Bulletin of the American Physical Society
58th Annual Meeting of the APS Division of Plasma Physics
Volume 61, Number 18
Monday–Friday, October 31–November 4 2016; San Jose, California
Session BP10: Poster Session I (Computational and Theoretical Techniques; C-Mod, International, ITER and Next Step Tokamak) Reconnection and Self-organizationPoster
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Room: Exhibit Hall 1 |
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BP10.00001: COMPUTATIONAL AND THEORETICAL TECHNIQUES |
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BP10.00002: ABSTRACT WITHDRAWN |
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BP10.00003: Conservative discontinuous Galerkin discretizations of the 2D incompressible Euler equation Francois Waelbroeck, Craig Michoski, Tess Bernard Discontinuous Galerkin (DG) methods provide local high-order adaptive numerical schemes for the solution of convection-diffusion problems. They combine the advantages of finite element and finite volume methods. In particular, DG methods automatically ensure the conservation of all first-order invariants provided that single-valued fluxes are prescribed at inter-element boundaries. For the 2D incompressible Euler equation, this implies that the discretized fluxes globally obey Gauss' and Stokes' laws exactly, and that they conserve total vorticity. Liu and Shu [J. Comp. Phys. 160, 577 (2000)] have shown that combining a continuous Galerkin (CG) solution of Poisson's equation with a central DG flux for the convection term leads to an algorithm that conserves the principal two quadratic invariants, namely the energy and enstrophy. Here, we present a discretization that applies the DG method to Poisson's equation as well as to the vorticity equation while maintaining conservation of the quadratic invariants. Using a DG algorithm for Poisson's equation can be advantageous when solving problems with mixed Dirichlet-Neuman boundary conditions such as for the injection of fluid through a slit (Bickley jet) or during compact toroid injection for tokamak startup. . [Preview Abstract] |
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BP10.00004: An optimal, fully implicit algorithm for the low-$\beta$ ``two-field'' two-fluid MHD model. Luis Chac\'on, Adam Stanier The low-$\beta$ ``two-field'' two-fluid magnetohydrodynamics model is appealing owing to its simplicity and its wide applicability in strongly magnetized plasmas. However, it supports fast dispersive waves that challenge its numerical integration, and demand efficient implicit integration methods. We propose an efficient, parallel, optimal nonlinearly implicit algorithm for the low-$\beta$ XMHD model based on physics-based preconditioned Jacobian-free Newton-Krylov (JFNK) methods.\footnote{L. Chac\'on and A. Stanier, \emph{J. Comput. Phys.}, submitted (2016)} The proposed preconditioner leverages earlier developments of effective physics-based preconditioners for MHD\footnote{L. Chac\'on, D. A. Knoll, and J. M. Finn, \emph{J. Comput. Phys.}, \textbf{178} (2002)} and high-$\beta$ extended MHD.\footnote{L. Chac\'on and D. A. Knoll, \emph{J. Comput. Phys.}, \textbf{188} (2003) } We demonstrate the performance of the algorithm with challenging numerical examples. In particular, we demonstrate optimal weak parallel scaling for a fixed implicit time step on grids up to 4096$\times$4096 on 4096 cores (the maximum available to us). At these resolutions, speedups with respect to explicit algorithms reach up to four orders of magnitude. [Preview Abstract] |
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BP10.00005: Advection-Dominant MHD Computation for External Kinks and Edge-Localized Modes C. R. Sovinec Separation of temporal and spatial scales is the primary consideration for computation of macroscopic dynamics in magnetically confined plasma. Dynamic shock capturing is not needed, but nonlinear external kinks and ELMs advect large gradients near the plasma surface. Using an implicit time-advance with Galerkin projection can be problematic in these applications when advection is stronger than dissipation on the spatial scale of the mesh. The applied math community has investigated many approaches to stabilizing numerical advection [Franca, Hauke, and Masud, CMAME 195, 1560]. One approach is the least-squares finite element method [Bochev and Gunzberger, SIAM Rev. 40, 789], which has previously been applied to MHD and plasma-fluid models [Adler, et al. SIAM J. Sci. Comput. 32, 229]. Here, we adapt this technique for MHD computation with the NIMROD code, starting with the scalar dependent fields that need to have definite sign: density and temperature. Time-splitting physical diffusion maintains the original size of the algebraic systems that are solved at each time-step. Upwinding explicit terms where derivatives are discontinuous avoids overshoot error while minimizing numerical dissipation. [Preview Abstract] |
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BP10.00006: Applications of continuous and orthogonal wavelet transforms to MHD and plasma turbulence Marie Farge, Kai Schneider Wavelet analysis and compression tools are presented and different applications to study MHD and plasma turbulence are illustrated. We use the continuous and the orthogonal wavelet transform to develop several statistical diagnostics based on the wavelet coefficients. We show how to extract coherent structures out of fully developed turbulent flows using wavelet-based denoising and describe multiscale numerical simulation schemes using wavelets. Several examples for analyzing, compressing and computing one, two and three dimensional turbulent MHD or plasma flows are presented.\\ Details can be found in M. Farge and K. Schneider. Wavelet transforms and their applications to MHD and plasma turbulence: a review. {\it J. Plasma Phys.}, {\bf 81}(6), 435810602, 2015. arXiv:1508:05650 [Preview Abstract] |
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BP10.00007: On Hamiltonian Magnetohydrodynamics: Lagrangian, Eulerian, and Dynamically Accessible Stability - Applications with Translation Symmetry P. J. Morrison, T. Andreussi, F. Pegoraro In a series of papers$^{\dagger}$ we have investigated general properties of equilibria and their stability in each of the Lagrangian, Eulerian, and Dynamically Accessible stability formulations of magnetohydrodynamics. In our latest work we compare and contrast stability results with these formulations for two applications: stratified convection and rotating pinch equilibrium configurations. The former example, emphasizes the role played entropy, while the later demonstrates the utility of a relabeling transformation that we introduced in our earlier work. Comparisons to classical works, in particular on interchange instability, are made. \\ \noindent $^{\dagger}$ T. Andreussi, P. J. Morrison, and F. Pegoraro, Phys. Plasmas, submitted (2016); ibid.\ {\bf 22}, 039903 (2015); ibid.\ {\bf 20}, 092104 (2013); ibid.\ {\bf19}, 052102 (2012), and Plasma Phy. Control. Fusion {\bf52}, 055001(2010). [Preview Abstract] |
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BP10.00008: Implementation and verification of Chapman-Enskog-like drift kinetic equations in NIMROD Eric Held, Joseph Jepson, Jeong-Young Ji Rigorous closure of the extended magnetohydrodynamic equations used in plasma fluid codes incorporates important effects for tokamak plasmas such as perturbed bootstrap current physics and generalized viscosity at low collisionality. In this work we discuss continuum numerical solutions of the Chapman-Enskog-like electron \footnote{J. J. Ramos, Phys Plasmas 17, 082502 (2010).} and ion \footnote{J. J. Ramos, Phys Plasmas 18, 102506 (2011).} drift kinetic equations which have been implemented recently in the NIMROD code. Among other things, these solutions supply the CGL electron stress closure for Ohms Law and CGL ion stress closure for the plasma flow evolution equation. Such closures are paramount to understanding the macroscopic stability properties of high-performance tokamak plasmas. Verification of the orthogonal nature of the Maxwellian and non-Maxwellian parts of the distribution function inherent in the adopted Chapman-Enskog-like approach is provided along with simulation results of neoclassical transport and the Spitzer thermalization and conduction problems. [Preview Abstract] |
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BP10.00009: Common Hamiltonian and topological properties of extended MHD models George Miloshevich, Manasvi Lingam, Philip Morrison Extended MHD, a 1-fluid model endowed with 2-fluid effects (electron inertia and Hall drift) possesses a Hamiltonian structure [1-4]. This formulation is described, as it unifies different classes of extended MHD models (including those that have mutually exclusive effects) [2]. The unification is further highlighted by showing that these models possess common topological invariants that are the generalizations of the fluid/magnetic helicity [3]. They can be expressed naturally in a knot-theoretic framework via the Jones polynomial by exploiting techniques from Chern-Simons theory. It is also shown that extended MHD exhibits other commonalities such as: generalized Kelvin circulation theorems, and the existence of two Lie-dragged 2-forms closely connected with generalizations of the fluid vorticity. \\ \noindent [1] H. M. Abdelhamid, Y. Kawazura & Z. Yoshida, J. Phys. A, 48, 235502 (2015) \\ \noindent [2] M. Lingam, P. J. Morison & G. Miloshevich, Phys. Plasmas, 22, 072111 (2015) \\ \noindent [3] M. Lingam, G. Miloshevich & P. J. Morrison, Phys. Lett. A, 380, 2400 (2016) \\ \noindent[4] E. C. D'Avignon, P. J. Morrison & M. Lingam, Phys. Plasmas, 23, 062101 (2016) \\ [Preview Abstract] |
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BP10.00010: Derivation of the Hall and Extended Magnetohydrodynamics Brackets Eric D'Avignon, Manasvi Lingam, Philip Morrison There are several plasma models intermediate in complexity between ideal magnetohydrodynamics (MHD) and two-fluid theory, with Hall and Extended MHD being two important examples. In this research we investigate several aspects of these theories, with the ultimate goal of deriving the noncanonical Poisson brackets used in their Hamiltonian formulations. We present fully Lagrangian actions for each, as opposed to the fully Eulerian, or mixed Eulerian-Lagrangian, actions that have appeared previously. As an important step in this process we exhibit each theory's two advected fluxes (in analogy to ideal MHD's advected magnetic flux), discovering also that with the correct choice of gauge they have corresponding Lie-dragged potentials resembling the electromagnetic vector potential, and associated conserved helicities. Finally, using the Euler-Lagrange map, we show how to derive the noncanonical Eulerian brackets from canonical Lagrangian ones. [Preview Abstract] |
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BP10.00011: Spectral methods for multiscale plasma-physics simulations Gian Luca Delzanno, Gianmarco Manzini, Juris Vencels, Stefano Markidis, Vadim Roytershteyn In this talk, we present the \emph{SpectralPlasmaSolver} (SPS) simulation method for the numerical approximation of the Vlasov-Maxwell equations. SPS either uses spectral methods both in physical and velocity space or combines spectral methods for the velocity space and a Discontinuous Galerkin (DG) discretization in space. The spectral methods are based on generalized Hermite's functions or Legendre polynomials, thus resulting in a time-dependent hyperbolic system for the spectral coefficients. The DG method is applied to numerically solve this system after a characteristic decomposition that properly ensures the upwinding in the scheme. This numerical approach can be seen as a generalization of the method of moment expansion and makes it possible to incorporate microscopic kinetic effects in a macroscale fluid-like behavior. The numerical approximation error for a given computational cost and the computational costs for a prescribed accuracy are orders of magnitude less than those provided by the standard PIC method. Moreover, conservation of physical quantities like mass, momentum, and energy can be proved theoretically. Finally, numerical examples are shown to prove the effectiveness of the approach. [Preview Abstract] |
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BP10.00012: Cascades and Spectra of Elastic Turbulence in 2D: Spinodal Decomposition & MHD Xiang Fan, Patrick Diamond, Luis Chacon We report on studies of turbulence in 2D spinodal decompositions of symmetric binary mixtures. This study emphasizes a comparison and contrast of the physics of spinodal turbulence with that of 2D MHD turbulence. The important similarities include basic equations, ideal quadratic conserved quantities, cascade directions and elastic waves. Turbulence in spinodal decomposition exhibits an elastic range when the Hinze scale is sufficiently larger than the dissipation scale, i.e. $L_H\ll L_d$. We show, using direct numerical simulation, that the mean square concentration spectrum $H^\psi_k\equiv \langle\psi^2\rangle_k$ (analogous to $H^A_k\equiv \langle A^2\rangle_k$ in MHD) scales as $k^{−7/3}$. This suggests an inverse cascade of $H^\psi$, corresponding to the case in MHD. However, we also show that, the kinetic energy spectrum scales as $k^{−3}$, as in the direct enstrophy cascade range for a 2D fluid (not MHD!). The resolution of this dilemma is that capillarity acts only at blob boundaries. This is in contrast to $B$ in MHD. Thus, as blob merger progresses, the packing fraction of interfaces decreases, thus explaining the outcome for the kinetic energy spectrum. [Preview Abstract] |
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BP10.00013: Global Gyrokinetic Simulation Model for Laboratory Magnetosphere Hua-sheng Xie, Wei-ke Ou, Yi Zhang, Shi-kang Du, Zi-cong Huang, Bo Li A global gyro-kinetic particle-in-cell code (GKD) is developed to study the micro-instabilties driven turbulent transport for magnetic dipole configuration. This configuration is relevant to several experiment devices, such as LDX at MIT, CTX at Columbia University and HDX at Harbin Institute of Technology. The major electrostatic drift instability in this system is entropy mode, which can be unstable even when ideal interchange mode is stable. For comparison, we also show the nonlinear results in Z-pinch and linear results with benchmark to linear eigenvalue solution. [Preview Abstract] |
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BP10.00014: A multi-model plasma simulation of collisionless magnetic reconnection I. A. M. Datta, U. Shumlak, A. Ho, S. T. Miller Collisionless magnetic reconnection is a process relevant to many areas of plasma physics in which energy stored in magnetic fields within highly conductive plasmas is rapidly converted to plasma energy. A full understanding of this phenomenon, however, is currently incomplete as models developed to date have difficulty explaining the fast reconnection rates often seen in nature, such as in the case of solar flares. Therefore, this behavior represents an area of much research in which various plasma models have been tested in order to understand the proper physics explaining the reconnection process. In this research, the WARPXM code developed at the University of Washington is used to study the problem using a hybrid multi-model simulation employing Hall-MHD and two-fluid plasma models. The simulation is performed on a decomposed domain where different plasma models are solved in different regions, depending on a trade-off between each model's physical accuracy and associated computational expense in each region. The code employs a discontinuous Galerkin (DG) finite element spatial discretization coupled with a Runge-Kutta scheme for time advancement and uses boundary conditions to couple the different plasma models. [Preview Abstract] |
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BP10.00015: Numerical simulations using a physics-based domain-decomposed plasma model A. Ho, U. Shumlak, I. A. M. Datta, S. T. Miller Plasma models have regimes of validity that depend on local parameters. The various models have different levels of physical fidelity and corresponding computational costs. For example, magnetohydrodynamic (MHD) plasma models assume a quasi-neutral fluid, but two-fluid plasma models do not. While two-fluid models are a superset of MHD models, they have to resolve electron dynamics and solve Maxwell’s equations. In many problems reduced models can adequately describe the plasma behavior in portions of the domain. Partitioning the domain to use a combination of MHD and two-fluid models in different parts of the domain can maintain the required physical fidelity while improving computational efficiency. Coupling between the models is handled using boundary conditions to convert the variable set of one constituent model to the variable set of another constituent model. This research investigates the coupling between multiple plasma models using a physics-based domain-decomposition. Comparisons are made on the accuracy and performance of a physics-based domain-decomposed plasma model with a single conventional plasma model of a plasma opening switch. [Preview Abstract] |
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BP10.00016: Variational and Hamiltonian techniques for plasma kinetic theory Alexander Close, Cesare Tronci Hamiltonian and variational methods have been particularly useful in the development of new kinetic and hybrid models. Here, we present a systematic construction that relates all these approaches. In particular, the Maxwell-Vlasov system is presented in both Lagrangian and Eulerian descriptions, and at the same time in both variational and Hamiltonian formulations. We unfold the relationship between all four pictures by using geometric techniques that include reduction by symmetry, gauge fixing and momentum maps. Eventually these tools are applied to hybrid kinetic-MHD systems to provide new variants of their low-gyrofrequency approximations. [Preview Abstract] |
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BP10.00017: Kinetic Global Modeling of Rare Gas Lasers Guy Parsey, John Verboncoeur, Andrew Christlieb Akin to diode-pumped alkali metal lasers, electronically excited states of rare gases (e.g. Ar and Kr) have been shown to operate as chemically inert three-level gain media for an optically pumped laser system. As opposed to vaporization heating, these systems rely on electric discharge to efficiently maintain a population of metastable states acting as the bottom laser level. We propose that a modified electron energy distribution (EEDF) in the electric heating can tune optically pumped rare gas laser (OPRGL) efficiencies. The EEDF factors into all plasma phase chemistry within the underlying reaction network, and is assumed to be maintained by discharge and electron sources. Using parameter scanning methods within the kinetic global modeling framework (KGMf), optimized EEDFs are found for metastable production and increasing OPRGL operational efficiencies. Finally, we investigate the feasibility of using a modified EEDF to drive a rare gas laser system without optical pumping. [Preview Abstract] |
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BP10.00018: On the ensemble averaging of PIC simulations R. J. B. Codur, F. S. Tsung, W. B. Mori Particle-in-cell simulations are used ubiquitously in plasma physics to study a variety of phenomena. They can be an efficient tool for modeling the Vlasov or Vlasov Fokker Planck equations in multi-dimensions. However, the PIC method actually models the Klimontovich equation for finite size particles. The Vlasov Fokker Planck equation can be derived as the ensemble average of the Klimontovich equation. We present results of studying Landau damping and Stimulated Raman Scattering using PIC simulations where we use identical “drivers” but change the random number generator seeds. We show that even for cases where a plasma wave is excited below the noise in a single simulation that the plasma wave can clearly be seen and studied if an ensemble average over O(10) simulations is made. Comparison between the results from an ensemble average and the subtraction technique[1] are also presented. In the subtraction technique two simulations, one with the other without the “driver” are conducted with the same random number generator seed and the results are subtracted. [1] V. K. Decyk, "Simulation of Microscopic Processes in Plasmas", PPG-1057 (1987). [Preview Abstract] |
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BP10.00019: Mitigating Particle Integration Error in Relativistic Laser-Plasma Simulations Adam Higuera, Kathleen Weichmann, Benjamin Cowan, John Cary In particle-in-cell simulations of laser wakefield accelerators with $a_0$ greater than unity, errors in particle trajectories produce incorrect beam charges and energies [1], predicting performance not realized in experiments such as the Texas Petawatt Laser [2]. In order to avoid these errors, the simulation time step must resolve a time scale smaller than the laser period by a factor of $a_0$. If the Yee scheme advances the fields with this time step, the laser wavelength must be over-resolved by a factor of $a_0$ to avoid dispersion errors. Here is presented and demonstrated with Vorpal [3] simulations, a new electromagnetic algorithm, building on previous work [4, 5, 6], correcting Yee dispersion for arbitrary sub-CFL time steps, reducing simulation times by $a_0$. \\ [1] A. V. Arefiev, et al., Physics of Plasmas (1994-present) 22, 013103 (2015). \\ [2] X. Wang, et al., Nature communications 4, 1988 (2013). \\ [3] C. Nieter and J. R. Cary, J. Comp. Phys. 196, 448 (2004). \\ [4] B. M. Cowan, et al., Phys. Rev. Special Topics- Accelerators and Beams 16, 041303 (2013). \\ [5] B. Finkelstein and R. Kastner, J. of Comp. Phys. 221, 422 (2007). \\ [6] R. Lehe, A. Lifschitz, C. Thaury, V. Malka, and X. Davoine, Physical Review Special Topics-Accelerators and Beams, 021301 (2013). [Preview Abstract] |
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BP10.00020: Exact Energy and Momentum Conservation in Variational Macro-Particle Plasma Models B. A. Shadwick, E. G. Evstatiev, Nam Nguyen We consider a class of variational macro-particle plasma models that exhibit simultaneous conservation of energy and momentum. These models retain translation invariance by using a Fourier representation of the electromagnetic fields in place of a spatial grid. That is, the Fourier amplitudes of the fields are the fundamental quantities. From the discrete Lagrangian, a canonical Hamiltonian system is obtained in the usual way, for which we introduce a symplectic integrator. We present a general formulation of the method with examples drawn from 1-1/2D studies of intense laser-plasma interactions. We comment on the relative merits of the Lagrangian vs. Hamiltonian formulations and discuss efficiency and practicality of using this technique in three dimensions. [Preview Abstract] |
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BP10.00021: A non-stochastic Coulomb collision algorithm for particle-in-cell methods Guangye Chen, Luis Chacon Coulomb collision modules in PIC simulations are typically Monte-Carlo-based. Monte Carlo is attractive for its simplicity, efficiency in high dimensions, and conservation properties. However, it is noisy, of low temporal order (typically $O(\sqrt{\Delta t}$), and has to resolve the collision frequency for accuracy.\footnote{Dimits, et. al., JCP, 228, p.4881 (2009)} In this study, we explore a non-stochastic, multiscale alternative to Monte Carlo for PIC. The approach is based on a Green-function-based reformulation\footnote{Hu, Krommes, PoP, 1, p. 863 (1994)} of the Vlasov-Fokker-Planck equation, which can be readily incorporated in modern multiscale collisionless PIC algorithms.\footnote{Chen, Chac\'on, and Barnes, JCP, 230, p.7018 (2011)} An asymptotic-preserving operator splitting approach allows the collisional step to be treated independently from the particles while preserving the multiscale character of the method. A significant element of novelty in our algorithm is the use of a machine learning algorithm that avoid a velocity space mesh for the collision step.\footnote{Yoon and Chang, PoP, 21, 032503 (2014)} The resulting algorithm is non-stochastic and first-order-accurate in time. We will demonstrate the method with several relaxation examples. [Preview Abstract] |
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BP10.00022: Sparse grid techniques for particle-in-cell schemes Lee Ricketson, Antoine Cerfon The particle-in-cell (PIC) method has long been the standard technique for kinetic plasma simulation across many applications. The downside, though, is that quantitatively accurate, 3-D simulations require vast computing resource. A prominent reason for this complexity is that the statistical figure of merit is the number of particles per cell. In 3-D, the number of cells grows rapidly with grid resolution, necessitating an astronomical number of particles. This is what we may call the curse of dimensionality. To address this challenge, we propose the use of sparse grids: by a clever combination of the results from a variety of grids, each of which is well resolved in at most one coordinate direction, we achieve similar accuracy to that of a full grid, with with many few grid cells, thereby dramatically reducing the statistical error. We present results from test cases that demonstrate the new scheme's accuracy and efficiency. [Preview Abstract] |
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BP10.00023: GPU Acceleration of Particle-In-Cell Methods Benjamin Cowan, John Cary, Scott Sides Graphics processing units (GPUs) have become key components in many supercomputing systems, as they can provide more computations relative to their cost and power consumption than conventional processors. However, to take full advantage of this capability, they require a strict programming model which involves single-instruction multiple-data execution as well as significant constraints on memory accesses. To bring the full power of GPUs to bear on plasma physics problems, we must adapt the computational methods to this new programming model. We have developed a GPU implementation of the particle-in-cell (PIC) method, one of the mainstays of plasma physics simulation. This framework is highly general and enables advanced PIC features such as high order particles and absorbing boundary conditions. The main elements of the PIC loop, including field interpolation and particle deposition, are designed to optimize memory access. We describe the performance of these algorithms and discuss some of the methods used. [Preview Abstract] |
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BP10.00024: Physics based optimization of Particle-in-Cell simulations on GPUs Stephen Abbott, Ed D'Azevedo We present progress in improving the performance of the gyrokinetic particle-in-cell (PIC) code XGC-1 on NVIDIA GPUs, as well as enhancements made to portability and developer productivity using OpenACC directives. Increasingly simulation codes are required to use heterogeneous accelerator resources on the most powerful supercomputing systems. PIC methods are well suited to these massively parallel accelerator architectures, as particles can largely be advanced independently within a time-step. Their advance must still, however, reference field data on underlying grid structures, which presents a significant performance bottleneck. Even ported to GPUs using CUDA Fortran, the XGC-1 electron push routine accounts for a significant portion of the code execution time. By applying physical insight to the motion of electrons across the device (and therefore field grids) we have developed techniques that increase performance of this kernel by up to 5X, compared to the original CUDA Fortran implementation. Architecture specific optimizations can be isolated in small `leaf' routines, which allows for a portable OpenACC implementation that performs nearly as well as the optimized CUDA. [Preview Abstract] |
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BP10.00025: Integral equation tools for 2D scattering of RF waves by blobs. lise-marie imbert-gerard We will present a numerical method for 2D scattering by blobs. The method is based on potential theory, and provides an integral formulation of the continuous problem. The formulation depends on the plasma density on the one hand, and on the incident wave on the other hand. The main challenge is then to discretize the volume integral term of the equation. A high order discretization scheme will be introduced. It relies on the identification of a near-field regime, close to the singluarity of the kernel, and a far-field regime. The precomputation phase is crucial to both the accuracy and the speed of the scheme.The resulting linear system is dense. It is solved thanks to a pre-existing fast direct solver, called HODLR, providing a compressed approximation of the inverse matrix. The method has been developped for the O mode equation, and numerical examples will be presented. The development of a similar method for the full cold plasma model is under investigation. The principal difficulty relies on deriving a well-posed integral formulation with a structure adapted to our discretization tools. Preliminary results in this direction will be discussed. [Preview Abstract] |
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BP10.00026: PlasmaPy: beginning a community developed Python package for plasma physics Nicholas A. Murphy, Yi-Min Huang In recent years, researchers in several disciplines have collaborated on community-developed open source Python packages such as Astropy, SunPy, and SpacePy. These packages provide core functionality, common frameworks for data analysis and visualization, and educational tools. We propose that our community begins the development of PlasmaPy: a new open source core Python package for plasma physics. PlasmaPy could include commonly used functions in plasma physics, easy-to-use plasma simulation codes, Grad-Shafranov solvers, eigenmode solvers, and tools to analyze both simulations and experiments. The development will include modern programming practices such as version control, embedding documentation in the code, unit tests, and avoiding premature optimization. We will describe early code development on PlasmaPy, and discuss plans moving forward. The success of PlasmaPy depends on active community involvement and a welcoming and inclusive environment, so anyone interested in joining this collaboration should contact the authors. [Preview Abstract] |
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BP10.00027: C-MOD, INTERNATIONAL, ITER AND NEXT STEP TOKAMAKS . [Preview Abstract] |
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BP10.00028: Examining Innovative Divertor and Main Chamber Options for a National Divertor Test Tokamak B. LaBombard, M. Umansky, D. Brunner, A.Q. Kuang, E. Marmar, G. Wallace, D. Whyte, S. Wukitch The US fusion community has identified a compelling need for a National Divertor Test Tokamak. The 2015 Community Planning Workshop on PMI called for a national working group to develop options. Important elements of a NDTT, adopted from the ADX [1] concept, include the ability to explore long-leg divertor `solutions for power exhaust and particle control' (Priority Research Direction B) and to employ inside-launch RF actuators combined with double-null topologies as `plasma solution for main chamber wall components, including tools for controllable sustained operation' (PRD-C). Here we examine new information on these ideas. The projected performance of super-X and X-point target long-leg divertors is looking very promising [2]; a stable fully-detached divertor condition handling an order-of-magnitude increase in power handling over conventional divertors may be possible. New experiments on Alcator C-Mod are addressing issues of high-field side versus low-field side heat flux sharing in double-null topologies and the screening of impurities that might originate from RF actuators placed in the high-field side -- both with favorable results. [1] Nuclear Fusion 55 (2015) 053020. [2] M. Umansky invited talk, this conference. [Preview Abstract] |
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BP10.00029: Scoping study for compact high-field superconducting net energy tokamaks R. T. Mumgaard, M. Greenwald, J. P. Freidberg, S. M. Wolfe, Z. S. Hartwig, D. Brunner, B. N. Sorbom, D. G. Whyte The continued development and commercialization of high temperature superconductors (HTS) may enable the construction of compact, net-energy tokamaks. HTS, in contrast to present generation low temperature superconductors, offers improved performance in high magnetic fields, higher current density, stronger materials, higher temperature operation, and simplified assembly. Using HTS along with community-consensus confinement physics (H98$=$1) may make it possible to achieve net-energy (Q\textgreater 1) or burning plasma conditions (Q\textgreater 5) in DIII-D or ASDEX-U sized, conventional aspect ratio tokamaks. It is shown that, by operating at high plasma current and density enabled by the high magnetic field (B\textgreater 10T), the required triple products may be achieved at plasma volumes under 20m$^{\mathrm{3}}$, major radii under 2m, with external heating powers under 40MW. This is at the scale of existing devices operated by laboratories, universities and companies. The trade-offs in the core heating, divertor heat exhaust, sustainment, stability, and proximity to known plasma physics limits are discussed in the context of the present tokamak experience base and the requirements for future devices. The resulting HTS-based design space is compared and contrasted to previous studies on high-field copper experiments with similar missions. The physics exploration conducted with such HTS devices could decrease the real and perceived risks of ITER exploitation, and aid in quickly developing commercially-applicable tokamak pilot plants and reactors. [Preview Abstract] |
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BP10.00030: The density dependence of H-mode access at high magnetic fields J.W. Hughes, D. Brunner, A.E. Hubbard, B. LaBombard, J. Rice, J. Terry, E. Tolman, I. Cziegler, E. Edlund Experimental investigations on Alcator C-Mod explore the power requirements, and local edge threshold conditions, for H-mode transitions, while accessing reactor-relevant plasma densities and toroidal magnetic fields from 2.5T to 8T. As on many tokamaks, the power threshold for H-mode $P_{th}$ does not increase monotonically with density, but actually rises significantly below a particular value of $\bar n_e}$ (the so-called `low-density limit' for H-mode). Such behavior can not be reproduced by current scaling laws used to project the power threshold for H-mode on future devices, which tend to assume a power law form, {\it e.g.} $P_{th} \sim B_T^x n_e^y$. Considerably more complicated dependencies are suggested by experiments, which indicate that the low-density branch moves to higher values of density as $B_T$ is increased. We extend this examination to magnetic fields that meet and surpass the ITER design field, and interpret the results in the context of candidate models to explain the upturn in $P_{th}$ at low density. [Preview Abstract] |
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BP10.00031: High Density H-Mode Behavior on Alcator C-Mod Elizabeth Tolman, Jerry Hughes, Brian LaBombard, Steve Wolfe Alcator C-Mod experiments have explored pedestal physics in high-density, stationary enhanced $D_\alpha$ (EDA) H-mode over a range of 2.7 to 7.8 T. Future high toroidal magnetic field devices may wish to operate in stationary ELM-suppressed regimes such as EDA H-Mode to benefit from high confinement while avoiding the risks posed by ELMs; such devices may also want to maximize plasma density. However, prior analysis of C-Mod EDA H-Modes at toroidal magnetic fields between 4.5 and 6 T shows that EDA H-mode Greenwald fraction scales inversely with magnetic field as $f_{GW} \sim B_T^{-.5}$, with only weak dependence on fueling. We use recent C-Mod experiments to extend this scaling to magnetic fields from 2.7 to 7.8 T. In addition, we characterize the shape of high-density C-Mod EDA H-Mode pedestals and study the response of both the pedestal and the edge to efforts to change $f_{GW}$ through gas puffing and modification of plasma current, with suggestions for potential connections to pedestal theory and modeling. [Preview Abstract] |
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BP10.00032: Gas-Puff Imaging Observations of the Edge Mode Driven by the ``Shoelace'' Antenna Woonghee Han, J. Terry, T. Golfinopoulos, S. Baek, D. Brunner, P. Ennever, B. LaBombard, E. Marmar Gas-Puff Imaging (GPI) routinely measures the spatially-resolved edge fluctuations in C-Mod plasmas. During the 2016 C-Mod campaign, the ``Shoelace'' antenna has been used to drive fluctuations in the edge plasma at frequencies and wavenumbers typical of the Quasi-Coherent Mode (QCM) which drives particle transport in the pedestal of ELM-less Enhanced D$_{\alpha }$ H-mode discharges. A ``Shoelace''-driven mode has been detected on fluctuation diagnostics that are magnetically mapped to the antenna. These diagnostics include GPI, the Mirror Langmuir Probe, the reflectometer, and Phase Contrast Imaging, and they all detect a mode in the plasma at the same driven frequency. GPI measures the radial profile of the mode amplitude and phase with the radial width of 6 mm. The poloidal wavenumber of the mode is evaluated to be $k_{\theta } \quad \approx $ 1.5 cm$^{\mathrm{-1}}$ near the low-field-side midplane, matching the structure imposed by the antenna winding. The measured mode amplitude, phase, and the poloidal wavenumber will be compared with those calculated from other diagnostics in order to characterize the property of the ``Shoelace''-driven mode in the edge plasma, which may provide further insight to QCM. [Preview Abstract] |
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BP10.00033: Statistics of fluctuation induced transport in the scrape-off layer of Alcator C-Mod Ralph Kube, Odd Erik Garcia, Audun Theodorsen, Brian LaBombard, James Terry The fluctuation induced transport in the scrape-off layer of Alcator C-Mod is investigated in an ohmically heated lower single-null discharge using Mirror Langmuir Probes. The probes are connected to a horizontal scanning probe which dwells at the outboard mid plane limiter radius and to electrodes in the outer divertor baffle. At the limiter radius the electron density, electron temperature and plasma potential are correlated with linear correlation coefficients r of approximately r=0.8. The bursts show a steep rise and a decay on a time scales of approximately 5 and 10 microseconds respectively. Amplitudes of bursts in the density, temperature, and plasma potential time series are correlated with r approximately 0.7-0.8. Conditionally averaged bursts in the radial particle and heat flux time series are less coherent and less reproducible, their amplitudes are correlated to the amplitude of bursts in the density time series with r=0.4. Statistics of the fluctuating plasma parameters at the outer divertor baffle are qualitatively similar to those at outboard midplane. Histograms, as well as statistics for level crossings and excess times spent above a given threshold for the time series compare favorably to a stochastic model for time series of scrape-off layer plasmas. [Preview Abstract] |
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BP10.00034: Reduction of ion transport and turbulence via dilution with nitrogen and neon injection in C-Mod deuterium plasmas M. Porkolab, P. Ennever, S.G. Baek, A.J. Creely, E.M. Edlund, J. Hughes, J.E. Rice, J.C. Rost, A.E. White, M.L. Reinke, G. Staebler, J. Candy Recent experiments on C-Mod ohmic plasmas and gyrokinetic studies indicated that dilution of deuterium plasmas by injection of nitrogen decreased the ion diffusivity and may also alter the direction of intrinsic toroidal rotation [1]. Simulations with TGLF and GYRO showed that dilution of deuterium ions in low density (LOC) plasmas increased the critical ion temperature gradient, while in high density (SOC) plasmas it decreased the stiffness. The density fluctuation spectrum measured in low q95 plasmas with Phase Contrast Imaging (PCI), and corroborated with spatially localized reflectometer measurements show a reduction of turbulence near r/a $=$ 0.8 with $k\rho_{s}\le $ 1, in agreement with modeling predictions in this region where the ion turbulence is well above marginal stability. Measurements also indicate that reversal of the toroidal rotation direction near the SOC-LOC transition may depend on ion collisionality rather than that of electrons. New experiments with neon seeding, which may be more relevant to ITER than with nitrogen seeding, show similar results. The impact of dilution on T$_{\mathrm{e}}$ turbulence as measured with CECE diagnostic will also be presented. [1] P. Ennever, et al., PoP 22, 072507 (2015). [Preview Abstract] |
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BP10.00035: Electron Temperature Gradient Scale Measurements in ICRF Heated Plasmas at Alcator C-Mod Saeid Houshmandyar, Perry E. Phillips, William L. Rowan, Nathaniel T. Howard, Martin Greenwald It is generally believed that the temperature gradient is a driving mechanism for the turbulent transport in hot and magnetically confined plasmas. A feature of many anomalous transport models is the critical threshold value ($L_{C})$ for the gradient scale length, above which both the turbulence and the heat transport increases. This threshold is also predicted by the recent multi-scale gyrokinetic simulations, which are focused on addressing the electron (and ion) heat transport in tokamaks [Howard \textit{et al}, Phys. Plasma \textbf{23}, 056109 (2016)]. Recently, we have established an accurate technique (B$_{\mathrm{T}}$-jog) to directly measure the electron temperature gradient scale length ($L_{Te}=T_{e}$/$\nabla T)$ profile, using a high-spatial resolution radiometer-based electron cyclotron emission (ECE) diagnostic [Houshmandyar \textit{et al}, RSI (2016)]. For the work presented here, electrons are heated by ion cyclotron range of frequencies (ICRF) through minority heating in L-mode plasmas at different power levels, TRANSP runs determine the electron heat fluxes and the scale lengths are measured through the B$_{\mathrm{T}}$-jog technique. Furthermore, the experiment is extended for different plasma current and electron densities by which the parametric dependence of $L_{C}$ on magnetic shear, safety factor and density will be investigated. [Preview Abstract] |
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BP10.00036: Simultaneous profile measurements of medium- and high-Z impurity concentrations (n$_{\mathrm{Z}}$/n$_{\mathrm{e}})$, T$_{\mathrm{e}}$ , $\Delta $Z$_{\mathrm{eff}}$ and n$_{\mathrm{e}}^{\mathrm{2}}$Z$_{\mathrm{eff}}$ in MCF plasmas from multi-energy x-rays Jacob Maddox, Luis Delgado-Aparicio, Novimir Pablant, Max Rutman, Ken Hill, Manfred Bitter, Matthew Reinke, John Rice Novel energy resolved measurements of x-ray emissions were used to characterize impurity concentrations, electron temperature, and $\Delta $Z$_{\mathrm{eff}}$ in a variety of Alcator C-Mod plasmas. A PILATUS2 detector programmed in a multi-energy configuration and used in a pinhole camera geometry provides the capability to function similar to a pulse height analyzer (PHA) but with full plasma profile views and sufficient spatial (\textasciitilde 1 cm), energy (\textasciitilde .5 keV), and temporal (\textasciitilde 10 ms) resolution. Each of the PILATUS2's \textasciitilde 100k (487x195) pixels can be set to an energy threshold, which sorts x-ray emissions into energy bins by counting only photons with energy above the threshold energy. By setting every 13th pixel row to the same energy bin and the 12 interjacent pixel rows to different energy bins on the PILATUS2 detector gives 38 poloidal sightlines (487 rows/13 energy bins). The number of photons detected in each energy bin depends on (n$_{\mathrm{Z}}$/n$_{\mathrm{e}})$, T$_{\mathrm{e}}$, and n$_{\mathrm{e}}^{\mathrm{2}}$Z$_{\mathrm{eff}}$, so that these plasma parameters can be extracted by fitting the data to an emission model, which includes free-free, free-bound, and bound-bound emissions from a De/H background plasma with perturbing medium and high-Z impurities, like intrinsic Mo, Fe, and Cu or injected W. Also, radial electron temperature profiles were measured during LHRF and ICRF and compared to Thomson scattering and ECE. [Preview Abstract] |
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BP10.00037: Complications with flush-mounted probe analysis beyond sheath-expansion A.Q. Kuang, B. LaBombard, D. Brunner In a reactor relevant divertor, the heat-flux onto the target plate would be too large and traditional proud Langmuir probes will melt. By making the probes flush with the surface of the target plate they become nearly as robust as the divertor plates themselves. However, without a theoretically rigorous derivation of the sheath thickness, sheath expansion has been a primary concern for the interpretation of flush mounted probe data [1,2]. Following the installation of a flush-mounted Langmuir probe system at Alcator C-Mod (toroidally-elongated and field-aligned to give it a `rail' geometry) that effectively mitigates the effects of sheath expansion down to incident field line angles of 0.5 degree [3], further complications have arisen that cannot be explained by sheath-expansion. The `rail' probes systematically measure lower densities and higher temperatures but have the same pressure. The evolution of the scrape-off layer profiles measured on the divertor target plate from sheath-limited to detached regimes is also different. These are indicative of important physics, perhaps unique to conditions in a vertical-target plate divertor with small field-line attack angles, that affects the I-V characteristics and is not currently included in probe data analyses. Controlled experiments performed at Alcator C-Mod mapped out this discrepancy and the results will be presented. [1] Gunn, J. P. (1997). \textit{Phys. of Plasma}. Vol. 4. p. 4435. [2] Weinlich, M. and Carlson, A. (1997). \textit{Phys. of Plasma}. Vol. 4. p. 2151. [3] A.Q., Kuang, et. al. (2016). \textit{Nucl. Mat. and Energy, }in review. [Preview Abstract] |
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BP10.00038: Experimental characterization of the lower hybrid wave field on the first pass using a magnetic probe array T. Shinya, S. G. Baek, G. M. Wallace, R. R. Parker, S. Shiraiwa, Y. Takase Experimental characterization of the lower hybrid (LH) wave propagation from the launcher to the core plasma is important to validate an antenna spectrum model and to identify parasitic wave-edge plasma interactions occurring in front of the launcher. On Alcator C-Mod, the wave frequency spectrum and dominant parallel wavenumber are characterized with two probe arrays installed near the edge plasma. The first one is mounted on a radially movable structure that is about 108 deg toroidally away from the launcher. A phasing scan experiment at moderate density suggests a resonance-cone propagation of the launched slow LH wave with a finite spectral width. As plasma density is raised, the measured power decreases, correlated with the observed loss of efficiency. Recently, the second probe array with an increased number of probes has been installed on a limiter that is 54 deg. toroidally away from the launcher, which is expected to be dominantly sensitive to the wave-field directly leaving the launcher. An initial measurement shows that the probe array detects a coherent wave field. A full-wave model to evaluate the wave electric-field pattern in front of the probe array is under development. If available, further experimental and modeling results will be presented. [Preview Abstract] |
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BP10.00039: Experimental Measurements of the Lower Hybrid Electric Field on Alcator C-Mod by Stark Effect Spectroscopy D. L. Hillis, R. Mumgaard, C. Lau, G. Wallace, S. Shiraiwa A new diagnostic was installed on Alcator C-Mod capable of determining both the magnitude and direction of the lower hybrid wave electric field, \textbf{E}$_{\mathrm{\mathbf{LH}}}$. The diagnostic, named SELHF (\textbf{S}tark \textbf{E}ffect \textbf{L}ower \textbf{H}ybrid \textbf{F}ield), simultaneously measures the two orthogonal polarization states of the D$_{\mathrm{\beta }}$ spectra by passive optical emission spectroscopy. The \textbf{E}$_{\mathrm{\mathbf{LH}}}$ vector is then determined by systematically fitting the spectrum to the EZSSS (\textbf{E}xplicit \textbf{Z}eeman-\textbf{S}tark \textbf{S}pectra \textbf{S}imulator) code which incorporates a fully quantum mechanical model comprising of the appropriate dynamic electric field and magnetic field operators. The SELHF diagnostic has 27 unique views of the LH launcher and surrounding space, each integrating over a \textasciitilde 3 cm in diameter sightline, which is comparable to the waveguide dimension. Two sightlines are simultaneously viewed, yielding four spectra per discharge. In this presentation the diagnostic setup will be given. The methodology behind the spectral modeling and the results of the associated error analysis, yielding the accuracy of the \textbf{E}$_{\mathrm{\mathbf{LH}}}$ vector information, will be presented. The initial experimental results compared against a 2D cold-plasma model in COMSOL will be discussed. Work supported by DoE Contract No. DE-FC02-99ER54512 on Alcator C-Mod, a Department of Energy Office of Science user facility. [Preview Abstract] |
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BP10.00040: Simulation analysis of current profile broadening via lower hybrid current drive in the EAST tokamak P. T. Bonoli, S. Shiraiwa, A. M. Garofalo, M. Lanctot, X. Z. Gong, B. Ding, S. Ding, G. Li, M. Li, H. Liu, B. Lyu, J. Qian, C. Yang, C. Holcomb, J. McClenaghan Experiments on EAST have recently demonstrated broadening of the current profile via the application of LHCD with systematic scans yielding lower internal inductance with higher density [1]. The radial penetration of LH waves is expected to decrease as the density increases as refractive effects become more important. In this paper we present analyses of these discharges using the GENRAY / CQL3D ray tracing / Fokker Planck model to investigate if the expected decrease in radial penetration at higher density is responsible for the profile of LHCD becoming more off-axis. This analysis will also investigate the effect of minor modifications in the incident wave spectrum on the damping location of the LH waves. [1] A. M. Garofalo et al, 26th IAEA Fusion Energy Conference, 17-22 October 2016, Kyoto, Japan. [Preview Abstract] |
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BP10.00041: Extending fullwave core ICRF simulation to SOL and antenna regions using FEM solver S. Shiraiwa, J. C. Wright A full wave simulation approach to solve a driven RF waves problem including hot core, SOL plasmas and possibly antenna is presented. This approach allows for exploiting advantages of two different way of representing wave field, namely treating spatially dispersive hot conductivity in a spectral solver and handling complicated geometry in SOL/antenna region using an unstructured mesh. Here, we compute a mode set in each region with the RF electric field excitation on the connecting boundary between core and edge regions. A mode corresponding to antenna excitation is also computed. By requiring the continuity of tangential RF electric and magnetic fields, the solution is obtained as unique superposition of these modes. In this work, TORIC core spectral solver is modified to allow for mode excitation, and the edge region of diverted Alcator C-Mod plasma is modeled using COMSOL FEM package. The reconstructed RF field is similar in the core region to TORIC stand-alone simulation. However, it contains higher poloidal modes near the edge and captures a wave bounced and propagating in the poloidal direction near the vacuum-plasma boundary. These features could play an important role when the single power pass absorption is modest. This new capability will enable antenna coupling calculations with a realistic load plasma, including collisional damping in realistic SOL plasma and other loss mechanisms such as RF sheath rectification. [Preview Abstract] |
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BP10.00042: Mode conversion in three ion species ICRF heating scenario Y. Lin, E. Edlund, P. Ennever, M. Porkolab, J. Wright, S. Wukitch Three-ion species ICRF heating has been studied on Alcator C-Mod and on JET [1]. It has been shown to heat the plasma and generate energetic particles. In a typical three-ion scenario, the plasma consists of \textasciitilde 60-70{\%} D, \textasciitilde 30-40{\%} H and a trace level (1{\%} or less) of $^{\mathrm{3}}$He. This species mixture creates two hybrid resonances (D-$^{\mathrm{3}}$He and $^{\mathrm{3}}$He-H) in the plasma, in the vicinity of the $^{\mathrm{3}}$He IC resonance (on both sides). The fast wave can undergo mode conversion (MC) to ion Bernstein waves and ion cyclotron waves at the two hybrid resonances. A phase contrast imaging (PCI) system has been used to measure the RF waves in the three-ion heating experiment. The experimentally measured MC locations and the separating distance between the two MC regions help to determine the concentration of the three species. The PCI signal amplitudes for the RF waves are found to be sensitive to RF and plasma parameters, including P$_{\mathrm{RF,}}$ T$_{\mathrm{e}}$, n$_{\mathrm{e}}$ and also the species mix concentration. The parameter dependences found in the experiment will be compared with ICRF code simulations. [1] Ye.O. Kazakov, invited talk, this conference. [Preview Abstract] |
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BP10.00043: An automated process for generating archival data files from MATLAB figures G.M. Wallace, M. Greenwald, J. Stillerman A new directive from the White House Office of Science and Technology Policy requires that all publications supported by federal funding agencies (\emph{e.g.} Department of Energy Office of Science, National Science Foundation) include machine-readable datasets for figures and tables\footnote{J.P. Holdren. MEMORANDUM FOR THE HEADS OF EXECUTIVE DEPARTMENTS AND AGENCIES. ``Increasing Access to the Results of Federally Funded Scientific Research.'' https://www.whitehouse.gov/sites/default/files/microsites/ostp/ ostp\_public\_access\_memo\_2013.pdf}. An automated script was developed at the PSFC to make this process easier for authors using the MATLAB plotting environment to create figures. All relevant data (x, y, z, errorbars) and metadata (line style, color, symbol shape, labels) are contained within the MATLAB .fig file created when saving a figure. The \emph{export\_fig} script extracts data and metadata from a .fig file and exports it into an HDF5 data file with no additional user input required. Support is included for a number of plot types including 2-D and 3-D line, contour, and surface plots, quiver plots, bar graphs, and histograms. [Preview Abstract] |
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BP10.00044: Analysis of MHD instabilities limiting high normalized beta operation in KSTAR Y.S. Park, S.A. Sabbagh, J.W. Berkery, J.M. Bialek, S.W. Yoon, J. Kim, Y.M. Jeon, J.G. Bak, W.H. Ko, S.H. Hahn, Y.K. In, M.J. Choi, S.G. Lee, J.G. Kwak, Y.K. Oh, H.K. Park, G.S. Yun, S.C. Jardin H-mode plasma operation in KSTAR reached high normalized beta up to 4.3 that significantly surpassed the computed $n=$1 ideal no-wall beta limit by a factor of 1.6. Pulse lengths at maximum normalized beta were extended to longer pulses by new, more rapid equilibrium control resulting in normalized beta greater than 3 sustained for 1 s. Analysis of these plasmas shows that low-$n$ global kink/ballooning or resistive wall modes (RWMs) were not the cause of the plasma termination. Kinetic modification of the ideal MHD $n=$1 stability criterion computed by the MISK code shows the kinetic RWM to be stable, which is consistent with the observed high normalized beta operation. An $m$/$n=$2/1 tearing mode onsets at high normalized beta greater than 3 that experimentally reduces normalized beta by more than 30{\%}. The stability of the observed 2/1 tearing mode examined by using the M3D-C$^{\mathrm{1}}$ code coupled with the EFIT reconstruction shows a stable 2/1 mode while the equilibrium is experimentally unstable to the 2/1 mode This result may imply that the mode is classically stable, and the pressuredriven neoclassical terms dominate over the current gradient term. Advances in the analysis from the recent run campaign will be reported. [Preview Abstract] |
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BP10.00045: Radio frequency bursts accompanied by the crash dynamics of edge-localized mode Minho Kim, Shekar G. Thatipamula, Gunsu S. Yun, Kangwook Kim, Yong-Un Nam Electromagnetic burst emissions in the radio frequency (RF) range (0.1\textasciitilde 1 GHz) from the KSTAR high confinement (H) -- mode plasma are detected using RF spectrometers. The RF burst emission is primarily associated with the crash dynamics of the edge-localized mode (ELM) observed by imaging diagnostics [G. S. Yun et al. Phys. Rev. Lett. 107, 045004 (2011); J. Lee et al. Phys. Rev. Lett. accepted (2016)]. A persistent emission appears in narrow band prior to the ELM crash, often overlapping with deuteron or proton ion cyclotron harmonics. The emission lines become more intense and broader toward crash, which is correlated with the structural change of the mode. At the onset of ELM crash, the emission turns wide band and is often followed by short intense bursts (2--3 $\mu $s) with rapid-frequency chirping in steps of deuteron or proton cyclotron frequency. Hence, the RF signals offer the scope for revealing the complex dynamics of the ELM crash. *Work supported by the National Research Foundation of Korea (NRF) under contract No. NRF-2014M1A7A1A03029881 and BK21$+$ program. [Preview Abstract] |
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BP10.00046: Supersonic Molecular Beam Injection Effects on Tokamak Plasma Applied Non-axisymmetric Magnetic Perturbation Hyunsun Han, Y. In, Y.M. Jeon, S.H. Hahn, K.D. Lee, Y.U. Nam, S.W. Yoon In KSTAR experiments, the change of tokamak plasma behavior by supersonic molecular beam injection (SMBI) was investigated by applying resonant magnetic perturbations(RMP) that could suppress edge localized modes (ELMs). When the SMBI is applied, the symptom representing ELM suppression by RMP is disappeared. The SMBI acts as a cold pulse on the plasma keeping the total confinement engergy constant. However, it makes plasma density increase and change the plasama collisionality which can play a role in the edge-pedestal build-up processing. [Preview Abstract] |
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BP10.00047: ELM study in KSTAR H-mode plasma using ECEI observations and edge simulation M. Kim, J. Lee, H.K. Park, G.S. Yun, J.M. Kwon, J.E. Lee, X.Q. Xu, S. Ku Full understanding of ELM physics is one of the most important issues to achieve stable plasma operation in high-performance. In KSTAR H-mode plasmas, ELM physics have been studied by a comparative study between measured ELM images by electron cyclotron emission imaging (ECEI) and edge simulations. In comparative study, the mode structure from the simulation is converted to a synthetic image. An agreement between two images provided high confidence on the study of ELM structure using ECEI images. Because an ELM cycle is already nonlinear phase through saturated linear phase when it is able to be observed, a nonlinear simulation is required for an advanced comparative study. By comparing the observed images and that from the BOUT$++$ nonlinear ELM simulation, the role of transport (e.g. heat and particle diffusion) and dissipation (e.g. resistivity, hyper-resistivity and viscosity) coefficient is under investigation. The discrepancies between the observed coherent mode structures on the inboard side during inter-ELM-crash periods with the BOUT$++$ simulation results are investigated. An XGC simulation, full-f gyrokinetic PIC code, is introduced to explain the discrepancies in HFS mode structure. The growth of HFS mode will be discussed in this comparative study. [Preview Abstract] |
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BP10.00048: Solitary perturbations prior to the partial collapse of the edge pedestal in KSTAR H-mode plasmas J.E. Lee, G.S. Yun, M.H. Kim, M. Kim, J. Lee, H.K. Park, M. Choi, W.H. Ko Solitary perturbations (SPs), localized both poloidally and radially, are frequently observed on the KSTAR tokamak within $\sim$100 $\mu$s before the partial collapse of the edge pedestal. The perturbation structure measured by 2D imaging diagnostic [1] is clearly distinguished from the quasi-steady filamentary modes that are routinely observed during the inter-crash period [2, 3]. In particular, the SPs have a low toroidal mode number (typically unity) and smaller pitch angle. The SPs are similar to the irregular mode structure with large amplitude [3] appearing near complete crash. The resemblance suggests that the generation of SPs is strongly connected to the crash mechanism. [1] G.S. Yun \textit{et al}, \textit{Rev. Sci. Instrum.} \textbf{81} 10D930 (2010) [2] J.E. Lee \textit{et al}, \textit{Nucl. Fusion} \textbf{55} 113035 (2015) [3] G.S. Yun \textit{et al}, \textit{Phys. Plasmas} \textbf{19} 056114 (2012) [Preview Abstract] |
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BP10.00049: Implementation of MSE Wavelength-Interpolation Background Subtraction on KSTAR Steven Scott, Robert Mumgaard A ten-channel polychrometer that simultaneously measures the Motional Stark Effect pi and sigma line polarized emission and two neighboring wavelengths near the MSE spectrum, previously used on Alcator C-Mod, will be implemented at KSTAR in FY17. This will provide accurate measurements of the partially-polarized MSE background emission even in situations where the background varies rapidly in time and space. Data analysis will be performed by a new, tokamak-independent data analysis suite that computes the signal amplitude at many harmonics of the photo-elastic modulator (PEM) frequency using a numerical-beat algorithm. The frequency and phase of the PEM drive signal is computed very accurately by examining successive rise-times of the drive, then reference sinusiodal waveforms are constructed at multiple harmonics. The reference waveform is numerically beat against the measured MSE signal to obtain the signal amplitudes at various PEM harmonics. Availability of signal amplitudes up to the 5$^{\mathrm{th}}$ PEM harmonic provides an accurate estimate of the PEM retardance during routine operation. Customizations to the hardware and software for implementation at KSTAR including corrections for Faraday rotation and beam overlap will be discussed. [Preview Abstract] |
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BP10.00050: Development of Integrated Magnetic and Kinetic Control-oriented Transport Model for q-profile Response Prediction in EAST Discharges Hexiang Wang, Eugenio Schuster, Tariq Rafiq, Arnold Kritz, Siye Ding Extensive research has been conducted to find high-performance operating scenarios characterized by high fusion gain, good confinement, plasma stability and possible steady-state operation. A key plasma property that is related to both the stability and performance of these advanced plasma scenarios is the safety factor profile. A key component of the EAST research program is the exploration of non-inductively driven steady-state plasmas with the recently upgraded heating and current drive capabilities that include lower hybrid current drive and neutral beam injection. Anticipating the need for tight regulation of the safety factor profile in these plasma scenarios, a first-principles-driven (FPD)control-oriented model is proposed to describe the safety factor profile evolution in EAST in response to the different actuators. The TRANSP simulation code is employed to tailor the FPD model to the EAST tokamak geometry and to convert it into a form suitable for control design. The FPD control-oriented model's prediction capabilities are demonstrated by comparing predictions with experimental data from EAST. [Preview Abstract] |
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BP10.00051: Predicting Electron and Ion Thermal Transport in EAST Discharges A.H. Kritz, T. Rafiq, A.Y. Pankin, S. Ding, H. Du, J. Ma, P.T. Bonoli The Multi-Mode (MMM7.1, T Rafiq et al., Phys. Plasmas 20, 032506 (2013)) and the Trapped Gyro-Landau Fluid (TGLF, G.M. Staebler, et al., Phys. Plasmas 14, 055909 (2007)) anomalous transport models are used in the PTRANSP code to predict the evolution of the electron and ion temperature profiles. Simulations are carried out using PT-SOLVER, a modular, parallel, and multi-regional solver particularly suited for stiff transport models. The predicted temperature profiles are compared with corresponding EAST experimental data. The MMM7.1 and TGLF models compute transport driven by electron and ion temperature gradient modes, and by trapped electron modes. In addition, MMM7.1 computes transport driven by kinetic and resistive ballooning modes. The neoclassical thermal transport is calculated using the NCLASS and NEO modules. The NUBEAM module and the LSC module are used for neutral beam and for lower hybrid heating and current drive. The self-consistent evolution of the equilibrium is obtained using the TEQ equilibrium code. The radial dependence of the contributions of the different instabilities to the anomalous transport is described, and the degree that the MMM7.1 and TGLF transport models yield temperature profiles that are consistent with EAST experimental data is illustrated. [Preview Abstract] |
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BP10.00052: The low density type III ELMy H-mode regime on JET-ILW: a low density H-mode compatible with a tungsten divertor? E. Delabie, J. C. Hillesheim, J. Mailloux, C. F. Maggi, F. Rimini, E. R. Solano The threshold power to access H-mode on JET-ILW has a minimum as function of density [1]. Power ramps in the low and high density branch show qualitatively very different behavior above threshold. In the high density branch, edge density and temperature abruptly increase after the L-H transition, and the plasma evolves into a type I ELMy H-mode. Transitions in the low density branch are gradual and lead to the formation of a temperature pedestal, without increase in edge density. These characteristics are reminiscent of the I-mode regime [2], but with high frequency ELM activity. The small ELMs allow stable H-mode operation with tolerable tungsten contamination, as long as both density and power stay below the type I ELM boundary. The density range in which the low density branch can be accessed scales favourably with toroidal field but unfavourably with isotope mass. At B$_T$=3.4T, a stable H-mode has been obtained at $ |
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BP10.00053: Recent Alfv\'{e}n Eigenmode measurements on JET V. Aslanyan, M. Porkolab, P. Woskov, P. Puglia, W. Pires de Sa, R. Galvao, L. Ruchko, S. Sharapov, S. Dorling, S. Dowson, M. Graham, T. Blackman, G. Jones, A. Goodyear, P. Blanchard, A. Fasoli, D. Testa, J. Figueiredo, C. Perez von Thun Alfv\'{e}n Eigenmodes (AE) have been observed in the latest JET campaigns, excited by ICRH-driven fast particles in D and DH plasmas. The detection of AEs allows determination of isotope abundance in recent experiments with mixed ion composition plasmas. A major upgrade to the Toroidal Alfv\'{e}n Eigenmode Active Antenna diagnostic at JET has opened the possibility to probe AEs with a wide range of toroidal mode numbers n and quantify their damping rate. A new 4 kW amplifier has been installed for each of six antennas to increase the output power and allow real time control of the relative phasing between the antennas. The diagnostic will be used to study the damping of alpha-driven AEs during the DT campaign planned on JET in support of ITER. Simulations with the MISHKA code are used to interpret the frequencies and radial localization of AEs. [Preview Abstract] |
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BP10.00054: Isotopic mass and fast ion effects in JET alpha heating plasmas Robert Budny Experiments to detect alpha heating were performed in TFTR (1994) [1] and in JET (DTE1 1997) [2]. Observations of alpha heating were reported. Hydrogenic isotopic mass effects were seen in TFTR, but were assumed to be negligible in JET although unexpectedly high T$_i$ was seen in the DT plasmas. A reanalysis [3] showed strong correlation of core T$_e$ and T$_i$ with isotopic mass A, and with the time delays of significant sawteeth. Here effects of fast ions are studied. Beam ion pressure is also correlated with suppression of significant sawteeth, but is not correlated as strongly with the core T$_e$ and T$_i$. Beam and alpha ion effects on confinement and heating are reported. $^a$See the Appendix of F. Romanelli et al., Proceedings of the 25th IAEA Fusion Energy Conference 2014, Saint Petersburg, Russia. [1] G.Taylor, {\it et al.,}, Phys. Review Lett. {\bf 76} 2722 (1996. [2] Thomas, {\it et al.,} Phys. Review Lett. {\bf 80} 5548 (1998). [3] R.V.Budny, Nucl. Fusion {\bf 56} 036013 (2016). [Preview Abstract] |
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BP10.00055: Measurement of turbulent electron temperature fluctuations on the ASDEX Upgrade tokamak using correlated Electron Cyclotron Emission S. Freethy, G. D. Conway, I. Classen, A. J. Creely, T. Happel, B. Vanovac, A. E. White First measurements of core (r/a < 0.95) turbulent electron temperature fluctuations made on the ASDEX Upgrade (AUG) tokamak using a Correlation Electron Cyclotron Emission (CECE) technique are presented. Validation of gyro-kinetic models against measurements of the underlying turbulent micro-structure are essential for developing predictive capabilities for future devices. In tokamak plasmas, turbulent temperature fluctuations are sufficiently broadband ($\sim$0.5MHz) and low-amplitude ($\sim$1\%) that conventional radiometer techniques are fundamentally unable to detect them and a correlation technique is required to further extract the signals. An application of the spectral decorrelation method had been designed and built for AUG. This CECE radiometer shares an optical path with a reflectometer and is sensitive to wavenumbers perpendicular to the magnetic field $k_\perp$ up to 0.76cm$^{-1}$ . An upgrade to the focusing mirror will increase this range to $k_\perp$ up to 1.4cm$^{-1}$. Measurements in Helium plasmas have been made at three radial locations simultaneously, providing a profile of the temperature fluctuation amplitude in the outer core of Electron Cyclotron Resonance Heated heated L-mode plasmas. New results and future plans will be presented. [Preview Abstract] |
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BP10.00056: Runaway electrons mitigation by 3D fields: new insights from ASDEX Upgrade and RFX-mod experiments. M. Gobbin, G. Papp, L. Marrelli, P.J. McCarthy, M. Nocente, G. Pautasso, W. Suttrop, P. Piovesan, D. Terranova, M. Valisa Disruption-generated runaway electron (RE) beams represent a severe threat for tokamak plasma-facing components, thus motivating the search of mitigation techniques. The application of optimized 3D fields might aid this purpose, as was recently investigated in ASDEX Upgrade and RFX-mod. In ASDEX Upgrade discharges, the application of n$=$1 resonant magnetic perturbations (RMPs) by the B-coils before and during the disruption results in a longer current quench time together with a lower RE current in the post-disruption phase. The strength of the observed effects depends on the upper-to-lower B-coil phasing, i.e. on the poloidal spectrum of the RMPs. These results are analyzed by means of numerical tools, like the guiding center code ORBIT, and the role of plasma response is also investigated. Similar experiments have been performed in RFX-mod low density plasmas where magnetic perturbations of various amplitudes, applied by non-axisymmetric coils, have been found to partially suppress REs. ORBIT simulations indicate, in this case, that RE orbit losses are associated to a raised level of stochasticity in the edge plasma region. [Preview Abstract] |
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BP10.00057: Overview of the EUROfusion Medium Size Tokamak scientific program Piero Martin, Stefano Coda, Thomas Eich, Antti Hakola, Hendrik Meyer The EUROfusion MST (Medium Size Tokamaks) task force is in charge of the European science programme in the ASDEX Upgrade, TCV and MAST-U tokamaks. This paper will present an overview of the main results obtained in the 2015/16 campaign in AUG and TCV and the future plans. We will discuss, among others, successful disruption and runaway electron control experiments with MGI and 3D fields, the achievement of full ELM suppression with RMP accompanied by the understanding of plasma response and the heat load pattern study, the exploration of regimes with impurity seeding at high P/R with 85 $\%$ radiation fraction and good confinement, the study of tungsten fuzz, where W samples with pre-formed nanostructures were exposed to H-mode Helium plasmas and the investigation on advanced divertor concepts. A survey of MHD limits and of MHD control in standard and high-beta regimes will be presented. The results from the AUG campaign dedicated to He plasmas in support of ITER initial operation will also be presented, as well as analysis of old MAST data that reveal interesting features in the filamentary transport. [Preview Abstract] |
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BP10.00058: Understanding the dynamics of the inductive plasma formation and its application to create doublet shaped plasma in the TCV tokamak Joyeeta Sinha, Stefano Coda, Basil Paul Duval, Cristian Galperti, Jean-Marc Moret, Holger Reimerdes The dynamics of the plasma formation in TCV are revisited with the goal of improving reliability and developing new scenarios such as the creation of doublet configurations. A database for the plasma formation scenarios in TCV reveals that 15$\%$ of the attempts to form a plasma fail during the burn-through phase. Plasma formation dynamics are greatly affected by the difference between programmed and obtained plasma current ramp rates that can lead to oscillations in $I_P$ when the $I_{P}$ feedback control is activated. This mismatch in $I_P$ also propagates into the radial position control. Failed burn-throughs occur when the Ohmic heating power is insufficient either since $I_P$ rises too slow or due to a combined effect of the $I_P$ feedback oscillations and a regularly occurring MHD instability. Several strategies to improve the present plasma formation scenario have been implemented. Based on the improved understanding of the plasma formation dynamics, a strategy has been developed to create and control a doublet configuration by merging of two droplet-shaped plasma requiring simultaneous breakdown at two locations. [Preview Abstract] |
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BP10.00059: Initial exploration of scenarios with Internal Transport Barrier in the first NBI-heated L-mode TCV plasmas Chiara Piron, Olivier Sauter, Stefano Coda, Antoine Merle, Alexander Karpushov, Leonardo Pigatto, Tommaso Bolzonella, Paolo Piovesan, Nicola Vianello Fully non-inductive operation of high performance plasmas is one of the main objectives of contemporary Tokamak research. In this perspective, plasmas with Internal Transport Barriers (ITBs) are an attractive scenario, since they can attain a high fraction of bootstrap current [1]. In this work we start exploring ITB scenarios on the Tokamak \`{a} Configuration Variable (TCV) heated by a newly available 1MW Neutral Beam Injector (NBI) [2]. Here we investigate for the first time in this device the impact of the additional NBI power on the performance and stability of L-mode plasmas with ITBs [3]. Results of both experimental data analyses and ASTRA transport simulations are presented. The work examines also the Magneto Hydro-Dynamics (MHD) activity and stability of the explored plasmas. In particular, the role of plasma magnetic equilibrium parameters, such as plasma elongation and triangularity, on the sustainment of these NBI-heated ITB scenarios is discussed. [1] R. C. Wolf et al 2003 Plasma Phys. Control. Fusion 45 R1 [2] A. N. Karpushov et al 2015 Fusion Eng. Des. 96-97 493 [3] S. Coda et al 2007 Nucl. Fusion 47 714 [Preview Abstract] |
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BP10.00060: Runaway electron behavior in the Frascati Tokamak Upgrade (FTU) Zana Popovic, Jose Ramon Martin-Solis, Basilio Esposito, Daniele Marocco, Federica Causa, Paolo Buratti, Luca Boncagni, Daniele Carnevale, Mateusz Gospodarczyk Several recent experiments in the FTU tokamak are dedicated to the study of runaway electrons (RE), both in the flattop and disruption phases of the discharge. Experiments have been carried out to evaluate the threshold electric field for RE generation during the flattop of ohmic discharges. The measured threshold electric field during RE electron generation and suppression experiments for a wide range of plasma parameters is found to be $\sim $2-5 times larger than predicted by the relativistic collisional theory, E$_{\mathrm{R}}=$n$_{\mathrm{e}}$e$^{\mathrm{3}}$ln$\Lambda $/4$\pi \varepsilon _{\mathrm{0}}^{\mathrm{2}}$m$_{\mathrm{e}}$c$^{\mathrm{2}}$, and is consistent with an increase of the critical field due to the RE synchrotron radiation. Runaway evolution has been numerically simulated using a test particle model including toroidal electric field acceleration, collisions and synchrotron radiation losses. Estimates of RE energy distribution are consistent with the measurements of two recently installed RE diagnostics: HXR-camera and RE Imaging and Spectroscopy (REIS) system. [Preview Abstract] |
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BP10.00061: Runaway electrons and ITER Allen Boozer ITER planning for avoiding runaway damage depends on magnetic surface breakup in fast relaxations. These arise in thermal quenches and in the spreading of impurities from massive gas injection or shattered pellets. Surface breakup would prevent a runaway to relativistic energies were it not for non-intercepting flux tubes, which contain magnetic field lines that do not intercept the walls. Such tubes persist near the magnetic axis and in the cores of islands but must dissipate before any confining surfaces re-form. Otherwise, a highly dangerous situation arises. Electrons that were trapped and accelerated in these flux tubes can fill a large volume of stochastic field lines and serve as a seed for the transfer of the full plasma current to runaways. If the outer confining surfaces are punctured, as by a drift into the wall, then the full runaway inventory will be lost in a short pulse along a narrow flux tube. Although not part of ITER planning, currents induced in the walls by the fast magnetic relaxation could be used to passively prevent outer surfaces re-forming. If magnetic surface breakup can be avoided during impurity injection, the plasma current could be terminated in tens of milliseconds by plasma cooling with no danger of runaway. [Preview Abstract] |
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BP10.00062: Real-time Numerical Solution for the Plasma Response Matrix for Disruption Avoidance in ITER Alexander Glasser, Egemen Kolemen, A.H. Glasser Real-time analysis of plasma stability is essential to any active feedback control system that performs ideal MHD disruption avoidance. Due to singularities and poor numerical conditioning endemic to ideal MHD models of tokamak plasmas, current state-of-the-art codes require serial operation, and are as yet inoperable on the sub-$\mathcal{O}$(1s) timescale required by ITER's MHD evolution time. In this work, low-toroidal-n ideal MHD modes are found in near real-time as solutions to a well-posed boundary value problem. Using a modified parallel shooting technique and linear methods to subdue numerical instability, such modes are integrated with parallelization across spatial and ‘temporal’ parts, via a Riccati approach. The resulting state transition matrix is shown to yield the desired plasma response matrix, which describes how magnetic perturbations may be employed to maintain plasma stability. Such an algorithm may be helpful in designing a control system to achieve ITER’s high-performance operational objectives. [Preview Abstract] |
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BP10.00063: Calculation of Neoclassical Ripple Transport in ITER using SFINCS Elizabeth Paul, Matt Landreman, Donald Spong, Francesca Poli Neoclassical interactions with non-axisymmetric magnetic fields cause a damping force known as neoclassical toroidal viscosity (NTV). The toroidal symmetry of ITER will be broken by the finite number of toroidal field coils and the presence of perturbing ferromagnetic structures such as test blanket modules (TBM) and ferritic inserts (FI). We compute 3D equilibrium magnetic fields for an ITER steady-state scenario using VMEC and calculate neoclassical transport quantities in the presence of these error fields using the Stellarator Fokker-Planck Iterative Neoclassical Conservative Solver (SFINCS) code. In the presence of both the FI and TBM, the net effect is a decrease in toroidal damping. The magnitude of NTV torque density at large radii ($ r/a \geq 0.7$) is comparable to the NBI torque density at small radii ($ r/a \leq 0.4$), but is opposite in direction. This could indicate the possibility of generating sheared flows. The magnetic field ripple does not significantly affect the neoclassical tokamak relationship between radial electric field and parallel flow velocity, and at $r/a \geq 0.7$ the ripple drives additional collisional heat flux comparable to the axisymmetric neoclassical flux. [Preview Abstract] |
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BP10.00064: Burn control of an ITER-like fusion reactor using fuzzy logic A. Sair Garcia-Amador, Julio J. Martinell The fuel burn in a fusion reactor has to be kept at a nearly constant rate in order to have a steady power exhaust. Here, we develop a control system based on a fuzzy logic controller in order that adjusts external parameters to keep the plasma temperature and density at the design values of a reactor of the characteristics of ITER. The control parameters chosen are the D-T refueling rate, the auxiliary heating power and a neutral helium beam. We use a fuzzy controller of the Mamdani type that uses a number of membership functions appropriate to produce a response to parameter deviations that minimizes the response time. The inference rules are determined in a way to provide stabilization to all perturbations of the temperature, density and alpha particle fraction. The dynamical response of the reactor is simulated with a 0D model that uses confinement times provided by the ITER scaling. We show that the system is feedback stabilized for a large range of parameters around the nominal values. The recovery time after a departure from the steady values is of the order of one second. We compare the results with another control system based on neural networks that was developed previously. [Preview Abstract] |
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BP10.00065: Can high fields save the tokamak? The challenge of steady-state operation for low cost compact reactors Jeffrey Freidberg, Akshunna Dogra, William Redman, Antoine Cerfon The development of high field, high temperature superconductors is thought to be a game changer for the development of fusion power based on the tokamak concept. We test the validity of this assertion for pilot plant scale reactors (Q $\sim$ 10) for two different but related missions: pulsed operation and steady-state operation. Specifically, we derive a set of analytic criteria that determines the basic design parameters of a given fusion reactor mission. As expected there are far more constraints than degrees of freedom in any given design application. However, by defining the mission of the reactor under consideration, we have been able to determine the subset of constraints that drive the design, and calculate the values for the key parameters characterizing the tokamak. Our conclusions are as follows: 1) for pulsed reactors, high field leads to more compact designs and thus cheaper reactors -- high B is the way to go; 2) steady-state reactors with H-mode like transport are large, even with high fields. The steady-state constraint is hard to satisfy in compact designs -- high B helps but is not enough; 3) I-mode like transport, when combined with high fields, yields relatively compact steady-state reactors -- why is there not more research on this favorable transport regime? [Preview Abstract] |
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BP10.00066: The High Field Compact Approach in Nuclear Fusion: Present and Foreseeable Developments vs. Damnatio Memoriae* P. Spillantini, B. Coppi, G. Grasso A confirmation of the fact that the most promising approach, in the effort to demonstrate experimentally that fusion burning D-T plasmas can reach near-ignition conditions [1], is that of high field compact (HFC) machines, has come from recent analyses [2] of confinement experiments conducted over the years. In fact, this approach can be adopted to begin investigations of D-D and $D-^{3}$He burning regimes. An important development that can be used in these experiments is that of high field super-conductor technology. This technology was pioneered with the adoption [3] and design of the largest (vertical field) coils of the Ignitor machine using $MgB_{2}$ super-conductors cooled to about $10^{o}$K. The use of hybrid magnets combining $MgB_{2}$ and high temperature super-conductors to reach the needed high fields for all the machine components has been proposed also with a specific configuration for envisioned future experiments [3]. A surprising occurrence, related to the ideas at the basis of the HFC machine approach has been the practice of the ``damnatio memoriae'' inflicted on their originators. *Sponsored in part by the U.S. D.O.E. [1] B. Coppi, 1721, 020003 (2016). [2] A.E. Costley, Nucl. Fus., 56, 066003 (2016). [3] B. Coppi, et al. Nucl. Fus., 55, 053011 (2015). [Preview Abstract] |
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BP10.00067: Verification and optimization of the CFETR baseline scenario D. Zhao, L.L. Lao, O. Meneghini, G.M. Staebler, J. Candy, S.P. Smith, P.B. Snyder, R. Prater, X. Chen, V.S. Chan, J. Li, J. Chen, N. Shi, W. Guo, C. Pan, X. Jian The baseline scenario of China Fusion Engineering Test Reactor (CFETR) was designed starting from 0D calculations. The CFETR baseline scenario satisfies the minimum goal of Fusion Nuclear Science Facility aimed at bridging the gaps between ITER and DEMO. 1.5D calculations are presented to verify the on-going efforts in higher-dimensional modeling of CFETR. Steady-state scenarios are calculated self-consistently by the OMFIT integrated modeling framework that includes EFIT for equilibrium, ONETWO for sources and current, TGYRO for transport. With 68MW of neutral beam power and 8MW of ECH injected to the plasma, the average ion temperature ${\textless$T_i\textgreater}$ is maintained at 15keV, while 150MW fusion power is produced. The neutral beams also drive 55$\%$ of the plasma current. Modest fast ion diffusion will reduce NBCD and affect the profile substantially. Top-launch ECH will increase the current drive and the power absorption rate. EPED model are being included. [Preview Abstract] |
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BP10.00068: Optimization of CFETR confinement by controlling rotation shear and pedestal collisionality Xiang Jian, Jiale Chen, Vincent Chan, Guoqiang Li, Ge Zhuang Optimization of a CFETR baseline scenario (Chan et al 2015 Nucl. Fusion. 55) with EC and NB H{\&}CD is performed using a multi-dimensional code suite. Rotation shear is controlled using NB, with injection angle being constrained to avoid edge heating and to maintain q\textunderscore min \textgreater 2. The NB power is adjusted to keep the plasma fully non-inductive. The NB energy that maximize the fusion gain Q is identified. Trade-off between the pedestal density and temperature is performed with the pedestal pressure fixed. It is found that Q increases with pedestal density, while the density peaking factor (DPF) remains unchanged. Linear analysis shows that the transport is dominated by TEM and ITG turbulence. Collisionality affects these turbulences in such a way that the induced changes in DPF cancel out. A weaker dependence of DPF makes higher density operation more favorable for fusion gain. [Preview Abstract] |
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BP10.00069: A Multi Fluid Analysis of the Ignition Criterion Luca Guazzotto, Riccardo Betti In magnetic confinement nuclear fusion experiments, performance with respect to ignition is expressed in terms of the Lawson criterion, a zero-dimensional, single-fluid, steady-state power balance expressing the plasma properties needed for ignition through the energy confinement time $\tau_E$ and the plasma temperature and density. Several improvements to the classical criterion are investigated. Ions, electrons and $\alpha$ particles are allowed to have different energy confinement times and energy coupling times are expressed through physics-based relations. The effect of multi-fluid physics is examined in a steady-state analysis and for the time-dependent case, which requires a nonlinear treatment more detailed than the standard ``$\dot T$ vs$.$ $T$'' single-fluid one. A one-dimensional analysis is also considered to investigate the importance of density and temperature profiles on the $\tau_E$ needed for ignition. Rather than by solving the 1D transport equations, this is done with a parametric study. \begin{enumerate} \item[[1$\! \! \!$]] J. D. Lawson, Proc. Phys. Soc. London Sect. B 70, 6 (1957) \item[[2$\! \! \!$]] J. P. Freidberg, Plasma Physics and Fusion Energy, Cambridge University Press, Cambridge UK, 2007 \end{enumerate} [Preview Abstract] |
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BP10.00070: RECONNECTION AND SELF ORGANIZATION |
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BP10.00071: Pressure and Density Scaling in the High-Energy Trapping Distribution During Reconnection Peter Montag, Jan Egedal The trapping distribution is a model of the electron distribution function that posits two regions of velocity space: a ``passing" particle region where electrons are fed in from an external Maxwellian distribution and a ``trapped" particle region with Maxwellian distribution in perpendicular velocity and uniform distribution in parallel velocity. The boundary between trapped and passing is determined by the parallel electric field and the magnetic mirror force. This has proven a simple but accurate model of the electron distribution function in the inflow region during reconnection, and the simplicity of this model allows for analytic calculation of the moments. The results of this calculation can be used to determine asymptotic forms of the scaling laws of the plasma parameters. Additionally, the model can be straightforwardly extended to the relativistic limit, and reasonably accurate approximations to the scaling laws in that limit are also obtained. [Preview Abstract] |
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BP10.00072: Cluster observation of electron energization during the magnetospheric reconnection. Harsha Gurram, Jan Egedal In situ spacecraft measurements in the Earths magnetosphere have shown that magnetic reconnection energizes the electrons and a source of the suprathermal electrons. This study investigates the electron distribution functions and electron heating recorded by the Cluster Mission during the reconnection event on August 21, 2002 in the interval 0754 to 0825. This event exhibits a flow reversal with the characteristic isotropic flat-top distribution around the flow reversal namely near the X-line. The distribution function measurements near reconnection reveal the presence of cold beams directed towards the X-line while the energized electrons are seen to be moving away from the reconnection region. The electrons see an increase in their bulk energy by a factor of 100 from the inflow to exhaust. The observed beam like features are in good agreement with the kinetic simulations and confirm the model for electron energization in reconnection exhaust[1]. [1]J.Egedal & W.Daughton,A.Le and A.L.Borg (2015), Phy. Plasmas [Preview Abstract] |
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BP10.00073: Pressure Anisotropy Probe for the Terrestrial Reconnection Experiment (TREX) Rachel Myers, Jan Egedal, Joseph Olson, Samuel Greess, Michael Clark, Paul Nonn, John Wallace, Cary Forest The Terrestrial Reconnection Experiment (TREX) at the Wisconsin Plasma Astrophysics Laboratory (WiPAL) studies magnetic reconnection primarily in the collisionless regime. In this regime, electron pressure anisotropy is expected to develop, deviating from traditional Hall reconnection dynamics and driving formation of large-scale current layers. In order to measure the anisotropy, a multi-tip electromagnetic probe similar to the M-probe described by Shadman [1], consisting of 32 Langmuir probe tips and two magnetic coils, has been constructed. Each tip is biased to a different potential, simultaneously measuring discrete parts of the full I-V characteristic. Pulsing the coil then locally increases the magnetic field, creating a magnetic mirror force to reflect electrons with large values of $v_{\perp}/v$. The change in electron velocity modifies the I-V characteristics and can be used to infer $p_{\parallel}/p_{\perp}$. Analysis with the new probe will be presented. [1] K. Shadman, Physics of Plasmas (2004). [Preview Abstract] |
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BP10.00074: Sub-ion scale plasmoids during collisionless reconnection on TREX Joseph Olson, Jan Egedal, Rachel Myers, Sam Greess, Mike Clark, John Wallace, Cary Forest The Terrestrial Reconnection Experiment (TREX), operating at the Wisconsin Plasma Astrophysics Laboratory\footnote{C.B. Forest \textit{et al.}, JPP (2015)}, is able to explore a collisionless regime inaccessible to previous reconnection experiments. To date, TREX has already achieved Lundquist numbers up to $10^4$ where kinetic effects, such as electron pressure anisotropy, become important to the reconnection dynamics\footnote{A. Le \textit{et al.}, JPP (2015)}. During a recent run campaign in this collisionless regime, the spontaneous formation of magnetic islands (plasmoids) inside the ion diffusion region was observed. It is known that long current layers are susceptible to tearing, leading to the formation of plasmoids, and that these plasmoids have strong effects on the reconnection rate and particle energization. However, contrary to theoretical and numerical predictions, the TREX experiments show that the plasmoid instability is active even when the current layer is less than one $d_i$ long\footnote{J. Olson \textit{et al.}, PRL (2016)}. Analysis of these events shows that smaller plasmoids occur at a higher rate than larger ones, suggesting that magnetic islands could be seeded in plasmas more effectively than previously thought. [Preview Abstract] |
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BP10.00075: Kinetic Structures Associated with Asymmetric Magnetic Reconnection in MMS Observations Blake Wetherton, Jan Egedal, Ari Le, William Daughton Magnetic reconnection is inherently linked to the kinetic behavior of electrons as they decouple from the field lines in the electron diffusion region. As such, the kinetic evolution of the electron distribution function is of particular interest. In fact, elucidating these electron dynamics is a significant goal of NASA's current Magnetospheric Multiscale (MMS) mission, which is now taking measurements in the magnetopause reconnection region. The asymmetric nature of the magnetopause gives rise to interesting particle dynamics, such as seemingly agyrotropic crescent-shaped electron distribution functions that are observed by MMS spacecraft. Using data from kinetic simulations and MMS spacecraft, this study examines electron kinetic structures in asymmetric reconnection. A drift kinetic model is used to interpret electron distribution function data and identify structures of the reconnection geometry. In particular, it is found that most of the observed agyrotropic features can be accounted for by well-magnetized electrons in the framework of drift kinetic theory. [Preview Abstract] |
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BP10.00076: Second Generation Magnetic Flux Array for the Terrestrial Reconnection Experiment (TREX) Samuel Greess, Jan Egedal, Joe Olson, John Wallace, Mike Clark, Cary Forest TREX, part of the Wisconsin Plasma Astrophysics Laboratory, studies magnetic reconnection in a variety of regimes. In its prior configuration, TREX used two coils inside a 3m spherical vacuum vessel filled with plasma to create a magnetic field opposing a background field from an external Helmholtz coil, driving reconnection. In order to study the reconnection process, we first constructed a 160 channel Magnetic Flux Array, which allowed us to infer the flux function, $\Psi $, and thus the toroidal component of the vector potential, \textbf{A}$\phi $, as a function of time over the array area. From \textbf{A}$\phi $, we further found the field geometry, current density, and reconnection rate [1]. Following the success of this array [2], a second array was constructed with similar parameters but with the addition of a thin stainless steel shield to reduce noise and a set of toroidal field Bdot coils. Data from this second array in the most recent run of TREX will be presented and compared to the results from the first array. [1] Kesich et al., Review of Scientific Instruments 79,063505 (2008). [2] Olson et al., PRL (2016) [Preview Abstract] |
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BP10.00077: Magnetic pumping as a source of particle heating Emily Lichko, Jan Egedal, William Daughton, Justin Kasper Magnetic pumping is a means of heating plasmas for both fusion and astrophysical applications. This study presents a generalized model, related to the compressional pumping model Fisk \& Gloeckler applied to the solar wind (2006). Unlike previous models, this model includes diffusion of the anisotropic features which develop in velocity space, thereby allowing energy to be transferred to the particles directly from the turbulence. By using various orderings, the drift kinetic equation can be reduced to a more general form of Parker's equation with an anisotropic distribution function. Through expansions in both pitch angle and in space, it can be shown that this equation has power law solutions and results in an overall heating of the plasma. This form of heating is related to transit-time damping. Kinetic simulations were performed to test the theoretical model and explore regimes where spatial and velocity diffusion are of the same order of importance, regimes not easily available to analytical calculations. These simulations appear to confirm the pumping model in the appropriate limits. \\ \\ Fisk L.A. \& Gloeckler, G. (2006), Astrophys. J. 640, L79. [Preview Abstract] |
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BP10.00078: Is there a fundamental principle for energy partitioning in a proto-typical reconnection layer? Masaaki Yamada, Jongsoo Yoo, Russell Kulsrud Recently, a quantitative inventory of magnetic energy conversion in a proto-typical reconnection layer was experimentally studied in MRX with a well-defined boundary [1,2]. This study concluded that about half the inflowing magnetic energy is converted to particle energy, while more energy is partitioned to ions. This observation was found to be consistent with numerical simulation results based on VPIC codes [3]. It was also found that features of energy conversion and partitioning do not strongly depend on the size of the analysis region. A question arises, whether there is a fundamental principle in the energy partitioning in a proto-typical reconnection layer. This talk presents our physics analysis of the energy conversion processes in the magnetic reconnection layer of two-fluid physics regime. The flows of electrons at the reconnection layer lead to a formation of strong electrostatic field in the reconnection plane causing ion acceleration and resultant ion heating. Based on the two-fluid features, a quantitative analytical model of energy partitioning will be presented. [1] M. Yamada et al, Nature Communications. $\bf{5}$, 4774 (2014) [2] M. Yamada et al, Phys. Plasmas, $\bf{23}$, 055402 (2016) [3] K.J. Bowers et al, Phys. Plasmas, $\bf{15}$, 055703 (2008) [Preview Abstract] |
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BP10.00079: Laboratory study of magnetic reconnection with a guide field and density asymmetry across the current sheet Hongxuan Zhu, J. Yoo, H. Ji, J. Jara-Almonte, W. Fox, M. Yamada It has been known that the diamagnetic drift can stabilize the tearing mode, which is used to explain incomplete reconnection during sawtooth oscillations in Tokamaks [1]. Swisdak et al. propose that reconnection with a strong guide field and pressure asymmetry is suppressed when the relative drift speed between ions and electrons along the outflow direction exceeds the upstream Alfv\'{e}n speed [2]. Swisdak's argument has been supported by space observations [3], but the exact mechanism of suppression has not been conclusively verified. We will conduct experiments in MRX to study suppression of reconnection with a strong guide field and density asymmetry. We will apply a guide field strength of about 2--3 times of the reconnecting field and achieve a density ratio up to 10. By systematically changing the guide field strength, we will investigate how the electron diamagnetic drift can affect profiles of the magnetic/electric field and patterns of the ion/electron flow. Finally, we will study how these modified field profiles and flow patterns contribute to reduction of the reconnection rate. [1] B. Rogers and L. Zakharov, Phys. Plasmas 2, 3420 (1995). [2] M. Swisdak et al., J. Geophys Res. 108, A5 (2003). [3] T. D. Phan et al., Geophys. Res. Lett. 40, 11 (2013). [Preview Abstract] |
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BP10.00080: Development and construction of a comprehensive set of research diagnostics for the FLARE user facility Jongsoo Yoo, J. Jara-Almonte, S. Majeski, S. Frank, H. Ji, M. Yamada FLARE (Facility for Laboratory Reconnection Experiments) will be operated as a flexible user facility, and so a complete set of research diagnostics is under development, including magnetic probe arrays, Langmuir probes, Mach probes, spectroscopic probes, and a laser interferometer. In order to accommodate the various requirements of users, large-scale (1 m), variable resolution (0.5–4 cm) magnetic probes have been designed, and are currently being prototyped. Moreover, a fully fiber-coupled laser interferometer has been designed to measure the line-integrated electron density. This fiber-coupled interferometer system will reduce the complexity of alignment processes and minimize maintenance of the system. Finally, improvements to the electrostatic probes and spectroscopic probes currently used in the Magnetic Reconnection Experiment (MRX) are discussed. The specifications of other subsystems, such as integrators and digitizers, are also presented. [Preview Abstract] |
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BP10.00081: Status of the FLARE (Facility for Laboratory Reconnection Experiments) Construction Project and Plans as a User Facility H. Ji, A. Bhattacharjee, S. Prager, W. Daughton, Y. Chen, R. Cutler, W. Fox, F. Hoffmann, M. Kalish, J. Jara-Almonte, C. Myers, Y. Ren, M. Yamada, J. Yoo, S.D. Bale, T. Carter, S. Dorfman, J. Drake, J. Egedal, J. Sarff, J. Wallace The FLARE device (flare.pppl.gov) is a new intermediate-scale plasma experiment under construction at Princeton for the studies of magnetic reconnection in the multiple X-line regimes directly relevant to space, solar, astrophysical, and fusion plasmas, as guided by a reconnection phase diagram [Ji \& Daughton, (2011)]. Most of major components either have been already fabricated or are near their completion, including the two most crucial magnets called flux cores. The hardware assembly and installation begin in this summer, followed by commissioning in 2017. Initial comprehensive set of research diagnostics will be constructed and installed also in 2017. The main diagnostics is an extensive set of magnetic probe arrays, covering multiple scales from local electron scales, to intermediate ion scales, and global MHD scales. The planned procedures and example topics as a user facility will be discussed. [Preview Abstract] |
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BP10.00082: Development of a new experimental device for long-duration magnetic reconnection in weakly ionized plasma Ryoma Yanai, Yasuhiro Kaminou, Kento Nishida, Michiaki Inomoto Magnetic reconnection is a universal phenomenon which determines global structure and energy conversion in magnetized plasmas. Many experimental studies have been carried out to explore the physics of magnetic reconnection in fully ionized condition. However, it is predicted that the behavior of magnetic reconnection in weakly ionized plasmas such as solar chromosphere plasma will show different behavior such as ambipolar diffusion caused by interaction with neutral particles. In this research, we are developing a new experimental device to uncover the importance of ambipolar diffusion during magnetic reconnection in weakly ionized plasmas. We employ an inverter-driven rotating magnetic fields technique, which is used for generating steady azimuthal plasma current, to establish long-duration (\textasciitilde 1 ms) anti-parallel reconnection with magnetic field of \textasciitilde 5 mT in weakly ionized plasma. We will present development status and initial results from the new experimental setup. This work was supported by JSPS A3 Foresight Program “Innovative Tokamak Plasma Startup and Current Drive in Spherical Torus”, Giant-in Aid for Scientific Research (KAKENHI) 15H05750, 15K14279, 26287143 and the NIFS Collaboration Research program (NIFS14KNWP004). [Preview Abstract] |
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BP10.00083: Measurement of Ohms Law and Transport with Two Interacting Flux Ropes. Walter Gekelman, Tim DeHaas, Steve Vincena, Bill Daughton Two flux ropes, which are kink unstable, and repeatedly collide, were generated in a laboratory magnetoplasma. All the electric field terms in Ohms law: $-\nabla \phi -\frac{\partial \vec{{A}}}{\partial t},\frac{1}{ne}\vec{{J}}\times \vec{{B}},\mbox{-}\frac{1}{ne}\nabla P,\vec{{u}}\times \vec{{B}}$ were measured at 48,000 spatial locations and thousands of time steps. All quantities oscillate at the flux rope collision frequency. The resistivity was derived from these quantities and could locally be 30 times the classical value. The resistivity, which was evaluated by integrating the electric field and current along 3D magnetic field is not largest at the quasi-seperatrix layer (QSL) where reconnection occurs. The relative size and spatial distribution of the Ohms law terms will be presented. The reconnection rate, $\Xi =\int\limits {\vec{{E}}\cdot d\vec{{l}}} $was largest near the QSL and could be positive or negative. Regions of negative resistivity exists (the volume integrated resistivity is positive) indicating dynamo action or the possibility of a non-local Ohms law. Volumetric temperature and density measurements are used to estimate electron heat transport and particle diffusion across the magnetic field. [Preview Abstract] |
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BP10.00084: Measurements of Magnetic Helicity within Two Interacting Flux Ropes Timothy DeHaas, Walter Gekelman Magnetic helicity (H$_{\mathrm{M}})$ has become a useful tool in the exploration of astrophysical plasmas. Its conservation in the MHD limit (and even some fluid approaches) constrains the global behavior of large plasma structures. One such astrophysical structure is a magnetic flux rope: a rope-like, current-carrying plasma embedded in an external magnetic field. Bundles of these ropes are commonly observed extending from the solar surface and can be found in the near-earth environment. In this well-diagnosed experiment (3D measurements of n$_{\mathrm{e}}$, T$_{\mathrm{e}}$, V$_{\mathrm{p}}$, \textbf{B}, \textbf{J}, \textbf{E}, \textbf{u}$_{\mathrm{\mathbf{flow}}})$, two magnetic flux ropes were generated in the Large Plasma Device at UCLA. These ropes were driven kink-unstable, commencing complex motion. As they interact, helicity conservation is broken in regions of reconnection, turbulence, and instabilities. The changes in helicity can be visualized as 1) the transport of helicity ($\phi $\textbf{B}$+$\textbf{E}$\times$ \textbf{A)} and 2) the dissipation of the helicity (-2\textbf{E}\textbullet \textbf{B}). Magnetic helicity is observed to have a negative sign and its counterpart, cross helicity, a positive one. These qualities oscillate 8{\%} peak-to-peak. As the ropes move and the topology of the field lines change, a quasi-separatrix layer (QSL) is formed. The volume averaged H$_{\mathrm{M}}$ and the largest value of Q both oscillate but not in phase. In addition to magnetic helicity, similar quantities such as self-helicity, mutual-helicity, vorticity, and canonical helicity are derived and will be presented. [Preview Abstract] |
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BP10.00085: Nonlinear interactions of kink-unstable flux ropes and shear Alfv\'{e}n waves S. Vincena, W. Gekelman, T. DeHaas, S.K.P. Tripathi Magnetic flux ropes and shear Alfv\'{e}n waves occur simultaneously in plasmas ranging from solar prominences, the solar wind, and the earth's magnetotail. If the flux ropes evolve to become unstable to the kink mode, interactions between the kink oscillations and the shear waves can arise, and may even lead to nonlinear phenomena. Experiments aimed at elucidating such interactions are performed in the upgraded Large Plasma Device at UCLA. Flux ropes are generated using a 20 cm $\times$ 20 cm LaB$_{6}$ cathode discharge (with L=18 m and $\beta\sim 0.1$.) The ropes are embedded in a otherwise current-free, cylindrical ($r=30$cm) ambient plasma produced by a second, BaO cathode. Shear Alfv\'{e}n waves are launched using either internal antennas, or by modulating the BaO cathode-anode discharge current. In the latter case, kink unstable oscillations and driven shear waves nonlinearly generate sidebands about the higher shear wave frequency (evident in power spectra) via three-wave coupling; this is demonstrated though bi-coherence calculations and k-matching. Informational complexity and entropy of the time series are also investigated. Future work will focus on antenna-launched waves to control amplitude and frequency, as well as a possible evolution to a turbulent state. [Preview Abstract] |
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BP10.00086: Hard X-Ray Burst Detected From Caltech Plasma Jet Experiment Magnetic Reconnection Event Ryan S. Marshall, Paul M. Bellan In the Caltech plasma jet experiment a 100 kA MHD driven jet becomes kink unstable leading to a Rayleigh-Taylor instability that quickly causes a magnetic reconnection event. Movies show that the Rayleigh-Taylor instability is simultaneous with voltage spikes across the electrodes that provide the current that drives the jet. Hard x-rays between 4 keV and 9 keV have now been observed using an x-ray scintillator detector mounted just outside of a kapton window on the vacuum chamber. Preliminary results indicate that the timing of the x-ray burst coincides with a voltage spike on the electrodes occurring in association with the Rayleigh-Taylor event. The x-ray signal accompanies the voltage spike and Rayleigh-Taylor event in approximately 50{\%} of the shots. A possible explanation for why the x-ray signal is sometimes missing is that the magnetic reconnection event may be localized to a specific region of the plasma outside the line of sight of the scintillator. The x-ray signal has also been seen accompanying the voltage spike when no Rayleigh-Taylor is observed. This may be due to the interframe timing on the camera being longer than the very short duration of the Rayleigh-Taylor instability. [Preview Abstract] |
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BP10.00087: Three-dimensional two-fluid investigation of 3D-localized magnetic reconnection and its relation to whistler waves Young Dae Yoon, Paul M. Bellan A full three-dimensional computer code was developed in order to simulate a 3D-localized magnetic reconnection. We assume an incompressible two-fluid regime where the ions are stationary, and electron inertia and Hall effects are present. We solve a single dimensionless differential equation for perturbed magnetic fields with arbitrary background fields. The code has successfully reproduced both experimental and analytic solutions to resonance and Gendrin mode whistler waves in a uniform background field. The code was then modified to model 3D-localized magnetic reconnection as a 3D-localized perturbation on a hyperbolic-tangent background field. Three-dimensional properties that are asymmetric in the out-of-plane direction have been observed. These properties pertained to magnetic field lines, electron currents and their convection. Helicity and energy have also been examined, as well as the addition of a guide field. [Preview Abstract] |
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BP10.00088: The role of kinetic ions in magnetic reconnection Adam Stanier, William Daughton, Andrei Simakov, Luis Chacon, Ari Le, Homa Karimabadi, Jonathan Ng, Amitava Bhattacharjee To explain many magnetised plasma phenomena in nature and the laboratory, it is important to understand how the rates of magnetic reconnection behave in large and weakly collisional systems. A key question concerns what physics must be retained within reduced models to be able to reproduce the reconnection rates and global behaviour of fully kinetic systems. Here we model the coalescence of magnetic islands with a range of guide fields that have application to the Earth's magnetosphere. It is demonstrated that the Hall-MHD model is able to reproduce the reconnection rates of the fully kinetic system only in the presence of a fairly strong guide field ($B_g\geq 3B_x$). In the weak guide field limit non-isotropic ion pressure tensor effects that are missing from Hall-MHD are crucial to describe many key features of this reconnection test-problem [1], including the peak and average rates, pile-up field, outflow velocity, and global evolution of the system. A hybrid model which retains the full kinetic physics for ions along with mass-less fluid electrons gives good agreement with fully kinetic results for the full range of guide fields considered. These results suggest that kinetic ions may be important for a large number of reconnection events in the Earth's magnetosphere. [Preview Abstract] |
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BP10.00089: Collisionless Magnetic Reconnection as an Ion Acceleration Mechanism of Low-$\beta$ Laboratory Plasmas Emanuele Cazzola, Davide Curreli, Giovanni Lapenta In this work we present the results from a series of fully-kinetic simulations of magnetic reconnection under typical laboratory plasma conditions. The highly-efficient energy conversion obtained from this process is of great interest for applications such as future electric propulsion systems and ion beam accelerators. We analysed initial configurations in low-beta conditions with reduced mass ratio of mi = 512me at magnetic fields between 200G and 5000G and electron temperatures between 0.5 and 10eV. The initial ion density and temperature are kept uniform and equal to 10$^{19}$ m$^{-3}$ and 0.0215eV (room temperature) respectively. The analysis has shown that the reconnection process under these conditions can accelerate ions up to velocities as high as a significant fraction of the inflow Alfven speed. The configuration showing the best scenario is further studied with a realistic mass ratio in terms of energetics and outflow ion momentum, with the latter featured by the traditionally used specific impulse. Finally, a more detailed analysis of the reconnection outflow has revealed the formation of different interesting set of shock structures, also recently seen from MHD simulations of relativistic plasmas and certainly subject of future more careful attention. [Preview Abstract] |
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BP10.00090: 3-D Electromagnetic Instabilities in Current Sheet Zhenyu Wang, Yu Lin, Xueyi Wang, Liu Chen, Kurt Tummel 3-D electromagnetic instabilities in a Harris current sheet with a finite guide magnetic field $B_{G}$ are systematically studied by employing the gyrokinetic electron and fully kinetic ion (GeFi) particle model with a realistic mass ratio $m_i/m_e$. Our studies show that lower-hybrid drift instability (LHDI) with $k\sqrt{\rho_i\rho_e} \sim 1$ and drift kink instability (DKI) and drift sausage instability (DSI) with $k\rho_i \sim 1$ are excited in the current sheet. The most unstable DKI is away from $\mathbf{k} \cdot \mathbf{B}=0$, and the most unstable DSI is at $\mathbf{k} \cdot \mathbf{B}=0$, where $\mathbf{k} \equiv (k_x, k_y)$, with $k_x$ being along the anti-parallel field direction and $k_y$ is along the current direction. On the other hand, an instability with a compressional magnetic field perturbation located at the center of current sheet is also excited under a relatively large $B_G$, and its maximum growth rate is at $\mathbf{k} \times \mathbf{B} = 0$. The presence and structure of these instabilities as a function of $B_G$ is presented. The GeFi simulation results are compared with those from the fully kinetic particle simulation. [Preview Abstract] |
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BP10.00091: Particle-in-cell simulations of Magnetic Field Generation, Evolution, and Reconnection in Laser-driven Plasmas Jack Matteucci, Clément Moissard, Will Fox, Amitava Bhattacharjee The advent of high-energy-density physics facilities has introduced the opportunity to experimentally investigate magnetic field dynamics relevant to both ICF and astrophysical plasmas. Recent experiments have demonstrated magnetic reconnection between colliding plasma plumes, where the reconnecting magnetic fields were self-generated in the plasma by the Biermann battery effect. In this study, we simulate these experiments from first principles using 2-D and 3-D particle-in-cell simulations. Simulations self-consistently demonstrate magnetic field generation by the Biermann battery effect, followed by advection by the Hall effect and ion flow. In 2-D simulations, we find in both the collisionless case and the semi-collisional case, defined by $eV_i \times B$ $\gg$ $R_{ei}/n_e$ (where $R_{ei}$ is the electron ion momentum transfer) that quantitative agreement with the generalized Ohm's law is only obtained with the inclusion of the pressure tensor. Finally, we document that significant field is destroyed at the reconnection site by the Biermann term, an inverse, `anti-Biermann' effect, which has not been considered previously in analysis of the experiment. The role of the anti-Biermann effect will be compared to standard reconnection mechanisms in 3-D reconnection simulations. [Preview Abstract] |
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BP10.00092: Visco-resistive plasmoid instability in Sweet-Parker current sheets Daniela Grasso, Luca Comisso The linear analysis by Loureiro et al. [1] is generalized to investigate the plasmoid instability in visco-resistive Sweet-Parker sheets [2]. We cover both the linear and nonlinear growth of the plasmoids. The linear growth rate and the wavenumber scale as $S^{1/4} (1+P_m)^{-5/8}$ and $S^{3/8} (1+P_m)^{-3/16}$ with respect to the Lundquist number $S$ and the magnetic Prandtl number $P_m$. The growth of the plasmoids slows down from an exponential growth to an algebraic growth when they enter into the nonlinear regime. The time-scale of the nonlinear growth of the plasmoids is found to be $\tau_{NL} \sim S^{-3/16} (1+P_m)^{19/32} \tau_{A,L}$. We also discuss how the plasmoid instability can enable fast magnetic reconnection [3] in visco-resistive plasmas [4]. In this regime, the global reconnection rate is shown to be $\left\langle {{\left. {d\psi /dt} \right|}_X} \right\rangle \approx 0.01 v_{A,u} B_u (1+P_m)^{-1/2}$ [2]. [1] N.F. Loureiro, A.A. Schekochihin and S.C. Cowley, Phys. Plasmas 14, 100703 (2007). [2] L. Comisso and D. Grasso, Phys. Plasmas 23, 032111 (2016) [3] A. Bhattacharjee, Y.-M. Huang, H. Yang and B. Rogers, Phys. Plasmas 16, 112102 (2009). [4] L. Comisso, D. Grasso and F.L. Waelbroeck, Phys. Plasmas 22, 042109 (2015). [Preview Abstract] |
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BP10.00093: Enhanced Electron Heating and Mixing in a 3D Kinetic Simulation for MMS Magnetopause Crossings with Weak Guide Fields Ari Le, William Daughton, Li-Jen Chen, Jan Egedal We present a 3D kinetic simulation of asymmetric reconnection with plasma parameters matching the MMS magetopause diffusion region crossing reported by Burch et al. (Science 2016). The simulation was performed with the code VPIC on LANL's Trinity machine, which enabled relatively high grid resolution and numerical particle numbers to resolve the electron diffusion region dynamics. The simulation not only reproduces the reported crescent distributions but also appears to account for new features observed by MMS in other diffusion region events with weak guide fields. Compared to a 2D simulation with the same plasma parameters, drift turbulence in the 3D simulation substantially enhances the mixing and parallel heating of electrons on the magnetosphere side. This modifies the reconnection rate inferred from a recently introduced electron mixing diagnostic. To the magnetosphere side of the in-plane magnetic null, the parallel electric field exhibits a bipolar structure with polarities opposite to the large-scale parallel electric field. The 3D structure of the X line and the particle signature of the inverted bipolar parallel electric field have been observed by MMS. [Preview Abstract] |
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BP10.00094: Generalized Plasmoid Instability in Time Evolving Current Sheets Luca Comisso, Manasvi Lingam, Yi-Min Huang, Amitava Bhattacharjee In the widely studied Sweet-Parker current sheets, the plasmoid instability grows at a rate proportional to $S$ (Lundquist number) raised to a fractional positive exponent [1,2]. This implies that in large S systems, Sweet-Parker current sheets cannot be attained as current layers are linearly unstable and disrupt before this state is achieved. Here, we formulate a quantitative and mathematically precise theory of the plasmoid instability in time evolving current sheets based on a principle of least time [3]. We obtain the scaling relations for the growth rate, number of plasmoids, aspect ratio, plasmoid width and onset time. They are shown to depend on the initial perturbation amplitude, the characteristic rate of current sheet evolution, and the Lundquist number. An important finding of this analysis is that the final results are not simple power laws. The detailed dynamics of the instability is also elucidated, and shown to comprise of a long period of quiescence followed by sudden growth over a short time scale. [1] N.F. Loureiro, A.A. Schekochihin and S.C. Cowley, Phys. Plasmas 14, 100703 (2007) [2] L. Comisso and D. Grasso, Phys. Plasmas 23, 032111 (2016) [3] L. Comisso, M. Lingam, Y.-M. Huang, A. Bhattacharjee, submitted to Phys. Rev. Lett. (2016) [Preview Abstract] |
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BP10.00095: Onset of Plasmoid Instability in an Evolving Current Sheet Yi-Min Huang, Luca Comisso, A. Bhattacharjee Abstract The scaling of plasmoid instability linear growth rate with respect to Lundquist number S in a Sweet-Parker current sheet, $\gamma\sim S^{1/4}$, indicates that at high S, the current sheet will break apart before it approaches the Sweet-Parker width. Therefore, a proper description for the onset of the plasmoid instability must incorporate the thinning process of the current sheet. We carry out a series of 2D simulations and develop diagnostics to separate fluctuations from an evolving background. It is found that the fluctuation amplitude starts to grow only when the linear growth rate is sufficiently large ($\gamma\tau_{A}\gtr sim 1$) to overcome convective losses. The linear growth rate continues to rise until the sizes of plasmoids become comparable to the inner layer width of the tearing mode. At this point the current sheet is disrupted and the instability enters the early nonlinear regime. The growth rate suddenly decreases, but the fluctuation amplitude continues to grow until it reaches nonlinear saturation. We identify important time scales of the instability development, as well as scalings for linear growth rate, current sheet width, and dominant wavenumber at current sheet disruption. A phenomenological model that reproduces simulation results is proposed. [Preview Abstract] |
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BP10.00096: Energy principle for a gyrofluid model and variational description of collisionless tearing modes Makoto Hirota, Philip J. Morrison Linear stability of a four-field gyrofluid model is investigated by formulating the corresponding "energy principle", which is well-known as an established tool for ideal magnetohydrodynamic (MHD) stability. By assuming static equilibria (no flow as well as no diamagnetic drift), the eigenvalue problem is shown to be self-adjoint and the most unstable mode can be found by minimizing a potential energy. The process of deriving this energy principle differs in many respects from the direct application of the energy-Casimir method. It can be shown by the energy principle that the ion's compressibility effect tends to diminish the growth rate (as is the case with ideal MHD) whereas the finite-Larmor-radius effect tends to enhance it. On the other hand, the stability boundary is not affected by them but determined by the incompressible-MHD potential energy with a destabilizing effect of the electron inertia. This energy principle is applied to collisionless tearing modes. By substituting a simple trial function that includes only two parameters and minimizing the potential energy with respect to them, the estimated growth rate is found to agree with the dispersion relations derived by asymptotic matching. The parameters are, in fact, related to the widths of two nested inner layers. [Preview Abstract] |
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BP10.00097: Proton acceleration in three-dimensional non-null magnetic reconnection Mahboub Hosseinpour In a 3D non-null magnetic reconnection the process of magnetic reconnection takes place in the absence of a null point where magnetic field vanishes. By randomly injecting a population of 10,000 protons, the trajectory and energy distribution of accelerated protons are investigated in the presence of magnetic and electric fields of a particular model of non-null magnetic reconnection. The results show that protons are accelerated along the magnetic field lines away from the non-null point only at azimuthal angles where the magnitude of electric field is strongest and therefore particles obtain kinetic energies on the order of thousands of MeV and even higher. Moreover, the energy distribution of the population depends strongly on the amplitude of the electric and magnetic fields. Comparison shows that a non-null magnetic reconnection is more efficient in accelerating protons to very high GeV energies than a null-point reconnection. [Preview Abstract] |
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BP10.00098: A nonlocal fluid closure for antiparallel reconnection Jonathan Ng, A Hakim, A Bhattacharjee The integration of kinetic effects in fluid models is an important problem in global simulations of the Earth’s magnetosphere and space weather modelling. In particular, it has been shown that ion kinetics play an important role in the dynamics of large reconnecting systems, and that fluid models can account of some of these effects[1,2] . Here we introduce a new fluid model and closure for collisionless magnetic reconnection and more general applications. Taking moments of the kinetic equation, we evolve the full pressure tensor for electrons and ions, which includes the off diagonal terms necessary for reconnection. Kinetic effects are recovered by using a nonlocal heat flux closure, which approximates linear Landau damping in the fluid framework [3]. Using the island coalescence problem as a test, we show how the nonlocal ion closure improves on the typical collisional closures used for ten-moment models and circumvents the need for a colllisional free parameter. Finally, we extend the closure to study guide-field reconnection and discuss the implementation of a twenty-moment model. [1] A. Stanier et al. Phys Rev Lett (2015) [2] J. Ng et al. Phys Plasmas (2015) [3] G. Hammett et al. Phys Rev Lett (1990) [Preview Abstract] |
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BP10.00099: PIC simulation studies of merging processes of spheromak-like and spherical-tokamak-like plasmoids Ritoku Horiuchi, Shunsuke Usami Two different types of merging processes of two plasmoids have been examined by means of two-dimensional PIC simulation. One is a counter helicity merging process of two spheromak-like (SP) plasmoids without any guide field component perpendicular to reconnection magnetic field. The other is a merging process of two spherical-tokamak-like (ST) plasmoids with a strong guide field in a reconnection region. In contrast to collisionless reconnection in an open system, most of plasma and energy are confined inside a newly formed plasmoid after the merging in the present simulation. By comparing the simulation results, we have examined the detailed mechanisms of merging and energy transfer processes for two cases, and clarified the guide field dependence. It is found that the merging process is suppressed due to the strong guide field for the ST case, while the EM energy is efficiently transferred to particles through the merging process for the SP case. The detailed mechanism will be discussed in the presentation. [Preview Abstract] |
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BP10.00100: Energy Conversion Mechanism for Electron Perpendicular Energy in High Guide-Field Reconnection Xuehan Guo, Ritoku Horiuchi, Yasuhiro Kaminou, Frank Cheng, Yasushi Ono The energy conversion mechanism for electron perpendicular energy, both the thermal and the kinetic energy, is investigated by means of two-dimensional, full-particle simulations in an open system. It is shown that electron perpendicular heating is mainly due to the breaking of magnetic moment conservation in separatrix region because the charge separation generates intense variation of electric field within the electron Larmor radius. Meanwhile, electron perpendicular acceleration takes place manly due to the polarization drift term as well as the curvature drift term of $\bm E \cdot \bm u_\perp$ in the downstream near the X-point. The enhanced electric field due to the charge separation there results in a significant effect of the polarization drift term on the dissipation of magnetic energy within the ion inertia length in the downstream. [Preview Abstract] |
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BP10.00101: Magneto-thermal Reconnection Processes, Related Angular Momentum Transport issues and Formation of High Energy Particle Populations* B. Coppi, B. Basu, A. Fletcher The two-fluid theory of magnetic reconnection [1], when the longitudinal electron thermal conductivity is relatively large, shows that the perturbed electron temperature tends to become singular [2] in the presence of a reconnected field component and an electron temperature gradient. A transverse thermal diffusivity can remove this singularity while a finite ``inductivity'' can remove the singularity of the corresponding plasma displacement [1]. Then i) a new ``magneto-thermal reconnection'' producing mode, driven by the electron temperature gradient, is found [2]; ii) the characteristic widths of the layers where reconnection takes place remain significant even when the relevant macroscopic distances are very large; iii) modes with phase velocities both in the electron diamagnetic velocity direction and in the opposite one are found. Their growth rates depend on small dissipative factors. The found modes can extract angular momentum from the plasma and thereby sustain a ``spontaneous rotation'' process [3]. Sponsored by the U.S. D.O.E. [1] B. Coppi, Phys. Fluids 8, 2273 (1965) and B. Coppi, B. Basu, et al. Nucl. Fus., 55, 093018 (2015). [2] B. Coppi, Plasma Phys. Reports, 42, 5, 383 (2016). [3] B. Coppi, Nucl. Fus. 42, (2002). [Preview Abstract] |
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BP10.00102: Magnetic reconnection in three-dimensional magnetohydrodynamic Taylor-Green flows Jinhua Hao, Yue Yang We develop the magnetic-surface field (MSF), a Lagrangian-based structure identification method, to study the evolution of magnetic surfaces in magnetohydrodynamics (MHD). Every isosurface of the MSF defines a magnetic surface consisting of magnetic lines. This method is rooted in the Alfven theorem, which is the analogue of the Helmholtz vorticity theorem to illustrate the “frozen-in” nature of magnetic fields. A two-time approach and a numerical dissipative regularization are introduced for evolving MSF in the conducting fluids with a finite conductivity. From the construction and evolution of MSFs in three-dimensional MHD Taylor-Green (TG-MHD) flows, the topological changes of magnetic surfaces and the reconnection of magnetic lines are characterized. By comparing the structural evolutions in a TG-MHD flow and in a Taylor-Green hydrodynamic (TG-HD) flow, we elucidate the effects of the Lorenz force on the evolution of magnetic surfaces and vortex surfaces. Moreover, we find that the significant changes in energy spectra and dissipation rates in the transition are related to the appearance of some characteristic magnetic and vortex surfaces. [Preview Abstract] |
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BP10.00103: Relativistic Magnetic Reconnection around rotating black holes Felipe Asenjo, Luca Comisso In recent years, the classical Sweet-Parker and Petschek models have been extended in the special relativistic regime, both for MHD plasmas [1] and two-fluid electron-positron plasmas [2]. Nevertheless, there could be situations, like in the vicinity of black holes, where also general relativistic effects can become important. Here, we calculate analytically the reconnection rate and other relevant quantities in a magnetic reconnection process around a rotating black hole. A striking result is that the black hole rotation is capable to produce an enhancement of the rate at which magnetic reconnection proceeds. [1] Y. E. Lyubarsky, Mon. Not. R. Astron. Soc. 358, 113 (2005). [2] L. Comisso and F.A. Asenjo, Phys. Rev. Lett. 113, 045001 (2014). [Preview Abstract] |
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BP10.00104: 3-D MHD modeling and stability analysis of jet and spheromak plasmas launched into a magnetized plasma. Dustin Fisher, Yue Zhang, Ben Wallace, Mark Gilmore, Ward Manchester, C. Nick Arge The Plasma Bubble Expansion Experiment (PBEX) at the University of New Mexico uses a coaxial plasma gun to launch jet and spheromak magnetic plasma configurations into the Helicon-Cathode (HelCat) plasma device. Plasma structures launched from the gun drag frozen-in magnetic flux into the background magnetic field of the chamber providing a rich set of dynamics to study magnetic turbulence, force-free magnetic spheromaks, and shocks. Preliminary modeling is presented using the highly-developed 3-D, MHD, BATS-R-US code developed at the University of Michigan. BATS-R-US employs an adaptive mesh refinement grid that enables the capture and resolution of shock structures and current sheets, and is particularly suited to model the parameter regime under investigation. CCD images and magnetic field data from the experiment suggest the stabilization of an m$=$1 kink mode trailing a plasma jet launched into a background magnetic field. Results from a linear stability code investigating the effect of shear-flow as a cause of this stabilization from magnetic tension forces on the jet will be presented. Initial analyses of a possible magnetic Rayleigh Taylor instability seen at the interface between launched spheromaks and their entraining background magnetic field will also be presented. [Preview Abstract] |
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BP10.00105: Dynamics of Magnetized Plasma Jets and Bubbles Launched into a Background Magnetized Plasma B. Wallace, Y. Zhang, D.M. Fisher, M. Gilmore The propagation of dense magnetized plasma, either collimated with mainly azimuthal B-field (jet) or toroidal with closed B-field (bubble), in a background plasma occurs in a number of solar and astrophysical cases. Such cases include coronal mass ejections moving in the background solar wind and extragalactic radio lobes expanding into the extragalactic medium. Understanding the detailed MHD behavior is crucial for correctly modeling these events. In order to further the understanding of such systems, we are investigating the injection of dense magnetized jets and bubbles into a lower density background magnetized plasma using a coaxial plasma gun and a background helicon or cathode plasma. In both jet and bubble cases, the MHD dynamics are found to be very different when launched into background plasma or magnetic field, as compared to vacuum. In the jet case, it is found that the inherent kink instability is stabilized by velocity shear developed due to added magnetic tension from the background field. In the bubble case, rather than directly relaxing to a minimum energy Taylor state (spheromak) as in vacuum, there is an expansion asymmetry and the bubble becomes Rayleigh-Taylor unstable on one side. Recent results will be presented. [Preview Abstract] |
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BP10.00106: The Mochi project: a field theory approach to plasma dynamics and self-organization Setthivoine You, Jens von der Linden, Eric Sander Lavine, Alexander Card, Evan Carroll The Mochi project is designed to study the interaction between plasma flows and magnetic fields from the point-of-view of canonical flux tubes. The Mochi Labjet experiment is being commissioned after achieving first plasma. Analytical and numerical tools are being developed to visualize canonical flux tubes. One analytical tool described here is a field theory approach to plasma dynamics and self-organization. A redefinition of the Lagrangian of a multi-particle system in fields reformulates the single-particle, kinetic, and fluid equations governing fluid and plasma dynamics as a single set of generalized Maxwell’s equations and Ohm’s law for canonical force-fields. The Lagrangian includes new terms representing the coupling between the motion of particle distributions, between distributions and electromagnetic fields, with relativistic contributions. The formulation shows that the concepts of self-organization and canonical helicity transport are applicable across single-particle, kinetic, and fluid regimes, at classical and relativistic scales. The theory gives the basis for comparing canonical helicity change to energy change in general systems. [Preview Abstract] |
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BP10.00107: The Topology of Canonical Flux Tubes in Flared Jet Geometry Eric Sander Lavine, Setthivoine You Magnetized plasma jets are generally modeled as magnetic flux tubes filled with flowing plasma governed by MHD. We outline here a more fundamental approach based on flux tubes of canonical vorticity. This approach extends the concept of magnetic flux tube evolution to include the effects of finite particle momentum and enables visualization of the topology of plasma jets in regimes beyond MHD. We examine the morphology of these canonical flux tubes for increasing electrical currents, different radial current profiles, different electron Mach numbers, and a fixed, flared, dipole magnetic field. Calculations of gauge-invariant relative canonical helicity track the evolution of magnetic, cross, and kinetic helicities in the system and show that ion flow fields can unwind to compensate for increasing magnetic twist. The results demonstrate that including a species' finite momentum can result in long, collimated canonical vorticity flux tubes even when the magnetic flux tube is flared. With finite momentum, particle density gradients must be normal to canonical vorticities not to magnetic fields, so observations of collimated astrophysical jets could be images of canonical vorticity flux tubes instead of magnetic flux tubes. [Preview Abstract] |
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BP10.00108: Exploring the use of Quadrature Moment Inversion Algorithms in Implicit PIC Simulation David Larson, Ian Bean We report on the use of quadrature moment inversion algorithms [1-3] in implicit particle-in-cell simulation. In particular, we explore their use as a natural means of closing the moment system in the fluid-kinetic PIC method [4]. Results are presented for test problems in 1D1V and extensions to fully implicit simulation are discussed. [1] R.O. Fox, J. Comp. Phys. 227 (2008), [2] O. Desjardins, et. al., J. Comp. Phys. 227 (2008), [3] Yuan, C., and R. O. Fox, J. Comp. Phys. 230 (2011), [4] Markidis, S., et al., J. Comp. Phys. 271 (2014). [Preview Abstract] |
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BP10.00109: Non-modal theory of the ion cyclotron turbulence of the inhomogeneous plasma with a shearing transverse current . Volodymyr S. Mykhaylenko, Volodymyr V. Mykhaylenko, Hae June Lee The non-modal theory of the ion cyclotron turbulence of the inhomogeneous plasma with a shearing transverse current is developed employing the methodology of the shearing modes. The governing equation is the nonlinear integral equation, which determines the temporal evolution of the perturbed electrostatic potential. It accounts for the nonlinear effect of the scattering of ions by the ensemble of ion cyclotron shearing modes. The solutions for this equation are derived for any time interval for the different values of the current velocity, of the velocity shear and wave numbers. The analysis of the temporal evolution of the anomalous ion heating is given. The applications of the developed theory to the space and laboratory plasma are discussed [Preview Abstract] |
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