Session K1: Plasma/Sherwood Poster Session I (2:00pm - 5:00pm)

Ion heating due to reconnection and turbulence in SSX

Ion heating is measured in the SSX device with a high resolution ion Doppler spectrometer. The SSX IDS instrument measures the width and Doppler shift of either the nascent $C_{III}$ impurity $229.7~nm$ line or a doped $He_{II}$ impurity $468.6~nm$ line to determine the temperature and line-averaged flow velocity. The velocity resolution of the instrument is $\le 5~km/s$.  There is enough signal to resolve the full line within an MHD dynamical time (about $1~\mu s$ in SSX). Spheromak merging in a new oblate flux conserver ($R=0.25~m, L=0.4~m$) has resulted in some stable configurations but often results in excitation of several unstable MHD modes. After reconnection and instability, we measure a period of ion heating with peak temperatures for carbon $T_C = 40~eV$ but for helium only $T_{He} = 20~eV$. Our results are consistent with temperature increasing with ion mass but only scaling like $\sqrt{M_i/m_p}$. We plan a more comprehensive study of the effect of reconnection and turbulence on ion heating for various ion masses (He, C, Xe). A new high purity gas delivery and mixing system is under construction. Results of ion heating with other ions will be presented.   

The Wheaton Impulsive Reconnection Experiment

A new experiment is beginning operation at Wheaton College for the study of impulsive magnetic reconnection in three dimensions. The experiment is composed of two parallel electrodes, linked by a magnetic arcade that is generated by a coil surrounding the electrodes. Current is driven along the arcade from one electrode to another, causing the arcade to inflate and become sheared. During the subsequent nonlinear evolution, the arcade may become unstable with strong driving and/or break off into a separated plasmoid. Fast imaging diagnostics and magnetic probe arrays will be used to follow the evolution of the arcade and identify sites where reconnection is taking place. The experimental components have been constructed and assembled. Power supply and fueling tests are underway with first plasmas anticipated early this summer. Work supported by U.S.D.O.E. grant DE-FG02-08ER55002.   

Experimental onset threshold and magnetic pressure pileup for 3D reconnection

Magnetic reconnection changes the topology of magnetic field lines to a lower energy state. This process can liberate stored magnetic field energy and accelerate particles during unsteady, explosive events. This is one of the most important processes in astrophysical, space and laboratory plasmas. The abrupt onset and cessation has been a long standing puzzle. We show the first three-dimensional (3D) laboratory example of onset and stagnation of magnetic reconnection between magnetized and parallel current channels (flux ropes) driven by magnetohydrodynamic (MHD) attraction and a 3D plasma current driven instability. Antiparallel magnetic field lines carried by these colliding flux ropes break and drive an electric field. The inflow soon exceeds a threshold for the formation of a reconnection current layer. Magnetic flux and pressure pile up just outside this layer, and eventually become large enough to support MHD back-reaction forces that stall the inflow and stagnate the reconnection process. * Supported by Los Alamos Laboratory Directed Research Development, Center for Magnetic Self Organization   

Transition between viscous and collisionless regimes of parallel flows damping in RFPs*

Strong ion heating is observed during sawtooth crashes in the Madison Symmetric Torus reversed field pinch (RFP) experiments. The mechanism of dissipation due to damping of parallel flows generated by tearing instabilities is examined. In collisional limit, the viscous dissipation is caused by the effect of parallel viscosity in Braginskii equations. Since the ion mean free path $\lambda $ exceeds the parallel scale length of the flows k$_{\vert \vert }^{-1}$ , the collisional formalism cannot provide reliable predictions. Several kinetic closures have been proposed in the past to incorporate kinetic effects into the plasma momentum equation in the form of Landau-like integral for the effective collisionless viscous force. To investigate the transition from viscous to collisonless regimes we develop an alternative approach based on numerical solution of the kinetic equation with Landau collisional operator. Direct computational modeling of the ion heating yields the rate of dissipation and allows us to follow the transition between two limiting cases as a function of the parameter k$_{\vert \vert }\lambda $. *The work supported by the N.S.F. and the U.S.D.O.E.   

Modeling of Multi-Interface, Diverging, Hydrodynamic Experiments for the National Ignition Facility

The National Ignition Facility will soon provide more than ten times the energy than was previously available on laser facilities. In the context of supernova-relevant hydrodynamics, this will enable experiments in which hydrodynamic instabilities develop from multiple, coupled interfaces in a diverging explosion. This presentation discusses the design of spherical and aspheric blast-wave-driven explosions, in which the relative masses of the layers are scaled to those within the star. The simulations probed the instability growth and multi-interface interactions to assess the diagnosability and experimental value of different designs using a variety of materials. Analysis of aspheric cases will determine the feasibility of extending the experiment to investigate aspheric supernova.   

Impurity Ion Heating by Cyclotron Absorption of Magnetic Turbulence in MST

Treating magnetic turbulence in the MST reversed field pinch device as an Alfv\'{e}nic cascade from globally unstable tearing modes, impurity ion heating from cyclotron damping of the turbulence is calculated. Numerical solution of the plasma dispersion relation yields a branch that is shear Alfv\'{e}n-like for low parallel wavenumber. At intermediate wavenumber the real part of the frequency tends toward the cyclotron frequency, while for higher wavenumber the frequency becomes zero at a critical value. Damping is strongest near the critical frequency$^{2}$. For parameter values of the experiment, the damping yields impurity heating rates consistent with the rise of impurity temperature during transient events of enhanced magnetic turbulence. Temperature evolution is modeled from a 0-D transport calculation, which also shows that collisional transfer from impurities to the bulk species can account for experimental values of the bulk species. The theory also describes the evolution of parallel and perpendicular temperatures. $^{2}$V. Tangri, et al., Phys. Plasmas \textbf{15}, 112501 (2008).   

Relativistic two-fluid waves in pulsar plasmas

A relativistic two-fluid approach for a streaming magnetized pair plasma is considered. Such a scenario corresponds to secondary plasmas created at the polar caps of pulsar magnetospheres. The model, in which instead of the magnetic field the generalized vorticity is frozen in the fluid, is investigated for propagating waves. For parallel propagation four transverse modes are found. Two of them are analogous to the R and L modes of the non-relativistic pair plasma limit. The other two are Alfv\'enic modes split into a fast and slow mode. The slow mode is cyclotron two-stream unstable at large wavelengths and always subluminous. The fast Alfv\'en mode is superluminous for large wavelengths only becoming subluminous at $k>2\sqrt{\gamma_{o}^2-1}$. In this incompressible approximation only the ordinary mode is present for perpendicular propagation. For oblique propagation the dispersion relation is numerically studied for finite and infinitely magnetic field and the results are qualitatively described.   

Energy and Cross-helicity cascades in driven magnetohydrodynamic turbulence

Magnetohydrodynamic (MHD) turbulence has been invoked to explain the observed power law scaling of the energy spectrum of fluctuations in the solar wind. Observations have also shown that turbulence consists of Alfv\'enic fluctuations that predominantly propagate away from the sun, indicating that the turbulence possesses cross-helicity, one of three MHD ideal invariants that cascades from large to small scales in the turbulent state. Moreover, there have been recent evidence from theory and numerical simulations that cross helicity plays a more fundamental role in determining the structure of the spectrum of magnetohydrodynamic turbulence, even when no overall cross-helicity is present. In order to elucidate the role of cross-helicity in the turbulence, we perform high resolution numerical simulations of MHD turbulence with and without cross-helicity. Based on our results, we propose that in the imbalanced case the Elsasser energy spectra have different amplitudes, nevertheless, their scaling is the same and consistent with the Iroshnikov-Kraichnan scaling, also observed in the balanced case.   

Dynamics of Solar Coronal Mass Ejections: Theory and New SECCHI Observation

The physical mechanisms of coronal mass ejections (CMEs) and flares have been an important open question in solar and by implication stellar physics. The physical connections between CMEs and these phenomena have also been a major question. The new SECCHI observations represent unprecedented opportunities to test and establish new understanding of CME physics both closer to and farther away from the Sun than was previously possible. In this paper, I will discuss new results from recent applications of a theoretical flux-rope model of CMEs (Chen JGR, 1996) to several CMEs and their dynamics observed to about 100 Rs (1/2 AU) by SECCHI. Forces acting on these CMEs are found to be dominated by the Lorentz hoop force in the inner corona and by the competition of the hoop force and retarding drag force in the outer corona and heliosphere. It is shown that the erupting flux-rope model governed by these forces is able to fit the observed CME trajectories throughout the SECCHI field of view out to approximately 1/2 AU, indicating that the model correctly captures the basic physics, i.e., forces and magnetic geometry, of acceleration and propagation of CMEs. It is also shown that the duration of the poloidal flux injection function chosen to fit the CME trajectory closely match the duration of the observed GOES X-ray light curves for both short-duration and long-duration flares.   

Plasma Flows in the Heliosheath

The Voyager spacecraft provide the first opportunity to study in situ the physics of the plasma in the heliosheath, the region of the shocked solar wind between the termination shock and the heliopause. The plasma flow speed at Voyager 2 is faster than that observed at Voyager 1, an unexpected finding. Flow in the T direction (RTN coordinates) is larger than in the N direction. This may indicate that the termination shock is wider in the T than N directions, but there is an alternate interpretation involving heliosheath flow patterns diverging from the stagnation point. The N component of the flow oscillates with a 110-day period whereas the T component is fairly constant. We suggest that these oscillations are due to a change in the shock orientation in the RN plane, perhaps caused by latitudinal changes in the solar wind.   

Current Sheet Formation and Self-Organization in Turbulent Plasmas

Self-Organization can be defined as the process by which a physical system, in the course of its evolution, changes its spatial structure, the form of its equations of motion, or key coefficients in those equations. A turbulent magnetohydrodynamic (MHD) fluid can exhibit self-organization, so defined. A turbulent MHD fluid with collisional resistivity has a low rate of dissipation of turbulent energy. However, as the turbulence develops, it forms thin current sheets in which the current density increases exponentially. When the electron drift speed becomes comparable to or exceeds the ion acoustic speed, plasma instabilities can enhance the resistivity, and thus the dissipation rate. In turbulent evolution of this kind, an MHD fluid can transform itself from a low dissipation to a high dissipation state. Calculations show that it is plausible that turbulence in the solar corona could exhibit this behavior.   

Long-Term Evolution of Magnetized Bubbles in Galaxy Clusters

An unsolved problem in active galactic nuclei (AGN) feedback on clusters is how to account for the the morphology and stability of buoyant bubbles and their interactions with the ambient intracluster medium (ICM). Appreciable magnetic energy has been observed in both cluster and radio lobe plasmas. We have performed nonlinear ideal magnetohydrodynamic simulations of the long term evolution of a magnetized low-density ``bubble'' plasma formed by a radio galaxy in a stratified cluster medium. It is found that about 3.5\% of the initial magnetic energy remains in the bubble after $\sim 8 \times 10^{9}$~years, and the initial magnetic bubble expansion is adiabatic. The bubble can survive for at least $8\times 10^9$~years due to the stabilizing effect of the bubble magnetic field on Rayleigh-Taylor and Kelvin-Holmholtz instabilities, possibly accounting for ``ghost cavities" as observed in Perseus-A. A filament structure spanning about 500~kpc is formed along the path of bubble motion. The mean value of the magnetic field inside this structure is $\sim 0.88$~$\mu$G at $\sim8\times10^9$~years. Finally, the initial bubble momentum and rotation have limited influence on the long term evolution of the bubble.   

Ideal Magnetohydrodynamic Simulations of Magnetic Bubble Expansion as a Model for Extragalactic Radio Lobes

Recent astronomical observations indicate that radio lobes are gigantic relaxed magnetized plasmas with kilo-to-megaparsec scale jets providing a source of magnetic energy from the galaxy to the lobes. Therefore we are conducting a laboratory plasma experiment, the Plasma Bubble Expansion Experiment (PBEX) in which a higher pressure magnetized plasma bubble (i.e., the lobe) is injected into a lower pressure background plasma (i.e., the intergalactic medium) to study key nonlinear plasma physics issues. Here we present detailed ideal magnetohydrodynamic (MHD) three-dimensional simulations of PBEX. First, the direction of bubble expansion depends on the ratio of the bubble toroidal to poloidal magnetic field, with a higher ratio leading to expansion predominantly in the direction of propagation and a lower ratio leading to expansion predominantly normal to the direction of propagation. Second, a leading MHD shock and a trailing slow-mode compressible MHD wave front are formed ahead of the bubble as it propagates into the background plasma. Third, the bubble expansion and propagation develop asymmetries about its propagation axis due to reconnection arising from numerical resistivity and to inhomogeneous angular momentum transport due to the background magnetic field. These results will help guide the initial experiments and diagnostic measurements on PBEX.   

Magnetic Bubble Expansion as an Experimental Model for Extra-Galactic Radio Lobes

The Plasma Bubble Expansion Experiment (PBEX) has begun laboratory experiments and coordinated nonlinear MHD simulations to address outstanding nonlinear plasma physics issues related to how magnetic energy and helicity carried by extra-galactic jets interacts with the intergalactic medium to form radio lobe structures. Experiments are being conducted in the 4 meter long, 50 cm diameter HELCAT linear plasma device at UNM. A pulsed magnetized coaxial gun ($\sim $10 kV, $\sim $100 kA, $\sim $2 mWb) forms and injects magnetized plasma bubbles perpendicularly into a lower pressure weakly magnetized background plasma formed by a helicon and/or hot cathode source in HELCAT. Experimental parameters can be adjusted so that important dimensionless parameters are relevant to the astrophysical context. Ideal MHD simulations show that an MHD shock develops ahead of the bubble as it propagates, and that the bubble develops asymmetries due to the background field [1]. First experimental data from plasma bubble injection into a background plasma, including magnetic probe measurements and high-speed camera imaging, will be presented. [1] W. Liu et al., Phys. Plasmas 15, 072905 (2008). Supported by NSF-AST/DOE grant AST-0613577 and LANL LDRD.   

Heating the Intra-Cluster Medium by Magnetic AGN Feedbacks

It is believed that AGN feedback from the SMBH at the central elliptical galaxy in galaxy clusters is a major source to heat the Intra-Cluster Medium (ICM) to avoid the catastrophic collapse of the cluster core. The morphologies of the jet/lobes of the radio galaxies and the sizes of the large X-ray cavities indicate that the energy of magnetic fields from AGNs may be a big fraction of the total AGN energy. We performed Cosmological MHD simulations of AGN feedbacks in Poynting flux-dominated limit at different stages of the cluster formation. We show that about 80\% of the injected magnetic energy ($\sim$10$^{61}$ erg) from the AGN is converted to the thermal and kinetic energy of the ICM. This energy is distributed through the ICM by driving shocks and forming bubbles by magnetic fields. While shocks heat the inner part of cluster core rapidly, the raising bubbles bring the injected energy to the outer region in longer time. The properties of cluster core are dramatically changed by the injection. The impact on cluster formation by the AGN feedbacks at different redshifts is discussed.   

Singletip Langmuir Measurements of UW-RWM Plasma

The rotating wall machine is a linear screw-pinch built to study the role of different wall boundary conditions on the resistive wall mode (RWM). Its plasma is created by a hexagonal array of seven electrostatic guns. The guns can be biased to discharge up to 1 kA of current each, firing independently or in tandem. The 20 cm diameter, 1.2 m long plasma column is held in place by a 600 G (max) axial guide field. A singletip Langmuir probe inserted from the opposite end of the chamber yields measurements of $T_e, n_e$ and $V_p$ in $r$ and $z$. The density fired from a single gun on the magnetic axis diffuses to the wall as it travels down the column, while the plasma from seven guns condenses in the center. I will present 2D Langmuir profiles and animations of the unbiased plasma column in several density and field configurations; biased plasma current measurements are an ongoing concern.   

Coster kronig transition and shake off probabilities in L$\alpha $ region of X-Ray satellites spectra

The X-ray satellite spectra arising due to 2p$_{3/2}^{-1}$3x$^{-1}$-3x$^{-1}$3d$^{-1}$ (x $\equiv $ s, p, d) transition array, in elements with Z = 40 to 92, have been calculated. The energies of various transitions of the array have been determined by using available Hartree-Fock-Slater data on 1s$^{-1}$-2p$^{-1}$3x$^{-1}$ and 2p$_{3/2}^{-1}$-3x$^{-1}$,3x'$^{-1}$ Auger transition energies and their relative intensities have been estimated by considering cross - sections of singly ionized 2x$^{-1}$ (x $\equiv $ s, p) states and then of subsequent Coster-Kronig and shake off processes. In both these processes initial single hole creation is the prime phenomenon and electron bombardment has been the primary source of energy. The calculated spectra have been compared with the measured satellite energies in L$\alpha _{1}$ spectra. Their intense peaks have been identified as the observed satellite lines. The one to one correspondence between the peaks in calculated spectra and the satellites in measured spectra has been established on the basis of the agreement between the separations in the peak energies and those in the measured satellite energies. It has been established that six satellites observed in the L$\alpha _{1}$ region of the X-ray spectra of various elements and named $\alpha _{3}$, $\alpha _{4}$, $\alpha _{5}$, $\alpha \prime $, $\alpha ^{ix}$ and $\alpha ^{x}$ in order of increasing energy are mainly emitted by 2p$_{3/2}^{-1}$3d$^{-1}$-3d$^{-2}$ transitions. On the basis of agreement between computed spectra and measured satellites, It is observed that the satellite $\alpha _{3 }$in $_{40}$Zr to $_{48}$Cd and $\alpha \prime $ in $_{74}$W to $_{92}$U is emitted by the superposition of the most intense transition $^{3}$F$_{4}-^{3}$F$_{4}$, contributing in order of decreasing intensity.   

Extreme Ultraviolet Spectroscopy of Highly Charged Tungsten for Magnetic Fusion Plasma Diagnostics

The NIST electron beam ion trap has been used to provide accurate transition wavelengths in the 2-20 nm spectral range for highly charged elements near Z=74 (tungsten).~ Spectra were recorded over a wide range of monoenergetic electron impact energies (2-27 keV), to produce charge states in the range of Q=37-65, corresponding to those expected in thermal plasmas with temperatures up to about 100,000,000 K (such as ITER).~ In addition to W, we also studied several elements with similar mass (Hf, Ta, and Au) in order to reveal isoelectronic trends.~ We have compared the measured spectral distribution of light to synthetic spectra computed using the NOMAD collisional-radiative code using atomic data generated by the FAC code.~   

Generation of Large-Scale Zonal Structures by Drift Flute Waves in High-Beta HED Plasmas

Our aim is to develop a more general analysis of nonlinear dynamics of drift-flute waves, applicable to arbitrary plasma beta and arbitrary spatial scales in comparison with the ion Larmor radius. This study is of interest for fundamental plasma theory as well as for the interpretation of Z-pinch and laboratory astrophysics experiments. Description of low-frequency waves and in particular drift flute waves in a high beta plasma, generally speaking, requires a kinetic approach, based on the Vlasov-Maxwell set of equations. In the present work we show that the alternative two-fluid description can adequately describe the ion perturbations with arbitrary ratio of the characteristic spatial scales to the ion Larmor radius in so-called Pade approximation. For this purpose reduced two-fluid hydrodynamic equations which describe nonlinear dynamics of the flute waves with arbitrary spatial scales and arbitrary plasma beta are derived. The linear dispersion relation of the flute waves and the Rayleigh-Taylor instability are analyzed. A general nonlinear dispersion relation which describes generation of large-scale zonal structures by the flute waves is presented and analyzed.   

Neoclassical Viscosities and Anomalous Flows in Stellarators

We present initial work to use neoclassical viscosities calculated with the PENTA code [1] in a transport model that includes Reynolds stress generation of flows [2]. The PENTA code uses a drift kinetic equation solver to calculate neoclassical viscosities and flows in general three-dimensional geometries over a range of collisionalities. The predicted neoclassical viscosities predicted by PENTA can be flux-surfaced average and applied in a 1-D transport model that includes anomalous flow generation. This combination of codes can be used to test the impact of stellarator geometry on anomalous flow generation. As a test case, we apply the code to modeling flows in the HSX stellarator. Due to variations in the neoclassical viscosities, HSX can have strong neoclassical flows in the core region. In turn, these neoclassical flows can provide a seed for anomalous flow generation. [1] D. A. Spong, Phys. Plasmas \textbf{12}, 056114 (2005). [2] D. E. Newman, et al., Phys. Plasmas \textbf{5}, 938 (1998).   

3D Global Fluid Simulations of Turbulence in LAPD

We present 3D global fluid simulations of the UCLA upgraded Large Plasma Device (LAPD). This device confines an 18-m-long, cylindrically symmetric plasma with a uniform magnetic field. The plasma in the simulations is generated by density and temperature sources inside the computational domain, and sheath boundary conditions are applied at the ends of the plasma column. In 3D simulations of the entire plasma, we observe strong, rotating intermittent density and temperature fluctuations driven by resistive driftwave turbulence with finite parallel wavenumbers. Analogous simulations carried out in the 2D limit (that is, assuming that the motions are purely interchange-like) display much weaker mode activity driven a Kelvin-Helmholtz instability. The properties and scaling of the turbulence and transport will be discussed.   

Simulations of transport and sheared flow in the helimak experiments

A two-dimensional fluid model that includes E x B convection, magnetic curvature, and plasma sources, is used to study the helimak experiments, a magnetized toroidal plasma with open field lines. The model equations evolve both the perturbations and equilibrium profiles of the plasma density, potential, and electron temperature. The profiles of plasma parameters, the sheared E x B flow, the fluctuation-induced transport, as well as statistics of the fluctuations obtained from the simulations are presented. The simulation results show good agreement with the experimental observations.   

Deriving magnetofluid models from action principles

An algorithmic prescription is described for building action principles for plasma magnetofluid models that are extensions of magnetohydrodynamics. The action principles naturally lead to physically important invariants and Hamiltonian structure. Also, a prescription for obtaining reduced fluid models is given. Examples relevant to laboratory plasma discharges and naturally occurring plasmas will be presented, including models with gyroviscosity and generalizations of Ohm's law.   

Action principle derivation of one-fluid models from two-fluid actions

Ideal MHD possesses a well-known action principle formulation when the theory is expressed in terms of Lagrangian (or material) variables [1]. Here we start with a general electromagnetic two-fluid action functional in Lagrangian variables and derive action principles for one-fluid models, including ideal MHD. [1] W.A. Newcomb, Nuclear Fusion: 1962 Suppl. Part 2, p. 451   

Modeling of Anomalous Transport in Tokamaks with FACETS code

The FACETS code, a whole-device integrated modeling code that self-consistently computes plasma profiles for the plasma core and edge in tokamaks, has been recently developed as a part of the SciDAC project for core-edge simulations. A choice of transport models is available in FACETS through the FMCFM interface~[1]. Transport models included in FMCFM have specific ranges of applicability, which can limit their use to parts of the plasma. In particular, the GLF23 transport model does not include the resistive ballooning effects that can be important in the tokamak pedestal region and GLF23 typically under-predicts the anomalous fluxes near the magnetic axis~[2]. The TGLF and GYRO transport models have similar limitations~[3]. A combination of transport models that covers the entire discharge domain is studied using FACETS in a realistic tokamak geometry. Effective diffusivities computed with the FMCFM transport models are extended to the region near the separatrix to be used in the UEDGE code within FACETS. \\ 1. S.~Vadlamani {\it et al.} (2009) %First time-dependent transport simulations using GYRO and NCLASS within FACETS (this meeting).\\ 2. T. Rafiq {\it et al.} (2009) %Simulation of electron thermal transport in H-mode discharges Submitted to Phys. Plasmas.\\ 3. C. Holland {\it et al.} (2008) %Validation of gyrokinetic transport simulations using %DIII-D core turbulence measurements Proc. of IAEA FEC (Switzerland, 2008)   

Progress of Time-dependent Transport Simulations Using GYRO and Neoclassical Models Within FACETS

Progress on the integration of the turbulent transport code GYRO and the neoclassical codes such as NCLASS into the FACETS (Framework Application for Core-Edge Transport Simulations) framework through the use of a multi-language Fortran/C/C++ friendly FMCFM (Framework for Modernization and Componentization of Fusion Modules) interface is presented. The FMCFM framework provides a common interface to varying fusion transport modules and libraries such as those in the National Transport Code Collaboration (NTCC) module library {[}1{]}. The interlanguage wrapper code is automatically generated. First results of coupled GYRO-NCLASS-FACETS simulations using realistic initial profiles and particle/heat sources are presented. \\ {[}1{]} A. H. Kritz \emph{et al}. Comp. Phys. Communications \textbf{164} ,108 (2004) \\ {[}2{]} See A. Pankin's \emph{et al.} presentation on transport models in FACETS (Sherwood 2009)\\   

Predictions of high $Q_{DT}$ in ITER H-mode plasmas

Time-dependent integrated predictions of performance metrics such as the fusion power P$_{DT}$, Q$_{DT}\equiv$ P$_{DT}/$P$_{ext}$, and alpha profiles are presented. The PTRANSP code (see R.V. Budny, R. Andre, G. Bateman, F. Halpern, C.E. Kessel, A. Kritz, and D. McCune, Nuclear Fusion {\bf 48} 075005, and F. Halpern, A. Kritz, G. Bateman, R.V. Budny, and D. McCune, Phys. Plasmas {\bf 15} 062505) is used, along with GLF23 to predict plasma profiles, NUBEAM for NNBI and alpha heating, TORIC for ICRH, and TORAY for ECRH. Effects of sawteeth mixing, beam steering, beam shine-through, radiation loss, ash accumulation, and toroidal rotation are included. A total heating of P$_{ext}$=73MW is assumed to achieve H-mode during the density and current ramp-up phase. Various mixes of NNBI, ICRH, and ECRH heating schemes are compared. After steady state conditions are achieved, P$_{ext}$ is stepped down to lower values to explore high $Q_{DT}$. Physics and computation uncertainties lead to ranges in predictions for P$_{DT}$ and Q$_{DT}$. Physics uncertainties include the L$\rightarrow$H and H$\rightarrow$L threshold powers, pedestal height, impurity and ash transport, and recycling. There are considerably more uncertainties predicting the peak value for Q$_{DT}$ than for P$_{DT}$.   

Dynamic Confinement of ITER Plasma by O-Mode Driver at Electron Cyclotron Frequency Range

A low B-field side launched electron cyclotron O-Mode driver\footnote{R. Prater et. al., \textit{Nucl. Fusion} 48, No 3 (March 2008).} leads to the dynamic rf confinement, in addition to rf turbulent heating, of ITER\footnote{E. P. Velikhov, History of the Russian Tokamak and the Tokamak Thermonuclear Fusion Research Worldwide That Led to ITER (Documentary movie; Stefan Studios Int'l, La Jolla, CA, 2008; {\copyright} E. P. Velikhov, V. Stefan.)} plasma. The scaling law for the local energy confinement time $\tau _{E}$ is evaluated ($\tau _{E}$ $\sim $ 3n$_{e}$T$_{e}$/2Q, where (3/2) n$_{e}$T$_{e}$ is the local plasma thermal energy density and Q is the local rf turbulent heating rate). The dynamics of unstable dissipative trapped particle modes (DTPM)\footnote{M N Rosenbluth, \textit{Phys. Scr.} T2A 104-109 ~ 1982}$^,$\footnote{B. B. Kadomtsev and O. P. Pogutse, Nucl. Fusion 11, 67 (1971).} strongly coupled to Trivelpiece-Gould (T-G) modes is studied for gyrotron frequency 170GHz; power$\sim $24 MW CW; and on-axis B-field $\sim $ 10T. In the case of dynamic stabilization of DTPM turbulence and for the heavily damped T-G modes, the energy confinement time scales as $\tau _{E}\sim $(I$_{0})^{-2}$, whereby I$_{0}$(W/m$^{2})$ is the O-Mode driver irradiance.   

Gyrocenter-Gauge Kinetic Algorithm for High Frequency Waves in Magnetized Plasmas

A kinetic particle-in-cell simulation algorithm for electromagnetic waves in gyrofrequency range has been developed based on the gyrocenter-gauge kinetic theory. The magnetized plasma system is simulated in the gyrocenter coordinate system. The gyrocenter distribution function F is sampled on the gyrocenter, parallel velocity, and magnetic moment coordinates. The gyrocenter-gauge function S is sampled on the Kruskal rings, and shares the first five coordinates with F. The moment integral of pull-back transformation from perturbed gyrocenter coordinate to unperturbed gyrocenter coordinate is directly calculated using the Monte-Carlo integration method, and an explicit difference scheme for Maxwell's equations in terms of potentials is adopted. The new Gyrocenter-Gauge (G-Gauge) algorithm has been successfully applied to the simulation studies of high frequency extraordinary wave, electron Bernstein wave, the mode conversion process between the extraordinary wave and the electron Bernstein wave in 1D inhomogeneous plasma, and the mode conversion between electron plasma wave and ion Bernstein wave in 2D plasma.   

Vorticity equation for gyrokinetic formulations

Traditionally, a gyrokinetic quasineutrality equation has been employed to calculate the electric field in delta-f gyrokinetic codes. The usual gyrokinetic quasineutrality is written to first order in an expansion in the ion Larmor radius over the tokamak minor radius, and it provides the correct result for short wavelengths, on the order of the ion Larmor radius. However, in tokamaks, this lowest order equation fails to give a self-consistent radial electric field for long wavelengths. To calculate the radial electric field, we need the toroidal rotation and hence we must keep the radial transport of toroidal angular momentum. This effect is missing in traditional gyrokinetics. By studying the time derivative of quasineutrality, known as the vorticity equation, we make explicit the effect of momentum transport and we prove that gyrokinetics has to be solved to higher order if the radial electric field is to be calculated from quasineutrality. As an alternative approach, we propose to employ a vorticity equation where only the terms that transport toroidal angular momentum must be calculated to higher order.   

Fusion-Fission Transmutation Scheme- Efficient Destruction of Nuclear Waste

A fusion-assisted transmutation system for the destruction of transuranic (TRU) waste is presented. Subcritical fusion-fission hybrids burn the intransigent transuranic residues (with most of the long lived bio-hazard) of a new fuel cycle that uses cheap light water reactors (LWRs) for the easily burned majority of the TRU. In the new fuel cycle, the number of hybrids needed to destroy a given amount of original LWR waste is 5-10 times less than the corresponding number of critical fast reactors. (Fast reactors, due to stability constraints, cannot burn the very poor quality TRU residue.) The new system comparably reduces the expensive reprocessing throughput. Realization of these advantages should lead to a great reduction in the cost of transmutation. The time needed for 99{\%} waste destruction would also be reduced from centuries to decades. The centerpiece of the fuel cycle is a high power density compact fusion neutron source (CFNS-100 MW, with major radius + minor radius $\sim $ 2.5 m), which is made possible by a super-X divertor. The physics and technology requirements of the CFNS are much less than the requirements of a pure fusion power source. Advantages of the system as part of a timely strategy to combat global warming are briefly described.   

Three-Dimensional Equilibrium Reconstruction: V3FIT

Equilibrium Reconstruction is an inverse problem, where the signals from experimental diagnostics are used to determine the parameters (current profile, pressure profile, toroidal flux), which specify an MHD equilibrium. The V3FIT code is an equilibrium reconstruction code that uses VMEC (a three-dimensional MHD equilibrium code) to solve the forward problem. Latest results will be shown, including geometrical constraints on the equilibrium (limiter positions) and improved profile specification.   

PIC modeling of ion heating in RFP-like plasma

Strong ion heating is observed during sawtooth crashes in the reversed field pinch (RFP). This effect can be partially explained as the heating due to viscous damping of localized plasma flows generated by tearing modes [1] at sawtooth crashes. Here we attempt a self-consistent modeling of the effect in fully kinetic particle in cell simulations in 2-D plane geometry with initial plasma equilibrium parameters relevant to those in RFP plasmas. The initial equilibrium is taken to be tearing unstable. Preliminary results show that when the proton to electron mass ratio is close to the realistic one, part of the magnetic field energy is converted to ion flow energy and then to ion thermal energy while the total electron energy is almost unchanged. 1. V.~A.~Svidzinski, G.~Fiksel, V.~V.~Mirnov, and S.~C.~Prager, Phys. Plasmas Vol. 15, p. 062511 (2008).   

Gyrokinetic studies of stellarator turbulent transport via Gene

We study the turbulence and turbulent transport in stellarators (and tokamaks), via analysis of simulation results from the 3D gyrokinetic code Gene\footnote{ P. Xanthopoulos, F. Jenko, Phys.Plasmas {\bf 13}, 092301 (2006).}, with particular emphasis on the configuration-dependence of turbulence characteristics. Present day stellarator designs seek to optimize stellarator neoclassical transport. With the advent of simulation codes like Gene, one can now seek to characterize and then optimize designs for TOTAL transport. The comparison between different configurations in stellarator parameter space is of 2 types, global and local. Global comparisons look at changes in plasma performance (eg, levels of turbulent fluxes and zonal flows, dependence of these on plasma gradients) between very different designs (eg, a QA versus a QI/QO design). Local comparisons look at the changes in performance between slight variants of the same design. Both aid in gaining insight into which geometric features (curvature, local and global shear, etc) are important in determining the turbulent characteristics.   

Nonlocal theory for the excitation of geodesic acoustic modes by drift waves

The geodesic acoustic modes (GAMs) are typically observed in the edge region of toroidal plasmas. Drift waves have been identified as a possible cause of excitation of GAMs by a resonant three-wave parametric process. A nonlocal theory of excitation of these modes in inhomogeneous plasmas typical of the edge region of tokamaks has been developed. The continuum GAM modes with coupling to the drift waves can generate discrete ``global'' unstable eigenmodes localized in the edge ``pedestal'' region of the plasma. These global eigenmodes have a two space scale character. The ``fast'' radial scale is determined by a three-wave frequency matching condition while the ``slow'' scale is determined by the ambient density and temperature inhomogeneity scale-lengths.   

The gyrokinetic free energy cascade driven by a magnetic field gradient

Recent progress in the theory of the gyrokinetic inertial range cascade has created an opportunity to revisit the problem of the free energy cascade in tokamaks with a fresh perspective. In this work, we develop a theory of grad-B-driven, quasi-two dimensional free energy cascade in the so-called nonlinear phase-mixing range, $k\rho_i \gg 1$. We compare the predictions of this theory with nonlinear simulations using GS2 and its streamlined version, AstroGK.   

Non-diffusive particle transport in a gyrokinetic Z-pinch with pitch-angle scattering

We have developed a new nonlinear, gyrokinetic, $\delta f$ PIC code with a pitch-angle scattering collision operator and a gyroaveraging method valid for large $k_{\perp}\rho_i$. We examine the collisional damping of zonal flows in the Z-pinch entropy mode, where gradients of plasma density and temperature drive a curvature-type instability for $k_{\perp}\rho_i >1$. This arrangement is useful for self-consistent particle tracking studies aimed at determining whether non-diffusive transport is relevant for describing radial transport in gyrokinetic microturbulence. Non-diffusive transport is a consequence of non-Gaussian random walks. Zonal flows in turbulence are likely to cause such random walks since short displacements are favored perpendicular to the zonal flows. A subset of particles for each value of $k_{\perp}\rho_i$ can be selected from the entire set of particles that determine the fields. Displacements of these particles can be tracked and used to determine the dependence of the mean square displacement on time as a function of particle energy. Observable results include power-law scaling of the variance of particle displacements and non-Gaussian displacement distribution functions. Results are compared to analytic expectations and other observations of non-diffusive transport in simpler simulations.   

Interfacing \textsc{vacuum} to \textsc{m3d-c1} and other nonlinear codes

In order to interface the linear 2-D (in equilibrium) \textsc {vacuum} code to nonlinear 3-D codes a buffer zone is assumed which separates the fully nonlinear region from the intrinsically linear vacuum region. Within the buffer zone the plasma can: 1) gradually transition radially to a vacuum-like (e.g., high resistive) virtual layer where it matches directly to the outer fields calculated by the \textsc{vacuum} code, or 2) abruptly transition through a thin resistive layer beyond which the fields are again calculated by the \textsc{vacuum} code. The latter solves for the magnetic scalar potential response to the normal field at the layer, which in both cases is assumed continuous. In case 1) the tangential fields are also continuous, but in case 2) the apropriate dicontinuities of the tangential fields across the resistive shell are accounted for. In the outer vacuum region the fields satisfy the outer boundary conditions and is Fourier analyzed in the toroidal angle $\phi$. Although the method is not restiicted to this, an example is presented where the scalar potential of the \textsc{vacuum} code matches on to the magnetic field decomposition used in the nonlinear \textsc{m3d-c1} code currently under development.   

$\delta f$ simulation of non-local neoclassical effects in tokamaks using Constants of Motion background distribution function.

While standard $\delta f$ simulation uses a local shifted Maxwellian for a background distribution, true collisionless neoclassical equilibrium distribution is a function of three Constants of Motion (CoM). The difference between CoM and local Maxwellian is due to particle orbit width, which can become very large for fast ions near sharp pressure gradients. Taking the CoM function as equilibrium in PIC simulations eliminates the large orbit contribution to the rapid growth of the particle weights. We illustrate this by simulating the radial transport using GTC-NEO code [2] which has been modified to support the new equilibrium. New challenges faced by the CoM based simulation include solving moment equations, implementing ion-ion collision operator and particle loading. We introduce deterministic collision oprator between CoM functions together with test-particle and field- paticle opeartors to simulate collisions. In presence of ion density, temperature and parallel flow gradients the new CoM based simulation produces much smaller particle weights compared to the local Maxwellian based results. We present results from the simulation of a system with sharp gradients as well as in presence of impurities using the new algorithm. [1] F. L. Hinton, TTF (2008). [2] W. X. Wang et. al., Physics of Plasmas 13, 082501 (2006).   

Radial Spreading of Drift Wave-Zonal Flow Turbulence via Soliton Formation

Recently, it has been shown that turbulence spreading is responsible for the local turbulence intensity dependence on the global nonuniform equilibrium properties, {\it i.e.} the size scaling of turbulent transport coefficients. In the present work, first we investigate the slab model for the spatio-temporal evolution of the drift wave(DW) radial envelope and zonal flow(ZF) amplitude. Stationary solution of the coupled partial differential equations in a simple limit yields formation of DW-ZF solitons. It is shown that the DW-ZF soliton structures propagate at group velocity which depends on the envelope peak amplitude. Additional interesting physics, {\it e.g.} birth/death, collision, and reflection of solitons, as well as turbulence bursting can also be observed due to effects of linear growth/damping, dissipation, equilibrium nonuniformities and soliton dynamics. The propagation of soliton causes significant radial spreading of DW turbulence and therefore can affect transport scaling by increasing the turbulent region. Discussion on the correspondence to the two-field DW-ZF description in toroidal geometry will also be presented.   

Toroidal Ion Temperature Gradient Modes and Angular Momentum Transfer$^1$

Toroidal modes driven by the ion temperature gradient$^2$ are commonly thought to be responsible for the observed transport of ion thermal energy in high temperature plasmas. These modes have a toroidal phase velocity in the direction of the ion diamagnetic velocity for a considerable range of their transverse wavelengths, but for some parameters the phase velocity reverses. Modes of odd parity - meaning the electrostatic potential is an odd function of the poloidal angle measured relative to the equatorial plane - are driven primarily by the combined effects of the geodesic curvature, ion temperature gradient, and shear of the magnetic field. The odd parity modes are not stabilized by collisionality to the same extent as are the even parity modes. Therefore, in the L-regime the odd modes can be excited near the edge of the plasma where $\eta_i$ can be significant. In this case the modes may be responsible for ejection of angular momentum in the ion diamagnetic velocity direction. Such ejection is required by the accretion theory of spontaneous rotation$^3$. Correlation with experiments on Alcator C-Mod is given. $^1$Sponsored in part by the US DOE and NSF. $^2$B. Coppi and F. Pegoraro, Nucl. Fus. 17, 969 (1977). $^3$B. Coppi, Nucl. Fus. 42, 1 (2002).   

Simulation of turbulence in tokamak plasmas with reversed magnetic shear

Electrostatic ITG and TEM turbulence in tokamak plasmas with reversed shear and integer $q$ minimum value are simulated using Gyrokinetic Toroidal Code (GTC). For the ITG case, electrostatic potential fluctuation gaps are observed in the minimum-$q$ region in the linear phase, with sizes comparable to the distances between adjacent rational surfaces. In the non-linear phase, the gaps are filled up due to turbulence spreading. For the TEM case, the mode grows only in the positive-shear side in the linear phase. In the non-linear phase, it diffuses into the negative-shear side.   

New Algorithm for Simulation of the Interaction of Intense Laser Light with a Multiscale Plasma

The kinetic simulation of the interaction of intense laser light with plasma for fast ignition is challenging. Conventional explicit, particle-in-cell (PIC) methods require temporally resolving the light wave and electron plasma frequencies and spatially resolving the light wavelength, electron Debye length, and skin depth for stability and accuracy. There is also a CFL stability condition on the speed of light. In a fast-ignition plasma, the electron density spans many orders of magnitude. The very underdense plasma is typically collisionless and the very overdense plasma is highly collisional. Fully electromagnetic, explicit PIC algorithms work well up to densities exceeding critical density, but are impractical in the highly overdense region where wave propagation is very restricted. We introduce a two-region algorithm for the simulation of fast ignition. For lower densities, we use an explicit, fully electromagnetic algorithm, and a variant of the explicit algorithm of Davies, et al., for the very overdense plasma using a reduction of Maxwell's equations and an Ohm's law. Spatial smoothing of the electric fields is required. Analysis and demonstrations are presented.   

Microwave Ionization of Hydrogen Atoms in the Presence of a Metal Wall

Computer simulations of hydrogen ionization were conducted using a one-dimensional classical model. A metal wall at varying distances was used in conjunction with varying strengths and frequencies of microwaves, and ionization probabilities were computed for a range of microwave parameters corresponding to experiments. It is clearly demonstrated that the presence of a metal wall can significantly lower the threshold for chaotic microwave ionization because of the effects of image charges in the wall. The results may be applicable to the sticking problem in muon-catalyzed fusion, e.g., a microwave ionization scheme in a sea of carbon nanotubes.   

Gyrofluid study of the energy spectrum near the ion Larmor radius

In the past, gyrofluid models have been used to study problems where finite Larmor-radius (FLR) effects are important. These models are computationally less expensive than full gyrokinetic computations, but still capture much of the relevant physics. We have developed a gyrofluid model that is valid for the regime with spatial scales close to the ion Larmor radius. Using this model, we explore the energy spectrum for wave numbers in this regime. Calculations are run on Graphical Processing Units (GPUs) which utilize a highly parallel architecture thus decreasing the overall computational cost.   

Finite beta effects in the Cyclone Base Case

It has loog been observed in Particle-in-Cell simulations of the Cyclone Base Case that simulations do not saturate at $\beta$ values well below the Kinetic Balooning Mode threshold. The dominant instabilities are broken up by the self-generated zonal flows in the early nonlinear stage, but subsequently lower $k_{\theta}$ modes slowly emerge and grow to large amplitude, leading to large streamer transport. Here we investigate this problem based on a new flux-tube code. Starting with the global GEM, all the equilibrium quantities, such as $B(r,\theta)$ and $T(r)$, are set to their values at the center (the flux-tube location). A linear $q(r)$ profile is still used to compute the toroidal shift when matching the two boundaries along the field line. This implementation differs from the earlier one chiefly in that additional terms in the equation of motion along ${\bf B}$, small but needed to preserve $P_{\zeta}$ as a constant of motion, are retained. These apparently have a stabilizing effect on low $k_{\theta}$ modes, allowing us to push $\beta$ closer to the KBM threshold. Collisions, radial boundary conditions and coarse-graining are all observed to strongly affect the nonlinear state at high $\beta$. Detailed results will be presented and compared with Eulerian simulations [Candy, Phys. Plasmas {\bf 12}, 072307 (2005)].   

Edge Turbulence Scaling Studies

Recent simulations of edge and SOL turbulence using the Lodestar SOLT code \footnote{J. R. Myra, D. A. Russell, and D. A. D'Ippolito, Phys. Plasmas {\bf 15}, 032304 (2008); D. A. D'Ippolito et al., paper IAEA-CN-165/TH/P4-17 (2008).} have addressed a number of related questions : nonlinear saturation mechanisms for edge turbulence, the role of sheared flow in regulating turbulence and blob generation, and the role of dissipation in these processes. Here, we examine the scaling of the turbulent particle and heat flux with various parameters, such as the linear damping of the zonal flows and the equilibrium gradients. We will investigate the question of whether the 2D edge turbulence exhibits a critical-gradient behavior seen on some experiments. The transition between different nonlinear saturation mechanisms will also be discussed.   

The Role of Passive Momentum Flux in Turbulence Saturation and Bursty Edge Transport

In edge transport, particle sources (typically ionization) sustain the density (but not the zonal velocity) profile against turbulence-induced losses. The conservation law for zonal momentum $<$nv$_{y}>$ implies a ``passive'' momentum flux associated with the radial particle flux of the form $<$nv$_{x}><$v$_{y}>$. When other linear zonal flow damping mechanisms are small, e.g. viscosity and drag, this nonlinear passive loss term competes with Reynolds stress $<$n$><$v$_{x}$v$_{y}>$ to establish a dynamical turbulence quasi-steady state, which is typically very bursty in character. We study the turbulent state in this regime, with attention to the saturation mechanisms of profile modification and zonal flow shear. Reduced dimensionality models are presented together with results from the SOLT turbulence code. We find that bursts are associated with the radial convective (i.e. passive) transport of the zero-velocity-shear point across the instability zone. Broader implications for the role of the v$_{y}$(x) profile will be discussed.   

Simulation of plasma sheath turbulence for magneto-inertial fusion (MIF)

A leading approach to achieve MIF is to use an imploding metal liner to compress magnetized target plasma to thermonuclear temperatures. For MIF applications, the magnetic field is parallel to the liner surface, which causes the ions, with their large gyro-radii, to positively charge the liner. This creates a strong ExB shear flow which can cause turbulence and regulate. Here we report on progress of the simulation studies of plasma sheath turbulence using a state-of-the-art VPIC [1] code. Baseline calculations are carried out examine the possibility of establishing a quiescent sheath plasma equilibrium in 1D for a flat liner surface and 2D for the shaped one, which should be unstable when 2D and 3D dynamics are allowed. The details of plasma sheath parameters from these runs, allows us to examine the regimes of various instabilities and their nonlinear saturation.\\[3pt] [1] K. J. Bowers, et al., ``Ultra high performance 3D electromagnetic relativistic kinetic plasma simulation,'' Phys. Plasmas 15, 055703 (2008).   

Global Rotational Instabilities with Vertical Field Reversal

Attempts to observe the Magnetorotational Instability in many laboratory experiments are complicated by turbulence due to the low magnetic Prandtl number ($Pm \equiv \nu/\eta$) of liquid metals. Recent experiments in the Los Alamos Flowing Magnetized Plasma (FMP) facility have shown that it is possible to sustain quasisteady rotation in a plasma annulus with $Pm > 1$. The plasma is supported by a rotational current drive, which can reverse the direction of the magnetic field in the interior. We examine the global linear stability of an idealized system in which a centrifugally supported plasma with differential toroidal rotation is threaded by a vertical field $B_z(r)$ which reverses sign in the interior of the plasma. A toroidal field $B_{\phi} \sim 1/r$ is also present. We find the necessary parameters for the excitation of the MRI. The effects of temperature and density gradients are also considered, as well as Hall terms. Consequences for the nonlinear regime are discussed.   

Non-stationary magnetized axially symmetric equilibrium

The equations of motion for a fully ionized hydrogenic plasma in applied coaxial electric and magnetic fields are analyzed, where the term for the Hall effect in the generalized Ohm's law equation picks up a factor of 1/2 relative to its usual expression. Magnetization of the medium is incorporated through the decomposition of the Hall term and the inclusion of the magnetization force, which is found to equal or exceed the gradient of the scalar pressure. A limit on the kinetic pressure obtains which corresponds to the usual limit of unity for a certain selection of parameters. Solutions of these equations for the free motion of the charges in the case of an infinite column with azimuthal symmetry are compared for various prescribed pressure profiles, where one finds that the profile near the outer edge plays an important role in the feasibility of the equilibrium.   

Relativistic Reconnection with Radiation

Relativistic reconnection is the likely mechanism for high energy emission in magnetar, pulsar, and black hole magnetospheres, as well as gamma ray bursts and jets in active galactic nuclei. In such astrophysical systems, the magnetic energy density greatly exceeds the particles' thermal and rest mass energy density. In the dissipation region of the reconnecting field, the large release of magnetic energy heats the plasma above the pair production threshold making the plasma optically thick to Thompson scattering. The increased opacity confines the released magnetic energy, which is converted into enhanced plasma outflow. The effect of radiation is incorporated via the Landau-Lifshitz prescription for the radiation reaction force, and the relativistic collision operator of Dzavakhishvili and Tsintsadze is employed to calculate the resistivity of the plasma.   

Dynamic Behavior of Peeling-Ballooning Modes in a Shifted-Circle Tokamak Equilibrium

Progress in understanding edge localized modes (ELMs) has been made by investigating the stability properties of peeling-ballooning modes. We focus on the linear and nonlinear evolution of the peeling-ballooning modes over the entire spectrum in a shifted-circle tokamak equilibrium, using the extended-MHD code NIMROD. The TOQ-generated equilibrium models an H-mode plasma with a pedestal pressure profile and parallel driven edge currents. ~A vacuum region is prescribed by a resistivity profile that transitions from a small to very large value at a specified location. We manipulate the modes that govern the pedestal evolution, by changing this location. Ballooning-like instabilities dominate distant vacuum cases, whereas peeling mode physics is expected to dominate as the vacuum approaches the pedestal. An extensive nonlinear study is planned in addition to a linear analysis as functions of the pedestal parameters and vacuum location. We present our linear results and nonlinear computational comparisons between the peeling-dominated and ballooning-dominated mode evolution.   

Double Interaction Process for the Ejection of Angular Momentum and Relevant Recoil*

The explanation of the spontaneous toroidal rotation in the L-confinement regime, according to the ``accretion theory''$^1$, requires the existence of a process ejecting angular momentum at the edge of the plasma column in the same direction as that of the ion diamagnetic velocity. The consequent recoil creates a local source of angular momentum, in the opposite direction, which then is transported from the edge to the center region. The ejection and recoil are described by a double interaction process, similar to that explaining the slide-away regime$^2$, whereby a single mode interacts at the same time with two particle populations. In this case we assume that a cold and a hot ion populations are present at the edge and are treated as collisional and collisionless, respectively. A temperature gradient (of the cold ions) driven mode ejects hot ions while accelerating them in the direction of the longitudinal mode phase velocity. The cold ions are transported inward and recoil in the (longitudinal) opposite direction. An analytic description of this process is given. The transport of angular momentum from the edge of the plasma column is attributed to a different category of modes such as velocity and temperature gradient (VTG) driven modes involving only the hot population. *Sponsored in part by the U.S. DOE. $^1$B. Coppi, $\it{Nucl. Fus.}$ $\bf{42}$ (2002); $^2$B. Coppi, F. Pegoraro, R. Pozzoli, G. Rewoldt, $ \it{Nucl. Fus.}$ $\bf{16}$ 309 (1976).   

Seeding Neoclassical Tearing Modes by resonant Pfirsch-Schl\"uter currents

Neoclassical tearing mode (NTM) excitation requires a seeding mechanism that initializes a magnetic island above a threshold value. Often, NTM seeding is correlated with the appearance of some other MHD event,such as a sawtooth crash. The conventional model to explain the island seeding is to account for toroidal mode coupling producing a resonant radial magnetic perturbation that causes a forced reconnection at the NTM rational surface. Differential rotation between the magnetic signal of the MHD event and the rational surface of the NTM can provide significant shielding. In this work, we offer another explanation for the seeding process. In addition to the MHD event producing a resonant radial magnetic perturbation, the magnitude of the magnetic field strength is altered; a 3-D helical deformation of $|B|$ occurs. Helically resonant components of $|B|$ together with a pressure gradient at the NTM's rational surface produce singular Pfirsch-Schluter currents that can ultimately produce seed islands. This is a prominent island producing mechanism in 3-D stellarator equilibria. Additionally, neoclassical viscosities arise in accordance with the 3-D deformations which can partially shield the resonant currents.   

Hall-MHD and Two-Fluid Plasma Equilibria and Stability

Following our work on Hall-MHD which is a one-fluid model, we proceed to investigate the two-fluid plasma equilibrium state. This was investigated previously typically for an axisymmetric configuration. A known variational principle was used to produce only a small number of equilibria. We have stronger results, where we can produce what can be shown to be all possible equilibrium states both axisymmetric and 3D configurations. We can recover ideal MHD with equilibrium flow by some limiting process. As in MHD, stability cannot be easily determined by an energy integral since the integral is not of a definite sign even for stable plasmas. Another limiting case of interest is classical compressible fluids with no magnetic field. Here different configurations have their own different features (such as the number of constants of the motion), and must be treated differently. We produce a stability criterion which appears to be substantially different from the one applicable to rotating MHD plasmas, and is easier to satisfy.   

Internal Kink Stability and Its Relation to Tokamak Sawteeth

Analysis of sawtooth cycles using the Porcelli model [1] for specific DIII-D discharges shows that several features of the stability do not follow the conventional picture. Notably, the ideal stability does not necessarily degrade during the ramp as the axis q drops. Instead, the stabilizing contributions are weakened largely due to the changing equilibrium conditions. The Porcelli and NOVA-K [2] models are compared against the experiments. The fast particle stability contribution from NOVA-K is sensitive of varying pitch angle distribution. Yet, using reconstructed equilibria, the simpler Porcelli model yields results in agreement with experiment. This is investigated by studying the dependence of the NOVA-K results on the distribution. Accurate modeling of the actual fast ion distribution is key and a method for obtaining this from the limited statistics of a Monte-Carlo simulation is described. \par\vskip3pt\noindent [1] F. Porcelli, et al., Plasma Phys. Control. Fusion 38 (1996) 2163. \par\vskip3pt\noindent [2] C.Z. Cheng, Physics Reports 211 (1992) 1.   

A Detailed Study of Kinetic Effects of Energetic Particles on Resistive MHD Stability

Kinetic effects of energetic particles can play a crucial role in the stability of the 2/1 tearing mode in tokamaks such as JET, JT-60U, and DIII-D, where the fraction of energetic particle $\beta _{frac}=\beta _{h}$/$\beta $ is high. Using model equilibria based on experimental reconstructions, the non-ideal MHD stability, linear, and nonlinear growth and evolution of the 2/1 mode is investigated including a $\delta f$ PIC model for the energetic particles coupled to the MHD solution. The linear growth of eigenfunctions is calculated at various $\beta _{N }$and $S$ ranging from the resistive unstable to the ideal unstable regime. Initial nonlinear effects are also investigated. It has been observed that energetic particles have significant damping and stabilizing effects at experimentally relevant $\beta _{N}$, $\beta _{frac}$, and $S$, and less weaker damping and stabilizing effects inat the ideal unstable regime, and cause a real frequency of the 2/1 mode. These results suggest that a qualitative extrapolation is reasonable for what to expect from energetic particle effects on resistive MHD modes in ITER.   

Modeling Fast Electron Acceleration and Confinement in MHD Simulations,

Simulations of disruptions and disruption mitigation have been carried out with the NIMROD code, and are ongoing. An unresolved issue for ITER is the problem of runaway electrons which may be subject to large avalanche amplification factors during the current quench. Two possibilities for avoiding large runaway current fractions are collisional suppression of runaway avalanching, and degraded fast electron confinement. The latter method relies on large MHD fluctuations persisting during the current quench, which can be explored with MHD simulations. A model for diagnosing fast electron acceleration and confinement has been implemented in NIMROD. The model is presented along with further development plans. Preliminary results of the model for massive gas injection simulations show prompt loss of fast electron populations in the thermal quench, which is seen in experiments. The effects of elongation on MHD fluctuation amplitudes during a mitigated disruption are also considered.   

Recent Advances in Fully Kinetic Simulations of Driven Magnetic Reconnection with Boundary Conditions Relevant to MRX

We present an overview of the recent kinetic simulations of driven magnetic reconnection with boundary conditions relevant to the Magnetic Reconnection eXperiment (MRX). In this effort, unique for reconnection studies, the data from a well-diagnosed dedicated reconnection experiment and state-of-the-art fully kinetic simulations are combined and used to guide both the simulation and the experimental campaigns${}^1$. The simulations are performed using the high-performance particle-in-cell code VPIC${}^2$. The Coulomb collisions are treated in VPIC using a well-known Monte-Carlo technique${}^3$ that models a full collision operator. This approach allowed us to systematically examine the influence of weak Coulomb collisions on the dynamical evolution and structure of the reconnection layer. Initial results of 3D simulations that allow current-aligned instabilities to develop are presented, and the possible role of these instabilities in the reconnection dynamics is discussed. [1] Ji {\em et al.} {\em GRL}, 35, L13106 (2008) and Dorfman {\em et al.}, {\em Phys. Plasmas} {\bf 15}, 102107 (2008) [2] {K. J. Bowers {\em et al.} Phys. Plasmas, v. {\bf 15}, p.~055703, 2008.} [3] {T. Takizuka and H. Abe, J. Comput. Phys., v. {\bf 25}, p. 205, 1977}   

Comparison of the Recently proposed Super Marx Generator Approach to Thermonuclear Ignition with the DT Laser Fusion-Fission Hybrid Concept (LIFE) by the Lawrence Livermore National Laboratory.

The recently proposed Super Marx pure deuterium micro-detonation ignition concept [1] is compared to the Lawrence Livermore National Ignition Facility (NIF) laser DT fusion-fission hybrid concept (LIFE) [2]. A typical example of the LIFE concept is a fusion gain 30, and a fission gain of 10, making up for a total gain of 300, with about 10 times more energy released into fission as compared to fusion. This means a substantial release of fission products, as in fusion-less pure fission reactors. In the Super Marx approach for the ignition of a pure deuterium micro-detonation gains of the same magnitude can in theory be reached. If the theoretical prediction can be supported by more elaborate calculations, the Super Marx approach is likely to make lasers obsolete as a means for the ignition of thermonuclear micro-explosions. [1] ``Ignition of a Deuterium Micro-Detonation with a Gigavolt Super Marx Generator,'' Winterberg, F., Journal of Fusion Energy, Springer, 2008. http://www.springerlink.com/content/r2j046177j331241/fulltext.pdf. [2] ``LIFE: Clean Energy from Nuclear Waste,'' https://lasers.llnl.gov/missions/energy{\_}for{\_}the{\_}future/life/   

Self-consistent full wave simulations of lower hybrid waves

Lower hybrid (LH) waves have the attractive property of damping strongly via electron Landau resonance on relatively fast tail electrons. These waves are well-suited to driving off-axis current profile control in reactor grade plasmas. The break down of WKB techniques at reflections from the plasma cutoff make traditional ray tracing techniques unreliable in the weak absorption limit. A massively parallel version of the TORIC full-wave electromagnetic field solver valid in the LH range of frequencies has been developed~[Wright, et al. \newblock {\em CCP}, \textbf{4}, 545 (2008)] and applied to scenarios at the density ($10^{14}$/cc) and magnetic field (5T) characteristic of devices such as Alcator C-Mod [Wright, et al. \newblock {\em PoP}, \textbf{16}, TBP (2009)]. We find that retaining full wave effects due to diffraction and focusing at caustics and reflections has a strong effect on the location of wave absorption. Lower hybrid waves strongly modify the electron distribution and form a quasilinear plateau. In order to include this effect and field solutions consistent with the distribution function, we have coupled the CQL3D Fokker-Planck code to the lower hybrid solver, TORLH~[Valeo, et al. \newblock {\em 17th RF Topical Conf.}, n933, p. 297, New York, 2007]. Through iteration, a self-consistent solution is obtained. We discuss the effects off the non-Maxwellian distribution on power deposition and HXR spectra.   

Coupled GEM-XGC Simulations of Edge Pedestal Plasmas

Global GEM gyrokinetic turbulence simulations of the edge pedestal are performed assuming closed flux surfaces and using numerical profiles obtained from the XGC neoclassical calculation\footnote{Y. Chen and S. Parker, Phys. Plasmas, 15 055905 (2008)}. The plasma profiles used in GEM are output from an XGC simulation of L-mode DIII-D plasmas. In electromagnetic turbulence simulations, the obtained anomalous transport diffusivities are much bigger than from simulations in the electrostatic limit. While electromagnetic energy transport diffusivity is comparable to experimental values, the particle transport diffusivity is too high, and it would cause a pedestal crash in the XGC calculation. Adding carbon impurity may reduce the level of particle transport. Work is under way to couple GEM and XGC under the EFFIS end-to-end Frame for Fusion Integrated Simulation.   

Enhanced Neoclassical Transport Caused by Chaos Near an Asymmetric Separatrix

Plasma loss due to apparatus asymmetries is a ubiquitous phenomenon in magnetic plasma confinement. Recent experiments have investigated the loss rate when a central squeeze potential is applied to a magnetized plasma column, creating two trapped particle populations separated by a separatrix. These populations react differently to the asymmetries, leading to a collisional boundary layer at the separatrix. A loss rate scaling as $\sqrt{\nu / B}$ due to the boundary layer is expected theoretically,\footnote{D.H.E. Dubin, Phys. Plasmas {\bf 15}, 072112 (2008).} provided that the separatrix itself is axisymmetric. However, when the separatrix is {\it asymmetric}, particles become trapped and detrapped as they follow collisionless orbits. This can lead to single-particle resonances and/or a chaotic region around the separatrix, giving enhanced transport. This effect may help explain a long-standing discrepancy between experiment and neoclassical theory, and could play an important role in tokamak and stellerator confinement. Theory and simulations of this collisionless chaotic transport will be presented.   

Nonlinear Simulation of Alfven Eigenmodes driven by Energetic Particles: Comparison between HMGC and TAEFL Codes

Hybrid-MHD-Gyrokinetic Code (HMGC) [1] and the gyrofluid code TAEFL [2,3] are used for nonlinear simulation of Alfven Eigenmodes in Tokamak plasma. We compare results obtained in two cases: (I) a case designed for cross-code benchmark of TAE excitation; (II) a case based on a dedicated DIII-D shot \#132707 where RSAE and TAE activity is observed. Differences between the numerical simulation results are discussed and future directions are outlined. [1] S. Briguglio, G. Vlad, F. Zonca and C. Kar, Phys. Plasmas 2 (1995) 3711. [2] D.A. Spong, B.A. Carreras and C.L. Hedrick, Phys. Fluids B4 (1992) 3316. [3] D.A. Spong, B.A. Carreras and C.L. Hedrick, Phys. Plasmas 1 (1994) 1503.   

Comparison of Monte-Carlo Ion Cyclotron Heating Model with Full-Wave Linear Absorption Model

To fully account for the wave-particle interaction physics in ion-cyclotron resonant frequency heating experiments, the 5-D Monte-Carlo code ORBIT-RF is being coupled with the 2-D full wave code AORSA to iteratively evolve ion distribution in x-v space that is used to update the dielectric tensor in AORSA for evaluating the full-wave fields. It is demonstrated that using the full-wave fields from a Maxwellian dielectric tensor in AORSA and confining the resonant ions to their initial orbits in ORBIT-RF, ORBIT-RF largely reproduces the AORSA linear wave absorption profiles for fundamental and higher harmonic ICRF heating. An exception is an observed inward shift of the ORBIT-RF absorption peak for high harmonics near the magnetic-axis compared with that of AORSA, which can be attributed to a finite orbit width effect. Analysis of power absorption in velocity space confirms that significant power is absorbed by energetic particles with their banana tips at resonance locations.   

Role of stable eignmodes in 3D ETG-driven turbulence

The role of stable eigenmodes in Electron-Temperature-Gradient driven (ETG) turbulence is investigated. Low-wavenumber stable eigenmodes are thought to play a role in the dissipation mechanism leading to saturation of CTEM[1] and ITG[2] turbulence. Evidence has been found that the formation of magnetic coherent structures and the transition to a turbulence regime with stronger magnetic fluctuations are dependent of the ETG low $k$ stable modes in 2D fixed-$k_z$ fluid simulations[3]. A 3D code has been constructed to investigate the role of stable modes in 3D sheared slab geometry. Magnetic structure formation and electromagnetic ETG turbulence will be discussed in detail. [1] P.~W. Terry, D.~A. Baver and S.~Gupta, Phys. Plasmas \textbf{13}, 022307 (2006). [2] R.~Gatto, P.~W. Terry and D.~A. Baver, Phys. Plasmas 13 022306 (2006). [3] J.-H. Kim and P.~W. Terry (2008), 50th Annual Meeting of the Division of Plasma Physics, APS.   

Magnetic self-organization in driven MHD turbulence

Magnetohydrodynamic turbulence is a starting point for modeling large-scale plasma motions in a variety of systems ranging from astrophysical objects to laboratory experiments. Ideal MHD system has three conserved quantities: energy, magnetic helicity and cross-helicity. In decaying turbulence, energy decays faster than the other two invariants, leading to creation of structures due to the process of self-organization. Magnetic self-organization is much less understood in driven MHD turbulence. In particular, the cross-helicity, an ideal invariant cascading toward small scales in a turbulent state, has only recently become an object of systematic study as it became clear that it plays a fundamental role in driven MHD turbulence. We will demonstrate that driven MHD turbulence spontaneously creates domains of positive and negative cross helicity, which possess a hierarchical structure: inside small domains there exist smaller and stronger polarized domains and so on. This leads to spontaneous alignment of magnetic and velocity fluctuations and progressive reduction of nonlinear interaction at small scales, and it significantly affects the spectrum and structure of turbulent MHD systems.   

Neutral effects on magnetized collisional plasma transport

Neutral particles present at the edge of plasma magnetic confinement devices can play an important role in plasma energy and momentum transport due to a strong coupling with the plasma ions through charge-exchange processes [1--5]. Specifically, neutral fractions of order one thousandth or less are sufficient to produce important corrections to neoclassical radial ion heat flux, parallel ion flow, and the radial electric field, at least in a collisional plasma. Such corrections were evaluated in Refs. [2--5]. However, no complete, self-consistent, drift-ordered fluid description for a partially-ionized collisional plasma was available when these results were obtained. We recently obtained such a description [6] and use it in this work to check the results of Refs. [2--5]. In particular, we evaluate neutral corrections to the Pfirsch-Schl\"{u}ter radial electric field in a fully-ionized plasma [7]. [1] R.D. Hazeltine {\it et al.}, Nucl. Fusion {\bf 32}, 3 (1992). [2] P.J. Catto {\it et al.}, Phys. Plasmas {\bf 5}, 3961 (1998). [3] T. F\"{u}l\"{o}p {\it et al.}, Phys. Plasmas {\bf 5}, 3969 (1998). [4] T. F\"{u}l\"{o}p {\it et al.}, Phys. Rev. Lett. {\bf 89}, 225003 (2002). [5] A.N. Simakov {\it et al.}, Phys. Plasmas {\bf 10}, 398 (2003). [6] A.N. Simakov, Plasma Phys. Control. Fusion, submitted. [7] P.J. Catto {\it et al.}, Phys. Plasmas {\bf 12}, 012501 (2005).   

Bounce-Transit and Drift Resonance and Neoclassical Toroidal Plasma Viscosity in Tokamaks

The importance of the resonance between the bounce frequency of the trapped particles and precession drift frequency in tokamaks to the low frequency magnetohydroynamic instabilities has been recognized for a long time. The resonance is also important in the transport processes as demonstrated by Park, et al. in calculating the neoclassical toroidal plasma viscosity [1]. They found that the transport fluxes are independent of the collision frequency, i.e., a resonant plateau regime. Here, we develop a theory for neoclassical toroidal plasma viscosity to include not only the bounce and drift resonance of the trapped particles but also the transit and drift resonance the circulating particles [2]. In the resonant plateau regime, our results are similar to those obtained by Park, et al., except that bounce average over the trapped particle trajectories is not performed and that the contributions from the circulating particles are included. In the collisional limit, it is found that the resonant plateau regime is connected to the Pfirsch-Schluter regime. [1] PARK, J.-K.,{\ldots}et al., IAEA,Fusion Energy Conference, Geneva, October 2008, Paper EX/5-3Rb. [2] SHAING, K. C., CHU, M. S., and SABBAGH, S. A., (to be submitted to Plasma Phys. Control. Fusion)   

Generating quasi-linear diffusion coefficients using the delta-f PIC method

Linear wave codes, AORSA and TORIC, used by the SciDAC Center for Simulation of Wave-Plasma Interaction couple to the bounce-averaged nonlinear Fokker-Planck code CQL3D through quasi-linear diffusion coefficients. Both AORSA and TORIC rely on the quasi-local approximation that only includes first-order parallel and perpendicular gradient variations of cyclotron frequency and ignores field line curvature along with temperature and density gradient effects. Previously, the delta-f particle-in-cell (DFPIC) method has been used for simulating ion-cyclotron fast wave behavior. Particle behavior such as multiple pass resonance, banana orbits, and superadiabaticity can also be examined with this method. We present recent results on using eqdisk fusion data to generate quasi-linear diffusion coefficients that permit the VORPAL code to compare to AORSA and TORIC and to eventually couple to CQL3D. The results are generated for a single toroidal mode using DFPIC simulations in RZ geometry.   

A matched asymptotic treatment of the reflection of LH waves from a cutoff

Ray tracing techniques can be used to estimate the propagation of RF fields in plasmas. However, for lower-hybrid waves there are discrepancies between the power density profiles calculated using full-wave codes and those calculated using ray tracing simulations [1]. Previous work suggests that this discrepancy could be caused by the reflections of the LH waves from the cutoff [2,3]. In this poster, we calculate the effect of reflections from the cutoff, in the context of ray tracing and the WKB approximation. Using a linearized dispersion matrix to model the plasma at the cutoff, we obtain a local solution for the LH field at the cutoff. This local solution differs from the standard Airy-like form because of the intrinsic vector nature of the fields. Our local solution is then matched asymptotically to incoming and outgoing LH waves. The matching coefficients can then be used to interpret the reflection at the cutoff as a scattering process, where incoming rays are related to outgoing rays by a scattering matrix. [1] P. Bonoli, et al., Phys. Plasmas 15, 056117 (2008) [2] J. Wright, APS-DPP 2008, VI2.00003 [3] A. Schmidt, APS-DPP 2008, JO3.00003 Supported by the DOE OFES.   

Novel visualization and computational methods for iterated conversions in tokamak RF heating

Mode conversion is of great interest as a tool for RF heating and control of flow and current in fusion devices. In a closed system, waves convert many times, leading to a complex interference pattern. To aid in visualization, we introduce the concept of a 'room' associated with each of two uncoupled modes, and illustrate the idea with a tokamak model for its two-dimensional poloidal cross-section (hence the ray phase space is four-dimensional). Each of the two dispersion surfaces, $D_{j }(x,y,k_{x},k_{y})$ = 0 for $j=$1,2, is three-dimensional, hence they can be visualized as two separate 3-spaces. The set of points where conversion can occur is a two-dimensional surface in each room. When a ray of type 1 in room 1 punctures the conversion surface, it continues in room 1 as a transmitted ray, but it also spawns a daughter ray of type 2 in room 2. Starting from a point on the conversion surface, we can follow a ray of either type in the relevant room to construct two maps, which take the conversion surface to itself. All possible sequences of conversions can be summarized by all possible combinations of the maps.   

Alfv\'{e}n mode structure/stability properties of stellarators and broken-symmetry tokamaks

Energetic particle driven shear Alfv\'{e}n wave (SAW) instabilities are frequently observed in both stellarator and tokamak experiments. Three-dimensional effects are present in all toroidal devices and can significantly influence both stability properties of energetic particle populations and their loss patterns on the first wall. Three-dimensional equilibrium variations in stellarators and broken symmetry tokamaks provide new couplings that increase the complexity and density of the Alfv\'{e}n mode spectrum. An eigenmode solver, the AE3D code, has been developed for calculating Alfv\'{e}n mode structures in such configurations and identifying the most likely modes for resonant energetic tail destabilization. Applications of this model to a variety of stellarators (LHD, TJ-II, HSX, QPS, NCSX) and broken symmetry tokamaks (ITER with TF ripple and ferritic materials) have been made and results will be presented. Possible extensions to include sound wave couplings and gyro-Landau closures will be discussed.   

Numerical study of laminar plasma dynamo in cylindrical and spherical geometries

We have performed the numerical investigation of possibility of laminar dynamo in two new experiments, Plasma Couette and Plasma Dynamo, which have been designed at the University of Wisconsin-Madison. The plasma is confined by a strong multipole magnetic field localized at the boundary of cylindrical (Plasma Couette) or spherical (Plasma Dynamo) chamber. Electrodes positioned between the magnet rings can be biased with arbitrary potentials so that Lorenz force $\mathbf{E}\times\mathbf{B}$ drives any given toroidal velocity profile at the surface. Using the extended MHD code, NIMROD, we have modeled several types of plasma flows appropriate for dynamo excitation. It is found that for high magnetic Reynolds numbers the counter-rotating von Karman flow (in cylinder) and Dudley-James flow (in sphere) can lead to self-generation of non-axisymmetric magnetic field. This field saturates at certain amplitude corresponding to a new stable equilibrium. The structure of this equilibrium is considered.   

High Energy Plasmas, General Relativity and Collective Modes in the Vicinity of Black Holes*

Plasmas around black holes can take different equilibrium configurations$^1$ from those known from fluid theory as the vertical Lorentz compression due to plasma currents can overtake that of the gravitational force. In a disk with a ``seed'' magnetic field, axisymmetric modes as well as tri-dimensional spirals can be excited by the combined effects of the radial gradient of the plasma rotation frequency and of the plasma pressure gradient$^2$. The spirals' properties depend strongly on their vertical structure$^3$. Axisymmetric modes can produce vertical counter-flows of thermal energy and particles and be candidates for the origin of the winds emanating from disks in Active Galactic Nuclei (AGN's)$^2$. The excitation of radially localized density spirals corotating with the plasma near a black hole can provide an explanation for$^4$ the observed Quasi Periodic Oscillations (QPO's) of the X-ray emission from compact objects. Convective spiral modes$^3$ that are purely oscillatory in time and not localized radially can acquire their amplitudes from coupling to unstable modes and provide transport$^3$ of angular momentum toward the outer region of the disk structure.*Sponsored in part by the U.S. DOE. $^1$B. Coppi and F. Rousseau, Ap. J., $\bf{641}$, 458 (2006). $^2$B. Coppi, Europhys. Letters $\bf{82}$, 19001 (2008). $^3$B. Coppi, MIT/LNS Report 08/08, submitted to A$\&$A (2008). $^4$B. Coppi and P. Rebusco, Paper P5.154, E.P.S. Conf. Pl. Phys. (Crete, 2008).   

Application of Scalable Solver Techniques to Magnetized Plasma Problems in 2D and 3D

New techniques have recently been developed for scalable parallel implicit solvers for extended MHD spectral element codes, using physics-based preconditioning to parabolize and reduce the order of the matrices to be solved, and either FETI-DP or Static Condensation to solve the resulting reduced matrices. During this development, these techniques have been found to be perfectly weakly scalable up to 64 processors on a simple ideal MHD wave propagation problem in a periodic plane. This presentation will describe the application of these techniques to more interesting and realistic problems of magnetized plasmas, including magnetic reconnection in 2D and the spheromak tilt mode in 3D. Comparisons will be given with previous solution methods.   

Gyrokinetic Models for Edge Plasmas

We have developed practical system of electromagnetic gyrokinetic equations for MFE edge simulations. This system 1) allows for large amplitude perturbations, 2) is consistent with energy conservation, and 3) minimizes the number of (difficult to implement) second-order terms needed. Because the relative perturbation amplitudes may be large, the operator in the gyrokinetic Poisson equation evolves with time, and the gyrocenter equations of motion used must retain specific second-order terms in order to maintain energy conservation. Methods for implementing the second-order terms in the equations of motion, and a useful finite-element discretization of the gyrokinetic Poisson equation have been developed. The latter results from a Galerkin approximation to Brizard's action variational principle. Because the magnetic field inhomogeneity scales are much longer than the radial plasma profile scales in the edge region, only the standard leading order terms (parallel streaming and magnetic drifts) need to be kept in the equilibrium portion of the gyrocenter equations of motion.   

Control of tearing modes in reversed field pinches above the ideal-wall tearing threshold

We have performed stability studies for RFP profiles with a resistive wall and with feedback based on sensing both the normal and tangential components of the magnetic field at the wall. In [Finn, J. M., Phys. Plasmas 13, 082504 (2006)] feedback results were obtained with a simple model using reduced resistive MHD. These results indicated that it is possible to stabilize resistive plasma modes above the ideal wall limit; it was found not to be possible to stabilize ideal plasma modes above their ideal wall threshold. The RFP model in this earlier paper involved a decreasing q profile, but of course the reduced MHD model is not an accurate model for an RFP. We have generalized these results to full resistive MHD in cylindrical geometry with RFP-like profiles. The results indicate as before that it is possible to stabilize above the tearing - ideal wall threshold but not above the ideal MHD ideal wall threshold. We will show the impact of the feedback schemes on several modes present in the system and present our interpretation.   

The Effect of Electron-Ion Equilibration on the Sunyaev-Zel'dovich Effect of Galaxy Clusters

Sunyaev-Zel'dovich effect (SZE) is a new observational probe that promises to provide new insights into cosmology and plasma astrophysics of galaxy clusters. The SZE is a distortion in the cosmic microwave background spectrum caused by hot electrons produced by shock-heating of intergalactic medium in the cluster outskirts. During this process, most of the kinetic energy goes into ions and little to electrons, causing the electron temperature to be considerably smaller than the ion temperature. Electrons and ions eventually equilibrate through Coulomb interactions, but this equilibration process is longer than the Hubble time in the outskirts of clusters. In this work, we investigate the electron-ion equilibration process in galaxy clusters and show how this process affects the SZE signals. We will also discuss implications for cluster gas evolution and cosmological constraints derived from upcoming SZE cluster surveys.   

Microwave Measurement of the n=2 Triplet P J=1-to-J=2 Fine-Structure Interval of Helium

The n=2 triplet P J=1-to-J=2 interval in helium has been measured to a precision of 350 Hz using the Ramsey method of separated oscillatory field. This 350-Hz measurement is the most precise to date of the n=2 triplet structure. Comparison between precise measurements of the n=2 triplet P fine structure and theoretical predictions will allow for a precise determination of the fine-structure constant when the current large discrepancy between experiment (PRL \textbf{95} 203001; PRL \textbf{87} 173002; PRL \textbf{84} 4321; Can J Phys \textbf{83} 301) and theory (PRL \textbf{97} 013002; Can J Phys \textbf{80} 1195) is resolved.