reconnection

The x-line of reconnection drifts in the outflow direction when the current sheet is asymmetric and has a guide field. In particular, reconnection can be choked off if the x-line drifts too fast. The energy conversion from the magnetic field to particles is hence significantly reduced. A suppression was suggested when the relative diamagnetic drift speed between electrons and ions exceeds the Alfv\'en speed based on the reconnecting magnetic field.\footnote{M. Swisdak et al., J. Geophys. Res., {\bf 108}, 1218, 2003} In this work, we re-visit this problem using Particle-in-Cell simulations. We break down the pressure gradient to a combination of density and temperature gradients, and find that the suppression effect from the temperature gradient is much weaker compared to that with a density gradient, consistent with a recent work using gyrokinetic simulations.\footnote{S. Kobayahsi et al., Phys. Plasmas, {\bf 21}, 04074, 2014} In addition, a wide range of parameters are explored to benchmark the theory, and the flux-breaking mechanism in these drifting x-lines is analyzed. This work has potential application at Earth's magnetopause and in Tokamak devices.\footnote{M. T. Beidler and P. Cassak, Phys. Rev. Let., {\bf 107}, 255002, 2011}   

3D Hall-mediated fast magnetic reconnection spontaneously initiated by a multi-scale instability cascade

The Caltech astrophysical jet experiment provides a highly resolved demonstration of the interaction between single fluid and 2-fluid scales and possibly kinetic scales as well. The jet evolves through the following sequence: (i) a current-carrying MHD-driven plasma jet self-forms, (ii) the jet undergoes a kink instability, (iii) the kink provides the environment for a secondary, Rayleigh-Taylor (RT) instability, (iv) the RT instability erodes the current channel radius to a scale smaller than ion skin depth to cause fast magnetic reconnection, (v) the reconnection emits broadband obliquely-propagating, right-hand circularly polarized whistler waves, and (vi) the reconnection energizes electrons and ions. The observation of the whistler waves confirms that the reconnection is in the Hall MHD regime (i.e., 2-fluid). An energetic extreme ultraviolet burst is observed at the location of reconnection indicating strong, localized electron heating. Spectroscopic measurement shows simultaneous fast ion heating. The analysis shows that electrons are plausibly heated by Ohmic dissipation, and that ions are plausibly heated stochastically, i.e., the guiding center approximation fails, a kinetic effect.   

Magnetic Field Shear in Kinetic Models Steps Toward Understanding Magnetic Reconnection Drivers

In the standard model for coronal mass ejections (CME) and/or solar flares, the free energy for the eruptive event resides in a strongly sheared magnetic. A pre-eruption force balance consists of an upward force due to the magnetic pressure of the sheared field and a downward tension due to overlying unsheared field. Magnetic reconnection disrupts this force balance; therefore, it is critical for understanding CME/flare initiation, to model the onset of reconnection driven by the build-up of magnetic shear. In MHD simulations, the application of a magnetic-field shear is a trivial matter. However, kinetic effects are dominant in the diffusion region and thus, it is important to examine this process with PIC simulations as well. The implementation of such a driver in PIC methods is challenging, however, and indicates the necessity of a true multiscale model for such processes in the solar environment. The field must be sheared self-consistently and indirectly to prevent the generation of waves that destroy the desired system. Plasma instabilities can arise nonetheless. Here, we show that we can control this instability and generate a predicted out-of-plane magnetic flux.   

Electron Energization During m=0 Magnetic Bursts in MST plasmas

MST reversed-field pinch plasmas develop magnetic modes with both a core-resonant poloidal mode m=1 structure and edge-resonant m=0 structure on the reversal surface. The impact of the m=0 modes on electron energization has been observed with Thomson scattering under plasma conditions with suppressed m=1 modes. Under such conditions, the m=0 modes undergo brief ($\sim$100 $\mu$s) bursts of localized magnetic activity. These bursts show a localized 4\% heating of electrons above a 600-900 eV background temperature, associated with a reduction of magnetic energy. An inward propagating cold pulse follows after the heating as a result of reduced confinement. Ensembles of hundreds of bursts are required to measure small relative heating, however single-shot results from MST's high repetition Thomson scattering diagnostic support the ensemble results. Analysis of Thomson scattering data also provides constraints on non-Maxwellian distributions and upcoming upgrades will improve the ability to resolve electron currents associated with the magnetic bursts.   

Collisionless reconnection driven bulk heating of electrons on TREX

The mechanism for particle heating during magnetic reconnection is an open topic in plasma physics research. Addressing this issue is a major concern for theory, observation, and experiment alike. Recently, a new model has been proposed to explain the bulk heating of electrons during collisionless reconnection, predicting that the heating scales inversely with the plasma beta [1]. The new Terrestrial Reconnection Experiment (TREX) aims to examine this energy partition in a laboratory plasma. By reducing the collisionality in the experiment, the upstream electron pressure should become anisotropic due to adiabatic trapping [2], making TREX the first reconnection experiment able to access the necessary parameters to study these plasma dynamics. Preliminary analysis from the TREX magnetic flux probe array will be presented, characterizing the electron diffusion region in for collisionless magnetic reconnection.\\[4pt] \\[1ex][1] A Le, et al., Phys. Rev. Lett. (submitted 2015). \\[1ex][2] J Egedal, et al., Phys. Plasmas 20(6) (2013).   

Theoretical Model for Electron Bulk Heating Resulting from Magnetic Reconnection

A new model predicts that the electron bulk heating resulting from collisionless magnetic reconnection scales directly with the upstream ratio of magnetic to electron pressure. The heating process involves two stages. First, the inflowing electrons are adiabatically trapped and heated by a parallel electric field [1]. Next, the electrons gain energy from the reconnection electric field as they undergo complex meandering motions in the electron diffusion region. Although these collisionless mechanisms lead to complex electron velocity distributions [2], a fluid treatment predicts the net electron heating and is in excellent quantitative agreement with both kinetic simulations and recent spacecraft observations [3]. \\[4pt] [1] Egedal et al., Phys. Plasmas 20, 061201 (2013)\\[0pt] [2] Ng et al., Phys. Rev. Lett. 106, 065002 (2011)\\[0pt] [3] Phan et al., Geophys. Res. Lett. 40.17, 4475-4480 (2013)   

The role of fluid compression in particle acceleration during magnetic reconnection

Previous theories of particle transport and acceleration have shown that fluid compression is the leading mechanism for particle acceleration or deceleration. However, the role of compression in particle acceleration during magnetic reconnection is unclear. Using fully kinetic simulations, we quantitatively investigate the effect of compression in particle acceleration and energy conversion during magnetic reconnection for a range of plasma beta and guide field. We show that compression has an important contribution in energy release and nonthermal particle acceleration when the guide field is smaller than the reconnecting component. For the case with small plasma beta, the compression leads to strong nonthermal particle distribution that resembles a power law. This results from kinetic simulations may help build a large-scale acceleration model in magnetic reconnection.   

The RFP dynamo: MHD to kinetic regimes

The hallmark of magnetic relaxation in an RFP plasma is profile flattening of ${\bf J_0\cdot B_0}/B^2$ effected by a dynamo-like emf in Ohm's law. This is well-studied in single-fluid MHD, but recent MST results and extended MHD modeling show that both $<\bf{V_1\times B}_1>$ and the Hall emf, $-<{\bf J_1\times B_1}>/en_e$, are important, revealing decoupled electron and ion motion. Since dynamo is current-related, the electron fluid emf, $<{\bf V_{e,1}\times B_1}>$, captures both effects. In MST, the electron flow is dominantly ${\bf V_{e,1}\approx E_1\times B_0}/B^2$, implying $<{\bf V_{e,1}\times B_1}>\approx<{\bf E_1\cdot B_1}>/B$. This and the Hall emf are measured in MST for comparison in Ohm's law. A finite-pressure response is also possible, e.g., ``diamagnetic dynamo", $\nabla\cdot< p_{e,1} {\bf B_1}>/en_e$, associated with diamagnetic drift, and ``kinetic dynamo" associated with collisionless streaming of electrons in a stochastic magnetic field. Correlation measurements $$ and $$ using FIR interferometry and Thomson scattering reveal these as small but finite in MST. A kinetic emf might be expected for any high-beta plasma with inhomogeneous pressure. Support by DOE/NSF   

A Unified Model of Astrophysical Plasma Turbulence

Turbulence profoundly affects particle transport and plasma heating in many astrophysical plasma environments, from galaxy clusters to the solar corona and solar wind to Earth's magnetosphere. Two seemingly incompatible models presently dominate plasma turbulence research: one views plasma turbulence as a sea of nonlinearly interacting Alfven waves, while the other focuses on the development of current sheets and their role as sites of enhanced dissipation. Here the generation of current sheets is shown to be a natural consequence of strong Alfven wave collisions, explained by constructive interference among the initial waves and nonlinearly generated modes. This discovery resolves the dichotomy between wave and coherent-structure models of plasma turbulence, leading to the expectation that Landau damping of the constituent Alfven waves plays a role in current sheet dissipation.   

Energy Transfer Mechanisms in Weakly Collisional Plasma Turbulence

We present a general picture of possible energy transfer mechanisms between particles and turbulent fields in weakly collisional plasmas. These mechanisms are the crucial steps leading to the dissipation of turbulence energy into plasma heat. We elucidate their significance as a function of spatial and velocity space. We also highlight ongoing effort with gyrokinetic simulations that support this picture. A range of plasma beta values suitable for space and astrophysical systems are considered in which one mechanism can play a more dominant role over another. Preliminary results will be discussed.   

Kinetic Simulations of Astrophysical Collisionless Turbulence

In many astrophysical systems collisionless plasma turbulence is thought to play a significant role in mitigating energy transport across scales. For example, local energy input from dissipation of turbulence is often invoked to explain the energy balance of the solar corona and the solar wind. At the same time, understanding of the dissipation mechanisms in collisionless plasma turbulence remains incomplete to say the least. We discuss our recent results from kinetic simulations of collisionless turbulence with parameters relevant to the solar wind. Specifically, large-scale hybrid simulations (fully kinetic ions and massless fluid electrons) are used to study ion anisotropies and dynamics of current sheets and magnetic reconnection at MHD scales. Fully kinetic particle-in-cell simulations are used to study the dynamics of turbulence at and below proton scales, focusing on formation of electron-scale current sheets and coupling between fluctuations at relatively low and high frequencies (compared to proton gyrofrequency).   

A Gyrokinetic Study of Intermittency and Coherent Structures in Kinetic Alfv\'{e}nic Turbulence

Turbulence is a ubiquitous process in space and astrophysical plasmas that serves to mediate the transfer of large-scale motions to small scales at which the turbulence can be dissipated and the plasma heated. In situ solar wind observations and direct numerical simulations demonstrate that sub-proton scale turbulence is dominated by highly anisotropic and intermittent, low frequency, kinetic Alfv\'{e}nic fluctuations. Previous gyrokinetic studies of kinetic Alfv\'{e}n wave turbulence have focused on the energy transport and wave-like properties of the turbulence; however, a recent gyrokinetic simulation examined the non-local and non-self-similar nature of the energy cascade. We use the same simulation data to examine the intermittency and coherent structures that are responsible for the non-local energy cascade.   

Phase mixing vs. nonlinear advection in drift-kinetic plasma turbulence

A scaling theory of drift-kinetic turbulence in a weakly collisional plasma is proposed, with account both of the nonlinear advection of the perturbed particle distribution by the fluctuating ExB flow and of its parallel phase mixing, which in a linear problem causes Landau damping. It is found that little free energy leaks into high velocity moments of the distribution, rendering the turbulence in the energetically relevant part of the wave-number space essentially fluid-like. The velocity-space free-energy spectra expressed in terms of Hermite moments are steep power laws and so the energy content of the phase space does not diverge and collisional heating due to long-wavelength perturbations vanishes at inifinitesimal collisionality (both in contrast with the linear problem). The ability of the energy to stay in the low moments is facilitated by ``anti-phase-mixing,'' which in the nonlinear system is due to the stochastic version of plasma echo (the advecting flow couples the phase-mixing and anti-phase-mixing perturbations). The partitioning of the wave-number space between the (energetically dominant) region where this is the case and the region where linear phase mixing wins its competition with nonlinear advection is governed by the ``critical balance'' between linear and nonlinear timescales, which for high Hermite moments splits into two thresholds, one demarcating the wave-number region where phase mixing predominates, the other where plasma echo does.   

Energy transfer and shear flow generation in plasma interchange turbulence

Energy transfer and ${\mathbf E} \times {\mathbf B}$ shear flow generation in plasma interchange turbulence are examined in a flux-driven system with both closed and open magnetic field lines. The nonlinear evolution of interchange turbulence shows the presence of two regimes characterized by low and high ${\mathbf E} \times {\mathbf B}$ flow shear. In the first regime, the mean ${\mathbf E} \times {\mathbf B}$ shear flow is at a relatively low level and the large-amplitude ${\mathbf E} \times {\mathbf B}$ velocity fluctuation dominates in the nonlinear saturated state. By increasing the heat flux that drives the system, the fluctuation-induced energy transfer becomes stronger and a transition to the second regime occurs, in which a high mean ${\mathbf E} \times {\mathbf B}$ flow shear is generated.   

Direct measurements and modeling of gradient-aligned cross-field ion flows near an absorbing boundary

Direct measurements of cross-field ion transport near boundaries are sought for validating transport models in magnetically confined plasmas. Using laser-induced fluorescence, we measured ion flows normal to an absorbing boundary that was aligned to be parallel to a uniform axial magnetic field in a helicon plasma. We used Langmuir and emissive probes to measure local density, temperature and plasma potential profiles in the same region. We then scanned ion-neutral collisionality by varying the ratio of the ion gyro-radius, $\rho_{i}$, and ion-neutral collision length, $\lambda $, over the range 0.34 $\le \rho_{i}$/$\lambda \le $1.60. Classical diffusion along density and potential gradients is sufficient to describe flow profiles for most cases but did not describe measurements well for 0.44 $\le \rho_{i}$/$\lambda \le $ 0.65. In these cases, cross-sections $\approx $3 times the classical prediction produced acceptable fits, and flow to the boundary was enhanced significantly. These enhanced flow cases exhibit spectra with low-frequency electrostatic fluctuations (f \textless 10 kHz) that are not observed in data described well by a classical diffusion model.   

Scaling of Electron Thermal Conductivity during the Transition between Slab and Mixed Slab-Toroidal ETG Mode

Transition from the slab to the toroidal branch of the electron temperature gradient (ETG) mode has been successfully achieved in a basic experiment in Columbia Linear Machine CLM [1]. We found a modest increase in saturated ETG potential fluctuations $ (\sim 2 \times) $ and a substantial increase in the power density of individual mode peaks $( \sim 4-5 \times) $ with increased levels of curvature. We have obtained a set of experimental scalings for electron thermal conductivity $ \chi_{\bot e}$ as a function of the inverse radius of curvature $ R_c ^{-1} $ for different fluctuation levels of the initial slab ETG mode. We found that thermal conductivity for pure slab modes is larger than it is for mixed slab-toroidal ETG modes with the same level of mode fluctuation. This effective reduction in diffusive transport can be partly explained by the flute nature of the toroidal ETG mode.\\[4pt] [1] A. Balbaky, V. Sokolov and A.K. Sen, Phys.Plasmas 22.   

2D Spinodal Decomposition in Forced Turbulence

Spinodal decomposition is a second order phase transition for binary fluid mixture, from one thermodynamic phase to form two coexisting phases. The governing equation for this coarsening process below critical temperature, Cahn-Hilliard Equation, is very similar to 2D MHD Equation, especially the conserved quantities have a close correspondence between each other, so theories for MHD turbulence are used to study spinodal decomposition in forced turbulence. Domain size is increased with time along with the inverse cascade, and the length scale can be arrested by a forced turbulence with direct cascade [1]. The two competing mechanisms lead to a stabilized domain size length scale, which can be characterized by Hinze Scale. The 2D spinodal decomposition in forced turbulence is studied by both theory and simulation with ``pixie2d.'' This work focuses on the relation between Hinze scale and spectra and cascades. Similarities and differences between spinodal decomposition and MHD are investigated. Also some transport properties are studied following MHD theories. This work is supported by the Department of Energy under Award Number DE-FG02-04ER54738. \\[4pt] [1] Perlekar, et al. Physical Review Letters 112.1 (2014): 014502.   

Flow driven inward particle flux and enstrophy production constraint on relaxation in Hasegawa-Wakatani turbulence

The relation between the physics of turbulent transport of particles and momentum is investigated, using the Hasegawa-Wakatani model, with both a density gradient and a quasi-equilibrium shear (zonal) flow. For axisymmetric $(k_\parallel = 0)$ fluctuations, pure KH instabilities, energized by the flow shear, relax the flow and drive an outward (down the density gradient) flux of particles $(\Gamma = \langle\tilde n\tilde v_x \rangle > 0$, where $\Gamma$ is the non-dimensional turbulent particle flux). However, for drift-KH instabilities of finite $k_\parallel$, flow enhanced pumping can locally drive an inward particle flux. Moreover, we use the positivity of the production of the fluctuation potential enstrophy to obtain a constraining relation between the momentum and particle transport. This constraint relation asserts that the turbulent vorticity flux $\Pi_{\omega}$ of a system which has a local inward particle flux $(\Gamma<0)$ must locally satisfy $\Pi_{\omega}<\Gamma<0$. This can lead to the change in the sign of the Reynolds work and relaxation of the flow shear at the radial location of the occurrence of the inward flux. Ongoing work focuses on determining the dependencies of the turbulent viscosity.   

Excitation of Kinetic Geodesic Acoustic Modes by Drift Waves in Nonuniform Plasmas

Spontaneous excitation of geodesic acoustic mode (GAM) by drift wave turbulence (DW), which is expected to play an important role in the DW saturation process, is investigated including effects of system nonuniformities and kinetic plasma response. The coupled equations describing the fully nonlinear interaction between GAM and DW are derived based on the nonlinear gyrokinetic theory, and then we solved both analytically and numerically to investigate the spatial-temporal evolution of the coupled DW-GAM system. Kinetic effects as well as nonuniformities due to diamagnetic frequency profile, finite radial envelope width of DW pump and GAM continuum are systematically included in the analysis. It is found that the parametric decay process is a convective instability for typical tokamak parameters, when finite group velocities of DW and GAM associated with kinetic effects and finite radial envelope width are taken into account. The nonlinearly driven GAM propagates at a group velocity, that, due to coupling with DW, is typically much larger than that predicted by the linear theory of GAM. When, however, nonuniformity of diamagnetic frequency is taken into account, the parametric decay process becomes, time asymptotically, a quasi-exponentially growing absolute instab   

Many mini-Maxwellian method for full 6D kinetic simulation of drift wave turbulence

It was recently shown that expansion of the full kinetic velocity distribution function as a sum of Gaussian Radial Basis Functions can exactly solve the nonlinear inverse-square force Fokker-Planck collision operator [1]. Here we apply this method of \textit{many} \textit{mini-Maxellians} to develop a new code for full 6D kinetic simulation of electrostatic drift wave turbulence with ion temperature gradient modes and adiabatic electrons in tokamak geometry. A linear Krook collision model keeps the local ion distribution function close to Maxwellian. The code is spectral in toroidal modes and formulated for delta-f and full-f, linear and nonlinear, local and global radial slice simulations. Suppression of irrelevant high-frequency ion cyclotron motion and short Debye length scales pose significant challenges for 6D simulations. The field solve compares a quasi-neutrality model with solution of the Poisson equation at large relative Debye length.\\[4pt] [1] E.\ Hirvijoki, J.\ Candy, E.\ Belli, and O.\ Embreus, ``The Gaussian Radial Basis Function Method for Plasma Kinetic Theory,'' submitted to Phys. Lett. A   

A Reduced Model of ExB and PV Staircase Formation and Dynamics

Staircases are patterns consisting of narrow, quasi-periodic corrugations interspersed by regions of partially flattened gradients or steps. Staircases are secondary pattern structures, produced by generalized ``negative diffusivity'' mechanisms, which trigger first order transitions. We develop a simple reduced model for PV gradient driven staircases, which evolves mean field and potential enstrophy density. Two different approaches yield the same model structure. The model conserves enstrophy, explicitly. Numerical solutions show the appearance of staircases, followed by multiple time scale step coalescence and competition dynamics. An interesting feature is that turbulence spreading is sufficient to maintain the step width. Further results and extensions will be discussed.   

Collisionless Zonal Flow Saturation for Weak Magnetic Shear

The damping of the zonal flow, either collisional or collisionless, plays an important role in regulating the drift wave-zonal flow system, and can affect the transport and confinement. The tertiary instability, e.g., a generalized Kelvin-Helmholtz (KH) instability driven by flow shear, has been suggested theoretically as a possible damping mechanism [Rogers 2000 PRL, Diamond 2005 PPCF]. The sensitivity of the tertiary mode to magnetic shear has not been quantified, especially in weak magnetic shear regimes. In this work, parametric scans using gyrokinetic simulation demonstrate that the zonal electric field energy normalized by the turbulence electric field energy decreases as magnetic shear decreases. With ITG drive artificially eliminated, the time evolution of the zonal structure indicates that the zonal electric field damps more rapidly at weak shear. This suggests larger collisionless zonal flow damping or larger effective turbulent viscosity at weak magnetic shear. The effects of the zonal components of specific variables, e.g., the parallel shear flow and the radial electric field, on tertiary instability, are also studied. Quantitative studies on the magnetic shear scaling of tertiary instability excitation and the collisionless zonal flow saturation are ongoing.   

Kinetic electron dynamics and short scales in gyrokinetic simulations

A recent study [1] with the flux-tube version of the Eulerian gyrokinetic code GENE showed how turbulence transport, both in the ion temperature gradient and trapped electron mode regime, is affected by the presence of fine radial structures on the fluctuating fields. These structures are located near low order mode rational surfaces and result from the non-adiabatic response of passing electrons. This study has now been pursued in global geometry with the gyrokinetic particle-in-cell code ORB5, for which a new quasi-neutrality field solver, valid to all orders in $k_\perp\rho$ ($k_\perp$ the perpendicular wavenumber and $\rho$ the Larmor radius), has been implemented using a finite element method similar to Ref. [2]. The linearized polarization drift term in this solver appears as an integral operator, involving a phase space integration evaluated on an Eulerian grid.\\[4pt] [1] J Dominski et al., {\it Phys. Plasmas} \textbf{22}, 062303 (2015)\\[0pt] [2] A Mishchenko et al., {\it Phys. Plasmas} {\bf 12}, 062305 (2005)   

Observation of edge turbulence spread by ECEI on the ELM-crash-suppressed plasmas in the KSTAR

The structure and dynamics of the ELM and edge turbulence modified by $n=1$ RMP have been studied during the ELM-crash-suppression phase by applying correlation analysis techniques on the measured ECEI signals. The ECEI shows that filamentary modes remained at theedge with frequent bursts during ELM-crash-suppression phase. The filamentary mode fluctuates in the range of $20$ kHz and the dynamics of the mode seems to be violent and complex compared to the ELMing H-mode phase. Correlation analysis shows corresponding fluctuations have long poloidal wavelength (or small poloidal wavenumber $k_{\theta}<1$ cm$^{-1}$) with smaller size compared to the filamentary mode, and average group velocity of $\sim3$ km/s along the electron diamagnetic direction, parallel wavelengths in the range of $2<\lambda_{||}<8$ m. The characteristic size in the order of $k_{\theta}\rho_s\sim0.1$ and velocimetry analysis suggest the resistive ballooning mode is a strong candidate for edge fluctuation in the ELM-crash-suppression phase.   

Symmetry Breaking by Parallel Flow Shear

Plasma rotation is important in reducing turbulent transport, suppressing MHD instabilities, and is beneficial to confinement. Intrinsic rotation without an external momentum input is of interest for its plausible application on ITER. $k_\|$ spectrum asymmetry is required for residual Reynolds stress that drives the intrinsic rotation. Parallel flows are reported in linear devices without magnetic shear. In CSDX, parallel flows are mostly peaked in the core [Thakur, et al. 2014]; more robust flows and reversed profiles are seen in PANTA [Oldenburger, et al. 2012]. A novel mechanism for symmetry breaking in momentum transport is proposed. Magnetic shear or mean flow profile are not required. A seed parallel flow shear (PFS) sets the sign of residual stress by selecting certain modes to grow faster. The resulted spectrum imbalance leads to a nonzero residual stress, which further drives a parallel flow with $\nabla n$ as the free energy source, adding to the shear until saturated by diffusion. Balanced flow gradient is set by $\Pi_\|^{Res}/\chi_\phi$. Residual stress is calculated for ITG turbulence and collisional drift wave turbulence where electron-ion and electron-neutral collisions are discussed and compared. Numerical simulation is proposed for testing the effect of PFS.   

2-D/3-D ECE imaging data for validation of turbulence simulations

The 2-D/3-D KSTAR ECEI diagnostic can provide a local 2-D/3-D measurement of ECE intensity. Application of spectral analysis techniques to the ECEI data allows local estimation of frequency spectra $S(f)$, wavenumber spectra $S(k)$, wavernumber and frequency spectra $S(k,f)$, and bispectra $b(f_1,f_2)$ of ECE intensity over the 2-D/3-D space, which can be used to validate turbulence simulations. However, the minimum detectable fluctuation amplitude and the maximum detectable wavenumber are limited by the temporal and spatial resolutions of the diagnostic system, respectively. Also, the finite measurement area of the diagnostic channel could introduce uncertainty in the spectra estimation. The limitations and accuracy of the ECEI estimated spectra have been tested by a synthetic ECEI diagnostic with the model and/or fluctuations calculated by GTS.   

Geodesic Curvature Effects in the WCMs

The favorable features of the steady state I-Regime [1,2] discovered on Alcator C-Mod recently make this regime a hopeful working regime for future burning plasma experiments. Accompanying the I-regime are the weakly coherent modes (WCMs)[1,2] with frequency around 200 kHz that propagate poloidally in the electron diamagnetic drift direction in the lab frame. The WCMs were interpreted [3,4] as certain type of heavy impurity modes in the 3-fluid framework in a 1-D plane magnetic field geometry. Once considering in a simplified toroidal magnetic field geometry, the geodesic curvature will play important roles in that the contribution of the geodesic compression may catch up with or outweighs that of the parallel compression in the plasma edge region where the fluctuations are highly localized. This geodesic coupling to the neighboring bands modifies the marginal stability condition and mode profiles in Refs.[3,4]. In the same framework, attempts will be made to interpret the concomitant low frequency ($\sim$ 20kHz) fluctuations as a type of impurity drift wave-like modes propagating in the ion diamagnetic drift direction.\\[4pt] [1] D.Whyte, et al., Nucl. Fusion,(2010).\\[0pt] [2] A.Hubbard, et al., Phys. Plasmas,(2011).\\[0pt] [3] B.Coppi, T.Zhou, Phys. Lett. A, 2916(2011).\\[0pt] [4] B.Coppi, T.Zhou, Phys. Plasmas, 012302(2012).\\[0pt] [5] I.Cziegler, MIT Ph.D. Thesis (2011).   

Study of intrinsic toroidal rotation in TCV discharges with microturbulence simulations

Plasma rotation and associated velocity shear are known to play an important role in the formation of transport barriers. In many current tokamaks the main source of toroidal rotation is the Neutral Beam Injection (NBI). However, in certain machines with no NBI, such as TCV, plasma rotation is still observed. This so-called intrinsic rotation is of much interest in view of ITER, given the relatively limited penetration depth of NBI beams in this device. Remarkable observations have been made on TCV, as reported in [A. Bortolon et al. 2006 Phys Rev. Lett. 97], exhibiting in particular a rotation inversion phenomenon occurring in conjunction with a relatively small change in the plasma density. A possible explanation for this behaviour has been suggested in form of a transition in the microturbulence with increasing collisionality ($\sim$density) from a dominantly TEM regime to a dominantly ITG regime. We are currently starting to analyse the intrinsic rotation observations on TCV in the framework of gyrokinetic turbulent transport modeling, performing flux-tube simulations with the local version of the GENE code [F. Jenko et al. 2000 Phys. Plasmas 7] at different minor radius positions, characterising the turbulence and computing the associated toroidal momentum flux.   

Universal instability, non-modal amplification, and subcritical turbulence

The ``universal instability'' has been discounted since studies in 1978 found this drift wave to be absolutely stable for nonzero magnetic shear. We challenge this finding and demonstrate a variety of interesting behaviors in this sheared slab system: (1) The 1978 work was limited to $k \rho < 1$, but we show in gyrokinetics the linear mode with shear can be absolutely unstable for $k \rho > 1$ even with no temperature gradients, no trapped particles, and no magnetic curvature [1]. (2) Even if the system is linearly stable, significant transient linear amplification can occur [2]. Flow shear is unnecessary for this growth, in contrast to Navier-Stokes linear transients. (3) Turbulence can be sustained even if all linear eigenmodes are decaying [2], as seen previously in fluid models [3-4] and which we demonstrate kinetically. We generalize a Navier-Stokes proof [5] that transient linear amplification is required for sustained turbulence. While unstable eigenmodes are not necessary for sustained turbulence, a modified eigenvalue problem does provide a necessary condition [2].\\[4pt] [1] Landreman et al PRL 114, 095003 (2015).\\[0pt] [2] Landreman et al J Plasma Phys 81, 905810501 (2015).\\[0pt] [3] Scott, PRL 65, 3289 (1990).\\[0pt] [4] Drake et al, PRL 75, 4222 (1995).\\[0pt] [5] DelSole, J Atmos Sci 61, 1086 (2004).   

On the nonlinear generation of zonal flows by turbulence in stellarators

Stellarators are a relatively fresh context in which to study zonal flows. As in tokamaks, the presence of these flows is thought to lessen the intensity of turbulence and transport. An interesting question is how the peculiarities of magnetic geometry affect the interaction between turbulence and zonal flows. In this work we investigate this question theoretically, and by direct numerical simulation. We generalize the secondary instability theory of Rogers, et al (2000) to allow for arbitrary magnetic field geometry, and test its predictions directly against gyrokinetic simulations. Our theoretical findings suggest that the turbulence should be less effective at driving zonal flows when it is localized within a flux surface, and we present a series of linear and nonlinear simulations demonstrating this effect. Because turbulence in stellarators tends to be spatially localized by features of the magnetic geometry, like the variation of curvature and shear, we argue that weaker zonal flows should be generally expected. However, this effect may be balanced by the enhancement of other saturation mechanisms unrelated to zonal flows, acting to lower the overall intensity of the turbulence.   

Investigating the Dimits Shift using the Second-order Cumulant Expansion Statistical Closure

The Dimits shift is the nonlinear upshift of the critical temperature gradient that signals the onset of collisionless ion-temperature-gradient-driven turbulence.\footnote{A. M. Dimits, et al., Phys. Plasmas \textbf{7}, 969 (2000).}$\!^,$\footnote{B. N. Rogers, et al., Phys. Rev. Lett. \textbf{85}, 5336 (2000).} This phenomenon is caused by the shearing away of turbulent streamers in the radial direction by poloidal zonal flows (ZFs). While the effect is witnessed in both gyrokinetic and gyrofluid simulations, there exists no analytical model that satisfactorily describes the mechanics through which it operates. In this work, a new model is developed by applying the second-order cumulant expansion closure to a simplified set of gyrofluid equations.\footnote{M. Ottaviani, et al., Phys. Rep. \textbf{283}, 121 (1997).} In particular, we calculate the threshold for the zonostrophic instability\footnote{K. Srinivasan and W. R. Young, J. Atmos. Sci. \textbf{69}, 1633 (2012).} of a two-field model, generalizing the work of Parker and Krommes\footnote{J. B. Parker and J. A. Krommes, New J. Phys. \textbf{16}, 035006 (2014).} on the modified Hasegawa--Mima equation, and assess whether the Reynolds-stress-generated ZFs can be destabilized in the model, thus indicating a Dimits shift.   

Derivation of the Direct-Interaction Approximation Using Novikov's Theorem

The direct-interaction approximation (DIA)\footnote{R. H. Kraichnan, J. Fluid Mech. {\bf5}, 497 (1959).} is a crucially important statistical closure for both neutral fluids and plasmas. Kraichnan's original derivation proceeded in $k$~space and assumed a large number~$N$ of interacting Fourier modes. That is problematic; the DIA can be formulated even for $N = 3$. In the present work an alternate $x$-space procedure based on Novikov's theorem is described. That theorem is a statement about the correlations of certain Gaussian functionals. Turbulence cannot be Gaussian due to nonlinearity, but Novikov's theorem can be used to formulate self-consistent equations for a Gaussian component of the turbulence. The DIA emerges under the assumption that certain higher-order correlations are small. In essence, this procedure is merely a restatement of Kraichnan's arguments, but it adds additional perspective because the assumption of large~$N$ is not required. Details can be found in a lengthy set of tutorial Lecture Notes.\footnote{J. A. Krommes, A tutorial introduction to the statistical theory of turbulent plasmas, a half-century after Kadomtsev's \textsl{Plasma Turbulence} and the resonance-broadening theory of Dupree and Weinstock, J. Plasma Phys., in press.}   

Unitary qubit extremely parallelized algorithms for coupled nonlinear Schrodinger equations

The nonlinear Schrodinger equation (NLS) is a ubiquitous equation occurring in plasma physics, nonlinear optics and in Bose Einstein condensates. Viewed from the BEC standpoint of phase transitions, the wave function is the order parameter and topological defects in that manifold are simply the vortices, which for a scalar NLS have quantized circulation. In multi-species NLS the topological nature of the vortices are radically different with some classes of vortices no longer having quantized circulation as in classical turbulence. Moreover, some of the vortex equivalence classes need no longer be Abelian. This strongly effects the permitted vortex reconnections. The effect of these structures on the spectral properties of the ensuing turbulence will be investigated. Our 3D algorithm is based on a novel unitary qubit lattice scheme that is ideally parallelized - tested up to 780 000 cores on Mira. This scheme is mesoscopic (like lattice Boltzmann), but fully unitary (unlike LB).   

Lattice Boltzmann LES for MHD Turbulence

Dellar's lattice Boltzmann (LB) model of 2D incompressible MHD introduced both a scalar velocity and vector magnetic distribution functions, which automatically enforces div B = 0 through the trace of an antisymmetric perturbed tensor. In the Smagorinsky LES model, the filtered Reynolds stresses are modeled by mean field gradient terms, with ad hoc closure eddy transport terms. Ansumali et. al. have developed an LES for Navier-Stokes turbulence by filtering the underlying mesoscopic LB. The filtered LB equations are then subjected to the Chapman-Enskog expansion. A Smagorinsky-like LES is recovered with no ad hoc assumptions other than the subgrid terms contribute only at the transport time scales. Here we extend these ideas to 2D MHD turbulence. The DNS data base is being generated from a multiple relaxation time (MRT) model with a quasi-entropic analytic scheme introduced recently by Karlin et. al. (2014) based on splitting the moment representation into various subgroups.   

Impurity Effects on Momentum Transport and Residual Stress

Impurities are inevitable during tokamak plasma operation because of strong interaction of plasma and plasma facing component and helium ash as a byproduct of fusion process. They cause problems such as radiation power loss and fusion fuel dilution. On the other hands, they are used to diagnosis plasma parameters (CES, XICS etc) and to suppress edge-localized mode by wall-coating. In this research, we study the impact of impurities on turbulence driven intrinsic rotation (via residual stress) in the context of the quasi-linear theory. A two-fluid formulation for main and impurity ions is employed to study ion temperature gradient modes in sheared slab geometry modified by the presence of impurities. An effective form of the parallel Reynolds stress is derived in the center of mass frame of a coupled main ion-impurity system. Analyses show that the contents and the radial profile of impurities have a strong influence on the residual stress. In particular, an impurity profile aligned with that of main ions is shown to cause a considerable reduction of the residual stress, which may lead to the reduction of turbulence driven intrinsic rotation.   

Bounce-averaged kinetic theory for a D-shape plasma and its application for ITG-TEM turbulence simulation

A general D-shape plasma with shaping effects including elongation, triangularity, and Shafranov shift has significant effects on the tokamak performance. Important physics phenomena in tokamaks associated with relatively low frequency fluctuations, such as ion temperature gradient (ITG) mode, trapped electron mode (TEM), and turbulence driven \textbf{E} $\times$ \textbf{B} flows etc., can be influenced by the shaping effects. Meanwhile, it has already been demonstrated that bounce-averaged kinetic theory is a sophisticated tool to provide a firm foundation for the description of such low frequency turbulence phenomena [1,2]. Thus, in this study, we extend the previous bounce-averaged kinetic theory to be applicable for a D-shape plasma by taking into account of the shaping effects. The extended bounce-averaged kinetic theory is self-consistent and can be used, for a computational simulation purpose, to study the shaping effects on the low frequency ITG-TEM turbulence in general tokamak geometry. We apply the extended theory to model kinetic electron responses in the gyrokinetic simulation code gKPSP [3]. Several benchmark simulation results will be presented to demonstrate the applicability and efficiency of the bounce-averaged kinetic electron model in general tokamak geometry. \\[4pt] [1] B.H. Fong and T.S. Hahm, Phys. Plasmas 6, 188 (1999)\\[0pt] [2] Y. Idomura et. al., J. Plasma Fusion Res. 6, 17 (2004)\\[0pt] [3] J.M. Kwon et. al., Phys. Plasmas 21, 013004 (2012)   

Turbulence driven particle pinch at the pedestal region in EAST

Existence of an anomalous inward particle flux in tokamak has been realized for a long time. Since particle transport up the density gradient particularly play a key role on the formation of edge pedestal in H-mode plasma, intensive efforts were made to identify the origin of particle pinch in tokamak. However, the mechanism of particle pinch is still a big challenge for plasma physics. In order to improve our understanding on inward particle pinch, turbulent transport have been investigated in boundary plasma with reciprocating Langmuir probe measurements on EAST. A broad turbulence is detected in pedestal after the L-H transition, which shows as fast (300kHz-500kHz) fluctuations in floating potential signals. It appears and gradually saturates after the dithering phase. The broad turbulence is ultimately terminated by the break out of ELMs. It is observed that most of the particle transport is outward directed before the emergence of broad turbulence. However, the particle transport is reversed to inward direction once the broad turbulence initializes in pedestal. Moreover, the edge pedestal starts to establish at the onset of the observed broad turbulence. It gradually stabilizes with the saturation of broad turbulence. During this period, the fluctuations and associated transport in the SOL are almost unaffected, which suggests a signature of particle pinch induced by the broad turbulence originating at the pedestal region.   

Initial results of LOC to SOC transition experiment in HL-2A tokamak

Dedicated experiment of LOC (linear Ohmic confinement) to SOC (saturated Ohmic confinement) transition was carried out in the HL-2A tokamak during the last campaign. The line-averaged density was ramped up from 0.6x10$^{19}$/m$^{3}$ to 1.5x10$^{19}$/m$^{3}$ under limiter configuration. The energy confinement time was observed to linearly increase with density and then saturate around line-averaged density $\sim$ 1.0x10$^{19}$/m3 (density in the core is around 2.0x10$^{19}$/m$^{3}$). The Shimomura density threshold was estimated as 1.9x10$^{19}$/m$^{3}$. A Langmiur probe array was plunged into the plasma during the whole density ramp up period, which measured the particle and momentum fluxes during the transition. Data from DBS and ECE will also be presented. The transition under divertor configuration was not found during density ramp up all the way to the density limit.   

A simple model for transport control as a possible mechanism for the I-mode and other enhanced confinement regimes

Over the last 2 decades, simple dynamical models have been able to capture a remarkable amount of the dynamics of the core and edge transport barriers found in many devices, including the often disconnected nature of the electron thermal transport channel sometimes observed in the presence of a standard (``ion channel'') barrier. By including in this rich though simple dynamic transport model an evolution equation for electron fluctuations we have investigated the interaction between the formation of the standard ion channel barrier and the somewhat less common electron channel barrier. Further adding to this model a simple model for phase effects, due to multiple instabilities, between the transported fields such as density and temperature, we can investigate whether the dynamics of more continuous transitions such as the I-mode can be captured and understood. If so, what can the model tell us about control knobs for these promising regimes?   

Progress in the study of magnetic dynamo generation processes by non-Gaussian, non-Markovian velocity fluctuations using meshless, Lagrangian numerical schemes

The generation of magnetic dynamos by turbulent velocity fields is traditionally studied, at the simplest level, by assuming near-Gaussian, random velocity fluctuations. This allows to express the effective electromotive force in terms of a piece proportional to the large-scale magnetic field (the $\alpha$-term) and another proportional to its curl (the $\beta$ term), once certain symmetry conditions are assumed. Physically, the $\alpha$-term is a measure of the mean helicity of the flow and drives the dynamo. Previously, we examined theoretically the consequences of assuming instead Levy-distributed, Lagrangianly-correlated velocity fields, which have been recently identified as relevant in regimes of near-marginal turbulence (superdiffusion) or in the presence of strong, stable sheared flows (subdiffusion). Here, we report on recent numerical progress on the study of these processes by implementing the kinematic dynamo equation using a meshless numerical method inspired by the SPH schemes frequently used in hydrodynamics. The results suggest that subdiffusive flows may importantly enhance the dynamo generation, even in the absence of mean helicity, which might be meaningful for the understanding of dynamo generation in situations where sheared, zonal flows are present.   

Characterization of non-diffusive transport in plasma turbulence by means of flux-gradient integro-differential kernels

A method to determine fractional transport exponents in systems dominated by fluid or plasma turbulence is proposed. The method is based on the estimation of the integro-differential kernel that relates values of the fluxes and gradients of the transported field, and its comparison with the family of analytical kernels of the linear fractional transport equation. Although use of this type of kernels has been explored before in this context, the methodology proposed here is rather unique since the connection with specific fractional equations is exploited from the start. The procedure has been designed to be particularly well-suited for application in experimental setups, taking advantage of the fact that kernel determination only requires temporal data of the transported field measured on an Eulerian grid. The simplicity and robustness of the method is tested first by using fabricated data from continuous-time random walk models built with prescribed transport characteristics. Its strengths are then illustrated on numerical Eulerian data gathered from simulations of a magnetically confined turbulent plasma in a near-critical regime, that is known to exhibit superdiffusive radial transport   

Coherent events in the phase of the Fourier spectrum of isotropic 2D turbulence

While studying turbulence it is common to analyze the Fourier transform of the evolved fields. However, most of these studies focus only on the amplitude of the Fourier transform, completely ignoring the complex phase. From the time of Kolmogorov, the slopes of the power spectrum have been extensively investigated. In contrast, studies of the phase are scarce, mainly due to the difficulties of its interpretation. Here, we continue previous studies on a 2D plasma turbulence model in which we showed that clear coherent patterns do appear in the complex phase of the Fourier spectrum, mainly within the dissipation range. These events have been shown to be associated with intermittent structures in real space.\footnote{J.M. Reynolds-Barredo et al., 54th APS (2012)} In this contribution, these results have also been obtained using the more general case of 2D incompressible Navier-Stokes equations, including different types of dissipation. The conclusions of our previous work remain in the sense that the coherent events continue to appear intermittently in the phase, being rather insensitive to the particular details of the model. This is the first time that such clear coherence patterns have been identified in the phase of the Fourier spectrum for a turbulence simulation.   

Control of ITBs in Fusion Self-Heated Plasmas

Simple dynamical models have been able to capture a remarkable amount of the dynamics of the transport barriers found in many devices, including the often disconnected nature of the electron thermal transport channel sometimes observed in the presence of a standard (``ion channel'') barrier. By including in this rich though simple dynamic transport model an evolution equation for electron fluctuations we have previously investigated the interaction between the formation of the standard ion channel barrier and the somewhat less common electron channel barrier. The electron channel formation and evolution is even more sensitive to the alignment of the various gradients making up the sheared radial electric field then the ion barrier is. Because of this sensitivity and coupling of the barrier dynamics, the dynamic evolution of the fusion self-heating profile can have a significant impact on the barrier location and dynamics. To investigate this, self-heating has been added this model and the impact of the self-heating on the formation and controllability of the various barriers is explored. It has been found that the evolution of the heating profiles can suppress or collapse the electron channel barrier. NBI and RF schemes will be investigated for profile/barrier control.   

Mechanisms of non-diffusive transport in a simple two-dimensional plasma fluid turbulence model

Ingredients for non-diffusive transport have been identified in a simple two-dimensional electrostatic plasma fluid turbulence model with a flux-driven background profile. The numerical model advances two turbulence fields (density and potential), and a flux-driven background profile. Directional dependent critical gradients coupled with the flux-driven profile enable super-diffusive transport. Sub-diffusive transport in the cross-flow direction occurs with an externally driven shear flow or a self-consistently generated flow. The competition between super-diffusive transport and sub-diffusive transport occurs in parameter regimes where the shear rate is sufficiently large enough to interfere with the super-diffusive transport induced by the radial critical gradient. A numerical extension to this model enables an investigation into the impact of a local perturbation on transport. This concept allows a comparison between passive scalar measurements and the Lagrangian trajectories in order to investigate the correspondence between transport measurements done experimentally and analytically. The transport quantification due to a local perturbation will also be applied to experimental edge plasma measurements.   

Triad interactions in multi-scale ITG/TEM/ETG turbulence

Most of turbulent transport studies assume scale separation between electron- and ion-scale turbulence. However, latest massively parallel simulations based on gyrokinetics reveal that multi-scale interactions between electron- and ion-scale turbulence can influence turbulent transport [S. Maeyama, Phys. Rev. Lett. 114, 255002 (2015)]. The physical mechanism is investigated by applying triad transfer analysis. It is revealed that short-wave-length ITG turbulent eddies stabilize electron-scale streamers. Additionally, it is found that electron-scale turbulence has a damping effect on zonal flows. As a result, turbulent transport spectrum obtained from the multi-scale turbulence simulation differs from the sum of ones obtained from single-scale simulations. We will discuss gyrokinetic triad transfer analysis and the applicability of its fluid approximation, and explain the physical mechanism of multi-scale interactions by means of triad transfer analysis.   

Global gyrokinetic simulations of microturbulence for TCV-relevant plasmas

Due to significant global effects, in smaller-sized tokamaks such as TCV local (flux-tube) microturbulence simulations are unable to fully reproduce experimental transport levels. We will therefore present results obtained with the global version of the gyrokinetic code GENE aiming at addressing two observations made on TCV. 1) Effect of negative triangularity: it has been experimentally demonstrated that half the heating power is required to maintain the same electron temperature profile when the sign of triangularity of the Last Closed Flux Surface is reversed from $\delta$=0.4 to -0.4 . Local simulations fail at reproducing both the actual transport level and positive/negative $\delta$ flux ratio. Therefore global simulations have been carried out with the aim of recovering the experimental results. 2) GAM physics: a complete multi-diagnostic characterization of the Geodesic Acoustic Mode has been reported from TCV. In particular the dependency of frequency, radial location and wave vector on plasma parameters have been experimentally investigated. Global runs modeling these TCV conditions will be discussed and simulations compared to experiments with the help of synthetic diagnostics.   

Effects of Multi-Point Current-Injection Feedback on Interchange Turbulence in a Dipole-Confined Plasma

Plasma confined by a strong dipole field exhibits low-frequency interchange turbulence, which previous experiments have shown responds locally to active feedback, primarily in the direction of the electron magnetic drift [1]. New experiments on the Collisionless Terella Experiment (CTX) use a system of two electrodes with 90$^\circ$ azimuthal separation to study the effects of multi-point current-injection feedback on interchange turbulence. Initial open-loop experiments to excite low-frequency waves at a variety of relative phases and amplitudes indicate a significantly stronger spatial coherence when two electrodes are used rather than one. These driven low-frequency waves also generate harmonics which can persist throughout the plasma. In a closed-loop active feedback configuration, this system may be used to regulate the turbulent dynamics in new ways.\\[4pt] [1] Roberts, Mauel, and Worstell, Phys Plasmas \textbf{22}, 055702 (2015).   

Statistical properties of the gyro-averaged standard map

A statistical study of the gyro-averaged standard map (GSM) is presented. The GSM is an area preserving map model proposed in [J. Fonseca, et al., Phys. of Plasmas \textbf{21}, 092310 (2014)] as a simplified description of finite Larmor radius (FLR) effects on ExB chaotic transport in magnetized plasmas with zonal flows perturbed by drift waves. The GSM's effective perturbation parameter, gamma, is proportional to the zero-order Bessel function of the particle's Larmor radius. In the limit of zero Larmor radius, the GSM reduces to the standard, Chirikov-Taylor map. We consider plasmas in thermal equilibrium and assume a Larmor radius' probability density function (pdf) resulting from a Maxwell-Boltzmann distribution. Since the particles have in general different Larmor radii, each orbit is computed using a different perturbation parameter, gamma. We present analytical and numerical computations of the pdf of gamma for a Maxwellian distribution. We also compute the pdf of global chaos, which gives the probability that a particle with a given Larmor radius exhibits global chaos, i.e. the probability that Kolmogorov-Arnold-Moser (KAM) transport barriers do not exist.   

The distinctions between amplitude and phase modulations in detecting nonlinear coupling

The amplitude and phase modulations are basic processing in plasma science. The amplitude modulation reflects the parametric instability. And Doppler shift mainly contributes the phase modulation due to plasma rotation in laboratory frame. The bispectral and envelop analysis are widely-used tools for detecting the nonlinear coupling. In this poster, artificial data and real experiment data are used to calculate both bispectra and envelop. The results show that both amplitude and phase modulations have significant amplitude in the bispectra and envelops. Particularly, the cross-phase between envelop and original signal reveals the distinctions of amplitude and phase modulations. Furthermore, the results discover that the basic bispectral analysis is not suitable for examining the nonlinear coupling in some cases.   

Potential Vorticity Dynamics and Models of Zonal Flow Formation

We describe the general theory of anisotropic flow formation in quasi-2D turbulence from the perspective on inhomogeneous potential vorticity (PV) mixing. The aim is to develop a vorticity transport operator, for use in modelling codes. The general structure of PV flux is deduced non-perturbatively using two relaxation models: the first is a mean field theory for the dynamics of selective decay based on the requirement that the mean PV flux dissipates potential enstrophy but conserves kinetic energy. The analyses show that the structure of PV flux has the form of a sum of a hyper-viscous and a viscous flux of PV. In the relaxed state, the ratio of the PV gradient to zonal flow velocity is homogenized. The homogenized quantity sets a constraint on the amplitudes of final-state PV and zonal flow. The second relaxation model is derived from a joint reflection symmetry principle, which constrains the PV flux driven by the deviation from the self-organized state. The form of PV flux contains, in addition to viscous and hyper-viscous terms, a nonlinear convective term, which can be generalized to an effective diffusion, on account of the gradient-dependent ballistic transport in avalanche-like systems. For both cases, the transport coefficients are calculated using perturbation theory.   

Realtime capable first principle based modelling of tokamak turbulent transport

Transport in the tokamak core is dominated by turbulence driven by plasma microinstabilities. When calculating turbulent fluxes, maintaining both a first-principle-based model and computational tractability is a strong constraint. We present a pathway to circumvent this constraint by emulating quasilinear gyrokinetic transport code output through a nonlinear regression using multilayer perceptron neural networks. This recovers the original code output, while accelerating the computing time by five orders of magnitude, allowing realtime applications. A proof-of-principle is presented based on the QuaLiKiz quasilinear transport model, using a training set of five input dimensions, relevant for ITG turbulence. The model is implemented in the RAPTOR real-time capable tokamak simulator, and simulates a 300s ITER discharge in 10s. Progress in generalizing the emulation to include 12 input dimensions is presented. This opens up new possibilities for interpretation of present-day experiments, scenario preparation and open-loop optimization, realtime controller design, realtime discharge supervision, and closed-loop trajectory optimization.   

Simulating Gyrokinetic/fluid hybrid electromagnetic modes in the total-f gyrokinetic code XGC1

XGC1 code has been extended to include the electronmagnetic capability using the hybrid model with gyrokinetic ions and fluid electrons. This feature will enable a more complete description of the MHD/fluid type mode activities including ELMs and low-n tearing modes. Their interaction with the kinetic neoclassical and microturbulence dynamics needs to be simulated together. Evolution of the background profile should also be captured self-consistently. We report recent development and verification of this hybrid model in the limit of small delta-B. The code has been verified for Alfven waves and ITG/KBM transition, and low-n resistive tearing modes. The KBM capability of XGC1 has been verified against the published results from Gyro, GEM, GS2, Gene, and GTC. Detailed verification of resistive tearing modes and kink modes in the toroidal geometry will be also presented. An implicit method is implemented in XGC1 to bypass the Courant condition caused by fast Alfven oscillations.   

Superdiffusion to normal diffusion: particle motion in three-dimensional force-free magnetic fields

Magnetic fields in regions of low plasma pressure and large currents, such as in interstellar space and gaseous nebulae, are force-free as the Lorentz force vanishes. The Arnold-Beltrami-Childress (ABC) field is an example of a three-dimensional, force-free, helical magnetic field. The field lines form complex and varied structures in space that are a mix of regular and chaotic lines of force. Charged particles moving in the region of chaotic field lines exhibit anomalous superdiffusion [1]. The sine field, or the Archontis field, is a special case of ABC field with the cosine terms left out. The lines of force of a sine field are completely chaotic in space. However, the diffusion of particles in the sine field is normal. The time evolution of an ensemble of particles can be divided into three domains. For short times, the motion is essentially ballistic. For intermediate times, the motion is characterized by a decay of the velocity autocorrelation function. For longer times, the particles undergo diffusion. We present results on the diffusion of field lines, and of particles, in the ABC and sine fields. In particular, the transition from superdiffusion to normal diffusion is discussed. \\[4pt] [1] A.K. Ram \textit{et al.}, \textit{Phys. Plasmas} \textbf{21}, 072309 (2014).   

Ion Transport in Collisional Unmagnetized Plasma With Multiple Ion Species

A fluid description of collisional unmagnetized plasma with multiple ion species is of interest for inertial confinement fusion (ICF). Different ions of the ICF capsule plasma can respond differently to the electric field and various gradient drives, resulting in important effects on the capsule implosion and performance not described by single-fluid equations. While multiple ion species plasma fluid descriptions exist, for example in [1], they are incomplete and lacking the calculations of the full array of transport coefficients. Herein, we attack the problem by appropriately generalizing the classical work of Braginskii [2] (a la Chapman-Enskog [3]) to a multi-component plasma. Having derived general equations for plasma transport coefficients, we then consider specific cases of deuterium-tritium plasma without and with presence of a gold component.\\[4pt] [1] V. M. Zhdanov, \textit{Transport Processes in Multicomponent Plasma} (Taylor {\&} Francis, New York, 2002).\\[0pt] [2] S. I. Braginskii, in \textit{Reviews of Plasma Physics}, edited by M. A. Leontovich (Consultants Bureau, New York, 1965), Vol. 1, p. 205.\\[0pt] [3] S. Chapman and T. G. Cowling, \textit{The Mathematical Theory of Non-uniform Gases} (Cambridge University Press, Cambridge, 1995).   

Origin of Non-diffusive Angular Momentum Transport and Spontaneous Rotation

The ``spontaneous rotation'' of axisymmetric plasmas has been confirmed to be connected [1] to the excitation of modes involving the extraction of angular momentum from the plasma column and the recoil of the background plasma in the opposite direction. Since the observed radial profiles of the toroidal rotation velocity are consistent with a transport equation for the angular momentum that is not, in general, of the diffusive type [1], a theoretical model is introduced to identify the modes that can be excited and lead to the presence of an angular momentum ``inflow'' contrary to the direction of diffusion flow. The considered class of modes involves significant electron temperature fluctuations, as evidenced by the experiments. After analyzing several options, the mode found to be most suitable [2] is a development of the toroidal ion temperature gradient mode [3].\\[4pt] [1] B. Coppi, 2000 IAEA Int. Fus. En. Conf. (Vienna, 2000) Paper TH-P1/17; and \textit{Nucl. Fus.} \textbf{42}, (2002) 1.\\[0pt] [2] B. Coppi, B. Basu, P. Montag, L. Sugiyama, T. Zhou, and P. Buratti, Paper presented at the 2014 IAEA Int. Fus. En. Conf. (St. Petersburg, 2014) TH-P7/10; submitted to \textit{Nucl. Fus}.\\[0pt] [3] B. Coppi, M. N. Rosenbluth, and R. Z. Sagdeev, \textit{Phys. Fluids} \textbf{10}, (1967) 582.   

Pressure anisotropy induced by velocity shear

In a collisionless magnetized plasma a sheared velocity field may lead to the anisotropization of an initial Maxwellian state. By including the full pressure tensor dynamics in a fluid plasma model, we show, analytically and numerically, that a sheared velocity field makes an initial isotropic state anisotropic and non-gyrotropic, i.e., makes the plasma pressure tensor anisotropic also in the plane perpendicular to the magnetic field. The propagation of transverse magneto-elastic waves in the anisotropic plasma affects the process of formation of a non-gyrotropic pressure and can lead to its spatial filamentation [1]. This plasma dynamics implies in particular that isotropic MHD equilibria cease to be equilibria in presence of a stationary sheared flow. Similarly, in the case of turbulence, where small-scale spatial inhomogeneities are naturally developed during the direct cascade, we may expect that isotropic turbulent states are not likely to exist whenever a full pressure tensor evolution is accounted for.\\[4pt] [1] D. Del Sarto, {\it et al.}. arXiv:1507.04895 (2015)   

Electron Parallel Closures

Electron parallel closures for ion charge number $Z=1$\footnote{J.-Y. Ji and E. D. Held, Phys. Plasmas {\bf 21}, 122116 (2014).} are extended for $Z>1$. Adopting the same form as the $Z=1$ kernels, parameters are computed for various $Z$. The parameters are smoothly varying in $Z$ and hence can be used to interpolate parameters and closures for noninteger, effective ion charge numbers. Electron parallel closures for $Z=1.8$ and 2.5 are presented as examples.   

Flow topology and Lagrangian conditional statistics in dissipative drift-wave turbulence

Lagrangian statistics in drift-wave turbulence, modeled by the Hasegawa-Wakatani system and its modified version, are investigated. The later shows the emergence of pronounced zonal flows. Different values of the adiabaticity parameter are considered. The main goal is to characterize the role of coherent structures (vortices and zonal flows) on the Lagrangian statistics of particles. Computationally intensive simulations following ensembles of test particles over hundreds of eddy turnover times are considered in statistically stationary turbulent flows. The flow topology is characterized using the Lagrangian Okubo-Weiss criterion [Kadoch et al, Phys. Rev. E \textbf{83} (2011)], and the flow is thus split into topologically different domains. In elliptic and hyperbolic regions, the probability density functions (pdfs) of the residence time have self-similar algebraic decaying tails. However, in the intermediate regions the pdfs do exhibit exponentially decaying tails. Topologically conditioned pdfs of the Lagrangian velocity and acceleration are also computed. The differences between the classical Hasegawa-Wakatani system and its modified version are assessed.   

Recently Observed Features of the Quasi-Coherent Mode and Relevant Theory

Recent experiments [1] have brought to light new features of the so-called Quasi Coherent Mode (QCM) observed when the EDA H-Confinement regime is produced by the Alcator C-Mod machine. This mode 1) has a phase velocity in the direction of the electron diamagnetic velocity in the reference frame where no equilibrium electric field is present; 2) involves relatively high electron temperature fluctuations; 3) is highly localized radially at the outer edge of the plasma column and extending beyond the Last Closed Magnetic Surface (LCMS). According to our theoretical model [2]. i) The relevant resistive mode driving factor is the sharp plasma pressure gradient developing at the edge when the plasma enters the EDA H-Regime. ii) A new kind of mode topology is identified. iii) The mode localization in the poloidal direction (ballooning) is related to the limited region around the equatorial plane where the pitch of the magnetic field is about constant [3]. The electron temperature fluctuations are consistent with the low thermal conductivity in the edge region.\\[4pt] [1] B. LaBombard, Bull. Am. Phys. Soc. 58, (2013) 367.\\[0pt] [2] B. Coppi, B. Basu, et. al., 2014 IAEA Int. Fus. En. Conf. TH-P7/10, submitted to Nucl. Fus.\\[0pt] [3] L. Sugiyama and H. R. Strauss, Phys. Plasmas 17, (2010) 06250.   

New Regime of Low Ion Collisionality in the Neoclassical Equilibrium of Tokamak Plasmas

The neoclassical description of an axisymmetric toroidal plasma equilibrium is formulated for an unconventionally low ordering of the collisionality that suits realistic thermonuclear fusion conditions. This requires a drift-kinetic analysis to the second order of the ion Larmor radius, which yields a new contribution to the leading solution for the non-Maxwellian part of the ion distribution function if the equilibrium geometry is not up-down symmetric. An explicit geometrical factor weighs this second Larmor-radius order, low-collisionality effect that modifies the neoclassical ion parallel flow and the ion contribution to the bootstrap current. For this low-collisionality neoclassical equilibrium solution, the pressure anisotropy part of the Chew-Goldberger-Low stress tensor is comparable to the gyroviscosity and their contributions to the flux-surface-averaged parallel momentum equation balance exactly.   

Simulating the coupled evolution of drift-wave turbulence and the tearing mode

Numerical simulations of turbulence and MHD instabilities such as the tearing mode can be computationally expensive and only recently have simulations begun to address their coupled, self-consistent interactions. The disparate scales involved in simulating the coupled evolution of small-scale turbulence and the larger-scale tearing mode make this a challenging numerical problem. Using the newly developed code, TURBO, we have performed nonlinear simulations of Hasegawa-Wakatani drift-wave turbulence coupled to Ohm's law. An equilibrium with prescribed stability properties and turbulent drives is used to examine the impact of drift-wave turbulence on the stability of the tearing mode and the energy transport between them in the context of a turbulent resistivity and turbulent viscosity. We find that the spatial structure of the density flux and these transport coefficients are asymmetric in the poloidal direction and peaked away from the X-point in the presence of an island in a poloidal flow. Similar effects are seen in simulations of ITG turbulence in the presence of a magnetic island and we discuss the connections to our work.   

Scaling of magnetic perturbation level for tearing mode turbulence during disruption

A model is presented regarding the magnetic perturbation saturation level for tearing turbulence during disruption. We consider a scenario where large scale tearing modes overlap with each other, break the flux surfaces and stir up a spectrum of small scale tearing modes. Two properties are of interest: one is the saturation level of turbulent perturbation, the other is the corresponding radial correlation length. The former is important because that the dominant contribution to the turbulent diffusion and hyper-resistivity scales as perturbation strength squared. The latter is important for transport of high energy particles in the random field. The aim of this model is to get a scaling of those two properties with respect to resistivity, instability drive and major geometry parameters. To this end, two specific cases are considered, one in which the flux surfaces are partially broken and the other when the whole plasma is stochastic. In both cases, we find the saturation level by balancing the linear drive which inject energy into the turbulence, and the forward cascade rate which transfer energy toward finer scales. The corresponding radial correlation length is then determined from the saturation level. Resistive MHD simulation are also presented to test the analytical model   

Model for transport driven by microtearing modes in tokamak discharges

Microtearing modes (MTMs) have been identified as a source of significant electron thermal transport in high beta tokamak discharges. A model for MTMs that can be installed in integrated predictive modeling codes is needed in order to improve the prediction of electron thermal transport and, consequently, the prediction of the evolution of the plasma in devices in which MTMs have a significant role. A unified fluid/kinetic approach is used in the development of a model for the transport driven by MTMs. The derivation includes the effects of electrostatic and magnetic fluctuations, collisionality, electron and ion temperature and density gradients and arbitrary curvature. MTMs are short-wavelength, ion scale electromagnetic instabilities which are driven by the electron temperature gradient in collisional plasma and propagate in the electron diamagnetic direction. The frequency of these modes is generally greater than the electron diamagnetic drift frequency, and the mode structure is extended along the magnetic field lines.   

Two-fluid MHD Regime of Drift Wave Instability

Drift wave instabilities contribute to the formation of edge turbulence and zonal flows, and thus are believed to play essential roles in the anomalous transport processes in tokamaks. Whereas drift waves are generally assumed to be local and electrostatic, experiments have often found regimes where the spatial scales and the magnetic components of drift waves approach those of magnetohydrodynamic (MHD) processes. In this work we study such a drift wave regime in a cylindrical magnetized plasma using a full two-fluid MHD model implemented in the NIMROD code. The linear dependency of growth rates on resistivity and the dispersion relation found in the NIMROD calculations qualitatively agree with theoretical analysis. As the azimuthal mode number increases, the drift modes become highly localized radially; however, unlike the conventional local approximation, the radial profile of the drift mode tends to shift toward the edge away from the center of the density gradient slope, suggesting the inhomogeneity of two-fluid effects.   

Seed Magnetic Islands Effect on Turbulence and Transport

Micro-turbulence is of great significance on the particle and energy transport, which have been widely investigated theoretically, experimentally and computationally. Its interaction with tearing mode, which can change the topology by creating a magnetic island and cause destructive consequences, have drawn a long-time interest among researchers. The pressure flattening within the magnetic island can decrease the bootstrap current, and thus influence the island evolution by triggering the neoclassical tearing modes. On one hand, turbulence strongly effects the density, temperature, and bootstrap current perturbations, which plays a key role in island physics. On the other hand, the flattened profiles within the island changes the density and temperature gradient, and the drive for turbulences in turn. In this work, self-consistent density, temperature profiles are constructed in presence of a seed magnetic island, and its effect on the turbulence is investigated.   

A Simulation Model for Drift Resistive Ballooning Turbulence Examining the Influence of Self-consistent Zonal Flows

Progress is reported on including self-consistent zonal flows in simulations of drift-resistive ballooning turbulence using the BOUT$++$ framework. Previous published work [1] addressed the simulation of L-mode edge turbulence in realistic single-null tokamak geometry using the BOUT three-dimensional fluid code that solves Braginskii-based fluid equations. The effects of imposed sheared ExB poloidal rotation were included, with a static radial electric field fitted to experimental data. In new work our goal is to include the self-consistent effects on the radial electric field driven by the microturbulence, which contributes to the sheared ExB poloidal rotation (zonal flow generation). We describe a model for including self-consistent zonal flows and an algorithm for maintaining underlying plasma profiles to enable the simulation of steady-state turbulence. We examine the role of Braginskii viscous forces in providing necessary dissipation when including axisymmetric perturbations. We also report on some of the numerical difficulties associated with including the axisymmetric component of the fluctuating fields. \\[4pt] [1] B. I. Cohen, M. V. Umansky, W. M. Nevins, M. A. Makowski, J. A. Boedo, D. Rudakov, G. M. McKee, and Z. Yan, Phys. Plasmas 20, 055906 (2013).   

Sub-Alfvenic Reduced Equations for Tokamak Plasmas

We present a system of reduced resistive MHD equations which are sub-Alfvenic with respect to ideal ballooning in large aspect ratio tokamak geometry.The low beta system allows dynamic evolution of full profiles. The system has the advantage that it is 2-dimensional in the transverse to $\mathbf{B}$, space variables. This allows significant analytical tractability as well as ease in numerical implementation. The linearized equations are shown to reproduce Mercier modes, resistive ballooning modes, tearing modes, sound waves, GAMs, the Stringer spinup, and Rosenbluth-Hinton zonal flows. The methodology developed allows extension to drift modes as well as to a hybrid system of moment and electromagnetic sub-gyro-drift-kinetic equations. Analytical and numerical benchmarks will be presented. We show that the system, which requires Laplace equation inversion to solve for electromagnetic potentials, is implementable numerically.   

Gyrofluid-Gyrokinetic Hybrid Turbulence Model

Gyrofluid models of tokamak turbulence are efficient compared to gyrokinetic models, in three senses. First, it is typically easier to develop one's intuition from fluid equations than kinetic equations. Second, because gyrofluid equations are only three-dimensional (instead of 5D or 6D), simulations with gyrofluid models require less memory than kinetic simulations and can therefore more easily fit on highly-optimized computing hardware, such as graphics processors. The third advantage is a result of the first two: one can develop and test ideas quickly with gyrofluid models. The disadvantage of gyrofluid models is their potential lack of physics fidelity. In this poster, we present our attempt to take full advantage of gyrofluid models, without sacrificing physics fidelity. Our approach is encapsulated in the Gryf-X code, which is an implementation of hybrid gyrofluid/gyrokinetic equations. The key improvements that we have brought to bear are: an improved understanding of the cascade of free energy simultaneously in $k_{\perp}$ and $v_{\perp}$; an improved model of zonal flow physics; and an implementation of the equations on modern heterogeneous computing platforms, both as a standalone simulation tool and as a component of TRINITY (a transport modeling code for tokamaks).   

Landau, Case, van Kampen and Collisionless Fluid Closures

Landau damping represents a fundamental paradox within plasma physics. The equations of motion of classical particles and fields are symmetric under time-reversal; yet, the open system formed by integration over velocity space is not invariant and damping results from phase-mixing. Here, it is shown that the Case-van Kampen theorem can be extended to magnetized plasmas: the linear eigenfunctions provide a complete representation of the particle distribution function and exponentially damped and growing eigenmodes must appear in pairs. The numerical Case-van Kampen transformation can performed efficiently in Fourier velocity space and allows fast timescales in the evolution of the system to be treated using exponential integration. On the other hand, fluid moments require integration over velocity space, and, thus, representation of Landau damping requires explicit introduction of the arrow of time through a collisionless damping operator. This operator captures linear phenomena at the cost of damping nonlinear phenomena such as the plasma echo. Numerical comparisons of these two rather different representations will be presented.   

Dependence of Turbulence Spatial Correlation Lengths on Plasma Rotation

We present the results from nonlinear gyrokinetic simulations in GS2 to investigate the parallel and perpendicular correlation lengths of electrostatic turbulence in tokamak plasmas with rotation. These correlation lengths are characterised for a range of parameters, including the E $ \times $ B shear, $\gamma_E$. We observe that the correlation lengths decrease as $ \gamma_E $ increases. Simulation results are compared against scaling laws deduced from the critical balance conjecture, which states that nonlinear perpendicular decorrelation times and parallel streaming times are comparable at all spatial scales.   

Benchmarking of the Gyrokinetic Microstability Codes GENE, GS2, and GYRO over a Range of Plasma Parameters

Comparing results (linear frequencies, eigenfunctions, and nonlinear fluxes) from different gyrokinetic codes as a means of verification (benchmarking) is only convincing if the codes agree over a wide range of plasma conditions. Otherwise, agreement may simply be fortuitous. We present here linear and nonlinear comparisons of the Eulerian codes GENE, GS2, and GYRO for a variety of JET discharges. The discharges include a simplified, 2-species, circular geometry case based on an actual JET discharge, an L-mode discharge with a significant fast ion pressure fraction, and a carbon-wall low triangularity hybrid discharge. All discharges were studied at rho=0.33 where significant ion temperature peaking is observed. The benchmarking is carried out to verify the GENE predictions that fast-ion-enhanced electromagnetic stabilization is the main contributor to the low ion heat flux.   

Investigation of plasma turbulence and geodesic acoustic modes using tangential phase-contrast imaging in the TCV tokamak

A tangential phase-contrast imaging (TPCI) diagnostic has been installed on the Tokamak \`a Configuration Variable (TCV) to measure plasma density fluctuations; by employing a spatial filtering technique, radially localized measurement can be performed from core plasma to the edge. The dependence of turbulence on plasma shape and radial position has been investigated, especially in the core region where local triangularity is vanishingly small. The measurements show a substantial reduction of turbulence amplitude from positive to negative triangularity, consistent with experimental observation of transport reduction on TCV and with non-linear gyrokinetic simulations. In addition, TPCI also measures the density component of the geodesic acoustic modes (GAM). The radial structure of GAM has been characterized in both single-frequency eigenmode and multi-mode regimes. Parametric studies were performed to investigate the dependence of GAM frequency, wavenumber, amplitude as well as GAM-turbulence interactions.   

Understanding rotation profile structures in ECH-heated plasmas using nonlinear gyrokinetic simulations

A non-diffusive momentum flux connecting edge momentum sources/sinks and core plasma flow is required to establish the off-axis peaked ion rotation profile typically observed in ECH-heated DIII-D plasmas without explicit external momentum input. The understanding of the formation of such profile structures provides an outstanding opportunity to test the physics of turbulence driving intrinsic rotation, and validate first-principles-based gyrokinetic simulation models. Nonlinear, global gyrokinetic simulations of DIII-D ECH plasmas indicate a substantial ITG fluctuation-induced residual stress generated around the region of peaked toroidal rotation, along with a diffusive momentum flux. The residual stress profile shows an anti-gradient, dipole structure, which is critical for accounting for the formation of the peaked rotation profile. It is showed that both turbulence intensity gradient and zonal flow ExB shear contribute to the generation of k// asymmetry needed for residual stress generation. By balancing the simulated residual stress and the momentum diffusion, a rotation profile is calculated. In general, the radial structure of core rotation profile is largely determined by the residual stress profile, while the amplitude of core rotation depends on the edge toroidal rotation velocity, which is determined by edge physics and used as a boundary condition in our model. The calculated core rotation profile is consistent with the experimental measurements. Also discussed is the modification of turbulence-generated Reynolds stress on poloidal rotation in those plasmas.   

ExB-Shear Effects on Magnetic-Flutter Diffusion of Electron-Drift Trajectories in ITG Turbulence

Magnetic-field stochasticity arises due to microtearing perturbations, which can be driven linearly [1] or nonlinearly [2], even at very modest values of the plasma beta. The resulting magnetic-flutter contribution may or may not be a significant component of the overall electron (particle and thermal) transport. Initial investigations [3] of the effect of ExB shear on electron-drift magnetic-flutter diffusion coefficient $D_{\mathrm{edr}}(r$,v$_{\vert \vert}$) using perturbed magnetic fields from GYRO simulations of ITG turbulence show two interesting results: 1) an absence of any peak in $D_{\mathrm{edr}}(r$,v$_{\vert \vert }$) at values of the ``resonant'' parallel velocity, v$_{\vert \vert}$, at which the ExB shear negates the magnetic shear, and 2) a significant increase in $D_{\mathrm{edr}}(r$,v$_{\vert \vert }$) for electrons with v$_{\vert \vert}$ surprisingly far from the resonant velocity. We explore these effects both through a more detailed quantification of the displacement and decorrelation rates of the orbits, as a function of parallel distance, and through a simplified model of electron drift motion in a poloidally localized turbulent magnetic field. Furthermore, we argue that a correct model will have ExB shearing of the perturbed magnetic field structures themselves, and we extend our investigations to include this effect. \\[4pt] [1] W. Guttenfelder, et al., Phys. Plasmas \textbf{19}, 056119 (2012);\\[0pt] [2] E. Wang, et al., Phys. Plasmas \textbf{18}, 056111 (2011);\\[0pt] [3] A. M. Dimits, et al., 2014 TTF Meeting.   

Power Threshold Minimum for L-H Transition in Collisional and Collisionless regimes

We study the physics of the power threshold $P_{th}(n)$ for L-H transition, by linking microscopics and macroscopics. The roles of the electron/ion heating ratio, electron-ion coupling in the threshold physics of the L$\to$H transition and the $P_{th,min}(n)$ are the primary foci. Our 1D predator-prey model reveals the puzzling decrease in $P_{th}(n)$ as the combination of an increase in collisional electron-to-ion energy transfer and an increase in the heating fraction coupled to the ions. Both processes strengthen the edge diamagnetic electric field needed to lock in the mean electric field shear for the $L\to H$ transition. Overal, the power threshold minimum emerges as a crossover between the threshold decrease caused by a rise in heat fraction coupled to ions (directly or indirectly, from electrons) and the threshold increase (at higher $n$) supported by the rise in shear flow damping. Turbulence driven shear flows are needed to trigger the transition by extracting energy from the turbulence. The electron/ion heating mix is important to the transition, in that it, together with electron-ion coupling, regulates the edge diamagnetic electric field shear. Collisionless turbulent electron-ion heat transfer processes and the pulsed fuel/heat deposition will also be discussed.   

DIII-D L-mode edge instabilities simulated in BOUT$++$

The well-known shortfall in predicted DIII-D tokamak L-mode edge transport [1] is investigated using various one and two-fluid models implemented in the BOUT$++$ code [2]. Five-[3] and six-field [4] models employed here contain the essential physics of peeling-ballooning modes, common in the H-mode edge, as well as drift-wave instabilities, predicted by various gyrokinetic and gyrofluid codes to dominate in the benchmark L-mode shot under investigation. We examine the extent to which instabilities driven at the separatrix can account for the systematic under-prediction of transport by these previous efforts. The focus is on the unstable linear spectrum for two domains: including and not including the separatrix. We compare one-fluid results (resistive ballooning unstable), two-fluid results (varying stability characteristics), and predictions from the gyrokinetic code GYRO [5] (driftwave dominant), to establish which models make meaningful contact with the experiment in which regimes and locations. We comment on numerical pitfalls within BOUT$++$ revealed in the present study. [1] T. L. Rhodes et al., Nucl. Fusion 51, 063022 (2011) [2] Dudson et al., Comp. Phys. Comm. V.180 (2009) 1467. [3] T.Y. Xia and X.Q. Xu, Phys. Plasmas 20, 052102 (2013) [4] T.Y. Xia, X.Q. Xu and P.W. Xi, Nucl. Fusion 53, 073009 (2013) [5] J. Candy and R.E. Waltz J. Comput. Phys. 186, 545 (2003)   

Nonlinear Interactions of Ion Temperature Gradient Microturbulence and Tearing Modes

We report progress on understanding the nonlinear interactions of ion temperature gradient turbulence and tearing modes using both analytic theory and numerical simulations, including some performed with the BOUT++ [1] framework. Using an electromagnetic five-field fluid model, results from two-dimensional simulations with static magnetic islands are first presented. It is found that the island width must exceed a threshold size (comparable to the turbulent correlation length in the no-island limit) to significantly impact the turbulence dynamics, with the primary impact being an increase in turbulent fluctuation and heat flux amplitudes. The turbulent radial heat flux is observed to localize near the island x-point, but does so asymmetrically. To quantify expected back-reaction of the turbulence on the tearing mode, an effective turbulent resistivity is quantified, and shown to be significantly (10x - 1000x) greater than the collisional resistivity used in the simulations. Progress on extending these results to three-dimensional simulations with dynamically evolving tearing mode islands will be presented, and implications of these results for predictive modeling of experiments discussed. \\[4pt] [1] B. Dudson et al., Comput. Phys. Comm. 180, 1467 (2009)   

Integrated core-edge tokamak simulations using a novel coordinate system for divertor detachment and heat-load studies

Simulating tokamak edge plasmas can often be difficult due to the X-point and divertor region having a different geometry than the rest of the plasma. For edge simulations, a field-aligned coordinate system is normally utilized so that the elongated structures along the field line can be resolved using less grid points while maintaining high resolution perpendicular to the field line. This introduces a singularity at the X-point and constrains the radial coordinate and the poloidal projection of the field-aligned coordinate to be orthogonal. We propose a new coordinate system that relaxes this constraint to allow arbitrary geometries to be matched in the poloidal plane while maintaining a field-aligned coordinate. This is useful at the divertor plate where field lines are not perpendicular to the surface and at the X-point where a close approach is desired. We implement a collisional two-fluid turbulence model using BOUT$++$ [1] to simulate an isolated divertor leg and investigate the effect of divertor plate angle on detachment and heat loads. We then couple edge simulations in BOUT$++$ with CENTORI [2], a core plasma fluid code, to study the evolution of the full plasma with these improved boundary conditions. \\[4pt] [1] B. Dudson, \textit{et al}, Comp Phys Comm, 9 (2009) 180.\\[0pt] [2] P. Knight, \textit{et al}, Comp Phys Comm, 11 (2012) 183.   

Microtearing Turbulence Limiting the JET-ILW Pedestal

The gyrokinetic GENE code is used to model instabilities and transport in the JET-ILW (ITER like wall) pedestal. Local GENE simulations identify microtearing modes (MTM) as the dominant low-k$_{\mathrm{y}}$ instability across most of the pedestal, with KBM unstable in a narrow region near the separatrix. Global simulations find that MTM growth rates are decreased by ExB shear, but to a lesser extent than electrostatic ITG/TEM-type modes, so that the MTM becomes relatively more prominent in the presence of ExB shear. A $\beta $ scan demonstrates local KBM to be unstable across the pedestal at lower $\beta $ (60 {\%} of the experimental value). As $\beta $ approaches and surpasses the experimental value, the KBM become more stable, and are limited to progressively narrower regions of the pedestal (consistent with the concept of second stability), while the MTM becomes more unstable and spans most of the pedestal. The absence of KBM is even more pronounced in global simulations. Nonlinear simulations of MTM turbulence using the experimental profiles produce transport levels that are comparable to experimental expectations, establishing the MTM as the likely mechanism limiting pedestal profile evolution in JET-ILW pedestals.   

Gyrokinetic study of impurity transport from neoclassical and turbulent mechanisms in and across H-mode pedestal

The edge gyrokinetic code XGC1 has been used to study impurity transport from combined neoclassical and turbulent mechanisms in and across a steep H-mode pedestal, in realistic magnetic separatrix geometry. Both low-Z and high-Z impurity transport are studied.. The effect on the turbulence and transport is found to be different whether the impurity radial profile gradient is in the same or opposite direction to the main ion profile gradient. Co-existence of the low- and high-Z impurities also makes difference in the transport of each species. Edge impurity behavior in NSTX, JET, and DIII-D tokamak plasma will be discussed.   

Kinetic Equations for the Plasma Edge

A hybrid fluid-kinetic framework for studying large-amplitude fluctuations in the edge of tokamak plasmas is presented. We derive equations for the behavior of an anisotropic plasma in the presence of both large fluctuations and steep gradients. The system consists of kinetic equations for electrons and ions, supplemented with fluid equations for the electromagnetic fields. In this way it builds upon both kinetic MHD and from the use of vorticity equations in gyrokinetics. This framework, by including both Alfv\'enic (including current-driven modes) and drift wave dynamics, can handle fully nonlinear perturbations such as erupting ELM filaments and blob-based turbulence. We not only present equations for such fast behavior, but also develop higher order equations that describe pedestal equilibria and slow scrape-off-layer dynamics. The relationship between this framework and existing collisional edge models is made clear.   

Beyond the standard plasma transport theory

The standard approach to transport in strongly magnetized plasmas, based upon an expansion in the gyro-radius over magnetic field scale length, has an illustrious, and successful history. It is however not a complete theory for plasma transport, and a number of phenomena which fall outside of its purview have recently attracted interest. The assumptions needed to derive the entire transport theory have only recently been explicitly laid out. Many of these assumptions are likely not widely appreciated, and the consequences of using the standard tools of transport theory to address phenomena which do not obey them are rather unclear. We discuss the consequences of these assumptions, and then turn our attention to the task of overcoming them. An avant-garde approach to modifying the standard theory to incorporate new physics will be introduced and applied to the loss of thermal ions in the edge. We study how the plasma remains quasi-neutral in the presence of this non-ambipolar transport, and consider the collisional re-filling of the loss cone. We will also briefly discuss other phenomena of interest that could be addressed using these techniques.   

Heat wave propagation due to power modulation in stochastic magnetic fields

Heat wave propagation due to power modulation in 3-dimensional chaotic magnetic fields is studied by solving the parallel heat transport equation using a Lagrangian-Green's function (LG) method [D. del-Castillo-Negrete et al., Phys. Rev. Letters 195004 (2011).] Going beyond previous works, we study time periodic sources using a novel Fourier-based numerical implementation of the LG method. The main problem addressed is the dependence of the heat wave propagation on the stochasticity (controlled by the amplitude of the magnetic field perturbation $\epsilon$) and the inverse penetration length $\gamma=\sqrt{\omega/ 2 \chi}$ (where $\chi$ is the parallel diffusivity and $\omega$ is the power modulation frequency). In all the cases considered there are no magnetic flux surfaces. However, radial transport is observed to depend strongly on $\epsilon$ and $\gamma$ due to the presence of {\em partial transport barriers}. Regions where the magnetic field connection length is large, correlate with regions where the radial propagation of the heat waves slows down and where the wave amplitude exhibits a steep gradient. Preliminary applications to recent heat pulse propagation experiments in DIII-D are discussed.   

Poloidal structure of the plasma edge with 3D magnetic fields

In the RFX-mod reversed-field pinch, when the magnetic field spontaneously develops a non axi-symmetric structure, also the plasma edge assumes a three dimensional shape. In previous RFX works, it has been shown that kinetic properties of the plasma (electron pressure, connection lengths, floating potential, influx, plasma flow) closely follow the symmetry of the 3D field, both in amplitude and phase, along the toroidal angle (i.e, the RFP perpendicular direction in the edge). Using a set of poloidally distributed diagnostics, it is shown that these same properties follow the poloidal periodicity (m$=$1) of the field. However, the behavior of the phase is more difficult to understand. In particular, the 3D modulation of the plasma potential can rotate in the poloidal direction with the typical velocity of 100m/s, similar in value with the phase velocity of the m$=$1 magnetic mode; or it can jump between inboard and outboard equatorial midplane. Moreover, when the floating potential structure rotates, there are preliminary indications that its direction depends on the plasma density: it follows the m$=$1 mode at higher density, and rotates in the opposite direction at lower density.   

Fast wave stabilization/destabilization of ion temperature gradient drift waves in a tokamak plasma

A kinetic description is developed for the stabilization/destabilization of ion temperature gradient drift waves by a large amplitude whistler wave. Parametric coupling of a whistler wave with the low frequency drift waves can yields whistler sidebands of their sum and difference frequencies. The whistler pump and sidebands can exert a ponderomotive force on electrons and modify the eigen-frequency of drift waves. This coupling process can lead to the stabilization/destabilization of drift waves, depending on the wave numbers of the interacting waves as well as the whistler pump power. The effectiveness of obliquely propagating whistler pump is also examined.   

Can we study the transport of MeV ions without generating fusion alphas?

The novel ion cyclotron resonance heating method, utilizing three ion species, allows the generation of energetic trace minorities in the MeV range [Ye. O. Kazakov et al., 2015, Nucl. Fusion 55, 032001]. We survey which aspects of alpha particle transport may be accessed experimentally without D-T operation, such as during the non-activated phase of ITER, through a numerical investigation of the transport properties of RF heated $\rm {}^3 He$ resonant ions in a $\rm {}^4He-H$ mixture plasma. The turbulent transport is simulated using the recently developed version of the gyrokinetic code GS2 that can handle strongly non-Maxwellian species [G. J. Wilkie et al., 2015, J. Plasma Phys. 81, 905810306], while the collisional transport is studied taking the temperature anisotropy of the $\rm {}^3 He$ species into account.   

Cross-diagnostic comparison of fluctuation measurements in a linear plasma column

The advent of fast imaging diagnostics, which provide two-dimensional measurements on relevant plasma time scales, has proven invaluable for interpreting plasma dynamics in laboratory devices. Despite its success, imaging remains a qualitative aid for many studies, because intensity is difficult to map onto a single physical variable for use in a theoretical model. This work continues our exploration of the relationship between visible-light and electrostatic probe measurements in the Controlled Shear Decorrelation Experiment (CSDX). CSDX is a well-characterized linear machine producing dense plasmas relevant to the tokamak edge ($T_e \sim 3$ eV, $n_e \sim 10^{13}$/cc). Visible light from ArI and ArII line emission is collected at high frame rates using a fast digital camera. Floating potential and ion-saturation current are measured by an array of electrostatic probe tips. We present a detailed comparison between imaging and probe measurements of fluctuations, including temporal, spatial, and spectral properties in various operational regimes.   

Effect of ion mass on transition to drift-zonal flow turbulence in the Controlled Shear Decorrelation eXperiment

The Controlled Shear De-correlation eXperiment (CSDX) is a helicon plasma device dedicated to studies of drift wave turbulence, zonal flow interaction and generation of intrinsic rotation in a cylindrical plasma configuration. Previous studies in argon plasma demonstrated existence of a weak turbulence driven azimuthally symmetric, radially sheared plasma flow [1]. More recent studies at higher B field with larger plasma size have shown the coexistence of radially separated multiple instabilities during the transition to strongly developed plasma turbulence [2]. To better understand the underlying mechanism and the role of the drift wave turbulence in the formation of the zonal shear layer and of the spatially separated multiple instabilities, we study the effects of the ion mass to further vary the effective system size via the parameter ($L_n/\rho_s$). Using an upgraded RF power source, we have achieved high-density helicon plasmas in gases such as argon, neon, helium, deut erium and hydrogen in CSDX. Therefore, the impact of the $\rho_s$ and isotope effect on turbulent transport, including the energy transfers and self-organization mechanisms between turbulence and sheared flows, will be addressed.\\[4pt] [1] GR Tynan et al 2006 PPCF\\[0pt] [2] SC Thakur et al 2014 PSST   

Initial Synthetic Diagnostics of Nonlinear Simulation of CSDX

The Controlled Shear Decorrelation Experiment (CSDX) linear plasma device provides a simple system for nonlinear studies of coupled drift-wave/zonal flow dynamics. We present numerical simulations of a minimal model of 3D collisional drift-wave physics in CSDX which evolves density, vorticity and electron temperature perturbations, implemented in the BOUndary Turbulence (BOUT++) framework [1]. Equilibrium electron density and temperature profiles are taken from experimental measurements [2]. We have verified the model with both linear analytical theory and nonlinear energy balance analysis. Results show that retaining the radial profile variation of plasma parameters has a significant impact on the simulation results. Application of synthetic Langmuir probes [3] to simulation results reveals that the effect of electron temperature fluctuations is significant for validation of model results against measurements of turbulence characteristics (e.g. fluctuation levels, flux, frequency spectra). Both of these effects are found to be needed for model predictions to be comparable to experimental observations. \\[4pt] [1] B. D. Dudson, et al., Comp. Phys. Comm. 180 (2009) 1467\\[0pt] [2] S. C. Thakur, et al., Physics of Plasmas 20, 012304 (2013)\\[0pt] [3] P. Ricci, et al., Physics of Plasmas 16, 055703 (2009)   

Transition from collisional drift-wave to multi-instability turbulence in a helicon plasma device

Recent studies in the Controlled Shear Decorrelation eXperiment reported a sharp non-monotonic global transition in the plasma dynamics during the transition to broadband turbulence [1]. Using a combination of probes, high speed imaging and laser induced fluorescence, we find that below a threshold magnetic field, the plasma is dominated by density gradient driven resistive drift waves. Above this threshold a new global equilibrium occurs, characterized by steepened density and ion temperature gradients and both azimuthal and parallel velocity shear layers, along with multiple plasma instabilities. At the center, high azimuthal mode number fluctuations are observed rotating in the ion diamagnetic drift direction, while in the density gradient region, drift waves propagate in the electron diamagnetic direction. Outside of this zone, velocity shear-driven fluctuations are observed. Simultaneously a very bright helicon blue core forms, and appears to be associated with a radial particle transport barrier. This new regime shows very rich plasma dynamics including intermittency, blobs, radial transport barrier, inward particle flux against density gradients [2] etc. Above the threshold conditions, linear stability analysis show co-existence of the ion temperature gradient (ITG) instability and velocity shear instability together with collisional electron drift waves. [1] S. C. Thakur \textit{et. al.}, \textit{PSST} \textbf{23} 044006 (2014) [2] L. Cui \textit{et. al.}, \textit{PoP }\textbf{22} 050704 (2015)   

Mach Probe Wakes are Important in Weakly Magnetized, Collisional Plasmas

Mach probes are often used as the diagnostic for flow in the scrape off layer (SOL) of tokamaks and in linear devices because of their low cost and ease of construction. However, proper interpretation of the Mach number has been debated, and interpretation methods use different calibration factors for different plasma parameters. The Controlled Shear Decorrelation eXperiment (CSDX) operates in an intermediate magnetization regime. To validate theories in this regime, measurements of the parallel ion velocity were made with Mach probes and laser induced fluorescence (LIF) at magnetic fields from 400 to 1600 gauss. We find that Mach probe measurements indicate higher velocities than LIF at fields above 400 gauss. Reduced downstream plasma density due to probe shadowing is a strong candidate for the cause of the discrepancy. An advective-diffusive model for the geometric shadowing and downstream plasma density is presented. When the model for the density drop is included, the Mach probe results agree with the LIF data. This result should be included by groups using Mach probes to measure parallel velocities in plasmas where the ion-neutral mean free path is shorter than the probe shadow length, Lps = $ a^2 C_s/D_{perp} $ in linear devices, the SOL, or divertor region of tokamaks.   

Characterization of Turbulence in the Texas Helimak

The Texas Helimak is an approximation to the cylindrical slab with large physical size compared to the correlation lengths of its instabilities and open magnetic field lines. As such, it functions efficiently as a test-bed for the physics of the SOL at low densities and temperatures that allow for the usage of Langmuir probe diagnostics. Much of the research performed on the device has focused on its high turbulent amplitudes. It was initially believed, both experimentally and theoretically, that the turbulence is dominated by a fluid drift wave. However, more recent evidence suggests that the identification of the Helimak instabilities is not so straightforward, but may vary with the connection length of the magnetic field lines through both drift wave and interchange instability regimes. In this work we document efforts to characterize the turbulence based on measurements of both parallel and perpendicular wavenumbers and other Langmuir probe data.   

Effect of Flow Shear on Simple Interchange Turbulence

The Helimak is an approximation to the infinite cylindrical slab with a size large compared with turbulence transverse scale lengths, but with open field lines of finite length. Interchange modes are the dominant instability. Flow profiles and shear can be greatly modified by the application of radial electric fields through external biasing of flux surfaces -- cylindrical shells. Measurements of the ion flow velocity profile are made by Doppler spectroscopy. The range of earlier measurements in argon has been expanded and new results for helium added. Local relations between flow shear and the level of non-linearly saturated density fluctuations are obtained. To extend the characterization of the turbulence, novel probes are being developed to measure the level of true plasma potential fluctuations. Work supported by the Department of Energy OFES DE-FG02-04ER54766.   

Development of Magnetically Insulated Baffled Probe Cluster for Measurement of Energy Flux and Particle Flux in the Texas Helimak

Progress is reported in employing magnetically insulated baffled (MIB) probes\footnote{\textit{RSI} 73, 3409, 2002; \textit{CPP} 44, 689 (2004); \textit{J. Phys. D} 44, 233001 (2011); \textit{RSI} 81, 10E129 (2010)} in the Texas Helimak\footnote{\textit{PoP} 21, 092302 (2014)}. Radial scans at the plasma edge of dc and ac space potential are presented. Like the Ball-Pen probe\footnote{\textit{CPP} 54, 279 (2014)}, the MIB probe shares the Langmuir probe simplicity and overcomes its shortcomings in the ability to make real-time measurements of plasma space potential, temperature, and energy/particle fluxes in magnetized plasma. By rotating the probe shaft to change the extent to which the baffle ``masks'' the probe collection area, the ratio between electron and ion probe current, and consequently the relative sensitivity of the floating-probe oscillations to space potential and electron/ion temperature, can be adjusted, thus allowing space potential fluctuations and electron/ion temperature fluctuations to be distinguished when measured at two different rotation angles. At the optimal rotation angle, the contribution of electron temperature and its fluctuations to the floating-potential measurement are eliminated and the space potential fluctuation phase is preserved.   

Simulation of runaway electrons in tokamak

Runaway electrons with relativisitc energy ($>$Mev) are generated in tokamaks when the acceleration by parallel electric field exceeds the drag due to Coulomb collisions with the bulk plasma. Carrying about 70\% of the ITER thermal current (15MA), they can possibly cause severe damage to tokamak facing components. Here we report the development of a solver for computing the evolution of runaway electron distribution in tokamak geometries. Essential effects from Coulomb collisions, radiation losses, toroidal effects and the radial transport are included on the same footings. Numerical techniques (implicit-explicit time-stepping, KT/NT central schemes) to overcome the difficulties arising from the wide spread of time scales in runaway electron dynamics and the hyperbolic nature of the relativistic Fokker-Planck equation will be discussed. We will use the solver to study two important physics: 1) the presence of stable point in the phase space and its relation to the electric field threshold [1]; 2) the radial transport of runaways in tokamak geometry [2] and its effects on the distribution function. Work supported by DOE via LANL-LDRD. \\[4pt] [1] P. Aleynikov \& B. Breizman, Phy. Rev. Lett. 114, 155001 (2015).\\[0pt] [2] X. Guan, H. Qin, N. Fisch, Phy. Plasmas 17, 092502 (2010).   

Reaction of runaway electron distributions to radiative processes

The emission of electromagnetic radiation by a charged particle in accelerated motion is associated with a reduction in its energy, accounted for by the inclusion of a radiation reaction force in the kinetic equation. For runaway electrons in plasmas, the dominant radiative processes are the emission of bremsstrahlung and synchrotron radiation. In this contribution, we investigate the impact of the associated radiation reaction forces on the runaway electron distribution, using both analytical and numerical studies, and discuss the corresponding change to the runaway electron growth rate, which can be substantial. We also report on the formation of non-monotonic features in the runaway electron tail as a consequence of the more complicated momentum-space dynamics in the presence of radiation reaction.   

Kinetic-MHD hybrid equilibrium model using a Monte-Carlo calculation of runaway electron distribution function

An axisymmetric MHD equilibrium model is studied to allow the inclusion of both beam inertia and energy spectrum for runaway electron beam. Following kinetic-MHD hybrid approach [1], we evaluate the RE beam current from the integrals of the RE distribution function. The distribution function is here evaluated by a relativistic guiding-center trace code ETC-Rel [2], where we have implemented the effects of collisions, radiations, and exponential growth into the code. Because to directly treat the Dreicer mechanism in particle simulations is time consuming, the primary RE source is modeled by a Monte-Carlo weighing scheme taking into account the instantaneous generation rate. This paper applies ETC-Rel to the parametric study of the MHD equilibrium with different RE beam parameters. Kinetic effects on the MHD equilibrium appears, e.g., as enhanced Shafranov shifts due to the inertia of highly relativistic electrons. A kinetic modification to the equilibrium becomes significant if the contribution of the beam inertia -- being increased with the total electron mass of multi-MeV RE populations -- becomes large enough to affect the radial force balance.\\[4pt] [1] E. V. Belova, et al., Phys. Plasmas 10, 3240 (2003);\\[0pt] [2] A. Matsuyama, et al., Nuclear Fusion 54, 123007 (2014).   

Suppression of runaway generation by SMBI in disruptions in J-TEXT tokamak

Runaway current generated in ITER disruption can lead to severe damage at plasma facing components. The generation and suppression of runaway electrons have been investigated in the J-TEXT tokamak. Runaway current was created with rapid argon injection by a massive gas injection (MGI) valve. Supersonic molecular beam injection (SMBI) as a highly efficient fueling method can provide a high beam velocity and deep penetration depth. A small amount of hydrogen injected by SMBI during the quiescent plasma current flattop can induce magnetic penetration, and then cause plasma instability which increases runaway electron loss rapidly. SMBI has been used to mitigate disruption generated runaway electrons in the J-TEXT tokamak. It is found that SMBI of hydrogen during plasma disruption can efficiently suppress runaway generation.   

Anomalous Doppler instability in tokamaks: first principles simulation and observations in MAST

The evolution in velocity space of minority suprathermal electron populations undergoing the anomalous Doppler instability (ADI) is investigated using fully nonlinear particle-in-cell simulations (W N Lai et al, Phys. Plasmas 20, 102122 (2013); and submitted (2015)) that self-consistently evolve particles and fields in a magnetized plasma. Electron trajectories during different stages of the ADI are captured, and are analyzed in relation to the excited electric fields and the overall velocity distribution of electrons. The time-evolution of the moments of the perpendicular electron distribution function is studied to test the range of applicability of analytical approximations that involve a quasilinear wave-driven diffusion operator. For some electrons, trapping and mirroring are observed during the saturation phase. Recent measurements of microwave and X-ray emission during edge localized mode (ELM) activity in the MAST tokamak imply acceleration of electrons parallel to the magnetic field combined with rapid acquisition of perpendicular momentum. This suggests (S J Freethy et al, Phys. Rev. Lett. 114, 125004 (2015)) that the ADI is operating on electrons accelerated by inductive electric fields generated by the initial ELM instability.   

Conservative large-angle collision operator for runaway avalanches

Avalanche runaway generation is the phenomenon whereby runaway electrons (REs) are generated due to large-angle collisions of thermal electrons with existing REs, leading to an exponential growth of the runaway current. These large-angle collisions are not described by the Fokker-Planck operator commonly employed to model collisions in plasmas, and have previously been accounted for by the addition of a particle source term in the kinetic equation [M. Rosenbluth et al., 1997, Nucl. Fusion 37, 1355; S. C. Chiu et al. 1998, Nucl. Fusion 38, 1711]. In this contribution we describe a new large-angle collision operator, derived as the high-energy limit of the linearized relativistic Boltzmann collision integral. This operator generalizes previous models of large-angle collisions to account for the full momentum dependence of the primary distribution and conserves particle number, momentum and energy, while also avoiding double counting of small- and large-angle collisions. The new operator is implemented in the 2D Fokker-Planck solver CODE [M. Landreman et al. 2014, Comp. Phys. Comm. 185, 847], with which we investigate its effect on the evolution of the runaway distribution.   

Probability and critical electric field for electron runaway

It is very important that we understand the physics of the runaway electron avalanche, both due to the need for runaway mitigation in disruptions in ITER, and the pure scientific merit. In this work we developed a new method to obtain the probability of an electron in momentum space to run away, by solving a time-independent PDE, alleviating the need for Monte-Carlo simulation. This PDE turns out to be adjoint to the electron kinetic equation. The new method is applied to calculate the avalanche growth rate and the threshold electric field. The results show that in the presence of synchrotron radiation and pitch angle scattering, the threshold electric field for the avalanche growth will increase to a value that is higher than the Connor-Hastie electric field. A series of kinetic simulations are conducted which confirms the findings. We also did a time-dependent simulation with increasing plasma density to simulate the gas-puffing runaway electron experiments in DIII-D, and the hard X-ray signal result shows qualitative agreement with the experiments for the threshold electric field.   

A multi-machine analysis of non-axisymmetric and rotating halo currents

Halo currents measured during tokamak disruptions exhibit non-axisymmetric and rotating features in several machines including Alcator C-Mod,\footnote{Granetz et al., \textit{Nucl. Fusion} \textbf{36}, 545 (1996)} ASDEX Upgrade,\footnote{Pautasso, et al., \textit{Nucl. Fusion} \textbf{51}, 043010 (2011)} and NSTX.\footnote{Gerhardt, \textit{Nucl. Fusion} \textbf{53}, 023005 (2013)} Such non-axisymmetries are of great interest to ITER because they can increase mechanical stresses during a disruption, especially if the rotation resonates with the natural frequencies of the vessel.\footnote{Hender et al., \textit{Nucl. Fusion} \textbf{47}, S128 (2007)} This paper presents an ITPA-initiated multi-machine analysis of these phenomena. The ITPA non-axisymmetric halo current database presently includes data from NSTX, DIII-D, AUG, and C-Mod. These data are analyzed here within a common numerical framework. Emphasis is placed on the evolution of the $n=1$ component of the halo current over the course of the disruption, as well as on how the non-axisymmetries and rotation depend on the equilibrium plasma parameters at the start of the disruption.   

Characteristic time for halo current growth and rotation

Halo currents, $I_h$, flow in part through plasma on open magnetic lines and in part through the walls. A halo current has the same function as the wall current of a resistive wall mode and arises when a kink cannot be wall stabilized. When flowing in the plasma, the halo current can produce no forces, so $\vec{j}_h =(j_{||}/B)\vec{B}$ with $\vec{B}\cdot\vec{\nabla}j_{||}/B=0$. To avoid too strong a coupling to stable kinks, the wall interception must be of sufficient toroidal extent, which implies the width of the halo current channel $\Delta_h\approx a I_h/I_p$, where $a I_h/I_p$ is the amplitude of the kink, $a$ is the minor radius, and $I_p$ is the plasma current. The equation for the growth of the halo current is $dI_h/dt=I_p/\tau_g$, where $\tau_g\approx (\mu_0/\eta_h)(a^2/4)/s_{eff}$ and $s_{eff}$ is a dimensionless stability coefficient. The rocket effect of the plasma flowing out of the two ends of the magnetic field lines in the halo can set the magnetic perturbation into toroidal rotation at a Mach number, $M_h$, comparable to unity. The rotation period is $\tau_r=(2\pi R_0/C_s)/M_h$, where $R_0$ is the major radius and $C_s=\sqrt{(T_e+T_i)/m_i}$ is the speed of sound. NSTX results appear consistent for $s_{eff}\sim 0.5$, $M_h\sim1$, and $T_{e,i}=10$eV.   

Prospects of ITER Instability Control

Prospects for real-time MHD stability analysis, plasma response calculations, and their use in ELM, NTM, RWM control and EFC will be discussed. ITER will need various controls to work together in order to achieve the stated goal of Q $\ge $ 10 for multiple minutes. These systems will allow operating at high beta while avoiding disruptions that may lead to damage to the reactor. However, it has not yet been demonstrated whether the combined real-time feedback control aim is feasible given the spectrum of plasma instabilities, the quality of the real-time diagnostic measurement/analysis, and the actuator set at ITER. We will explain challenges of instability control for ITER based on experimental and simulation results. We will demonstrate that it will not be possible to parameterize all possible disruption avoidance and ramp down scenarios that ITER may encounter. An alternative approach based on real-time MHD stability analysis and plasma response calculations, and its use in ELM, NTM, RWM control and EFC, will be demonstrated.   

Real-time Stability Analysis for Disruption Avoidance in ITER

ITER is intended to operate at plasma parameters approaching the frontier of achievable stability limits. And yet, plasma disruptions at ITER must be kept to a bare minimum to avoid damage to its plasma-facing structures. These competing goals necessitate real-time plasma stability analysis and feedback control at ITER. This work aims to develop a mechanism for real-time analysis of a large and virulent class of disruptions driven by the rapid growth of ideal MHD unstable modes in tokamak equilibria. Such modes will be identified by a parallelized, low-latency implementation of A.H. Glasser's well-tested DCON (Direct Criterion of Newcomb) code, which measures the energetics of modes in the bulk plasma fluid, as well as M.S. Chance's VACUUM code, which measures the same in the vacuum between the plasma and tokamak chamber wall. Parallelization of these codes is intended to achieve a time-savings of 40x, thereby reducing latency to a timescale of order 100ms and making the codes viable for ideal MHD stability control at ITER. The hardware used to achieve this parallelization will be an Intel Xeon Phi server with 77 cores (308 threads).   

ITER Disruption Mitigation System Design

The disruption mitigation system for ITER is under design and will require injection of up to 10 kPa-m3 of deuterium, helium, neon, or argon material for thermal mitigation and up to 100 kPa-m3 of material for suppression of runaway electrons. A hybrid unit compatible with the ITER nuclear, thermal and magnetic field environment is being developed. The unit incorporates a fast gas valve for massive gas injection (MGI) and a shattered pellet injector (SPI) to inject a massive spray of small particles, and can be operated as an SPI with a frozen pellet or an MGI without a pellet. Three ITER upper port locations will have three SPI/MGI units with a common delivery tube. One equatorial port location has space for sixteen similar SPI/MGI units.   

Physics and Engineering Design of the ITER Electron Cyclotron Emission Diagnostic

Electron temperature (T$_{\mathrm{e}})$ measurements and consequent electron thermal transport inferences will be critical to the non-active phases of ITER operation and will take on added importance during the alpha heating phase. Here, we describe our design for the diagnostic that will measure spatial and temporal profiles of T$_{\mathrm{e}}$ using electron cyclotron emission (ECE). Other measurement capability includes high frequency instabilities (e.g. ELMs, NTMs, and TAEs). Since results from TFTR and JET suggest that Thomson Scattering and ECE differ at high T$_{\mathrm{e}}$ due to driven non-Maxwellian distributions, non-thermal features of the ITER electron distribution must be documented. The ITER environment presents other challenges including space limitations, vacuum requirements, and very high-neutron-fluence. Plasma control in ITER will require real-time T$_{\mathrm{e}}$. The diagnosic design that evolved from these sometimes-conflicting needs and requirements will be described component by component with special emphasis on the integration to form a single effective diagnostic system.   

Component tests for the ITER Ion Cyclotron Transmission Line and Matching System - Status and Plans

New $Z_{0} = 50 \Omega$ gas-cooled component designs for the ITER Ion Cyclotron Heating and Current Drive System have been successfully tested at high RF power levels. They include two types featuring spoke-ring assembly (SRA) inner conductor supports: $20^{\circ}$ elbows, and variable length assembly bellows, both achieving RF voltages $>$ 35 kV peak, and currents $\sim 760$ A peak during quasi-steady state operation. The SRA utilizes mechanically preloaded fused quartz spokes, increasing lateral load handling capability. Components with SRA supports have been seismically tested, with no variation in low power electrical performance detected after testing. A 3 MW four-port switch has also been successfully tested at high RF power, and tests of a 6 MW hybrid power splitter are planned in the near future. Latest results will be presented. Plans for arc localization tests in a 60 m SRA transmission line run, and RF tests of $Z_{0} = 50 \Omega$ and $Z_{0} = 20 \Omega$ matching components with water-cooled inner conductors will also be discussed.   

DiMES Tests of W Leading Edge Power Loading in DIII-D

In a transient melt experiment in JET, the power to a $\sim$1-mm-high leading edge on a W lamella in the bulk-W outer divertor was lower than expected from the geometry by factors of 5 and 2 for L-mode and H-mode discharges, respectively. We checked this surprising result in DIII-D with 3 W blocks (10 mm square) mounted radially side-by-side in DiMES with leading edges of 0.0, 0.3, 1.0 mm, single null L-mode plasmas, OSP just outside ``0.0'' block, limited scans (NBI+ECH), B-field incident at 1.5$^{\circ}$ or 2.5$^{\circ}$, and viewed, as in JET, from above with 0.2mm/pixel resolution IRTV. Langmuir probes measured parallel power to the target. We compared probe and IR data with a detailed thermal model of the blocks and concluded provisionally that we did not reproduce the power deficit found in JET. Blurred IR images complicated fitting of temperature distributions from the thermal model. We plan an experiment with both L- and H-mode He plasmas before the APS meeting.   

Study of ITER Steady-State High q$_{min}$ Scenarios Using FASTRAN/IPS Integrated Transport Modeling

A high q$_{min}$ (q$_{min}$ $>$ 2) operational scenario has been identified as a possible candidate to achieve ITER baseline goals. This scenario requires a broad current profile with high bootstrap fraction, which in turn requires a relatively large pedestal height. The goal of this study is to identify an operational space for ITER high-q$_{min}$ steady-state scenarios via self-consistent integrated modeling using the IPS/FASTRAN framework with EPED providing the edge pedestal height. FASTRAN is an iterative numerical procedure that integrates a variety of models (transport, heating, CD, equilibrium and stability) and has been shown to reproduce most features of DIII-D high beta discharges with a stationary current profile. The FASTRAN solver has been implemented in the Integrated Plasma Simulator (IPS) framework. The sensitivity of this operating space to uncertainties in the transport and pedestal predictions will be studied.   

Analysis of multidimensional signals as classifiers for machine learning prediction of disruptions

ITER and future tokamaks beyond will require systems to predict oncoming disruptions so that damage to the machine can be avoided or mitigated. The use of supervised machine learning has proven to be successful in predicting the onset of disruptions with higher accuracy than a simple locked-mode detector, but only zero-dimensional time trace signals have been considered to examine this. We present initial results from our analysis of multidimensional signals (time + spatial dimensions) from the JET database to identify higher fidelity, physics-based classifiers that would allow the development of disruption prediction tools that are portable between machines.   

Survey of heating and current drive for K-DEMO

We present calculations of heating and current drive by neutral beam injection and by RF waves in the ion-cyclotron, lower-hybrid, and electron cyclotron frequency ranges for the steady-state burn conditions in a K-DEMO configuration with Ip$=$12.3 MA, a$=$2.1 m, Ro$=$6.8 m, Bo$=$7.4 T, ne-bar$=$1.1E20 /m3, T(0)$=$40 keV, and Zeff$=$1.5. Deposition from an ITER-like NBI system was calculated for quasi-tangential geometry with a horizontal beam axis; the axis elevation was scanned from Z$=$0 (the tokamak midplane) to Z$=$2.2 m. Peak deposition varies from r/a$=$0.1-0.65, the CD efficiency is 40-55 A/kW. A scan of ICRH frequency will reveal the windows of high CD efficiency that lie between absorption bands of the ion species (thermal D, T, He, Ar, and W, fast alphas and D). A scan of poloidal location for a 5 GHz lower-hybrid wave launcher varied the current profile shape in the periphery (no driven current for r/a \textless 0.65), and CD efficiency of 40-50 A/kW. The electron cyclotron survey varied the frequency, launcher poloidal location, and the poloidal and toroidal direction of the launched waves. A single frequency and poloidal position can achieve 25 A/kW over nearly the full range r/a$=$0.13-0.6 with, but up to 50 A/kW at r/a$=$0.5 is achievable at some locations with higher frequencies.   

Generic Magnetic Fusion Reactor Revisited

The original Generic Magnetic Fusion Reactor paper was published in 1986. This update describes what has changed in 30 years [1]. Notably, the construction of ITER is providing important benchmark numbers for technologies and costs. In addition, we use a more conservative neutron wall flux and fluence. But these cost-increasing factors are offset by greater optimism on the thermal-electric conversion efficiency and potential availability. The main examples show the cost of electricity (COE) as a function of aspect ratio and neutron flux to the first wall. The dependence of the COE on availability, thermo-electric efficiency, electrical power output, and the present day's low interest rates is also discussed. Interestingly, at fixed aspect ratio there is a shallow minimum in the COE at neutron flux around 2.5 MW/m$^{2}$. The possibility of operating with only a small COE penalty at even lower wall loadings (to 1.0 MW/m$^{2}$ at larger plant size) and the use of niobium-titanium coils are also investigated.\\[4pt] [1] J.Sheffield and S.L. Milora, ``Generic Magnetic Fusion Reactor Revisited,'' submitted to Fusion Science and Technology, June 2015.   

Popularity of the Compact Machine Approach in Fusion Research and Pioneering Role of the Ignitor Program

Several factors have led to an increase in popularity for the pursuit of advanced fusion research by compact machines. The Ignitor program has started this line of research on fusion burning plasmas as a development of the Alcator and Frascati Torus projects motivated more by basic physics considerations than speed and cost. Advances in high field superconducting magnets followed within the Ignitor program [1,2] have broadened the perspectives for its development. High values of $n\tau $ are expected considering $n$ related to ${{\bar{J}}_{\parallel }}\sim {{{{\bar{B}}}_{p}}}/{{\bar{a}}}\;$ ($\bar{a}=$mean plasma radius and ${{\bar{B}}_{p}}=$ mean poloidal field) and that $\tau$ has a favorable dependence on $I_{p}$, the total plasma current. If $ nT\propto {\bar{B}_{p}^{2}}/{\left( 2{{\mu }_{0}} \right)} $, the reactivity ${{n}^{2}}\left\langle {{\sigma }_{F}}v \right\rangle \propto {{n}^{2}}{{T}^{2}}\propto\bar B^{4}_{p}$. Thus a main guiding feature for advanced fusion burning experiments is that of appropriate and combined high values of the ${{\bar{B}}_{p}}$ and $I_{p}$ parameters, minimizing the input power of auxiliary heating systems.\\[4pt] [1] B. Coppi, \textit{et al., Nucl. Fus}. 53, (2013) 104013.\\[0pt] [2] B. Coppi, \textit{et al., Nucl. Fus}. 55 (2015) 053011.   

Tokamak Scenario Trajectory Optimization Using Fast Integrated Simulations

We employ a fast integrated tokamak simulator, METIS, for optimizing tokamak discharge trajectories. METIS is based on scaling laws and simplified transport equations, validated on existing experiments and capable of simulating a full tokamak discharge in about 1 minute. Rapid free-boundary equilibrium post-processing using FREEBIE provides estimates of PF coil currents or forces. We employ several optimization strategies for optimizing key trajectories, such as Ip or heating power, of a model ITER hybrid discharge. Local and global algorithms with single or multiple objective functions show how to reach optimum performance, stationarity or minimum flux consumption. We constrain fundamental operation parameters, such as ramp-up rate, PF coils currents and forces or heating power. As an example, we demonstrate the benefit of current over-shoot for hybrid mode, consistent with previous results. This particular optimization took less than 2 hours on a single PC. Overall, we have established a powerful approach for rapid, non-linear tokamak scenario optimization, including operational constraints, pertinent to existing and future devices design and operation.   

Pioneering Structural Solutions for Compact High Field Experiments Developed for the Alcator and the Ignitor Programs

Recently there has been an increased awareness of the fact that the line of research based on compact high field machines is the most promising to approach ignition conditions in DT burning plasmas and has acquired new perspectives for its applications. Then the technological solutions [1] that have made these machines possible have become subject to new attention and, in some cases, to rediscovery. The Alcator Program and, followed by Ignitor Program, has led to invent the coupled air-core former poloidal field system that has made compact machine possible and has been adopted on all advanced toroidal machines that came after Alcator. A recently rediscovered solution aimed at reducing the mechanical stresses in the inner legs of the toroidal magnet coils is the ``Upper and Lower Bracing Rings'' system that has had a key role in the design of the Ignitor machine and its evolution. Another solution to minimize the machine dimensions while maintaining high toroidal fields [2], in order to achieve high plasma current densities, is that of ``bucking and wedging'' of the toroidal magnet by coupling it mechanically to the central solenoid. [1] B. Coppi and M. Salvetti, MIT Report 02/06 (2002). [2] B. Coppi, $\textit{Nucl. Fusion}$ $\textbf{55}$, 053011 (2015).