Bulletin of the American Physical Society
2006 APS April Meeting
Saturday–Tuesday, April 22–25, 2006; Dallas, TX
Session K1: Poster Session: Magnetically Confined Plasma I 
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Room: Hyatt Regency Dallas Marsalis Hall B, 2:00pm  5:00pm 

K1.00001: Kinetic SelfOrganization of Microinstabilities in Astrophysical and in Laboratory Plasmas Giovanni Lapenta Microinstabilities can be considered as effective collisions. The small scale electromagnetic fluctuations due to microinstabilties can be considered as collisions on the particles, leading to a similar pointlike and instantaneouslike change in the particle momentum. This paradigm, the anomalous transport paradigm, requires us to derive theories that can predict the correct transport parameters (particularly the anomalous viscosity and anomalous resistivity) from the properties of the microinstabilties. Our recent work [13] has shown that another possible effect of microinstabilties is to lead to a direct macroscopic change in the equilibrium by affecting the plasma flow, temperature anisotropy and current profile on a macroscopic level. Our previous work has focused on space and astrophysical systems. But similar effects can be considered for experimental plasmas. A particularly intriguing possible analogy is with zonal flows and ``angular momentum generation'' believed to be happening in accretion disks in astrophysical systems [4] and with the ``spontaneous toroidal rotation'' of axisymmetric plasmas in fusion devices such as Jet and Alcator CMod [5]. [1] G. Lapenta, J.U. Brackbill, W.S. Daughton, Phys. Plasmas, 10, 1577 (2003). [2] W. Daughton, G. Lapenta, P. Ricci, Phys. Rev. Lett., 93, 105004, 2004 [3] P. Ricci, J.U. Brackbill, W.S. Daughton, G. Lapenta, Phys. Plasmas, 11, 4102, 2004. [4] B. Coppi 2002 Nucl. Fusion 42 14 [5] E. S. Marmar, et al., Fusion Energy 2002 (IAEA, Vienna) Paper OV/41 [Preview Abstract] 

K1.00002: Emergence of large scale magnetic fields by relaxation in laboratory and astrophysical plasmas Xianzhu Tang, Allen Boozer Magnetic relaxation is an extreme form of selforganization by which magnetic energy and helicity injected on small scales are transported to and accumulated on system scale magnetic fields by plasma fluctuations. Many fusion concepts rely on magnetic relaxation to generate and sustain the confining magnetic field. Examples include the reversed field pinch, spheromak, and spherical torus. Naturally occurring plasmas such as that in the giant radio lobes powered by the accretion disks of supermassive black holes are also subject to magnetic relaxation. A unified physics description of these relaxation processes can be found by an analogy to the familiar driven nonlinear oscillator. The fully relaxed Taylor state corresponds to the linear oscillator limit, where a primary resonance confines the energy input to the system scale magnetic fields. Like a nonlinear oscillator, the linear resonances are regularized by any of plasma inertia, finite pressure, and nonuniform normalized parallel current density in a partially relaxed plasma. The bifurcated regularized solutions are shown to have distinct physics interpretation and significance, and are intimately connected to the nonlinear dynamics that facilitate the relaxation. References:X.Z.Tang and A.H.Boozer, PRL, 225004 (2005); PRL, 155002 (2005); Phys. Plasmas, 102102 (2005). [Preview Abstract] 

K1.00003: Fractional diffusion models of nonlocal transport Diego delCastilloNegrete A class of models based on the use of fractional derivative operators is proposed to describe nonlocal transport in magnetically confined plasmas. Fractional operators incorporate in a unified framework nonFickian transport, nonMarkovian (“memory”) effects, and nondiffusive scaling. Recently, this formalism was applied to study transport in pressuregradientdriven plasma turbulence [1]. Here we present new results that incorporate finitesize domain effects, boundary conditions, sources, spatially dependent diffusivities, and general asymmetric fractional operators. The model is applied to describe, at a phenomenological level, nondiffusive, nonlocal transport processes observed in fusion plasmas, including anomalous confinement time scaling, “uphill” transport, rapid coldpulse propagation, and onaxis peaking with offaxis fuelling. [1] D. delCastilloNegrete, et al., Phys. Plasmas 11, 3854 (2004); Phys. Rev. Lett. 94,065003 (2005). [Preview Abstract] 

K1.00004: Nondiffusive transport in electron temperature gradient turbulence Kyle Gustafson, Diego del Castillo Negrete, Michael Barnes, William Dorland Numerical studies of electron temperature gradient turbulence (ETG) indicate that nonlinear effects boost the observed transport beyond the level expected from quasilinear analysis. In particular, the formation of radially extended streamers seems to facilitate rapid transport. We use the nonlinear gyrokinetic code GS2 to study transport of tracers through streamers embedded in ${\bf E}\times {\bf B}$ turbulence. In particular, we explore the role of such coherent structures in inducing long particle displacements (Levyflight), and study the nonGaussian scaling of the probability density function in space and time. Motivated by previous studies in pressuregradient driven plasma turbulence and flows with similar topology, we explore the use of fractional diffusion operators to model transport by streamers in ETG turbulence. Fractional diffusion operators are integrodifferential operators providing a natural mathematical framework to describe nonGaussian and nonMarkovian (memorydependent) transport processes. [Preview Abstract] 

K1.00005: Sources and Sinks of Zonal Flow Shear in Tokamak Microturbulence. Andris Dimits, Dan Shumaker, William Nevins The relative contributions of various physics terms to the driving and damping of the zonal flows in gyrokinetic simulations of toroidal ion temperature gradient (ITG) turbulence are investigated using a specialized simulation diagnostic. The development and verification of this diagnostic, which directly evaluates contributions of the terms to the rate of change of the mean squared zonal flow shear, were presented previously (A.M. Dimits et al. APSDPP02 meeting). We have found that in the turbulent finitetransport regime of toroidal ITG turbulence, the zonal flow shear is generated primarily through the Reynolds' stress term and dissipated by the transittime damping terms. Application of an analogous diagnostic to experiments would require modification of the approach to use measurements of the flow field quantities in a small number of localized regions instead of over full fluxsurfaces. Our simulations have addressed this by showing that useful zonalflowbalance information can be obtained with as few as four poloidal samples. [Preview Abstract] 

K1.00006: Calculation of SelfConsistent Turbulence and Transport in the Tokamak Edge M.V. Umansky, T.D. Rognlien, R.H. Cohen, L.L. LoDestro, X.Q. Xu Results of a selfconsistent simulation of turbulence and transport in the tokamak edge are presented. The calculations are done with the transport code UEDGE and the turbulence code BOUT. The turbulence fluxes and background profile data are exchanged between the codes using effective iteration schemes. A midplane limiter case is presented here. The limiter causes parallel plasma losses that strongly affect the radial plasma profiles, and the limiter sheath supports conductingwall instabilities. Two regimes are observed: (i) weakly intermittent turbulence when the flow shear is large, and (ii) strongly intermittent turbulence when the flow shear is small. The weakly intermittent regime is characterized by small, frequent transport bursts. In this case a large separation of time scales between turbulence and transport allows efficient coupling of turbulence and transport, yielding selfconsistent quasi stationary solutions. The strongly intermittent regime is characterized by large infrequent bursts of transport. In this case the coupling method based on separation of time scales loses its efficiency since the time scales of transport and turbulence overlap, and important nonlinear response functions, e.g. the material erosion rate, can not be correctly described by the timeaverage profiles. [Preview Abstract] 

K1.00007: Microinstabilities in quasihelically symmetric stellarators Tariq Rafiq, Chris Hegna The linear stability of electron drift modes, dissipative trapped electron modes (DTEM) and ITG modes is investigated in the electrostatic limit using ballooning formalism. For all these modes, a shooting technique is used and WKB type boundary conditions are applied. The threedimensional equilibria is calculated for a quasihelically symmetric (QHS) stellarator and a configuration whose symmetry is spoiled by the presence of mirror contribution to the magnetic spectrum. The dependence of the drift wave spectrum of stable and unstable modes, on various equilibrium parameters are investigated. The DTEM growth rate is calculated using perturbative approach. Multiple classes of helicallylocalized and toroidallylocalized eigenfunctions in the ballooning space are taken into account. The helically trapped modes are found to be most destabilizing in the QHS configuration, while in the Mirror configuration the toroidally trapped modes are found unstable. The magnitude of the growth rate is found to be higher in the Mirror configuration except for cases with peaked density profiles. [Preview Abstract] 

K1.00008: Existence of Magnetic Surfaces in 3D Configurations A.D. Turnbull A general expression is derived for the existence of magnetic surfaces in 3D. The expression is valid in an arbitrary coordinate system, which is important when axisymmetry is violated. In the general case, surfaces exist if and only if a simple 1D equation, equivalent to \textbf{B}{\textbullet}$\nabla $F, has solutions F with certain desired conditions imposed. For example, F must be periodic in anglelike coordinates and monotonic in radiallike variable, s. Applied to a torus, the fact that surfaces are guaranteed to exist with any special symmetry, drops out trivially from this formulation. One can also use alternative representations for \textbf{B}, such as the Clebsch form, to obtain further insight into the conditions where solutions exist. Analogous expressions are also obtained for the existence of current surfaces. Conditions can then be obtained for the existence of both current and magnetic surfaces, yielding criteria for proper nested flux surfaces. Force balance then imposes additional conditions; for ideal MHD, the key condition is the obvious one that \textbf{B}x($\nabla $x\textbf{B}) can be written as the gradient of a potential, which can then be equated to the pressure. [Preview Abstract] 

K1.00009: Rotation Profiles in DIIID From Neoclassical Viscosity R.W. Johnson, W.M. Stacey, J. Mandrekas Radial and poloidal profiles of rotation and density are calculated using neoclassical viscosity for a variety of discharges in DIIID. Several confinement regimes (\underline {L}mode, \underline {L}mode with \underline {I}nternal \underline {T}ransport \underline {B}arrier, \underline {H}mode, and \underline {H}mode with \underline {Q}uiescent \underline {D}ouble \underline {B}arrier) are investigated. Predicted toroidal velocities agree reasonably well with measured values for all regimes. Poloidal density asymmetries remain within 1020{\%} of the fluxsurface average value. Toroidal velocity is shown to have a poloidal profile rather than rotating rigidly. Transport of angular momentum is shown to arise mostly from gyroviscosity whilst leaving room for other (anomalous) transport mechanisms. [Preview Abstract] 

K1.00010: Methodology of Nonlinear Solver Module, GCNM, as an NTCC Module and SWIM Component H.E. St. John, L.L. Lao, M. Murakami, J.M. Park The success of stiff, drift wave type transport models such as GLF23 has necessitated introduction of new methods for solving transport equations. A Globally Convergent Newton Method (GCNM) module, which is part of the ``Predictive Transp'' project, and which will be one of the optional solvers in the SWIM project was developed to deal with this issue. GCNM is a Newtonbased solver for small sets ($<$500) of nonlinear equations typically encountered in the space and time discretized versions of transport equations. GCNM was designed to be used by other transport codes which must supply the time dependent sources required to solve the equations. For time independent situations GCNM can be used to directly find steadystate solutions without coupling to other codes. This has proved advantageous in ITER AT modeling where the current relaxation time is sufficiently large to preclude timestepping methods. We describe the initial release of the module and its use. [Preview Abstract] 

K1.00011: Coherent Structures in Magnetic Confinement Systems W. Horton Coherent structures are longlived, nonlinear localized solutions of the selfconsistient plasmaelectromagnetic field equations. They contain appreciable energy density and control various transport and magnetic reconnection processes in plasmas. These structures are selfbinding from the nonlinearity balancing, or overcoming, the wave dispersion of energy in smaller amplitude structures. The structures evolve out of the nonlinear interactions in various instabilities or external driving fields. The theoretical basis for these structures are reviewed giving examples from various plasma instabilities and their reduced descriptions from the appropriate partial differential equations. A classic example from drift waves is the formation of monopole, dipole and tripolar vortex structures which have been created in both laboratory and simulation experiments. For vortices, the long lifetime and nonlinear interactions of the structures can be understood with conservation laws of angular momentum given by the vorticity field associated with dynamics. Other morphologies include mushrooms, KelvinHelmholtz vorticity rollup, streamers and blobs. We show simulation movies of various examples drawn from ETG modes in NSTX, Hmode like shear flow layers in LAPD and the vortices measured with soft xray tomography in the GAMMA 10 tandem mirror. Coherent currentsheet structures form in driven magnetic reconnection layers and control the rate of transformation of magnetic energy to flow and thermal energy. [Preview Abstract] 

K1.00012: An Incompressible Fluid Model for HighSpeed Pellet Propagation in Guidetubes F.W. Perkins This work reports theoretical models developed to support optimization of pelletfueling. Experiments show pellet penetration will be optimized by highfieldside, highspeed launch. In present pellet systems, acceleration takes place outside the main tokamak chamber and pellets must propagate at high velocity through curved guide tubes to reach the desired HFS launch point. If the pellet velocity V exceeds a critical value V$_c$$\approx$ 300m/s, then centrifugal force will breakup the pellet in agreement with observations. In the limit V$>>$V$_c$, the pellet material can be modeled as an incompressible granular fluid of DT dust fragments and an equation is developed for its length l along the guide tube. The solution shows that l depends only on the angle the guide tube bends and not on the pellet speed. If a vnotch guide tube is used with a rightangle bend, the pellet as emerges as a highly elongated DT dust cloud, essentially a fluid jet. Further analysis shows this jet to be unstable and breakup into a series of droplets is expected. Ablation calculations based on droplet size result in poor penetration. [Preview Abstract] 

K1.00013: Physics with Reduced Parameters by the Ignitor Experiment G. Cenacchi, A. Airoldi, D. Farina, B. Coppi The Ignitor experiment is designed to produce plasma currents up to 11 MA and magnetic fields up to 13 T \footnote{B. Coppi, A. Airoldi, et al., \itshape{Nucl. Fusion} \upshape \textbf {41}, 1953 (2001)}, but its operational life will include ``preparatory'' discharges at reduced machine parameters that are expected to access significant plasma regimes. In this context a careful analysis has been carried out to verify the consistency of the plasma parameters to be obtained, in particular the ideal ignition conditions in DT plasmas with considerable pulse lengths, with the characteristics of the poloidal and toroidal field systems. To this end many simulations were carried out by the JETTO code, that is capable of taking into account the evolution of relevant freeboundary plasma equilibria. Two scenarios with magnetic fields up to 9 T and appropriate levels of injected (RF) heating were investigated: ``limiter'' (no Xpoint) configurations with plasma currents up to 7 MA, and double Xpoint configurations with plasma currents up to 6 MA. Proper programming of the density evolution and of the RF injection lead to reach and to maintain steady state conditions with peak temperatures around 6 keV (ideal ignition for the considered profiles) and significant $\alpha$particle production. The relevant pulse flattop length can be about 8 seconds. [Preview Abstract] 

K1.00014: MHD modeling of disruption mitigation by highpressure gas jet on Alcator CMod V.A. Izzo, R.S. Granetz, M.L. Reinke, D.G. Whyte, M. Bakhtiari MHD plays an important role in a massivegasjetinduced thermal quench in the case that only shallow impurity penetration is possible. This is seen in a series of NIMROD simulations with an assumed fixed penetration depth and a simple impurity radiation model. These simulations qualitatively reproduce several characteristics of a real CMod thermal quench triggered by gas jet injection. The simulations predict the fastest quench when the impurities penetrate to the q=2 surface, with an increasing delay preceding the quench as the separation between the penetration depth and q=2 increases. This prediction can be tested experimentally by scanning the q$_{95}$ of the target plasma over a wide range of values. By coupling NIMROD with the 0D radiation code KPRAD, simulations with accurate radiation rates, tracking all charge state populations, are possible for several gas species. In addition, models for neutral penetration and subsequent impurity mixing are included in the code with the goal of achieving quantitative predictability for gas jet disruption mitigation. Initial results from the new code are presented. Accuracy of the impurity penetration and mixing is assessed by comparison with experimental bolometry data. [Preview Abstract] 

K1.00015: MultiScale Interaction of a Tearing Mode with Drift Wave Turbulence: A Minimal SelfConsistent Model Chris McDevitt, Pat Diamond A minimal selfconsistent model of the multiscale interaction of a tearing mode with drift wave turbulence is presented. For simplicity, we consider a tearing instability in a cylindrical plasma interacting with electrostatic drift waves. Wave kinetics and adiabatic theory are used to treat the feedback of tearing mode flows on the drift waves via shearing and radial advection. The stresses exerted by the selfconsistently evolved drift wave population density on the tearing mode are calculated by mean field methods. The principal effect of the drift waves is to pump the resonant lowm mode via a negative viscosity, consistent with the classical notion of an inverse cascade in quasi2D turbulence. We study, two types of lowm, resonant structures. The first is a localized, electrostatic vortex mode, the width of which is set by resistively dissipated magnetic field line bending, and whose growth rate is given by $\gamma=\left(\left \nu_{T}\right^{2/3}/\eta^{1/3}\right)\left(v_{A}q_{y}/L_{s} \right)^{2/3}$, where $\nu_{T}$ is the turbulent viscosity. The second is like a usual tearing mode, which matches the interior layer (with negative viscosity) to an MHD exterior, via $\Delta^{\prime}$ . Outgoing wave boundary conditions are imposed in order to effect the match. The growth rate in the turbulent viscosity dominated regime is given by $\gamma=\left(\eta^{5/6}/ \left\nu_{T}\right^{1/6}\right)\left(q_{y}v_{A}/L_{s}\right) ^{1/3}\Delta^{\prime}$ . [Preview Abstract] 

K1.00016: Transport of dust particles in fusion devices A.Yu. Pigarov, S.I. Krasheninnikov Large production rates and spreading of dust throughout the device volume are very important safety issues for nextstep fusion projects (both: magnetic and inertial). A physical model for dust transport includes the dynamics dustplasma, dustturbulence, and dustsurface interactions. The dynamics is strongly coupled to heating, charging, erosion, evaporation, and thermochemical properties of dust particles. Recent developments in the model and their impact on the dust motion are highlighted. The model is incorporated into the DUSTT code [A.Pigarov, PoP 12 (2005) 122508]. Results of carbondust dynamics and transport in plasma are shown for NSTX and DIIID tokamaks. The simulations demonstrate that dust particles can be very mobile, accelerate to large velocities ($>$100 m/s), and penetrate deeply toward plasma core. Predictions for dust penetration into ITER plasma are also presented. Under standard tokamak plasma conditions, dust particles experience the net erosion or sublimation. However, as discussed, in some cases (for example, parasitic plasmas that occur underneath a dome), the dust particles can even grow from net deposition when a lowTe lowdensity plasma contains significant concentrations of impurities. Modeling is presented for transport of dust particles outside the working chamber, i.e. in pumping or diagnostics ports. Results of multiparametric analysis of dust penetrability are discussed. Work supported by USDoE grant DEFG0204ER54739. [Preview Abstract] 

K1.00017: Stability of zonal flows in finite beta tokamak plasmas Parvez Guzdar, Robert Kleva The generation of zonal flow in finite beta plasmas is an active area of research. These flows play a significant role in determining the level of transport caused by the resistive driftAlfven and driftballooning modes which occur in the edge region of tokamak plasmas. Thus understanding the stability of zonal flows can provide key understanding of the transitions triggered in the edge region. We have developed a new eigenvalue code to investigate the stability of zonal flows in finite beta plasmas. The code determines the eigenvalues and eigenmodes associated with all branches of modes present in the given system of equations. We will primarily focus on results for the tokamak edge plasmas where finite beta effects are enhanced by steep pressure gradients and high safety factor q. We will present results of the stability of the zonal flows as a function of the two key dimensionless parameters, the classical ideal ballooning stability parameter and the diamagnetic parameter. The relevance of this study to regulating edge transport will be discussed. [Preview Abstract] 

K1.00018: Dimensionless scaling laws of confinement in fusion plasmas with the 5D nonlinear GYrokinetic SEmiLAgrangian code (GYSELA) V. Grandgirard et al. This work addresses nonlinear global gyrokinetic simulations of ITG turbulence in a simple toroidal geometry with the GYSELA code. This code solves the gyrokinetic equation for ions, coupled to a quasielectroneutrality condition. The electron response is assumed adiabatic. The particularity of GYSELA code is to solve the VlasovPoisson like system on a fixed grid with a SemiLagrangian (SL) scheme $[1]$ for the entire distribution function. The 4D nonlinear driftkinetic version of the code has already shown the interest of such a SL method $[2]$. The energy conservation, which is recognized as a key test of validity, was achieved with an accuracy better than $2.5\%$. Results with the new 5D version of GYSELA will be presented, in particular a scan of turbulent transport for several values of the normalized gyroradius $\rho$star. The aim is to determine the dimensionless scaling law of confinement and to compare it with previous studies in this field $[3]$$[4]$.\vspace{10pt}\\ $[1]$ E. Sonnendr\"{u}cker et al, Journal of Comput. Physics, 149, 201220, 1999.\\ $[2]$ V. Grandgirard et al, accepted in Journal of Comput. Physics.\\ $[3]$ J. Candy and R.E. Waltz, Phys. Rev. Lett. 91, 2003.\\ $[4]$ Z. Lin et al., Phys. Rev. Lett. 82, 2002.\\ [Preview Abstract] 

K1.00019: A new Xray imaging Crystal Spectrometer for Measurements of the IonTemperature Profile in Tokamak Plasmas * M. Bitter, C. Bush, K. W. Hill, L. Roquemore, B. Stratton, D. Mastrovito, P. Beiersdorfer, M. F. Gu, J. E. Rice Future large tokamaks, such as ITER, require new diagnostic concepts for measurements of the iontemperature profile, since the currently used methods, which are based on neutral chargeexchange recombination spectroscopy, may not be applicable due to the fact that, at high plasma densities, neutral beams will not penetrate to the core of the plasma. An alternative method relies on Doppler broadening measurements of Xray lines emitted from highly charged highZ ions. However, the Xray crystal spectrometers, used so far, have recorded spectra from only a single sightline through the plasma and have therefore provided only a single point of an iontemperature profile. Therefore, a new Xray imaging crystal spectrometer is presently being developed. This spectrometer consists of a spherically bent crystal and a twodimensional positionsensitive detector and can simultaneously record spectra from multiple sightlines through the plasma. The spatial resolution in the plasma of about 13 cm is only determined by the height of the crystal and the Bragg angle. The paper will present the spectrometer concept and results obtained with a prototype instrument. * Work supported by DOE contract DEAC0276CH03073 and DOE grant 1083 [Preview Abstract] 

K1.00020: Simulation of plasma and impurity parallel flows, blob dynamics and crossfield transport asymmetry effects in tokamak SOL A.Yu. Pigarov, S.I. Krasheninnikov, G. Yu, B. LaBombard, T.D. Rognlien Recent experiments on several tokamaks have showed strong crossfield (CF) plasma convection due to intermittency (e.g., blobs) as well as the existence of largeMachnumber parallel plasma flows (LPPFs) in the SOL. Here we, firstly, report on the progress in our studies of dynamics and stability of coherent structures (blobs, dips) based on comprehensive 2D edge turbulence models. Secondly, multifluid 2D simulations of edge plasma and neutral gas transport are performed with the UEDGE code to explore potential driving mechanisms of LPPFs. We employ multiion diffusiveandconvective model for anomalous CF plasma transport. The model introduces asymmetric (ballooninglike) 2D profiles for CF transport coefficients, which are adjusted to match a representative set of experimental data. The UEDGE results on LPPFs are presented for SN Lmode shots in NSTX, CMod, and DIIID tokamaks. The roles of asymmetric intermittent CF transport, magnetic configuration and classical drifts in affecting the plasma flows are highlighted. The influence of these flows on divertor detachment, material migration, and main chamber recycling are discussed. Finally, we analyze the behavior of impurity ions in the SN SOL. Impurity sources and parallel flows of impurity ions are simulated with UEDGE under assumption of high LFS/HFS asymmetry of CF transport. Simulations show that in Lmode shots all charge states of impurity ions are highly entrained by background plasma flows. In the far SOL, impurity ions tend to have the same flow velocity as the deuterium ions, so that impurities are highly supersonic when the deuterium plasma flow is nearsonic. The outboard mainchamber wall can be an important net source of impurities, whereas both divertors can behave as net sinks for impurities. Work performed under USDoE grant DEFG0204ER54739. [Preview Abstract] 

K1.00021: ECRH and its effects on neoclassical transport in stellarators JaeChun Seol, C.C. Hegna The effect of ECRH heating on the neoclassical transport of conventional stellarators is addressed. In the absence of symmetry, neoclassical transport of stellarators is not favorable in the lowcollisional regime. This transport mechanism is particularly important in ECRH heated plasmas where a large energetic trapped electron population is produced. However, a selfconsistently generated EXB poloidal drift reduces the direct loss of trapped particles. A large radial electric field is built up by energetic trapped particles generated by electron cyclotron resonance heating (ECRH) yielding the ``electron root.'' We present a calculation that proceeds by solving for the lowest order electron distribution function using a FokkerPlanck equation for ECRH. Energetic electron generation is modeled using a quasilinear model ECRH diffusion. The radial particle fluxes are calculated by solving the 1$^{st}$ order FokkerPlanck equation. The radial electric field is determined from the ambipolarity condition of the particle fluxes. Implications for the achievement of electron root and associated enhanced confinement regimes will be addressed. For sufficiently large applied ECRH fields, the quasilinear description of waveparticle interaction is not generally valid. Efforts to extend the diffusion operator to account for nonlinear effects will be addressed. * Research is supported by U.S. Department of Energy Grant No. DEFG0299ER54546 [Preview Abstract] 

K1.00022: TwoFluid Plasma Steady States Linda Sugiyama, H.R. Strauss, J. Breslau, G. Fu Twofluid plasma models, which allow the electron and ion fluids to move independently, have important consequences for magnetically confined plasma behavior, compared to MHD. Twofluid steady states can be described analytically in terms of the canonical momenta and generalized vorticities of the two species (eg [1]), but the models contain free functions and do not really describe the conditions that hold in nonlinear numerical simulations. The plasma edge and surrounding vacuum region, which supplies global boundary conditions for the plasma in MHD, possesses additional degrees of freedom in a twofluid model, including possible large localized poloidal flows, radial electric fields, and separate species pressure gradients. Nonfluid, kinetic effects may also be important. These questions are investigated for high temperature fusion plasmas. with the help of the M3D initial value code.\\ \leftline{[1] L.C. Steinhauer, \emph{Phys. Plasmas} \textbf{6} 2734 (1999).} [Preview Abstract] 

K1.00023: Magnetic island induced bootstrap current on island evolution K.C. Shaing In a previous paper [K. C. Shaing, and D. A. Spong, Phys. Plasmas \textbf{13}, 2006], the effects of the even component (relative to the mode rational surface) of the magnetic island induced bootstrap current on the island dynamics in tokamaks are investigated, The magnetic island induced bootstrap current is a consequence of the symmetry breaking associated with a magnetic island embedded in an equilibrium magnetic field. It is found that island induced bootstrap current density contributes a term that is proportional to the width of the island, and the poloidal plasma beta, the ratio of the plasma pressure to the poloidal magnetic field pressure, to the island evolution equation. This term imposes a lower limit on the absolute value of the tearing mode stability parameter for the island to be unstable at high poloidal plasma beta. The theory is extended here to including the effects of the odd component of the magnetic island induced bootstrap current on the island evolution equation by taking into account the asymmetric island shape relative to the mode rational surface in the derivation of the island evolution equation. [Preview Abstract] 

K1.00024: Simulation of the time development of EBW emission from NSTX J. Preinhaelter, J. Urban, G. Taylor, S. Diem, L. Vahala, G. Vahala Time evolution of ECE spectra in 2040GHz range were simulated for NSTX plasmas. The code is based on the full wave solution of the cold plasma wave propagation used for determination of EBWXO and EBWX mode conversion efficiencies and on the determination of the effective radiation temperature from simultaneous solution of EBW ray evolution and integration of the radiative transfer equation. The method was successfully used for determination of the central temperature in NSTX from detected EBW signal at 16.5GHz [1]. The time development of the frequency spectra of EBW emission from the new NSTX antenna is simulated. For the shots ({\#}117970{\#}117982), the most intense radiation occurs at f = 25GHz. In this case EBW starts at the plasma center and is radiated mainly from the second harmonic [2]. We obtained detailed information how the ECE intensity is connected with the plasma parameters so the simulations allow determination of the EBW usability for plasma diagnostics and proposal of parameters for ECCD application. [1] J. Preinhaelter et al, 16th Topical Conf. on RF Power in Plasmas, Park City, Utah, B05, AIP Conference Proceedings 787,ed. Stephen J. Wukitch, Paul T. Bonoli,(2005), 349352. [2] J. Urban, J. Preinhaelter, G. Taylor, L. Vahala, G. Vahala: \textbf{ }\textit{Simulation of ECE frequency spectra for NSTX and comparison with new radiometer results.} 47th APSDPP, October, 2005. Denver, Colorado *Work supported by U.S. Dept. of Energy. [Preview Abstract] 

K1.00025: Recent Progress Toward an Integrated Particle Simulation of Plasma Edge C.S. Chang, S.H. Ku, W.W. Lee, S. Parker, Z. Lin, J. Cummings, M. Adams, F. Hinton, S. Ethier A SciDAC Fusion Simulation Prototype Center has recently been formed in an effort to understand the edge pedestal physics. The main activity is (a) to build a gyrokinetic particle code for the edge plasma, which spans the region from the pedestal top to the first wall and (b) to construct an integrated simulation framework for coupling of the edge kinetic code with a twofluid MHD code for an immediate application to the physics of the pedestalELM cycle. The gyrokinetic particle code is for an integrated simulation of the neoclassical kinetic ionelectron physics together with the turbulence and neutral physics, in a realistic wall and flux surface geometry for the present and future tokamak devices. A twofluid MHD code is for easier modeling of the ELM crash, in close coupling with the kinetic code. Even though the main part of the pedestal exists inside the separatrix surface, the pedestal physics is most likely coupled to the scrapeoff layer plasma properties. Thus, a comprehensive understanding of the edge plasma dynamics will be necessary. We will report our recent progresses in the 5D edge neoclassical physics simulation and understandings, numerical work in the selfconsistent turbulence simulation, and kineticMHD coupling of ELM activity. [Preview Abstract] 

K1.00026: Progress on longtime kinetic simulation of tokamak turbulence with very weak dissipation Scott Parker, Yang Chen, Jason Kahut Recent progress on convergence studies of longtime simulations for both electrontemperaturegradient (ETG) and iontemperaturegradient driven microturbulence will be reported. It was surprising to us to find that lownoise ETG turbulence simulations are wellconverged with rather modest particle number (3070 million particles). Progress on the particlecontinuum method [Vadlamani et al., {\it Comp. Phys. Comm.}, 209 {\bf 164} (2004)] will also be reported. The particlecontinuum method is really a general class of a variety of methods and has been shown to solve the socalled ``growing weight problem" in twodimensional simulations. The method is implemented in fourdimensions with the $\mu \nabla B$ force neglected. In this case, $v_\parallel$ is a constant of motion and resetting of the particle $\delta f$ on a fourdimensional grid is more reasonable. Discussion of issues related to applying particle continuum method in five dimensions will also be presented. Work supported by DOE SciDAC Gyrokinetic Particle Simulation Center and Center for Plasma Edge Simulation. [Preview Abstract] 

K1.00027: Novel aspects of linear wave conversion in burning plasmas A. J. Brizard, E. R. Tracy, A. N. Kaufman We report on our investigation of several novel aspects of linear wave conversion (a.k.a. mode conversion) in burning plasmas. These include (1) the effects of an inverted population of energetic particles (e.g., fusion products), giving rise to negativeenergy modes [1] and, thus, lead to absolute instabilities when counterpropagating rays of opposite energy signs resonantly interact [2]; and (2) the triplication of conversion due to the presence of internal transport barriers (associated with shearflow layers) overlapping the conversion region. \newline \vfill \noindent [1] A.~J.~Brizard and A.~N.~Kaufman, Phys.~Rev.~Lett.~ {\bf 76}, 1639 (1996); Phys.~Plasmas {\bf 3}, 64 (1996). \newline \noindent [2] A.~J.~Brizard, J.~J.~Morehead, A.~N.~Kaufman, and E.~R.~Tracy, Phys.~Rev.~Lett.~{\bf 77}, 1500 (1996); Phys.~Plasmas {\bf 5}, 45 (1998). [Preview Abstract] 

K1.00028: Anomalous Absorption of X2Driver Pump Power in DIIID Tokamak Plasma Via Relativistic Electron Bernstein Modes and Lower Hybrid Waves V. Stefan Recently\footnote{V. Stefan. Anomalous Absorption of REB Modes Due to Raman and Brillouin Scattering, and Two EBMode Decay of X2Driver in DIIID Tokamak Plasma.16$^{th}$ Topical Conf. on RF Power in Plasmas [Park City, 2005]V. Stefan. Enhanced Thermonuclear Yield Due to LowHarmonic REB Modes in Spherical Tokamak Plasmas. Sherwood2005 [Stateline, Nevada, USA]} I have reported on anomalous absorption of relativistic electron Bernstein modes (REB) for various driverplasma parameters in Spherical Tokamaks and DIIID Tokamak. plasma. Here I focus on X2Driver Pump decay in DIIID Tokamak plasma involving lowerhybrid waves (LHW).This channel involves the Brillouin scattering of X2Mode into another (X2)'mode coupled to the lowerhybrid waves (LHW). The nonlinearly generated (X2)'Mode propagates toward the second harmonic electron cyclotron layer, whereby it is absorbed through REBMode conversion, as in case of linear propagationabsorption channel. This leads to a strongly localized absorption. The weak LHWs are collisionally absorbed in the dense plasma region transferring the energy to ion plasma componentbulk plasma heating. The secondary decays of X2, X1, and EB modes, are taken into account in evaluation of energy confinement time in multiion plasmas [Preview Abstract] 

K1.00029: Coulomb Collision Algorithms for Particle Codes Bruce Cohen This paper surveys some of the particle code algorithms used to model Coulomb collisions in fully ionized plasmas, e.g., pairwise operators such as the TakizukaAbe$^{1}$ scheme and extensions$^{2}$, Langevin equation collision operators$^{3,4}$, and partially linearized gyrokinetic collisions operators for strongly magnetized plasmas.$^{5,6,7}$ Some recent experience is reported.$^{8 }$ Issues such as physics completeness, accuracy, and comparative algorithm performance are highlighted. 1. T. Takizuka and H. Abe, J. Comput. Phys. \textbf{25}, 205 (1977). 2. K. Nanbu, Phys. Rev. E \textbf{55}, 4642 (1997). 3. M.E. Jones, et al., J. Comp. Phys. \textbf{123}, 169 (1996). 4. W.M. Manheimer, M. Lampe, and G. Joyce, et al., J. Comp. Phys. \textbf{138}, 565 (1997). 5. X.Q. Xu and M.N. Rosenbluth, Phys. Fluids B \textbf{3}, 627 (1991). 6. A.M. Dimits and B.I. Cohen, Phys. Rev. E \textbf{49}, 709 (1994). 7. Z. Lin, W. M. Tang, and W. W. Lee, \textit{Phys.Plasmas }\textbf{2}, 2975 (August 1995). 8. B.I. Cohen, et al., ``Effects of ionion collisions and inhomogeneity in twodimensional kinetic ion simulations of stimulated Brillouin backscattering,'' accepted for publication in Phys. Plasmas (2006). [Preview Abstract] 

K1.00030: Modelling the effect of toroidal plasma rotation on driftmagnetohydrodynamic modes in tokamaks Ian Chapman, Tim Hender, Sergei Sharapov, Guido Huysmans, Anatolii Mikhailovskii A new code, MISHKAF has been developed in order to investigate linear MHD stability of ideal and resistive eigenmodes with respect to the effects of toroidal rotation in tokamaks in general toroidal geometry with the ion diamagnetic drift effect taken into account. Benchmark tests show good accordance with analytic theory for the stability limits of the n/m=1/1 internal kink mode with respect to toroidal rotation. Also, the stabilizing effect of the ion diamagnetic drift frequency on the internal kink mode is found to be more effective at finite flow shear. The stabilization of ballooning modes by toroidal rotation agrees well with analytic predictions if the local magnetic shear is below a critical value, above which no stabilization is exhibited. The effect of high flow shear is also analyzed for sawtoothing discharges in MAST, where it is found that stabilization of the n=1 internal kink mode by toroidal rotation may account for the observed sawtooth period increase. This work was funded by EURATOM and UK EPSRC. [Preview Abstract] 

K1.00031: Real geometry gyrokinetic PIC computations of ion turbulence in advanced tokamak discharges with SUMMIT/PG3EQ{\_}NC JeanNoel Leboeuf, Viktor Decyk, Terry Rhodes, Andris Dimits, Dan Shumaker The PG3EQ{\_}NC module within the SUMMIT Gyrokinetic PIC FORTRAN90 Framework makes possible 3D nonlinear toroidal computations of ion turbulence in the real geometry of DIIID discharges. This is accomplished with the use of local, field line following, quasiballooning coordinates and through a direct interface with DIIID equilibrium data via the EFIT and ONETWO codes, as well as Holger Saint John's PLOTEQ code for the (R, Z) position of each flux surface. The effect of real geometry is being elucidated with CYCLONE shot {\#}81499 by comparing results from PGEQ{\_}NC to those of its circular counterpart. The PG3EQ{\_}NC module is also being used to model ion channel turbulence in advanced tokamak discharges {\#} 118561 and 120327. Linear results will be compared to growth rate calculations with the GKS code. Nonlinear results will also be compared with scattering measurements of turbulence, as well as with accessible measurements of fluctuation amplitudes and spectra from other diagnostics. [Preview Abstract] 

K1.00032: Effects of Plasma Shaping on Nonlinear Gyrokinetic Turbulence E. A. Belli, G. W. Hammett, W. Dorland The effects of flux surface shape on the gyrokinetic stability and transport of tokamak plasmas have been studied using the GS2 code. Studies of the scaling of nonlinear turbulence with shaping parameters have been performed starting with a representative JETlike flux surface and artificially varying elongation, triangularity and their radial gradients together using the Miller analytic equilibrium formalism\footnote{R. Miller, et al, Phys. Plasmas {\bf 5}, 973 (1998).} to approach the circular limit via linear interpolation. Both linearly and nonlinearly, high shaping was found to be a stabilizing influence on the ITG turbulence, and a scaling of the heat flux with elongation of $\chi \sim \kappa^{1.5}$ or $\kappa^{2}$ (depending on the triangularity) was observed. While this is not as strong as empirical elongation scalings, it was also found that high shaping results in a larger Dimits upshift of the nonlinear critical gradient due to enhanced zonal flows. The effects of electromagnetic dynamics coupled with shaping are also presented. For electromagnetic runs, beta is varied with shaping to keep the Troyonnormalized beta fixed while also holding $q_{95}$ fixed. These results indicate that beta strongly affects the electron transport, particularly for more circular plasmas, and may lead to unsaturated transport in some cases, even well below the linear ballooning limit. [Preview Abstract] 

K1.00033: The Columbus Concept M. Salvetti, B. Coppi A spectrum of experiments is required for a ``Science First'' approach to fusion research\footnote{B. Coppi, MITRLE Report PTP02/04 (2002), Presentation to the NRC}. The possible discovery of new phenomena and the understanding of known ones, i.e. sawtooth oscillations, under fusion burning conditions will cetainly influence the design of future fusion reactors. The Columbus concept\footnote{B. Coppi and M. Salvetti, MITRLE Report PTP02/06} takes advantage of the Ignitor R$\&$D effort,including the construction of full size component prototypes. Relative to Ignitor, Columbus is characterized by increased linear dimensions ($R_0 \cong 1.5$ m is the plasma torus major radius) and by lower current densities in the magnets and within the plasma column. The toroidal magnetic field is decreased by the factor 12.6/13 and the average poloidal field produced by the plasma current is about equal to that of Ignitor for comparable values of the magnetic safety factor ($q_0$). The reference plasma current is $I_p \cong 12.2 $ MA, the value that ITER would produce for the same $q_0$ but without reaching ignition. The machine is based on cryogenic resistive magnet technologies and an optimized plasma confinement configuration which allow it to reach (real) ignition conditions by fusion reactions. Columbus is proposed for construction in the U.S. [Preview Abstract] 

K1.00034: Nonlinear Two Fluid and Kinetic ELM Simulations H.R. Strauss, L. Sugiyama, C.S. Chang, S. Ku, B. Hientzsch, J. Breslau, W. Park, R. Samtaney, M. Adams, S. Jardin Simulations of ELMs using dissipative MHD, two fluid MHD, and neoclassical kinetic physics models are being carried out using the M3D code [1]. Resistive MHD simulations of nonlinear edge pressure and current driven instabilities have been performed, initialized with realistic DIIID equilibria. Simulations show the saturation of the modes and relaxation of equilbrium profiles. Linear simulations including two fluid effects show the stabilization of toroidal mode number n = 10 modes, when the Hall parameter H, the ratio of ion skin depth to major radius, exceeds a threshhold. Nonlinear simulations are being done including gyroviscous stabilization. Kinetic effects are incorporated by coupling with the XGC code [2], which is able to simulate the edge plasma density and pressure pedestal buildup. These profiles are being used to initialize M3D simulations of an ELM crash and pedestal relaxation. The goal is to simulate an ELM cycle. \break [1] Park, W., Belova, E.V., Fu, G.Y., Tang, X.Z., Strauss, H.R., Sugiyama, L.E., Phys. Plas. 6, 1796 (1999).\break [2] Chang, C.S., Ku, S., and Weitzner, H., Phys. Plas. 11, 2649 (2004) [Preview Abstract] 

K1.00035: Is the Adabatic Ion Approximation Valid for ElectronTemperatureGradient Turbulence Simulations? J. Candy, R.E. Waltz, C. EstradaMila Gyrokinetic simulations of electrontemperaturegradientdriven turbulence normally rely upon an adiabatic ion (AI) approximation for numerical tractability. GYRO simulations using the AI approximation show that, in some regions of parameter space, simulations give rise to unbounded levels of turbulence. Such a result cannot be physical, suggesting a breakdown of the model equations. More expensive simulations which include the correct nonadiabatic ion response, on the other hand, are wellbehaved and give rise to physically sensible levels of electron heat transport. We explore this topic in detail, departing from a lowshear, lowtransport ETGAI test case and moving to the hightransport regime. We remark that the lowshear departure point has been the subject of a previous benchmark effort [1], for which four codes (GYRO, GS2, PG3EQ and GENE) are in mutual agreement. \newline [1] W. Nevins, \textit{et al.,} Bull. Am. Phys. Soc. \textbf{50}, 180 (2005), APS invited paper KI14. [Preview Abstract] 

K1.00036: Phase Space Structures in Toroidal Ion Temperature Gradient Turbulence T.H. Watanabe, H. Sugama, W. Horton The velocity space structures of the ion distribution function associated with toroidal ion temperature gradient (ITG) driven turbulence is shown for the almost collisionless regime relevant to burning fusion plasmas. The zonal flows are taken into account and the geodesic acoustic mode (GAM) is reproduced with the neoclassical polarization from the trapped ions as well as the ballistic mode structures. Detailed plots of the ion velocity space showing clearly the different response of the trapped and passing ions in the zonal flows and the ITG modes are presented. The fine scale structures are resolved with velocity grid of $1025\times65$ which resolves the structures down to $\nu_{*i} =0.04$ deep into the banana regime. Runs are sufficiently long in time to establish a steady state in which the entropy production from the ion temperature gradient is followed through the turbulence and dissipated with a LenardBernstein collision operator on the smalles scale of the velocity grid. The resulting gyroBohm coefficient for is 1.4 for the usual Cyclone DIIID base case as reported in Watanabe and Sugama 2006. [Preview Abstract] 

K1.00037: Relation between Radial and Axial Losses in Tandem Mirrors J. Pratt, W. Horton, H.L. Berk The tandem mirror still remains a potentially attractive magnetic confinement geometry. The absence of toroidal curvature and internal plasma parallel current gives the system strongly favorable stability. Additionally, GAMMA10 experimental results demonstrate that sheared rotation can suppress turbulent radial losses. For an MHD stable system, we investigate the interplay between drift wave (ITG, ETG and Bohm) radial transport and axial losses. Using empirical energy confinement scaling laws from large ITER and ISS databases as upper bounds on the radial loss rates, we simulate radial transport using a transport barrier dynamics (TBD) code. Simulations are carried out for a machine of volume $212 ~\rm m^3$ (central cell length/radius $30 \rm ~m/1.5$ m) with central cell field $3 ~T$. ITER stores $7022 $ MJ of energy in the toroidal magnetic field; in our tandem mirror design this energy is reduced to $954$ MJ. Our simulations show that high core temperatures result in long Pastukhov loss times; drift wave radial transport dominates, except at the plasma edge, where pitch angle scattering causes losses. [Preview Abstract] 

K1.00038: Gyrokinetic Simulations of OffAxis Minimumq Profile Corrugations R.E. Waltz, K.H. Burrell, J. Candy, M.E. Austin Quasiequilibrium radial \textit{profile corrugations} in the electron temperature gradient (ETG) are found at lowest order singular surfaces in global gyrokinetic (GYRO) code simulations of monotonic and offaxis minimumq DIIID discharges. The profile corrugation in the gradients are time average components of the zonal flows. As the off axis minimumq=2 surfaces enters the plasma the corrugations are measurably large and appear to trigger an internal transport barrier (ITB). The corrugation in the electron temperature gradient have the bumpdipbump structure seen in the DIIID experiments. \textit{These profile corrugations constitute the first direct experimental observation of zonal flows in a tokamak plasma} and confirm the physical reality of corrugations in a way not previously possible. Contrary to previous claims there is no dip in transport flow associated with the minimumq ``gap'' in singular surface density. There is a strong dip in ion energy flow from the strong ExB shear corrugation and consistent with an ITB. [Preview Abstract] 

K1.00039: Nonlinear dynamics of turbulence driven vortex flows at low$q$ resonances P.H. Diamond, O.D. Gurcan, C.J. McDevitt, T.S. Hahm Motivated by recent observations of transport barrier formation near integer $q$ surfaces, we consider the theory of turbulence driven vortex flows at lowq resonances. The essence of the problem is to understand the spatial relationship between profile modification at resonance and the profile steepening immediately nearby. Flattening can be due to lowm resonant vortex modes driven by turbulence in a manner similar to zonal flows or the direct effect of secondary structures on profiles. Both will flatten turbulence intensity profiles on resonance, but steepen it nearby, thus enhancing shear flow drive by Reynolds stress and so producing a barrier. The key issue is to understand how low$q $ resonances modify the envelope, since it is this structure which ultimately controls the shear flow. We study envelope modifications expected at lowq surfaces, and examine the effect of turbulence spreading on the intensity profiles. We aim to elucidate te bifurcation threshold for barrier formation. \newline \newline References\newline [1] M. Austin, APS Invited Talk, 2005 \newline [2] C. J. McDevitt and P. H. Diamond, submitted to {\it Phys.Plasmas}, (2005) [Preview Abstract] 

K1.00040: Nonlinear Growth of a Linetied gMode Near Marginal Stability P. Zhu, C. C. Hegna, C. R. Sovinec A theoretical framework has been developed for the study of the nonlinear gravitational ($g$) mode of a linetied flux tube near marginal stability. The theory is based on an expansion using two small parameters, $\epsilon\sim {\mbox{\boldmath $\xi$}}/L_{\rm eq}\ll 1$, and $n^{1}\sim k_\parallel/k_\perp\ll 1$, with ${\mbox{\boldmath $\xi$}}$ denoting the plasma displacement, $L_{\rm eq}$ the characteristic equilibrium scale, $k_\parallel$ and $k_\perp$ the dominant wavenumber of perturbation parallel and perpendicular to equilibrium magnetic field lines respectively. When $\epsilon\sim n^{1}$, the CowleyArtun regime is recovered where plasma is to the lowest order incompressible~[S.~C. Cowley and M. Artun, Phys. Rep., {\bf 283}, 185211 (1997)]. The detonation regime where the nonlinear growth of the mode is finitetime singular is a narrower subset of the CowleyArtun regime. However, the validity of this regime breaks down when $\epsilon\gg n^{1}$. In the intermediate nonlinear phase when $\epsilon\sim n^{1/2}$, the lowest order plasma compression [$\sim\nabla\cdot{\mbox{\boldmath $\xi$}}\sim{\cal O}(1)$] is nonzero. Direct MHD simulations with both a finite difference code and NIMROD indicate that the mode remains bounded in magnitude with a slightly reduced nonlinear growth [P. Zhu, A. Bhattacharjee, and K. Germaschewski, to appear in PRL (2006); P. Zhu, C.~C. Hegna, and C.~R. Sovinec, DPP2005]. During this phase, the coupled growth of the mode amplitude ${\mbox{\boldmath $\xi$}}$ and plasma compression may contribute to a nonlinear stabilization. The corresponding governing model equations for this intermediate nonlinear phase are derived. [Preview Abstract] 

K1.00041: Theory of turbulence spreading by penetrative convection and mode coupling O.D. Gurcan, P.H. Diamond, C.J. McDevitt, T.S. Hahm The intensity of inhomogenous turbulence may spread via avalanches or nonlocal mode couplings. These two processes are related and while mode coupling provides a mechanism for spreading, avalanches also, evolve the turbulence profile separately. Avalanches are the result of accumulation of density gradient in time at a slower time scale, resulting in intermittent, ``convective'' transport. It is essential to incorporate this effect to understand profile evolution and thus ``penetrative convection,'' which necessarily implies spreading. Here we consider a model that incorporates the effects of zonal flows, zonal ``density'' and fluctuationfluctuation mode couplings as well as linear growth, nonlinear damping and linear group propagation. We use an EDQNM type analysis of simple driftwave turbulence within the HasegawaWakatani model, to compute the effect of mode coupling between different $k_y$ modes. We observe it is predominantly the internal energy [i.e. $\widetilde{n}^2$], that is nonlinearly affected by these processes, whereas kinetic energy [i.e. $ \nabla \widetilde{\Phi}^2$] simply follows due to linear coupling. Features, which distinguish between spreading by mode coupling and by penetrative convection will be elucidated and discussed. [Preview Abstract] 

K1.00042: Equilibrium limits in the LDX experiment Luca Guazzotto, Jeffrey Freidberg, Jay Kesner The Levitated Dipole Experiment (LDX) is an experiment based on an innovative magnetic confinement concept, which allows the confinement of high beta (~1) plasmas. A critical figure of merit for such an experiment is the maximum beta that can be achieved during operation. In general, both equilibrium and stability limits must be determined. The present work focuses on the former limit. If toroidal effects are neglected, it is possible to determine the equilibrium beta limit analytically. LDX plasma has however a tight aspect ratio and toroidal curvature must therefore be considered. In the present work, equilibrium calculations obtained with the code FLOW [1] are presented. The code allows for arbitrary geometry, and has the additional properties of allowing toroidal flow and anisotropy to be included in the problem. Both properties are relevant to LDX, since LDX plasmas are expected to have macroscopic toroidal flow and finite anisotropy, due to the heating process. Numerical and analytical results are presented and discussed. [1] L. Guazzotto, R. Betti, J. Manickam and S. Kaye, Phys. Plasmas 11, 604 (2004) [Preview Abstract] 

K1.00043: Kinetic stability of internal kink in ITER Bo Hu, R. Betti, J. Manickam ITER's standard operation baseline scenario is susceptible to the $m/n=1/1$ internal kink instability. Kinetic effects modify the inertia and the perturbed energy of the mode, which are important to determine the mode stability. Numerical results are obtained for different $q$profiles and plasma betas for ITERlike realistic equilibria using the QSOLVER and PEST1 codes and a kinetic postprocessor. The MHD branch is found to be fully stabilized by the trapped particle compressibility. The stability of the fishbone branch is also greatly affected by the kinetic effects. The trapped electrons contribute a KruskalOberman term because electron collisionalty is much smaller than the mode frequency. Since the bounce frequency of the trapped thermal ions in the core region is close to the mode frequency, the trapped ion compressibility is reduced and damping is increased. Depending on the size of the $q=1$ radius, the trapped alpha particles can be stabilizing or destabilizing. The kinetic ion inertia enhancement(including damping) is also considered and provides a stabilizing effect. The fishbone branch is found to be stable if the $q=1$ radius is below a critical value. [Preview Abstract] 

K1.00044: Influence of Collisionality and Density Peaking on Thermal Transport F. Bombarda, B. Coppi A consensus has formed around the idea that electron collisionality plays a major role in determining the quality of thermal transport in toroidal plasmas. Future burning plasma experiments will operate at similar, relatively low values of the dimensionless collionality parameter $\nu_*$, but at densities that for ITER are close to the critical density and for Ignitor, thanks to its high current density, are about half that value. The trends of the energy confinement time with collisionality have been analyzed for early Ohmic plasmas in Alcator CMod and FTU. The former showed an almost linear correlation with $1/\nu_*$ followed by a saturated regime; the latter was characterized, at the time, by high impurity content and did not display any clear trend. For more recent, and cleaner, FTU data, the behaviour of $\tau_E$ as function of density and density profile peaking has been studied, for simple Ohmic and pellet injection discharges. The results have been compared with theory\footnote{B. Coppi, M.I.T.RLE Report PTP 04/07, Cambridge 2004}. In order to ensure fine profile density control in Ignitor, especially during the critical phase of the initial current rise, a fast pellet injector is being built in collaboration between ENEA and ORNL. Possible experiments to be carried out on existing machines are presented that could add further support to the proposed ignition scenarios for Ignitor. [Preview Abstract] 

K1.00045: Renormalized linear gyrokinetics and recovery of ideal magnetohydrodynamics L.J. Zheng, M. Kotschenreuther, J. W. Van Dam The gyrokinetic formalism provides expeditious means for the kinetic analysis of both macro and micro plasma instabilities. In this work, we revisit linear electromagnetic gyrokinetics theory and find that the ${\boldmath J}_0{\boldmath\times} \delta{\boldmath B}$ effect on force balance is missing and the FLR effect is not retained fully in the conventional formalism. We show that two key modifications are needed to get consistent ordering in gyrokinetics: First, the gyrophasedependent part of the perturbed distribution function, as well as its coupling to the gyrophaseindependent distribution function, should be retained. Second, the solution of the equilibrium gyrokinetic distribution function should be carried out to sufficiently high order. With these modifications we can recover linear MHD from this new gyrokinetic formalism. New effects and potential future applications of this gyrokinetic theory will be discussed ({\it e.g.}, to resistive wall modes). [Preview Abstract] 

K1.00046: Effect of sheared axial flow on the stability of the interchange mode in a hardcore Zpinch plasma Jeffrey Freidberg, Alexei Kouznetsov, Jay Kesner It is well known that a static (i.e. \textbf{v}=0 ) closed field line configuration, such as a Zpinch, levitated dipole, or hardcore Zpinch, can be stabilized against ideal MHD interchange modes if the plasma pressure falls off sufficiently rapidly with respect to increasing minor radius. The stabilizing effect is provided by plasma compressibility. However, many laboratory plasmas exhibit sheared velocity flows, \textbf{v}$' \neq$ 0, (due to nonambipolar plasma transport) and this flow affects marginal stability. An analysis has been carried out to investigate the effect of axially sheared flow on ideal MHD stability in a hardcore Zpinch. Specifically, the goal is to learn whether sheared flow is good, bad, or neutral for MHD stability? Analytic calculations of marginal stability for several idealistic velocity profiles have been carried out. It is found that all three options are possible depending on the shape of the shear profile. This reflects the competition between the destabilizing KelvinHemholtz effect and the fact that shear makes it more difficult for interchange perturbations to form. Also numerical calculations will be presented using more realistic experimental profiles of pressure and velocity to compare with the idealized analytic profile results. [Preview Abstract] 

K1.00047: MultiScale Interaction of a Tearing Mode with Drift Wave Turbulence: A Minimal SelfConsistent Model C.J. McDevitt, P.H. Diamond A minimal selfconsistent model of the multiscale interaction of a tearing mode with drift wave turbulence is presented. We first consider the problem of a tearing instability in a cylindrical plasma interacting with electrostatic drift waves. Wave kinetics and adiabatic theory are used to treat the feedback of tearing mode flows on the drift waves via shearing and radial advection. The stresses exerted by the selfconsistently evolved drift wave population density on the tearing mode are calculated by mean field methods. The principal effect of the drift waves is to pump the resonant lowm mode via a negative viscosity, consistent with the classical notion of an inverse cascade in quasiD turbulence. This mechanism is similar to that by which drift wave turbulence drives zonal flows. The magnitude of the turbulent stresses is consistent with a gyroBohm diffusivity, and thus exceeds the magnitude of the inertia term for the tearing mode. We study, two types of lowm, resonant structures. The first is a localized, electrostatic vortex mode and the second is like a usual tearing mode, which matches the viscoresistive layer (with negative viscosity) to an MHD exterior. Outgoing wave boundary conditions are imposed in order to effect the match. Extensions to the Rutherford regime and inclusion of turbulence spreading effects will be discussed. [Preview Abstract] 

K1.00048: Progress on gyrokinetic simulation of highn energetic particle driven instabilities Yang Chen, Scott Parker, Guoyong Fu A hybrid model, in which ions are described by the gyrokinetic equations and electrons are treated as a massless fluid, has been developed for arbitrary shape flux surfaces and equilibrium profiles, based on the GEM turbulence simulation code ( Y.~Chen and S.~E.~Parker, J. Comp. Phys. 189 (2003). The perturbed magnetic field is given by $\delta {\bf B}_\perp=\nabla A_\parallel\times{\bf b}$, with $A_\parallel$ given by the parallel Ampere's law. The electric field is given by ${\bf E}=\nabla \phi(\partial A_\parallel/\partial t) {\bf b}$, with $\phi$ obtained from the quasineutrality condition. The primary coupling of the hot particles to the bulk plasma comes from the hot particle term in the quasineutrality condition. This hybrid model can be shown to reduce to the MHD equations for the shear Alfv\'en modes under the assumption $E_\parallel=0$. Linear simulation shows the existence of global modes with TAE features in terms of mode location and frequency. However, small variation in the equilibrium profiles (such as qprofile and temperature profile) often leads to strongly unstable unphysical mode peaking at the inner midplane. We will attemp to resolve this difficulty, either by improving the electron model or by improving numerical algorithms to avoid the unphysical modes. [Preview Abstract] 

K1.00049: Fluctuations and Correlations in tokamak plasmas B. Li, R.D. Hazeltine The relation between stationary fluctuations of equilibrium states and irreversible processes is described. The wavenumber dependence of spatial correlations in homogeneous systems is obtained from Einstein distribution, and the mean square of fluctuations is then calculated. Using the fluctuationdissipation theorem and a convective diffusion equation, the power spectrum and autocorrelation function are computed. The results are compared with the observed plasma density fluctuations in tokamak experiments. [Preview Abstract] 

K1.00050: Tempest Neoclassical Simulation of Fusion Edge Plasmas X.Q. Xu, Z. Xiong, B.I. Cohen, R.H. Cohen, M. Dorr, J. Hittinger, G.D. Kerbel, W.M. Nevins, T.D. Rognlien We are developing a continuum gyrokinetic fullF code, TEMPEST, to simulate edge plasmas. The geometry is that of a fully diverted tokamak and so includes boundary conditions for both closed magnetic flux surfaces and open field lines. The code, presently 4dimensional (2D2V), includes kinetic ions and electrons, a gyrokinetic Poisson solver for electric field, and the nonlinear FokkerPlanck collision operator. Here we present the simulation results of neoclassical transport with Boltzmann electrons. In a large aspect ratio circular geometry, excellent agreement is found for neoclassical equilibrium with parallel flows in the banana regime without a temperature gradient. In divertor geometry, it is found that the endloss of particles and energy induces pedestallike density and temperature profiles inside the magnetic separatrix and parallel flow stronger than the neoclassical predictions in the SOL. The impact of the Xpoint divertor geometry on the selfconsistent electric field and geoacoustic oscillations will be reported. We will also discuss the status of extending TEMPEST into a 5D code. [Preview Abstract] 

K1.00051: A finite volume FokkerPlanck collision operator in constantsofmotion coordinates Z. Xiong, X. Q. Xu, B. I. Cohen, R. Cohen, M. R. Dorr, J. A. Hittinger, G. Kerbel, W. M. Nevins, T. Rognlien TEMPEST is a 5D gyrokinetic continuum code for edge plasmas. Constants of motion, namely, the total energy $E$ and the magnetic moment $\mu$, are chosen as coordinate s because of their advantage in minimizing numerical diffusion in advection operato rs. Most existing collision operators are written in other coordinates; using them by interpolating is shown to be less satisfactory in maintaining overall numerical accuracy and conservation. Here we develop a FokkerPlanck collision operator directly in $(E,\mu)$ space usin g a finite volume approach. The $(E, \mu)$ grid is Cartesian, and the turning point boundary represents a straight line cutting through the grid that separates the ph ysical and nonphysical zones. The resulting cutcells are treated by a cellmergin g technique to ensure a complete particle conservation. A two dimensional fourth or der reconstruction scheme is devised to achieve good numerical accuracy with modest number of grid points. The new collision operator will be benchmarked by numerical examples. [Preview Abstract] 

K1.00052: Collisional tests and an extension of the TEMPEST continuum gyrokinetic code R.H. Cohen, M. Dorr, J. Hittinger, G. Kerbel, W.M. Nevins, T. Rognlien, Z. Xiong, X.Q. Xu An important requirement of a kinetic code for edge plasmas is the ability to accurately treat the effect of colllisions over a broad range of collisionalities. To test the interaction of collisions and parallel streaming, TEMPEST has been compared with published analytic\footnote{F. Najmabadi, R.W. Conn and R.H. Cohen, Nucl. Fusion 24, 75 (1984); T.D. Rognlien and T.A. Cutler, Nucl. Fusion 20, 1003 (1980).} and numerical (Monte Carlo, bounceaveraged FokkerPlanck) results for endloss of particles confined by combined electrostatic and magnetic wells. Good agreement is found over a wide range of collisionality, confining potential and mirror ratio, and the required velocity space resolution is modest. We also describe progress toward extension of (4dimensional) TEMPEST into a ``kinetic edge transport code'' (a kinetic counterpart of UEDGE). The extension includes averaging of the gyrokinetic equations over fast timescales and approximating the averaged quadratic terms by diffusion terms which respect the boundaries of inaccessable regions in phase space. [Preview Abstract] 

K1.00053: Discrete particle noise in a nonlinearly saturated plasma Thomas Jenkins, W. W. Lee Understanding discrete particle noise in an equilibrium plasma has been an important topic since the early days of particlein cell (PIC) simulation [1]. In this paper, particle noise in a nonlinearly saturated system is investigated. We investigate the usefulness of the fluctuationdissipation theorem (FDT) in a regime where drift instabilities are nonlinearly saturated. We obtain excellent agreement between the simulation results and our theoretical predictions of the noise properties. It is found that discrete particle noise always enhances the particle and thermal transport in the plasma, in agreement with the second law of thermodynamics. [1] C.K. Birdsall and A.B. Langdon, {\it Plasma Physics via Computer Simulation}, McGrawHill, New York (1985). [Preview Abstract] 

K1.00054: Implementation and Verification of Twofluid Modeling in NIMROD C. R. Sovinec, H. Tian, D. C. Barnes, A. Y. Pankin, D. D. Schnack A secondorder time advance for the twofluid plasma model with equilibrium flow and drift has been developed and implemented in the NIMROD fusion MHD code. The algorithm retains the leapfrog character of the MHD algorithm [JCP 195, p. 355 (2004)] but solves separate implicit advances for each field. Analysis shows that this approach is numerically stable at arbitrarily large timestep when advection and drift terms, including gyroviscosity, are timecentered in each segment of the leapfrog. Implementation relies on Krylov methods with sparse approximate matrices solved directly for preconditioning and with matrixfree computations in the Krylovspace iterations. The implementation is tested on linear wave, interchange, and magnetic reconnection problems where analytic results are readily available. [Preview Abstract] 

K1.00055: Profile Consistency and Resistive Relaxation of FieldReversed Configurations Elena Belova Twodimensional numerical simulations are used to study resistive evolution and selforganization in FieldReversed Configurations (FRC). It is shown that FRCs with various initial profiles and separatix shapes obtained by solving the GradShafranov equation, evolve through resistive relaxation toward a specific family of FRC equilibria with flat current profile and approximately elliptic separatrix shape. This class of profiles is shown to be an attractor, and the FRC in the relaxed state evolves in a selfsimilar manner. Axisymmetric simulation of FRC formation by the counterhelicity spheromak merging also show formation of FRCs with elliptical shape and approximately flat current profiles independent of the initial conditions, implying that this class of equilibria may correspond to a minimumenergy state. Unlike the forcefree relaxed states in the lowbeta plasmas, twodimensional FRCs evolve towards zerohelicity, diamagnetic state, in which current is perpendicular to the magnetic field. An attempt is made to describe these states by a relaxation theory with two integral constraints. [Preview Abstract] 

K1.00056: Finite Ion Orbit Effects on Magnetic Islands in Toroidal Plasmas Xinzheng Liu, Chris Hegna A kinetic theory for the interaction of ions with an isolated magnetic island in tokamak plasma is presented. We examine islands whose characteristic widths are larger than ion gyro radius but comparable to the ion banana width. In this regime, the ion response to the island has a nonlocal feature due to the banana drifts. When solving the drift kinetic equation for ions, a change in coordinates is used to account for this behavior. A bounce averaging procedure is developed to separate out and solve the lower order distribution function. Constraint relationships found from transport equations and collision operators are used to determine the distribution function, which is treated in different velocity regions. A selfconsistent calculation for the electrostatic potential is proposed. The perturbed current is composed of the bootstrap current and the perpendicular neoclassical enhanced ion polarization current. The closure parallel current is calculated and compared with some recent numerical results. Using this current in Rutherford equation, the island width evolution equation is determined. A pair of selfconsistent equations for the island width and rotation frequency is to be derived. The results are to be compared with calculations for large island width so as to yield a description of magnetic island width evolution from subbanana width to macroscopic scale lengths. [Preview Abstract] 

K1.00057: Direct Comparison of Gyrokinetic Turbulence Simulations with Phase Contrast Imaging Fluctuation Measurements Darin Ernst, A. Long, N. Basse, L. Lin, M. Porkolab, W. Dorland We have developed a synthetic diagnostic$^1$ for the GS2 gyrokinetic code for direct comparisons with phase contrast imaging (PCI) measurements of density fluctuations in Alcator CMod. The gyrokinetic simulation is carried out in a local, field line following fluxtube, while PCI measures density fluctuations along 32 chords passing vertically through the plasma crosssection.$^2$ Transforming from Clebsch to cartesian coordinates, and integrating appropriately over portions of the flux tube viewed by the diagnostic, yields a density fluctuation spectrum versus wavenumber $k_R$ in the major radius direction. To achieve vertical localization, we examine an ITB case in which the spectrum is dominated by a strong trapped electron mode, localized near the halfradius. The wavelength spectrum from the simulations, using the synthetic diagnostic, closely reproduces the PCI spectrum. Contributions from $k_{\psi}$, where $\mathbf{B}=\nabla \alpha \times \nabla \psi $, downshift the GS2 $k_{\alpha}$ spectrum to improve upon our previous raw comparison with the PCI $k_R$ spectrum.$^3$ \\ $^1$A. Long, D. R. Ernst \textit{et al.,} Bull. Am. Phys. Soc. \textbf{50}(8) p. 153, GP1.48, also \urllink{p. 235, LP1.37} {http://www.psfc.mit.edu/research/alcator/pubs/APS/APS2005/ernst.pdf}. $^2$N. P. Basse \textit{et al.,} Phys. Plasmas \textbf{12}, 052512 (2005). $^3$D. R. Ernst \textit{et al.,} 2004 IAEA Fusion Energy Conference, \urllink{IAEACN116/TH/41} {http://wwwnaweb.iaea.org/napc/physics/fec/fec2004/datasets/TH41.html}, see also Phys. Plasmas \textbf{11} (2004) 2637. [Preview Abstract] 

K1.00058: Energy conserving and phase space area preserving fluidkinetic plasma equations H. Vernon Wong Low frequency fluidkinetic plasma equations, in which the total energy is conserved and the particle trajectories preserve their phase space area, are discussed. In a recent driftkinetic analysis of the Vlasov equation [1], exact to order $\epsilon^ 2$, where the ordering parameter $\epsilon $ is formally proportional to $m/e$ (maximal ordering), these conservation properties are satisfied. Many terms, however, are typically small, and it is often the case that subsidiary orderings can be introduced to reduce the number of relevant terms and thereby simplify the equations. A procedure for introducing subsidiary orderings is described, while at the same time maintaining the above conservation properties, and a reduced set of fluid kinetic equations is presented, equations which can be used to simulate the low frequency electromagnetic behaviour of magnetized plasmas. [1] H. Vernon Wong Phys. Plasmas 12, 112305 (2005) [Preview Abstract] 

K1.00059: Feedback stabilization of resistive and ideal plasma modes with a resistive wall above the ideal wall limit John M. Finn It has previously been found in tokamaks that feedback based on sensing the tangential component of the magnetic field at the wall is more effective than that based on the normal component of the field. We find that proportional feedback sensing the tangential component is capable of stabilization above the limit for tearing stability with an ideal wall. This stabilization occurs in a small range of parameters. If feedback is based on sensing a combination of the tangential and normal components, resistive plasma stability can be achieved in a large range of parameters above the ideal wall resistive plasma limit. In this regime, plasma rotation (or complex gain) is deleterious because it interferes with the control flux penetrating the wall. For ideal plasma modes, it is possible to get stabilization in the whole regime where wall stabilization occurs, albeit with possibly very large control parameters. In contrast to resistive plasma modes, it appears that stabilization above this range, where ideal plasma modes are unstable even with an ideal wall, is not possible. The relationship with the 'virtual shell' concept of Bishop will be discussed. This observation leads to the possibility in RPFs that singlehelicity or quasisinglehelicity states can be obtained by controlling all unstable m=1 modes except for the primary singlehelicity mode. Another possibility involves controlling the amplitude of the m=0, n=1 mode, which is typically stable but is driven by coupling of m=1 modes with different n. [Preview Abstract] 

K1.00060: Electron Cyclotron Current Drive by Bernstein Waves A.K. Ram, J. Decker, Y. Peysson The high$\beta$ plasmas in spherical tori (ST), like in NSTX, are overdense to the traditional X and O modes in the electron cyclotron range of frequencies (ECRF). However, in the same frequency range electron Bernstein waves (EBW) can propagate in ST plasmas and damp effectively on electrons at the Dopplershifed electron cyclotron resonance or its harmonics. Since externally generated current is necessary for steady state operation and for controlling the current profile, we examine the role of EBWs in STs. We find that EBWs can generate plasma current by the Ohkawa scheme in the outer half of the plasma and the FischBoozer scheme in the core of the plasma. The current drive efficiency is much higher with EBWs than with the traditional ECRF waves as the EBWs interact with more energetic electrons. We will discuss the properties of EBWs and their interaction with electrons for current drive. Results from two codes, one which solves the fully relativistic plasma dielectric tensor and the other which solves the drift kinetic equation for electrons, will also be presented. [Preview Abstract] 
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