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At least 235 records · Page 13

An asymptotic-preserving Lagrangian algorithm for the time-dependent anisotropic heat transport equation

We propose a Lagrangian numerical algorithm for a time-dependent, anisotropic temperature transport equation in magnetized plasmas in the large guide field regime. The approach is based on an analytical integral formal solution of the parallel (i.e., along the magnetic field) transport equation with sources, and it is able to accommodate both local and non-local parallel heat flux closures. The numerical implementation is based on an operator-split formulation, with two straightforward steps: a perpendicular transport step (including sources), and a Lagrangian (field-line integral) parallel transport step. Algorithmically, the first step is amenable to the use of modern iterative methods, while the second step has a fixed cost per degree of freedom (and is therefore scalable). Accuracy-wise, the approach is free from the numerical pollution introduced by the discrete parallel transport term when the perpendicular to parallel transport coefficient ratio X ⊥ /X ∥ becomes arbitrarily small, and is shown to capture the correct limiting solution when ε = X⊥L 2 ∥ /X1L 2 ⊥ → 0 (with L∥∙ L⊥ , the parallel and perpendicular diffusion length scales, respectively). Therefore, the approach is asymptotic-preserving. We demonstrate the capabilities of the scheme with several numerical experiments with varying magnetic field complexity in two dimensions, including the case of transport across a magnetic island.

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Predicting operational windows of ELMs suppression by resonant magnetic perturbations in the DIII-D and KSTAR tokamaks

A newly developed plasma response model, combining the nonlinear two-fluid MHD code TM1 and toroidal MHD code GPEC run in ideal mode, quantitatively predicts the narrow isolated q 95 windows (Δq 95 ~ 0.1) of ELM suppression by n = 1, 2 and 3 resonant magnetic perturbations (RMPs) in both DIII-D and KSTAR tokamaks across a wide range of plasma parameters. The key physics that unites both experimental observations and our simulations is the close alignment of essential resonant q-surfaces and the location of the top of the pedestal prior to an ELM. This alignment permits an applied RMP to produce field penetration due to the lower E × B rotation at the pedestal top rather than being screened. The model successfully predicts that narrow magnetic islands form when resonant field penetration occurs at the top of pedestal, and these islands are easily screened when q 95 moves off resonance, leading to very narrow windows of ELM suppression (typically Δq 95 ~ 0.1). Furthermore, the observed reduction in the pedestal height is also well captured by the calculated classical collisional transport across the island. We recover observed q 95 , β N and plasma shape dependence of ELM suppression due to the effect of magnetic islands on pedestal transport and Peeling-Ballooning- Mode (PBM) stability. Importantly, experiments do occasionally observe wide windows of ELM suppression (Δq 95 > 0.5). Our model reveals that at low pedestal-top density multiple islands open, leading to wide operational windows of ELM suppression consistent with experiment. The model indicates that wide q95 windows of ELM suppression can be achieved at substantially higher pedestal pressure with less confinement degradation in DIII-D by operating at higher toroidal mode number (n = 4) RMPs. As a result, this can have significant implications for the operation of the ITER ELM control coils for maintaining high confinement together with ELM suppression.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Electron acceleration in three-dimensional magnetic reconnection with a guide field

Kinetic simulations of 3D collisionless magnetic reconnection with a guide field show a dramatic enhancement of energetic electron production when compared with 2D systems. In the 2D systems, electrons are trapped in magnetic islands that limit their energy gain, whereas in the 3D systems the filamentation of the current layer leads to a stochastic magnetic field that enables the electrons to access volume-filling acceleration regions. The dominant accelerator of the most energetic electrons is a Fermi-like mechanism associated with reflection of charged particles from contracting field lines.

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ELECTRON ACCELERATION BY CASCADING RECONNECTION IN THE SOLAR CORONA. I. MAGNETIC GRADIENT AND CURVATURE DRIFT EFFECTS

We investigate the electron acceleration by magnetic gradient and curvature drift effects in cascading magnetic reconnection of a coronal current sheet via a test particle method in the framework of the guiding center approximation. After several Alfvén transit times, most of the electrons injected at the current sheet are still trapped in the magnetic islands. A small fraction of the injected electrons precipitate into the chromosphere. The acceleration of trapped electrons is dominated by the magnetic curvature drifts, which change the parallel momentum of the electron, and appears to be more efficient than the acceleration of precipitating electrons, which is dominated by the perpendicular momentum change caused by the magnetic gradient drifts. With the resulting trapped energetic electron distribution, the corresponding hard X-ray (HXR) radiation spectra are calculated using an optically thin Bremsstrahlung model. Trapped electrons may explain flare loop top HXR emission as well as the observed bright spots along current sheets trailing coronal mass ejections. The asymmetry of precipitating electrons with respect to the polarity inversion line may contribute to the observed asymmetry of footpoint emission.

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Instability interplay in a magnetized streaming plasma

The interplay between the Kelvin-Helmholtz, the Rayleigh-Taylor and the Magnetic Re-connection instabilities in a magnetized inhomogeneous plasma with a sheared velocity field is investigated within the framework of a two-dimensional, two fluid model. This magnetic configuration is of interest for the investigation of the mixing process between the solar wind plasma and the Earth's magnetospheric plasma at low latitudes at the magnetospheric flank.It is found that the combined role of the density inhomogeneity and of the in-plane magnetic field during the development of the Kelvin Helmholtz instability is multi faceted. It leads to small scale magnetic islands through the development of induced magnetic field line reconnection but at the same time the in-plane magnetic field preserves the global coherence of the vortex merging process (vortex pairing).

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IS THE MAGNETIC FIELD IN THE HELIOSHEATH LAMINAR OR A TURBULENT SEA OF BUBBLES?

All current global models of the heliosphere are based on the assumption that the magnetic field in the heliosheath, in the region close to the heliopause (HP), is laminar. We argue that in that region the heliospheric magnetic field is not laminar but instead consists of magnetic bubbles. We refer to it as the bubble-dominated heliosheath region. Recently, we proposed that the annihilation of the 'sectored' magnetic field within the heliosheath as it is compressed on its approach to the HP produces anomalous cosmic rays and also energetic electrons. As a product of the annihilation of the sectored magnetic field, densely packed magnetic islands (which further interact to form magnetic bubbles) are produced. These magnetic islands/bubbles will be convected with ambient flows as the sector region is carried to higher latitudes filling the heliosheath. We further argue that the magnetic islands/bubbles will develop upstream within the heliosheath. As a result, the magnetic field in the heliosheath sector region will be disordered well upstream of the HP. We present a three-dimensional MHD simulation with very high numerical resolution that captures the north-south boundaries of the sector region. We show that due to the high pressure of the interstellar magnetic field a north-south asymmetry develops such that the disordered sectored region fills a large portion of the northern part of the heliosphere with a smaller extension in the southern hemisphere. We suggest that this scenario is supported by the following changes that occurred around 2008 and from 2009.16 onward: (1) the sudden decrease in the intensity of low energy electrons (0.02-1.5 MeV) detected by Voyager 2, (2) a sharp reduction in the intensity of fluctuations of the radial flow, and (3) the dramatic differences in intensity trends between galactic cosmic ray electrons (3.8-59 MeV) at Voyager 1 and 2. We argue that these observations are a consequence of Voyager 2 leaving the sector region of disordered field during these periods and crossing into a region of unipolar laminar field.

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A POROUS, LAYERED HELIOPAUSE

The picture of the heliopause (HP)-the boundary between the domains of the Sun and the local interstellar medium (LISM)-as a pristine interface with a large rotation in the magnetic field fails to describe recent Voyager 1 (V1) data. Magnetohydrodynamic (MHD) simulations of the global heliosphere reveal that the rotation angle of the magnetic field across the HP at V1 is small. Particle-in-cell simulations, based on cuts through the MHD model at V1's location, suggest that the sectored region of the heliosheath (HS) produces large-scale magnetic islands that reconnect with the interstellar magnetic field while mixing LISM and HS plasma. Cuts across the simulation reveal multiple, anti-correlated jumps in the number densities of LISM and HS particles, similar to those observed, at the magnetic separatrices. A model is presented, based on both the observations and simulations, of the HP as a porous, multi-layered structure threaded by magnetic fields. This model further suggests that contrary to the conclusions of recent papers, V1 has already crossed the HP.

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The plasmoid instability during asymmetric inflow magnetic reconnection

Theoretical studies of the plasmoid instability generally assume that the reconnecting magnetic fields are symmetric. We relax this assumption by performing two-dimensional resistive magnetohydrodynamic simulations of the plasmoid instability during asymmetric inflow magnetic reconnection. Magnetic asymmetry modifies the onset, scaling, and dynamics of this instability. Magnetic islands develop preferentially into the weak magnetic field upstream region. Outflow jets from individual X-points impact plasmoids obliquely rather than directly as in the symmetric case. Consequently, deposition of momentum by the outflow jets into the plasmoids is less efficient, the plasmoids develop net vorticity, and shear flow slows down secondary merging between islands. Secondary merging events have asymmetry along both the inflow and outflow directions. Downstream plasma is more turbulent in cases with magnetic asymmetry because islands are able to roll around each other after exiting the current sheet. As in the symmetric case, plasmoid formation facilitates faster reconnection for at least small and moderate magnetic asymmetries. However, when the upstream magnetic field strengths differ by a factor of 4, the reconnection rate plateaus at a lower value than expected from scaling the symmetric results. We perform a parameter study to investigate the onset of the plasmoid instability as a function of magnetic asymmetry and domain size. There exist domain sizes for which symmetric simulations are stable but asymmetric simulations are unstable, suggesting that moderate magnetic asymmetry is somewhat destabilizing. We discuss the implications for plasmoid and flux rope formation in solar eruptions, laboratory reconnection experiments, and space plasmas. The differences between symmetric and asymmetric simulations provide some hints regarding the nature of the three-dimensional plasmoid instability.

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Magnetic field in a finite toroidal domain

The magnetic field structure in a domain surrounded by a closed toroidal magnetic surface is analyzed. It is shown that ergodization of magnetic field lines is possible even in a regular field configuration (with nonvanishing toroidal component). A unified approach is used to describe magnetic fields with nested toroidal (possibly asymmetric) flux surfaces, magnetic islands, and ergodic field lines.

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Energetic particle transport in 3D equilibrium. Final report

In this project, we have further developed the state-of-the-art fusion simulation code, gyrokinetic toroidal code (GTC), for studying the energetic particle (EP) transport in the 3D equilibrium. We have applied the new capabilities to simulate the EP transport by the Alfven eigenmodes in stellarators and by 3D magnetic islands in tokamaks. As part of V&V efforts for 3D capability, the 3D capabilities of GTC have been applied to study thermal transport in stellarators and tokamak with 3D magnetic fields by microturbulence, which could cause additional EP loss. Effects magnetic islands on neoclassical bootstrap current have also been studied. The computational capability developed and physics learned in this project are in support of fusion SciDAC Center for Integrated Simulation of Energetic Particles in Burning Plasmas (ISEP). During this project, the PI has supervised 6 postdoctoral researchers and 4 PhD students at the University of California, Irvine. A complete list of 49 publications and 23 invited talks partially supported by this grant since 7/2015 appears at the end of this report. Five key publications closely related to this project are highlighted in this report.

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Reconnection dynamics with secondary tearing instability in compressible Hall plasmas

The dynamics of a secondary tearing instability is systematically investigated based on compressible Hall magnetohydrodynamic. It is found that in the early nonlinear phase of magnetic reconnection before onset of the secondary tearing instability, the geometry of the magnetic field in the reconnection region tends to form a Y-type structure in a weak Hall regime, instead of an X-type structure in a strong Hall regime. A new scaling law is found that the maximum reconnection rate in the early nonlinear stage is proportional to the square of the ion inertial length (γ∝d{sub i}{sup 2}) in the weak Hall regime. In the late nonlinear phase, the thin elongated current sheet associated with the Y-type geometry of the magnetic field breaks up to form a magnetic island due to a secondary tearing instability. After the onset of the secondary tearing mode, the reconnection rate is substantially boosted by the formation of the X-type geometries of magnetic field in the reconnection regions. With a strong Hall effect, the maximum reconnection rate linearly increases with the increase of the ion inertial length (γ∝d{sub i})

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A semi-analytical model of RF condensation that can handle localized power depositions

A nonlinear effect, RF (radio frequency) condensation, can be used to facilitate RF stabilization of magnetic islands. Previously studied semi-analytical models for RF condensation are suited mainly for broad deposition profiles and are unable to handle power depositions that are localized in the interior of a magnetic island. The power deposition profile of electron cyclotron waves, in particular, can be highly localized near a cyclotron resonance. Here, a model is developed that can handle both localized profiles and broad profiles. This allows a comparison of RF condensation for narrow vs broad deposition profiles, and it allows a study of the dependence of RF condensation of localized deposition profiles on key parameters.

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Particle energization in 3D magnetic reconnection of relativistic pair plasmas

We present large scale 3D particle-in-cell simulations to examine particle energization in magnetic reconnection of relativistic electron-positron (pair) plasmas. The initial configuration is set up as a relativistic Harris equilibrium without a guide field. These simulations are large enough to accommodate a sufficient number of tearing and kink modes. Contrary to the non-relativistic limit, the linear tearing instability is faster than the linear kink instability, at least in our specific parameters. We find that the magnetic energy dissipation is first facilitated by the tearing instability and followed by the secondary kink instability. Particles are mostly energized inside the magnetic islands during the tearing stage due to the spatially varying electric fields produced by the outflows from reconnection. Secondary kink instability leads to additional particle acceleration. Accelerated particles are, however, observed to be thermalized quickly. The large amplitude of the vertical magnetic field resulting from the tearing modes by the secondary kink modes further help thermalizing the non-thermal particles generated from the secondary kink instability. Implications of these results for astrophysics are briefly discussed.

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Collaborative research: Dynamics of electrostatic solitary waves and their effects on current layers

The project has accomplished the following achievements including the goals outlined in the original proposal. Generation and measurements of Debye-scale electron holes in laboratory: We have generated by beam injections electron solitary waves in the LAPD experiments. The measurements were made possible by the fabrication of the state-of-the-art microprobes at UCLA to measure Debye-scale electric fields [Chiang et al., 2011]. We obtained a result that challenged the state of knowledge about electron hole generation. We found that the electron holes were not due to two-stream instability, but generated by a current-driven instability that also generated whistler-mode waves [Lefebvre et al., 2011, 2010b]. Most of the grant supported a young research scientist Bertrand Lefebvre who led the dissemination of the laboratory experimental results. In addition to two publications, our work relevant to the laboratory experiments on electron holes has resulted in 7 invited talks [Chen, 2007, 2009; Pickett et al., 2009a; Lefebvre et al., 2010a; Pickett et al., 2010; Chen et al., 2011c, b] (including those given by the co-I Jolene Pickett) and 2 contributed talks [Lefebvre et al., 2009b, a]. Discovery of elecctron phase-space-hole structure in the reconnection electron layer: Our theoretical analyses and simulations under this project led to the discovery of an inversion electric field layer whose phase-space signature is an electron hole within the electron diffusion layer in 2D anti-parallel reconnection [Chen et al., 2011a]. We carried out particle tracing studies to understand the electron orbits that result in the phase-space hole structure. Most importantly, we showed that the current density in the electron layer is limited in collisionless reconnection with negligible guide field by the cyclotron turning of meandering electrons. Comparison of electrostatic solitary waves in current layers observed by Cluster and in LAPD: We compared the ESWs observed in a supersubstorm by the Cluster spacecraft and those measured in LAPD. One of the similarities in the characteristics of ESWs observed in space and in LAPD is that the time duration tends to be approximately the inverse of the electron plasma frequency [Pickett et al., 2009b]. Discovery of suprathermal electron bursts inside a series of magnetic islands: Our effort in examining the roles of ESWs in reconnection current layers resulted in the serendipitous discovery that was published in Nature Physics. In earth’s magnetosphere, we observed through the measurements from the four Cluster spacecraft, a series of magnetic islands and suprathermal electron bursts within the islands. The islands were identified to be effectively acceleration sites for electrons [Chen et al., 2008, 2009].

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IMPACT OF TEMPERATURE-DEPENDENT RESISTIVITY AND THERMAL CONDUCTION ON PLASMOID INSTABILITIES IN CURRENT SHEETS IN THE SOLAR CORONA

In this paper, we investigate, by means of two-dimensional magnetohydrodynamic simulations, the impact of temperature-dependent resistivity and thermal conduction on the development of plasmoid instabilities in reconnecting current sheets in the solar corona. We find that the plasma temperature in the current-sheet region increases with time and it becomes greater than that in the inflow region. As secondary magnetic islands appear, the highest temperature is not always found at the reconnection X-points, but also inside the secondary islands. One of the effects of anisotropic thermal conduction is to decrease the temperature of the reconnecting X-points and transfer the heat into the O-points, the plasmoids, where it gets trapped. In the cases with temperature-dependent magnetic diffusivity, {eta} {approx} T {sup -3/2}, the decrease in plasma temperature at the X-points leads to (1) an increase in the magnetic diffusivity until the characteristic time for magnetic diffusion becomes comparable to that of thermal conduction, (2) an increase in the reconnection rate, and (3) more efficient conversion of magnetic energy into thermal energy and kinetic energy of bulk motions. These results provide further explanation of the rapid release of magnetic energy into heat and kinetic energy seen during flares and coronal mass ejections. In this work, we demonstrate that the consideration of anisotropic thermal conduction and Spitzer-type, temperature-dependent magnetic diffusivity, as in the real solar corona, are crucially important for explaining the occurrence of fast reconnection during solar eruptions.

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SIMULTANEOUS OBSERVATION OF RECONNECTION INFLOW AND OUTFLOW ASSOCIATED WITH THE 2010 AUGUST 18 SOLAR FLARE

We report the simultaneous extreme-ultraviolet observation of magnetic reconnection inflow and outflow in a flare on 2010 August 18 observed by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory. We found that during the rise phase of the flare, some plasma blobs appeared in the sheet structure above the hot loops. The plasma blobs were ejected bidirectionally along the sheet structure (outflow), at the same time as the threads visible in extreme-ultraviolet images moved toward the sheet structure (inflow). The upward and downward ejection velocities are 220-460 km s{sup -1} and 250-280 km s{sup -1}, respectively. The inflow speed changed from 90 km s{sup -1} to 12 km s{sup -1} in 5 minutes. By using these velocities, we estimated the nondimensional reconnection rate, which we found to vary during this period from 0.20 to 0.055. We also found that the plasma blobs in the sheet structure collided or merged with each other before they were ejected from the sheet structure. We hypothesize that the sheet structure is the current sheet and that these plasma blobs are plasmoids or magnetic islands, which could be important for understanding the dynamics of the reconnection region.

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CICART Center For Integrated Computation And Analysis Of Reconnection And Turbulence

CICART is a partnership between the University of New Hampshire (UNH) and Dartmouth College. CICART addresses two important science needs of the DoE: the basic understanding of magnetic reconnection and turbulence that strongly impacts the performance of fusion plasmas, and the development of new mathematical and computational tools that enable the modeling and control of these phenomena. The principal participants of CICART constitute an interdisciplinary group, drawn from the communities of applied mathematics, astrophysics, computational physics, fluid dynamics, and fusion physics. It is a main premise of CICART that fundamental aspects of magnetic reconnection and turbulence in fusion devices, smaller-scale laboratory experiments, and space and astrophysical plasmas can be viewed from a common perspective, and that progress in understanding in any of these interconnected fields is likely to lead to progress in others. The establishment of CICART has strongly impacted the education and research mission of a new Program in Integrated Applied Mathematics in the College of Engineering and Applied Sciences at UNH by enabling the recruitment of a tenure-track faculty member, supported equally by UNH and CICART, and the establishment of an IBM-UNH Computing Alliance. The proposed areas of research in magnetic reconnection and turbulence in astrophysical, space, and laboratory plasmas include the following topics: (A) Reconnection and secondary instabilities in large high-Lundquist-number plasmas, (B) Particle acceleration in the presence of multiple magnetic islands, (C) Gyrokinetic reconnection: comparison with fluid and particle-in-cell models, (D) Imbalanced turbulence, (E) Ion heating, and (F) Turbulence in laboratory (including fusion-relevant) experiments. These theoretical studies make active use of three high-performance computer simulation codes: (1) The Magnetic Reconnection Code, based on extended two-fluid (or Hall MHD) equations, in an Adaptive Mesh Refinement (AMR) framework, (2) the Particle Simulation Code, a fully electromagnetic 3D Particle-In-Cell (PIC) code that includes a collision operator, and (3) GS2, an Eulerian, electromagnetic, kinetic code that is widely used in the fusion program, and simulates the nonlinear gyrokinetic equations, together with a self-consistent set of Maxwell’s equations.

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Wide Operational Windows of Edge-Localized Mode Suppression by Resonant Magnetic Perturbations in the DIII-D Tokamak

Edge-Localized-Mode (ELM) suppression by resonant magnetic perturbations (RMPs) generally occurs over very narrow ranges of the plasma current (or magnetic safety factor $q_{95}$) in the DIII-D tokamak. However, wide $q_{95}$ ranges of ELM suppression are needed for the safety and operational flexibility of ITER and future reactors. In DIII-D ITER Similar Shape (ISS) plasmas with $n$=3 RMPs, the range of $q_{95}$ for ELM suppression is found to increase with decreasing electron density. Nonlinear two-fluid MHD simulations reproduce the observed $q_{95}$ windows of ELM suppression and the dependence on plasma density, based on the conditions for resonant field penetration at the top of the pedestal. When the RMP amplitude is close to the threshold for resonant field penetration, only narrow isolated magnetic islands form near the top of the pedestal, leading to narrow $q_{95}$ windows of ELM suppression. However, as the threshold for field penetration decreases with decreasing density, resonant field penetration can take place over a wider range of $q_{95}$. For sufficiently low density (penetration threshold) multiple magnetic islands form near the top of the pedestal giving rise to continuous $q_{95}$ windows of ELM suppression. The model predicts that wide $q_{95}$ windows of ELM suppression can be achieved at substantially higher pedestal pressure in DIII-D by shifting to higher toroidal mode number ($n$=4) RMPs.

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