PPPL

Invited Talks

Scientists of the Theory Department are frequently invited to give presentations at major physics and computing conferences.

The following presents a selection of the Invited Presentations given by Theory Staff and their collaborators.

Upcoming

  • 59th Annual Meeting of the APS Division of Plasma Physics
    Plasmoid Instability in Forming Current Sheets
    (abstract)
    L. Comisso
    #s180, Monday, 23 Oct 2017, 10:45am
    The plasmoid instability has had a transformative effect in our understanding of magnetic reconnection in a multitude of systems. By preventing the formation of highly elongated reconnection layers, it has proven to be crucial in enabling the rapid energy conversion rates that are characteristic of many plasma phenomena. In the well-known Sweet-Parker current sheets, the growth of the plasmoid instability occurs at a rate that is proportional to the Lundquist number (S) raised to a positive exponent. For this reason, in large-S systems, Sweet-Parker current sheets cannot be attained as current layers are linearly unstable and undergo disruption before the Sweet-Parker state is attained. Here, we present a quantitative theory of the plasmoid instability in time-evolving current sheets based on a principle of least time [1]. We obtain analytical expressions for the growth rate, number of plasmoids, plasmoid width, current sheet aspect ratio and onset time for fast reconnection. They are shown to depend on the Lundquist number, the magnetic Prandtl number, the noise of the system, the characteristic rate of current sheet evolution, as well as the thinning process [1,2]. We validate the obtained analytical scaling relations by comparing them against the full numerical solutions of the principle of least time. Furthermore, we show that the plasmoid instability exhibits a quiescence period followed by a rapid growth over a short timescale [1,2,3].
    [1] L. Comisso, M. Lingam et al., Phys. Plasmas 23, 100702 (2016)
    [2] L. Comisso, M. Lingam et al., arXiv:1707.01862
    [3] Y.-M. Huang, L. Comisso & A. Bhattacharjee, arXiv:1707.01863
  • 59th Annual Meeting of the APS Division of Plasma Physics
    L-H Transition using XGC
    (abstract)
    S. Ku
    #s181, Monday, 23 Oct 2017, 10:45am
    Abstract.
    [1] A. First, B. Second et al., citation
  • 59th Annual Meeting of the APS Division of Plasma Physics
    MRI and Dynamo
    (abstract)
    M. Kunz
    #s182, Monday, 23 Oct 2017, 10:45am
    Abstract.
    [1] A. First, B. Second et al., citation
  • 59th Annual Meeting of the APS Division of Plasma Physics
    Halo Currents/Forces During Disruptions using M3D-C1
    (abstract)
    D. Pfefferlé
    #s183, Monday, 23 Oct 2017, 10:45am
    Abstract.
    [1] A. First, B. Second et al., citation
  • 59th Annual Meeting of the APS Division of Plasma Physics
    Laser-Plasma Interactions in Magnetized Environment
    (abstract)
    Y. Shi
    #s184, Monday, 23 Oct 2017, 10:45am
    Propagation and scattering of lasers present new phenomena and applications when the plasma medium become magnetized. Starting from mega-Gauss magnetic fields, laser scattering becomes manifestly anisotropic [1]. By arranging beams at special angles, one may be able to optimize laser-plasma coupling in magnetized environment. In stronger giga-Gauss magnetic field, laser propagation becomes modified by relativistic quantum effects [2]. The modified wave dispersion relation enables correct interpretation of Faraday rotation measurements of strong magnetic fields, as well as correct extraction of plasma parameters from the X-ray spectra of pulsars. In addition, magnetized plasmas can be utilized to mediate laser pulse compression [3]. Using magnetic resonances, it is not only possible to produce optic pulses of higher intensity, but also possible to amplify UV and soft X-ray pulses that cannot be compressed using existing technology.
    [1] Yuan Shi, Hong Qin & Nathaniel J. Fisch, arXiv:1705.09758
    [2] Yuan Shi, Nathaniel J. Fisch & Hong Qin, Phys. Rev. A 94, 012124 (2016)
    [3] Yuan Shi, Hong Qin & Nathaniel J. Fisch, Phys. Rev. E 95, 023211 (2017)
  • 59th Annual Meeting of the APS Division of Plasma Physics
    (Rosenbluth Prize): Shear Current Dynamo
    (abstract)
    J. Squire
    #s185, Monday, 23 Oct 2017, 10:45am
    Abstract.
    [1] A. First, B. Second et al., citation
  • 59th Annual Meeting of the APS Division of Plasma Physics
    Parasitic momentum flux in the tokamak core
    (abstract)
    T. Stoltzfus-Dueck
    #s186, Monday, 23 Oct 2017, 10:45am
    Tokamak plasmas rotate spontaneously without applied torque. This intrinsic rotation is important for future low-torque devices such as ITER, since rotation stabilizes certain instabilities. In the mid-radius “gradient region,” which reaches from the sawtooth inversion radius out to the pedestal top, intrinsic rotation profiles may be either flat or hollow, and can transition suddenly between these two states, an unexplained phenomenon referred to as rotation reversal. Theoretical efforts to explain the mid-radius rotation shear have largely focused on quasilinear models, in which the phase relationships of some selected instability result in a nondiffusive momentum flux (“residual stress”). In contrast, the present work demonstrates the existence of a robust, fully nonlinear symmetry-breaking momentum flux that follows from the free-energy flow in phase space and does not depend on any assumed linear eigenmode structure. The physical origin is an often-neglected portion of the radial ${\bf E}\times{\bf B}$ drift, which is shown to drive a symmetry-breaking outward flux of co-current momentum whenever free energy is transferred from the electrostatic potential to ion parallel flows [1]. The fully nonlinear derivation relies only on conservation properties and symmetry, thus retaining the important contribution of damped modes. The resulting rotation peaking is counter-current and scales as temperature over plasma current. As first demonstrated by Landau [2], this free-energy transfer (thus also the corresponding residual stress) becomes inactive when frequencies are much higher than the ion transit frequency, which allows sudden transitions between hollow and flat profiles. Simple estimates suggest that this mechanism may be consistent with experimental observations.
    [1] T. Stoltzfus-Dueck, Phys. Plasmas 24, 030702 (2017)
    [2] L. Landau, J. Exp. Theor. Phys. 16, 574 (1946); English translation in J. Phys. (USSR) 10, 25 (1946)
  • 59th Annual Meeting of the APS Division of Plasma Physics
    Fast Magnetic Reconnection Mediated by Electron Pressure Gradient in MRX
    (abstract)
    W. Fox
    #s187, Monday, 23 Oct 2017, 10:45am
    Abstract.
    [1] A. First, B. Second et al., citation
  • 59th Annual Meeting of the APS Division of Plasma Physics
    ELMS using M3D-C1
    (abstract)
    B. Lyons
    #s188, Monday, 23 Oct 2017, 10:45am
    Abstract.
    [1] A. First, B. Second et al., citation

Past

  • 1st Asia-Pacific Conference on Plasma Physics, Chengdu
    Frontiers in energetic particle research in fusion
    N.N. Gorelenkov, abstract
    [#s189, 18 Sep 2017]
    The area of energetic particle (EP) physics in fusion research has been actively studied in recent decades. Significant progress has been recently reviewed in preparations for burning plasmas (BP) [1]. This talk highlights several high priority topics to be addressed in the near future in view of broadening the active fusion studies by the Asia-Pacific researches.
    The first topic remains to be important and critical for achieving the burning fusion conditions. It is on the predictions of EP transport in the presence of Alfvén Eigenmodes (AE) driven by superthermal, super-Alfvénic fast ions. In present devices AEs are observed in steady state or chirping frequency regimes driven by the confined energetic ions. Their profiles are characterized by the critical pressure gradients which in their turn are determined predominantly by the background thermal plasma dampings. Relatively simple reduced models as well as sophisticated initial value codes are developed now to uncover the underlying physics behind the relaxation of the fast ion distributions.
    Another priority topic we cover is the high frequency cyclotron instabilities responsible for Ion Cyclotron Emission (ICE) [2]. Intensively studied in the past this topic is again of special interest for future BP experiments where heavy neutron and gamma radiations make it difficult in general for diagnostics to operate. At the same time measuring the magnetic field oscillations at the plasma edge is a relatively simple task but can be a powerful diagnostic tool for fusion products. In particular in JET experiments it was shown that ICE power signal is proportional to the neutron flux intensity which makes the case for ICE to be used as a diagnostic. This topic needs a breakthrough in order to be a viable tool for fusion research.
    Finally we are covering the mechanisms when EP driven high frequency Alfvénic modes in ST devices lead to effective thermal electron transport as previously reported. Several ideas are considered such as the stochastic motion of thermal electrons in the presence of high frequency modes as well as the direct beam power channeling via the resonant excitation of the kinetic shear Alfvén waves. Theoretical estimates suggest that these ideas are plausible mechanisms for fusion plasmas in STs [3] and maybe relevant to conventional tokamaks. The suggested topics are important and timely now in order to identify possible new directions of the research for the fusion community.
    [1] N.N. Gorelenkov, S. Pinches & K. Toi, Nucl. Fusion 54, 125001 (2014)
    [2] N.N. Gorelenkov, New J. Phys. 18, 105010 (2016)
    [3] E. Belova, N.N. Gorelenkov et al., Phys. Rev. Lett. 115, 015001 (2015)
  • 1st Asia-Pacific Conference on Plasma Physics, Chengdu
    Parasitic Momentum Flux in the Tokamak Core
    T. Stoltzfus-Dueck, abstract
    [#s486, 18 Sep 2017]

  • 15th IAEA Technical Meeting on the Energetic Particles in Magnetic Confinement Systems, Princeton, NJ, 2017;
    Likelihood for Alfvénic instability bifurcation in experiments
    Vinícius Duarte, abstract
    [#s482, 05 Sep 2017]
    Energetic-particle-driven instabilities can seriously limit the performance of present-day and next-generation fusion devices. We apply a criterion [1] for the likely nature of fast ion redistribution in tokamaks to be in the convective or diffusive nonlinear regimes. The criterion, which is shown to be rather sensitive to the relative strength of collisional or micro-turbulent scattering and drag processes, ultimately translates into a condition for the applicability of reduced quasilinear modeling for realistic tokamak eigenmodes scenarios. The criterion is tested and validated against different machines, where the chirping mode behavior is shown to be in accord with the model. It has been found that the anomalous fast ion transport is a likely mediator of the bifurcation between the fixed-frequency mode behavior and rapid chirping in tokamaks. In addition, micro-turbulence appears to resolve the disparity with respect to the ubiquitous chirping observation in spherical tokamaks and its rarer occurrence in conventional tokamaks. In NSTX, the tendency for chirping is further studied in terms of the beam beta and the plasma rotation shear. For more accurate quantitative assessment, numerical simulations of the effects of electrostatic ion temperature gradient turbulence on chirping are presently being pursued using the GTS code.
    [1] V.N. Duarte, H.L. Berk et al., Nucl. Fusion 57, 054001 (2017)
  • The Exploratory Plasma and Fusion Research Workshop (EPR) 2017 conference
    Three-dimensional plasmoid-mediated reconnection in tokamaks
    F. Ebrahimi, abstract
    [#s190, 01 Aug 2017]

    Plasmoid-mediated reconnection is examined using global nonlinear three-dimensional resistive MHD simulations in a spherical tokamak for two cases: 1) generation of closed flux surfaces during helicity injection experiments for start-up current-drive (for solenoid-free tokamak design) and 2) nonlinear edge localized modes. An initial poloidal flux is created, in this case utilizing the helicity injection technique, in the presence of a toroidal guide field. A rare, classical example of plasmoid formation in a large-scale toroidal fusion plasma has been demonstrated during helicity injection, where the injected magnetic field lines are oppositely directed near the injection region and form elongated Sweet-Parker current sheets.[1] At high Lundquist number a transition to plasmoid instability has been shown. This is the first observation of plasmoid instability in a laboratory device configuration predicted by realistic MHD NIMROD simulations and then supported by experimental camera images from NSTX. Second, it is shown that the 3-D non-axisymmetric magnetic fluctuations could arise due to edge current-sheet instabilities. It is found that i) regardless of non-axisymmetric 3-D edge perturbations, large volume flux closure [2] is formed during start-up helicity injection, ii) 3-D magnetic fluctuations can cause local flux amplification to trigger axisymmetric reconnecting plasmoids formation at the reconnection site.[3] We also show coherent current-carrying filament structures (sometimes referred to as 3-D plasmoids) wrapped around the torus that are nonlinearly formed due to nonaxisymmetric reconnecting current sheet instabilities, the so called peeling-like edge localized modes.[4] These fast growing modes saturate by breaking axisymmetric current layers isolated near the plasma edge and go through repetitive relaxation cycles by expelling current radially outward and relaxing it back. The longstanding problem of quasiperiodic ELMs cycles is explained through the edge reconnection process.
    [1] F. Ebrahimi, R. Raman, Phys. Rev. Lett. 114, 205003 (2015)
    [2] F. Ebrahimi, R. Raman, Nucl. Fusion Lett. 56, 044002 (2016)
    [3] F. Ebrahimi, Phys. Plasmas 23, 120705 (2016)
    [4] F. Ebrahimi, Phys. Plasmas 24, 056119 (2017)

  • 230th AAS, Austin Texas
    Laboratory Observation of High-Mach Number, Laser-Driven Magnetized Collisionless Shocks
    D.B. Schaeffer, abstract, slides
    [#s439, 07 Jul 2017]
    Collisionless shocks are common phenomena in space and astrophysical systems, including solar and planetary winds, coronal mass ejections, supernovae remnants, and the jets of active galactic nuclei, and in many the shocks are believed to efficiently accelerate particles to some of the highest observed energies. Only recently, however, have laser and diagnostic capabilities evolved sufficiently to allow the detailed study in the laboratory of the microphysics of collisionless shocks over a large parameter regime. We present the first laboratory generation of high-Mach number magnetized collisionless shocks created through the interaction of an expanding laser-driven plasma with a magnetized ambient plasma. Time-resolved, two-dimensional imaging of plasma density and magnetic fields shows the formation and evolution of a supercritical shock propagating at magnetosonic Mach number $M_{ms}\approx12$. Particle-in-cell simulations constrained by experimental data further detail the shock formation and separate dynamics of the multi-ion-species ambient plasma. The results show that the shocks form on timescales as fast as one gyroperiod, aided by the efficient coupling of energy, and the generation of a magnetic barrier, between the piston and ambient ions. The development of this experimental platform complements present remote sensing and spacecraft observations, and opens the way for controlled laboratory investigations of high-Mach number collisionless shocks, including the mechanisms and efficiency of particle acceleration. The platform is also flexible, allowing us to study shocks in different magnetic field geometries, in different ambient plasma conditions, and in relation to other effects in magnetized, high-Mach number plasmas such as magnetic reconnection or the Weibel instability.
  • PASC17 Conference, Lausanne, Switzerland
    Gyrokinetic Particle Codes at Exascale: Challenges and Opportunities
    Stéphane Ethier, abstract, slides
    [#s480, 26 Jun 2017]
    2016 has seen the start of an ambitious new initiative at the US Department of Energy: The Exascale Computing Project (https://exascaleproject.org). ECP brings together domain scientists, applied mathematicians, computer scientists, and engineers to work in collaboration to accelerate the development of exascale hardware and software. On the software side, 15 applications were fully funded (+7 seed efforts), as well as 4 “co-design” centers and 35 software development projects. This presentation will give an insider’s view of the exascale project and, in particular, of the funded application on “High-Fidelity Whole Device Modeling of Magnetically Confined Fusion Plasma”. This project aims at developing an exascale-ready framework for the whole-device simulation of tokamak fusion devices. One of the main tasks in this effort is the coupling of the core turbulence delta-f code GENE with the edge turbulence total-f code XGC1.
  • 2017 IPELS
    ​​Laboratory Observation of High-Mach Number, Laser-Driven Magnetized Collisionless Shocks
    D.B. Schaeffer, abstract, slides
    [#s440, 23 Jun 2017]
    Collisionless shocks are common phenomena in space and astrophysical systems, including solar and planetary winds, coronal mass ejections, supernovae remnants, and the jets of active galactic nuclei. Of particular interest are the class of high-Mach number shocks, which are believed to efficiently accelerate particles to some of the highest observed energies. Only recently, however, have laser and diagnostic capabilities evolved sufficiently to allow the detailed study in the laboratory of the microphysics of collisionless shocks over a large parameter regime. We present the first laboratory generation of high-Mach number magnetized collisionless shocks created through the interaction of an expanding laser-driven plasma with a magnetized ambient plasma. Time-resolved, two-dimensional imaging of plasma density and magnetic fields shows the formation and evolution of a supercritical shock propagating at magnetosonic Mach number $M_{ms}\approx12$. Particle-in-cell simulations constrained by experimental data further detail the shock formation and separate dynamics of the multi-ion-species ambient plasma. The results show that the shocks form on timescales as fast as one gyroperiod, aided by the efficient coupling of energy, and the generation of a magnetic barrier, between the piston and ambient ions. The development of this experimental platform complements present remote sensing and spacecraft observations, and opens the way for controlled laboratory investigations of high-Mach number collisionless shocks, including the mechanisms and efficiency of particle acceleration. The platform is also flexible, allowing us to study shocks in different magnetic field geometries, in different ambient plasma conditions, and in relation to other effects in magnetized, high-Mach number plasmas such as magnetic reconnection or the Weibel instability.
  • EXB Plasmas for Space and Industrial Applications
    Electron-wall interactions and their consequences on transport
    I.D. Kaganovich, abstract, slides
    [#s209, 21 Jun 2017]
    The purpose of the talk is to give an overview of accomplishments at PPPL in predictive control of electron kinetics in low-pressure plasmas relevant to ${\bf E} \times {\bf B}$ discharges. We show using specific examples that this progress was made possible by synergy between full-scale particle-in- cell simulations, analytical models, and experiments. For low-pressure devices, the electron velocity distribution function (EVDF) is non-Maxwellian and, correspondingly, the wall potential is strongly modified. Electron emission strongly influences the wall potential and also leads to the enhanced ${\bf E} \times {\bf B}$ transport [1]. Nonlinear coupling between EVDF and the wall potential causes additional kinetic instabilities and can cause the relaxation sheath oscillations [2]. We also studied electron beam interaction with the plasma and collisionless transfer of the beam energy to plasma electrons [3]. When secondary electron emission (SEE) needs to be controlled, special surfaces can be used for the SEE mitigation [4]. Our current work includes implementing modern Poisson solvers into the Large Scale Plasma (LSP) particle-in- cell (PIC) code [5] which enables multidimensional PIC simulations. This enhanced PPPL-modified LSP code is being applied to study several low-temperature plasma technologies, including anomalous transport in closed drift ${\bf E} \times {\bf B}$ devices [6,7].
    [1] Hongyue Wang, Michael D Campanell et al., J. Phys. D - Appl. Phys. 47, 405204 (2014)
    [2] M. D. Campanell, A.V. Khrabrov & I.D. Kaganovich, Phys. Plasmas 19, 123513 (2012)
    [3] D. Sydorenko, I.D. Kaganovich et al., Phys. Plasmas 22, 123510 (2015)
    [3] I. D. Kaganovich & D. Sydorenko, Phys. Plasmas 23, 112116 (2016)
    [3] D. Sydorenko, I.D. Kaganovich et al., Phys. Plasmas 23, 122119 (2016)
    [4] Charles Swanson & Igor D. Kaganovich, J. Appl. Phys. 120, 213302 (2016), submitted (2017)
    [5] Johan Carlsson, Alexander Khrabrov et al., Plasma Sources Sci. Technol. 26, 014003 (2016).
    [6] J. Carlssonet al., to be submitted to Frontiers in Physics, section Plasma Physics (2017)
    [7] S. Baalrud and I.D. Kaganovich, “Plasma Theory: Role and Recent Trends” in “2017 Plasma Roadmap”, J. Phys. D: Appl. Phys. (2017).
  • International Workshop on the Interrelationship between Plasma Experiments in the Laboratory and in Space (IPELS 2017)
    Three-dimensional coherent plasmoids in current-carrying plasma
    F. Ebrahimi, abstract, slides
    [#s192, 20 Jun 2017]
    Plasmoid-mediated reconnection is examined using nonlinear three-dimensional resistive MHD simulations in a global toroidal geometry. An initial poloidal flux is created, in this case utilizing the helicity injection technique, in the presence of a toroidal guide field. We explore the physics of plasmoids reconnection for flux closure during plasma formation. Two types of current sheets are formed during flux expansion. First, a rare, classical example of plasmoid formation in a tokamak is demonstrated during helicity injection, where the injected magnetic field lines are oppositely directed near the injection region and form elongated Sweet-Parker current sheets (primary reconnecting current sheet). At high Lundquist number a transition to plasmoid instability has been shown in a large-scale toroidal fusion plasma.1 Consistent with the theory, fundamental characteristics of the plasmoid instability, including fast reconnection rate, have been observed in these realistic simulations. Second, edge current sheets are formed due to the poloidal flux compression near the plasma edge and shown to provide the free energy for non-axisymmetric magnetic fluctuations, the 3-D edge current-sheet instabilities. The role of these 3-D magnetic fluctuations in the onset of axisymmetric current-carrying plasmoids is examined. It is found that 3-D magnetic fluctuations can cause local flux amplification to trigger axisymmetric reconnecting plasmoids formation at the reconnection site.2 We also show coherent current-carrying filament (ribbon-like) structures wrapped around the torus that are nonlinearly formed due to nonaxisymmetric reconnecting current sheet instabilities, the so called peeling-like edge localized modes.3 These fast growing modes saturate by breaking axisymmetric current layers isolated near the plasma edge and go through repetitive relaxation cycles by expelling current radially outward and relaxing it back. The 3-D coherent current-carrying filament structures and their nonlinear dynamics due to the dynamo effect are relevant to flares, which also exhibit ejection of field-aligned filamentary structures into the surrounding space.
    [1] F. Ebrahimi, R. Raman, Phys. Rev. Lett. 114, 205003 (2015)
    [2] F. Ebrahimi, Phys. Plasmas 23, 120705 (2016)
    [3] F. Ebrahimi, arxiv.org/abs/1702.02696.
  • 44th International Conference on Plasma Science (ICOPS)
    Amplification due to the two-stream instability of self-electric and magnetic fields of an ion or electron beam propagating in background plasma
    I.D. Kaganovich, abstract, slides
    [#s208, 21 May 2017]
    Propagation of charged particle beams in background plasma as a method of space charge neutralization has been shown to achieve high degrees of charge and current neutralization and therefore can enable nearly ballistic propagation and focusing of charged particle beams. Correspondingly, use of plasmas for propagation of charged particle beams has important applications for transport and focusing of intense particle beams in electric propulsion, inertial fusion and high energy density laboratory plasma physics. However, the streaming of beam ions through a background plasma can lead to development of the two-stream instability between the beam ions and the plasma electrons [1,2]. The electric and magnetic self-fields enhanced by the two-stream instability can lead to defocusing of the ion beam and fast scattering of an electron beam. Using particle-in-cell (PIC) simulations, we study the scaling of the instability-driven self- electromagnetic fields and consequent defocusing forces with the background plasma density and beam ion mass. We identify plasma parameters where the defocusing forces can be reduced.
    [1] Erinc Tokluoglu and Igor D. Kaganovich, Phys. Plasmas 22, 040701 (2015)
    [2] Edward A. Startsev, Igor D. Kaganovich and Ronald C. Davidson, Nucl. Instr. Meth. Phys. Res. A 773, 80 (2014).
  • The International Sherwood Fusion Theory Conference, Annapolis
    Gyrokinetic simulation of a fast L-H bifurcation dynamics in a realistic diverted tokamak edge geometry
    [#s159, 02 May 2017]
    Despite its critical importance in the fusion program and over 30 years of H-mode operation, there has been no fundamental understanding at the kinetic level on how the H-mode bifurcation occurs. We report the first observation of an edge transport barrier formation event in an electrostatic gyrokinetic simulation carried out in a realistic C-Mod like diverted tokamak edge geometry under strong forcing by a high rate of heat deposition. The results show that the synergistic action between two multiscale dynamics, the turbulent Reynolds-stress driven [1] and the neoclassical X-point orbit loss drive [2] sheared ${\bf E}\times{\bf B}$ flows, works together to quench turbulent transport and form a transport barrier just inside the last closed magnetic flux surface. The synergism helps reconcile experimental reports of the key role of turbulent stress in the bifurcation [3] with some other experimental observations that ascribe the bifurcation to X-point orbit loss/neoclassical effects [4,5]. The synergism could also explain other experimental observations that identified a strong correlation between the L-H transition and the orbit loss driven ${\bf E}\times{\bf B}$ shearing rate [6]. The synergism is consistent with the general experimental observation that the L-H bifurcation is more difficult with the $\nabla B$-drift away from the single-null X-point, in which the X-point orbit-loss effect is weaker [2].
    [1] P.H. Diamond, S-I Itoh et al., Plasma Phys. Controlled Fusion 47, R35 (2005)
    [2] C.S. Chang, Seunghoe Kue & H. Weitzner, Phys. Plasmas 9, 3884 (2002)
    [3] G.R. Tynan, M. Xu et al., Nucl. Fusion 53, 073053 (2013)
    [4] T. Kobayashi, K. Itoh et al., Phys. Rev. Lett. 111, 035002 (2013)
    [5] M. Cavedon, T. Pütterich et al., Nucl. Fusion 57, 014002 (2017)
    [6] D.J. Battaglia, C.S. Chang et al., Nucl. Fusion 53, 113032 (2017)
    [7] S.M. Kaye, R. Maingi et al., Nucl. Fusion 51, 113109 (2011)
  • The International Sherwood Fusion Theory Conference, Annapolis
    Parasitic momentum flux in the tokamak core
    T. Stoltzfus-Dueck, abstract, slides
    [#s160, 01 May 2017]
    Tokamak plasmas rotate spontaneously in the absence of applied torque. This so-called 'intrinsic rotation' may be very important for future low-torque devices such as ITER, since rotation can stabilize certain instabilities. In the mid-radius 'gradient region,' which reaches from the sawtooth inversion radius out to the pedestal top, intrinsic rotation profiles are sometimes flat and sometimes hollow. Profiles may even transition suddenly between these two states, an unexplained phenomenon referred to as rotation reversal. Theoretical efforts to identify the origin of the mid-radius rotation shear have focused primarily on quasilinear models, in which the phase relationships of some selected instability result in a nondiffusive momentum flux ("residual stress"). In contrast to these efforts, the present work demonstrates the existence of a robust, fully nonlinear symmetry-breaking momentum flux that follows from the free-energy flow in phase space and does not depend on any assumed linear eigenmode structure. The physical origin is an often-neglected portion of the radial ExB drift, which is shown to drive a symmetry-breaking outward flux of co-current momentum whenever free energy is transferred from the electrostatic potential to ion parallel flows [1]. The resulting rotation peaking is counter-current and scales as temperature over plasma current. As originally demonstrated by Landau [2], this free-energy transfer (thus also the corresponding residual stress) becomes inactive when frequencies are much higher than the ion transit frequency, which may explain the observed relation of density and counter-current rotation peaking in the core. Simple estimates suggest that this mechanism may be consistent with experimental observations, in both hollow and flat rotation regimes.
    [1] T. Stoltzfus-Dueck, Phys. Plasmas 24, 030702 (2017)
    [2] L. Landau, J. Exp. Theor. Phys. 16, 574 (1946); English translation in J. Phys. (USSR) 10, 25 (1946)
  • Transport Task Force (TTF) Meeting, Williamsburg, VA, 2017.
    Quasilinear relaxation formalism for energetic particle interaction with Alfvénic modes
    Vinícius Duarte, abstract, slides
    [#s483, 27 Apr 2017]
    Energetic-particle-driven instabilities limit the performance of present-day and next-generation fusion devices. We propose a criterion for the likely nature of losses of fast ions in tokamaks to be in the convective or diffusive nonlinear regimes. The criterion, which is shown to be rather sensitive to collisional and micro-turbulent processes, ultimately translates into a condition for the applicability of quasilinear modelling for realistic tokamak eigenmodes scenarios. The criterion is tested and validated against NSTX and DIII-D where the chirping mode behavior is shown to satisfy this criterion. We then propose a resonance- broadened quasilinear framework in which the relevant variables are chosen to be the invariants of the unperturbed resonant particle Hamiltonian. The formulation describes distribution function evolution in phase space and captures both regimes of isolated and overlapping modes. We show how linear perturbative MHD codes can be used to provide information such as eigenstructures, resonance surfaces and mode-particle interaction matrix elements, all of which are necessary for realistic modelling of experimental discharges. Preliminary numerical results are discussed, as well as the prospects of using the resonance-broadened quasilinear model for whole-device simulation through proper interfacing with global transport codes.
  • 11th West Lake International Symposium on Energetic Particle Physics and Microturbulence, Hangzhou
    Nonlinear simulations of beam-driven compressional Alfvén eigenmodes in NSTX
    E. Belova, abstract, slides
    [#s157, 24 Apr 2017]
    Results of 3D nonlinear simulations of neutral-beam- driven compressional Alfvén eigenmodes (CAEs) in the National Spherical Torus Experiment (NSTX) are presented. Hybrid MHD- particle simulations for the H-mode NSTX discharge using the HYM code show unstable CAE modes for a range of toroidal mode numbers, $n = 4 - 9$, and frequencies below the ion cyclotron frequency. It is found that the essential feature of CAEs is their coupling to kinetic Alfvén wave (KAW) that occurs on the high-field side at the Alfvén resonance location. High-frequency Alfvén eigenmodes are frequently observed in beam-heated NSTX plasmas, and have been linked to flattening of the electron temperature profiles at high beam power. Coupling between CAE and KAW suggests a new mechanism to explain these observations, namely an energy channeling mechanism, in which beam driven CAEs dissipate their energy at the resonance location, therefore significantly modifying the energy deposition profile. The numerical model in the HYM code allows a full kinetic description of the beam ions, including the cyclotron resonances, but a one fluid MHD description is used to model the thermal plasma; therefore, the radial width of KAW is determined by the beam ion Larmor radius. Nonlinear simulations demonstrate that CAEs can channel the energy of the beam ions from the injection region near the magnetic axis to the location of the resonant mode conversion at the edge of the beam density profile. A set of nonlinear simulations show that the CAE instability saturates due to nonlinear particle trapping, and a large fraction of beam energy can be transferred to several unstable CAEs of relatively large amplitudes and absorbed at the resonant location. Absorption rate shows a strong scaling with the beam power.
  • US-Japan Workshop and School on Magnetic Reconnection
    General Theory of the Plasmoid Instability
    L. Comisso, abstract, slides
    [#s137, 21 Mar 2017]
    We present the recent formulation of a general theory of the onset and development of the plasmoid instability [1]. We consider the general problem of a reconnecting current sheet that can evolve in time, rather than assuming a fixed Sweet-Parker current sheet. The new theoretical framework has lead to completely new results, which have shown that previously obtained power laws are insufficient to capture the correct properties of the plasmoid instability. The new scaling laws are shown to depend on the initial perturbation amplitude, the characteristic rate of current sheet evolution, and the Lundquist number. 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] L. Comisso, M. Lingam et al., Phys. Plasmas 23, 100702 (2016)
  • Ion Propulsion and Accelerator Industrial Applications workshop (IPAIA), Italy
    Experimental and Theoretical Study of Ion Beam Neutralization by Plasma
    Igor Kaganovich, slides
    [#s207, 01 Mar 2017]
  • IAEA Technical Meeting on Uncertainty Assessment and Benchmark Experiments for Atomic and Molecular Data for Fusion Applications
    Sensitivity of Tokamak Transport Modeling to Atomic Physics Data: Some Examples
    D.P. Stotler, abstract, slides
    [#s191, 19 Dec 2016]
    A central concern in the design of burning plasma devices, such as ITER or DEMO, is that they represent extrapolations in dimensionless parameters from existing devices. The only means by which one can confidently predict their operation is via a well validated simulation based upon a first principles, or as close as possible, model. Accurate atomic physics data are essential to this task, not only for these predictive applications, but also for the validation of the model against the available data. In this talk, we present examples illustrating the sensitivity of such simulations to uncertainties in atomic physics data. The Gas Puff Imaging (GPI) diagnostic [1] provides spatially and temporally resolved data ideal for validating plasma turbulence simulations. To date, those validation tests have been based on statistical characterizations of the turbulence, such as correlation lengths and times. In using those data, one must account for the spatial extent of the neutral gas cloud that is being “lit” by the plasma turbulence. Neutral transport simulations of that gas cloud have essentially no free parameters and are themselves amenable to quantitative validation tests [2]. We will describe a couple of these, utilizing deuterium or helium gas puffs, and examine the sensitivity of the results to the atomic physics data for those systems. The use of tungsten in ITER as a principal plasma facing material has led to its introduction in a growing number of existing devices. Experiments conducted on those surfaces are frequently targeted at assessing tungsten erosion and its transport into the tokamak core. We will highlight two such recent investigations. In both cases, factor-of-a-few variations in the tungsten atomic physics data result in order of magnitude, or more, changes in the analysis results [3]. Finally, the drive towards truly first principles simulations entails, at least in some regimes, a shift from fluid descriptions of the plasma to ones that are fully kinetic [4]. The development of ever more capable computers and simulation algorithms has been steadily relaxing restrictions on the dimensionality and spatial coverage of such simulations. As they become more detailed and practical, additional atomic physics data will be required, e.g., doubly differential ionization cross sections. [This work is supported by U.S. DOE Contracts DE-AC02-09CH11466 (PPPL), DE-FC02-99ER54512 (MIT), DE-AC05-00OR22725 (ORNL), and DE-AC52-07NA27344 (LLNL).]
    [1] S.J. Zweben, D.P. Stotler et al., Plasma Phys. Control. Fusion 56, 095010 (2014)
    [2] B. Cao, D.P. Stotler et al., Fusion Sci. Tech. 64, 29 (2013)
    [3] J.D. Elder, P.C. Stangeby et al., J. Nucl. Mat. Energy, in press (2017)
    [4] D. Tskhakaya, Contrib. Plasma Phys. 56, 698 (2016)
  • Seminar, University of Maryland
    Modeling Tokamak Transients with M3D-C1
    N. Ferraro, slides
    [#s453, 30 Nov 2016]
  • 58th Annual Meeting of the APS Division of Plasma Physics
    Extending geometrical optics: A Lagrangian theory for vector waves
    D. Ruiz, abstract, slides
    [#s65, 04 Nov 2016]
    Even diffraction aside, the commonly known equations of geometrical optics (GO) are not entirely accurate. GO considers wave rays as classical particles, which are completely described by their coordinates and momenta; but rays have another degree of freedom, namely, polarization. As a result, wave rays can behave as particles with spin. A well-known example of polarization dynamics is wave-mode conversion, which can be interpreted as rotation of the (classical) “wave spin”. However, there are other less-known manifestations of the wave spin, such as polarization precession and polarization-driven bending of ray trajectories. This talk presents recent advances in extending and reformulating GO as a first-principle Lagrangian theory, whose effective-gauge Hamiltonian governs both mentioned polarization phenomena simultaneously. Examples and numerical results are presented. When applied to classical waves, the theory correctly predicts the polarization-driven divergence of left- and right- polarized electromagnetic waves in isotropic media, such as dielectrics and non-magnetized plasmas. In the case of particles with spin, the formalism also yields a point-particle Lagrangian model for the Dirac electron, i.e. the relativistic spin-1/2 electron, which includes both the Stern-Gerlach spin potential and the Bargmann-Michel-Telegdi spin precession. Additionally, the same theory contributes, perhaps unexpectedly, to the understanding of ponderomotive effects in both wave and particle dynamics; e.g., the formalism allows to obtain the ponderomotive Hamiltonian for a Dirac electron interacting with an arbitrarily large electromagnetic laser field with spin effects included. [Supported by the NNSA SSAA Program through DOE Research Grant No. DE-NA0002948, by the U.S. DOE through Contract No. DE-AC02-09CH11466, and by the U.S. DOD NDSEG Fellowship through Contract No. 32-CFR-168a.]
  • 58th Annual Meeting of the APS Division of Plasma Physics
    Radiation effects on the runaway electron avalanche
    C. Liu, abstract, slides
    [#s67, 04 Nov 2016]
    Runaway electrons are a critical area of research into tokamak disruptions. A thermal quench on ITER can result in avalanche production of a large amount of runaway electrons and a transfer of the plasma current to be carried by runaway electrons. The potential damage caused by the highly energetic electron beam poses a significant challenge for ITER to achieve its mission. It is therefore extremely important to have a quantitative understanding of the avalanche process, including (1) the critical energy for an electron to run away to relativistic energy, and (2) the avalanche growth rate dependence on electric field, which is related to the poloidal flux change required for an e-fold in current. It is found that the radiative energy loss of runaway electrons plays an important role in determining these two quantities. In this talk we discuss three kinds of radiation from runaway electrons, synchrotron radiation, Cerenkov radiation, and electron cyclotron emission (ECE) radiation. Synchrotron radiation, which mainly comes from the cyclotron motion of highly relativistic runaway electrons, dominates the energy loss of runaway electrons in the high-energy regime. The Cerenkov radiation from runaway electrons gives an additional correction to the Coulomb logarithm in the collision operator, which changes the avalanche growth rate. The ECE emission [1] mainly comes from electrons in the energy suprathermal rangee $1.2 <\gamma < 3$, which and gives an important approach to diagnose the runaway electron distribution in momentum and pitch angle. To study the runaway electron dynamics in momentum space including all the radiation and scattering effects, we use a novel tool, the adjoint method [2] to obtain both the runaway probability and the expected slowing-down time. The method is then combined with kinetic simulations to calculate the avalanche threshold and growth rate.
    [1] C. Paz-Soldan, R.J. La Haye et al., Nucl. Fusion 56, 056010 (2016)
    [2] Chang Liu, Dylan P. Brennan et al., Phys. Plasmas 23, 010702 (2016)
  • 58th Annual Meeting of the APS Division of Plasma Physics
    Plasmoids formation in a laboratory and large-volume flux closure during simulations of Coaxial Helicity Injection in NSTX-U
    F. Ebrahimi, abstract, slides
    [#s66, 31 Oct 2016]
    In NSTX-U, transient Coaxial Helicity Injection (CHI) is the primary method for current generation without reliance on the solenoid. A CHI discharge is generated by driving current along open field lines (the injector flux) that connect the inner and outer divertor plates on NSTX/NSTX-U, and has generated over 200kA of toroidal current on closed flux surfaces in NSTX. Extrapolation of the concept to larger devices requires an improved understanding of the physics of flux closure and the governing parameters that maximizes the fraction of injected flux that is converted to useful closed flux. Here, through comprehensive resistive MHD NIMROD simulations conducted for the NSTX and NSTX-U geometries, two new major findings will be reported. First, formation of an elongated Sweet-Parker current sheet and a transition to plasmoid instability has for the first time been demonstrated by realistic global simulations [1]. This is the first observation of plasmoid instability in a laboratory device configuration predicted by realistic MHD simulations and then supported by experimental camera images from NSTX. Second, simulations have now, for the first time, been able to show large fraction conversion of injected open flux to closed flux in the NSTX-U geometry [2]. Consistent with the experiment, simulations also show that reconnection could occur at every stage of the helicity injection phase. The influence of 3D effects, and the parameter range that supports these important new findings is now being studied to understand the impact of toroidal magnetic field and the electron temperature, both of which are projected to increase in larger ST devices.
    [1] F. Ebrahimi & R. Raman, Phys. Rev. Lett. 114, 205003 (2015)
    [2] F. Ebrahimi & R. Raman, Nucl. Fusion 56, 044002 (2016)
  • 58th Annual Meeting of the APS Division of Plasma Physics
    Understanding and Predicting Profile Structure and Parametric Scaling of Intrinsic Rotation
    W. Wang, abstract
    [#s68, 31 Oct 2016]
    The main focus of this talk is on developing physical understanding and a first-principles-based model for predicting intrinsic rotation profiles in magnetic fusion experiments, including ITER. It is shown for the first time that turbulent fluctuation-driven residual stress (a non-diffusive component of momentum flux) can account for both the shape and magnitude of the observed intrinsic toroidal rotation profile. The orientation and structure of typical residual stress profile is shown to have a complicated dependence on multiple physics parameters including turbulence type, q-profile structure, and collisionality, through which possible rotation profile optimization can be developed. Fluctuation-generated poloidal Reynolds stress, which displays a very similar radial structure, is also shown to significantly modify the poloidal rotation in a way consistent with experimental observations.
  • 58th Annual Meeting of the APS Division of Plasma Physics
    Laser-Driven Magnetized Collisionless Shocks
    D.B. Schaeffer, slides
    [#s438, 31 Oct 2016]
  • 26th IAEA Fusion Energy Conference
    Gyrokinetic projection of the divertor heat-flux width from present tokamaks to ITER
    C-S. Chang, abstract, slides
    [#s98, 19 Oct 2016]
    The edge gyrokinetic code XGC1 shows that the divertor heat flux width $\lambda_q$ in between ELMs of Type-I ELMy H-modes in two representative types of present tokamaks (DIII-D type for conventional aspect ratio and NSTX type for tight aspect ratio) is set mostly by the ion neoclassical orbit spread, which is proportional to $1/I_P$ , while the blobby turbulent spread plays a minor role. This explains the $1/I_P$ scaling of the heat flux width observed in present tokamaks. On the other hand, the XGC1 studies for ITER H-mode like plasmas show that $\lambda_q$ is mostly set by the blobby turbulent spread, with the heat flux width being about 5X wider than that extrapolated from the $1/I_P$ scaling. This result suggests that the achievement of cold divertor plasmas and partial detachment required for power load and W impurity source control may be more readily achieved and be of simpler control issue than predicted on the basis of the $1/I_P$ scaling. A systematic ongoing validation study of the XGC1 results on various existing tokamaks will also be presented, including JET that is the closest existing device to ITER.
  • 26th IAEA Fusion Energy Conference
    Penetration and amplification of resonant perturbations in 3D ideal-MHD equilibria
    S.R. Hudson, abstract, slides
    [#s69, 17 Oct 2016]
    The nature of ideal-MHD equilibria in three-dimensional geometry is profoundly affected by resonant surfaces, which beget a non-analytic dependence of the equilibrium on the boundary. Furthermore, non-physical currents arise in equilibria with continuously-nested magnetic surfaces and smooth pressure and rotational-transform profiles. We demonstrate that three-dimensional, ideal-MHD equilibria with nested surfaces and $\delta$-function current-densities that produce a discontinuous rotational-transform are well defined and can be computed both perturbatively and using fully-nonlinear equilibrium calculations. The results are of direct practical importance: we predict that resonant magnetic perturbations penetrate past the rational surface (i.e. “shielding” is incomplete, even in purely ideal-MHD) and that the perturbation is amplified by plasma pressure, increasingly so as stability limits are approached.
  • Joint Varenna - Lausanne International Workshop
    3D MHD equilibria with current sheets, magnetic islands, and chaos in stellarators and tokamaks
    J. Loizu, abstract, slides
    [#s84, 29 Aug 2016]
    Two outstanding questions regarding MHD equilibria in toroidally confined plasmas are: how to reliably compute 3D MHD equilibria (1) in the ideal limit where current sheets are predicted to form at resonant rational surfaces, and (2) in partially relaxed plasmas where flux-surfaces, islands, and chaos coexist? The first question is of fundamental importance for MHD theory and has potential experimental implications. In fact, it has been observed experimentally that under certain conditions self-healing of islands can occur and thus current sheet formation is expected on small scales [1]. Moreover, the understanding of the ideal plasma response to resonant magnetic perturbations (RMPs) in tokamaks is incomplete and still under debate [2]. The second question is clearly vital for a proper description of the magnetic field that is consistent with the established pressure and current profiles. In particular, the $\beta$-limit in stellarators is most likely set by equilibrium degradation rather than stability [3]. In order to address these questions, a theory based on a generalized energy principle, referred to as multi-region, relaxed MHD (MRxMHD) [4], was developed and bridges the gap between Taylor’s relaxation theory and ideal MHD. Using the SPEC code [5], a numerical implementation of MRxMHD, we provide the first numerical proof of the existence of singular current densities and a novel theoretical guideline for the computation of three-dimensional ideal MHD equilibria with current sheets [6]. As an example, we provide new predictions for the ideal response to RMPs in tokamaks, together with an unprecedented verification between linearly and nonlinearly perturbed equilibria [7, 8]. Finally, we use SPEC in stellarator geometry to perform equilibrium calculations for W7-X in experimentally-relevant scenarios, thereby providing new quantitative insights for the effect of pressure and bootstrap current on the generation of magnetic islands and ergodic fields.
    [1] Y. Narushima, K.Y. Watanabe et al., Nucl. Fusion 48, 075010 (2008)
    [2] A.D. Turnbull, N.M. Ferraro et al., Phys. Plasmas 20, 056114 (2013)
    [3] M. Drevlak, D. Monticello & A. Reiman, Nucl. Fusion 45, 731 (2005)
    [4] M.J. Hole, S.R. Hudson & R.L. Dewar, Nucl. Fusion 47, 746 (2007)
    [5] S.R. Hudson, R.L. Dewar et al., Phys. Plasmas 19, 112502 (2012)
    [6] J. Loizu, S.R. Hudson et al., Phys. Plasmas 22, 022501 (2015)
    [7] J. Loizu, S.R. Hudson et al., Phys. Plasmas 22, 090704 (2015)
    [8] J. Loizu, S.R. Hudson et al., Phys. Plasmas 23, 055703 (2016)
  • Quo vadis - Complex plasmas
    Electron Emission Effects in Bounded and Dusty Plasma
    I.D. Kaganovich, abstract, slides
    [#s95, 01 Aug 2016]

    Photon, electron and ion bombardment of materials leads to the emission of electrons from the materials. This so-called secondary electron emission (SEE phenomenon is a common link between particle-surface interactions in plasmas, particle accelerators, light sources, and space environments. The plasma-surface interaction in the presence of a strong electron emission is omnipresent in numerous plasma applications such as, for example, cathodes, emissive probes, divertor plasma, surface discharges, dusty plasma, plasma thrusters and plasma processing. In a plasma system, electron and ion fluxes to the wall are determined by particles velocity distribution functions and by the sheath potential, which are consistent with the wall properties. Electrons with sufficient energy to overcome the wall sheath potential and ions accelerated by the sheath potential can impact the wall and produce secondary electrons. The secondary electron emission can then reduce the sheath potential, leading to an increased loss of plasma electrons to the wall, increased wall heating, and increased cooling of the bulk plasma.

    Although the role of the secondary electron emission in the above processes and applications has been acknowledged, its effects are neither well characterized nor well understood and therefore, cannot be reliably predicted. For example, electron emission significantly changes the space-charge distribution around emissive probes, adding uncertainty to plasma potential measurements. This status quo is in a great part due to a complex synergistic nature of particle-surface interactions, which often involves a coupling between impinging particles and materials properties and surface geometry. This coupling is particularly strong for plasma-surface interactions. In this problem, plasma and materials sciences are not separable – the plasma and surface interact and evolve together. The plasma science challenges are i) to develop an understanding of SEE effects on plasma and plasma effects on SEE, including but not limited to heating and energy relaxation of emitted electrons in the plasma through collisions and collective effects, surface recombination, surface charging, and surface breakdown, ii) to characterize SEE properties and SEE effects directly in plasma rather than in vacuum as it is commonly done, and iii) to develop control of SEE effects. The materials and surfaces sciences challenges are to understand i) how surface evolves from interaction with plasma, ii) how these surface and materials modifications affect the SEE from these materials, and iii) how to control SEE properties of materials. For example, changing surface properties with various coatings or due to wall erosion, trapping of emitted particles in complex surfaces, nanoscale effects all can significantly alter the electron emission properties of plasma facing surfaces.

  • 21st International Symposium on Heavy Ion Inertial Fusion
    Update on Beam-Plasma Interaction Research at Princeton Plasma Physics Laboratory
    I.D. Kaganovich (presented by E.P. Gilson), abstract, slides
    [#s78, 19 Jul 2016]
    We have performed experimental and theoretical studies of beam neutralization by background plasma. Near-complete space-charge neutralization is required for the transverse compression of high-perveance ion beams for ion-beam-driven warm dense matter experiments and heavy ion fusion. One approach to beam neutralization is to fill the region immediately before the target with sufficiently dense plasma. The plasma provides a charge-neutralizing medium for beam propagation and makes it possible to achieve a high degree of compression beyond the space-charge limit. Experiments were performed on the Princeton Advanced Test Stand to investigate the degree of charge neutralization for different methods of neutralization [1]. A high-perveance 38 keV Ar+ beam was propagated in a plasma produced in a Ferroelectric Plasma Source (FEPS) discharge. By comparing the measured beam radius with the envelope model for space-charge expansion, it was determined that a charge neutralization fraction of 98% is attainable with sufficiently dense FEPS plasma and 83% with neutralization by plasma produced from a background gas. The transverse electrostatic potential of the ion beam is reduced from 15 V before neutralization to 0.3 V, implying that the energy of the neutralizing electrons is below 0.3 eV. Measurements of the time-evolution of beam radius show that near-complete charge neutralization is established 5 μs after the driving pulse is applied to the FEPS and can last for 35 μs. Numerical simulations of effects of the two-stream instability on the propagation of ion beam in background plasma were performed. Development of the two-stream instability between the beam ions and plasma electrons may lead to beam breakup, a slowing down of the beam particles, acceleration of the plasma particles, and transfer of the beam energy to the plasma particles and wave excitations. Making use of the particle-in-cell code LSP, a one-dimensional Vlasov code, the effects of the two-stream instability on beam propagation over a wide range of beam and plasma parameters were simulated. Because of the two-stream instability, the plasma electrons can be accelerated to velocities twice as high as the beam velocity. The resulting return current of the accelerated electrons may completely change the structure of the beam self-magnetic field, thereby changing its effect on the beam from focusing to defocusing. Therefore, previous theories of beam self-electromagnetic fields that did not take into account the effects of the two-stream instability must be significantly modified [2,3]. As a result of the two-stream instability, an ion beam pulse can generate an electron beam propagating ahead of the ion beam pulse and perturb plasma ahead of the ion beam pulse [4]. One simple method to avoid two-stream instability is to use tenuous plasma that can well neutralize ion beam space charge provided enough electrons can be supplied to the beam pulse from the plasma volume or chamber sides [5]. The associated change in plasma parameters affects the two-stream instability and causes its decay. This effect can be observed on the National Drift Compression Experiment-II (NDCX-II) facility by measuring the spot size of the extracted beamlet propagating through several meters of plasma. This research is supported by the U.S. Department of Energy.
    [1] Anton D. Stepanov, Eric P. Gilson et al., Phys. Plasmas 23, 043113 (2016)
    [2] Erinc Tokluoglu & Igor D. Kaganovich, Phys. Plasmas 22, 040701 (2015)
    [3] Edward A. Startsev, Igor Kaganovich & Ronald C. Davidson, Nucl. Instr. Meth. Phys. Res. A 733, 75 (2014)
    [4] Kentaro Hara & Igor D. Kaganovich, to be submitted to Phys. Plasmas
    [5] William Berdanier, Prabir K. Roy & Igor Kaganovich, Phys. Plasmas 22, 013104 (2015)
  • 21st International Symposium on Heavy Ion Inertial Fusion
    Special Lecture in Honor of Ron Davidson
    E.P. Gilson, slides
    [#s79, 18 Jul 2016]
  • PASC16 Conference, Lausanne, Switzerland
    Gyrokinetic Particle Codes at Exascale: Challenges and Opportunities
    Stéphane Ethier, abstract, slides
    [#s479, 08 Jun 2016]
    Particle-in-Cell (PIC) codes will be among the first applications to run at the exascale due to their high scalability and excellent data locality. This is especially true for relativistic PIC codes that simulate very fast phenomena where fields are time-advanced along with the particles. However, the time scale covered by these simulations is extremely short and of limited usefulness for magnetic fusion research. The gyrokinetic approximation of the Valsov equation, on the other hand, allows for much larger time scales by mathematically integrating out the fast cyclotron motion of ions in magnetized plasmas. Global gyrokinetic PIC codes, which implement this method, have been very successful but also more challenging to scale than their “classical” counterparts due to the gyrokinetic formulation and the need to solve a Poisson equation. This talk describes several computational schemes that have allowed the GK-PIC codes to overcome some of these issues and scale to petascale.
  • 10th West Lake International Symposium on Magnetic Fusion
    12th Asia Pacific Plasma Theory Conference, Hangzhou, China

    Kinetic Plasma Turbulence Simulations on Top Supercomputers Worldwide
    W. Tang, abstract, slides
    [#s99, 09 May 2016]

    A major challenge for supercomputing today is to demonstrate how advances in HPC technology translate to accelerated progress in key application domains. This is the focus of an exciting new program in the US called the “National Strategic Computing Initiative (NSCI)” – announced by President Obama as an Executive Order on July 29, 2015 involving all research & development (R&D) programs in the country to “enhance strategic advantage in HPC for security, competitiveness, and discovery.” A strong focus in key application domains is to accelerate progress in advanced codes that model complex physical systems -- especially with respect to reduction in “time-to-solution” as well as “energy to solution.” It is understood that if properly validated against experimental measurements/observational data and verified with mathematical tests and computational benchmarks, these codes can greatly improve much-needed predictive capability in many strategically important areas of interest.

    Computational advances in magnetic fusion energy research have produced global particle-in-cell (PIC) simulations of turbulent kinetic dynamics for which computer run-time and problem size scale very well with the number of processors on massively parallel many-core supercomputers. For example, the GTC-Princeton (GTC-P) code, which has been developed with a “co-design” focus, has demonstrated the effective usage of the full power of current leadership class computational platforms worldwide at the petascale and beyond to produce efficient nonlinear PIC simulations that have advanced progress in understanding the complex nature of plasma turbulence and confinement in fusion systems for the largest problem sizes. Instead of the familiar Fortran-90 language, this is a modern code written in C and deploying OpenMP/MPI, CUDA, and OpenACC programming strategies with a strong focus on performance optimization of key operational functions within particle-in-cell codes in general. This has produced significant advances in scalability, performance, and portability on path-to-exascale supercomputing systems worldwide. Results have provided strong encouragement for being able to include increasingly realistic dynamics in extreme-scale computing campaigns with the goal of enabling predictive simulations characterized by unprecedented physics resolution/realism needed to help accelerate progress in delivering fusion energy.

  • 10th West Lake International Symposium on Magnetic Fusion
    12th Asia Pacific Plasma Theory Conference, Hangzhou, China

    Computation of Multi-Region, Relaxed MHD Equilibria
    S.R. Hudson, abstract, slides
    [#s100, 09 May 2016]

    We describe the construction of stepped-pressure equilibria as extrema of a multi-region, relaxed magnetohydrodynamic (MHD) energy functional that combines elements of ideal MHD and Taylor relaxation, and which we call MRxMHD. The model is compatible with Hamiltonian chaos theory and allows the three-dimensional MHD equilibrium problem to be formulated in a well-posed manner suitable for computation, and numerical solutions are constructed using the stepped-pressure equilibrium code, SPEC. Highlights of recent calculations will be presented and discussed, including: that the self-organized single-helical-axis (SHAx) and double-axis (DAx) states in reversed field pinch experiments can be reproduced; that MRxMHD can recover ideal MHD; and the SPEC code is used to compute (for the first time) the singular current densities predicted in ideal MHD equilibria in three-dimensional geometry and a new class of solution to the ideal MHD equilibrium equation will be presented. Some ongoing developments of MRxMHD and SPEC will be discussed, including: vacuum verification calculations of W7-X equilibria; free-boundary, non-up-down symmetric DIIID calculations, and including a non-trivial flow into the energy principle.

  • 2016 International Sherwood Fusion Theory Conference
    Adjoint method and runaway electron dynamics in momentum space
    C. Liu, abstract, slides
    [#s71, 06 Apr 2016]
    Runaway electron physics is an important aspect of the post-thermal collapse in disruptions, and is a critical area for current research. Theoretical and experimental studies have shown that various kinds of kinetic effects, including the drag force, the pitch angle scattering, and the synchrotron and bremsstrahlung radiation can change the runaway electron distribution in momentum space. In this study, we use a novel tool, the adjoint method [1], to study the runaway electron momentum space structure. The adjoint method includes all the aforementioned kinetic effects, and overcomes some of the limitations of previous methods such as the test-particle and Monte-Carlo methods. Using the adjoint method, one can obtain results like the runaway probability function and the expected slowing-down time. Theses results are consistent with previous studies, including the increase of the critical electric field for runaway electron growth due to radiation effects [2] and the runaway electron hysteresis [3]. In addition, we use the adjoint method to study the role of large angle scattering in the runaway electron population decay when the electric field is close to but less than the critical value (the marginal case). For this case, we develop a new collision operator for runaway electrons that includes both small and large angle scattering self-consistently. In contrast with the common belief that small angle scattering is much more important than large angle scattering in weakly coupled plasmas, we find that for the marginal case large-angle scattering plays an important role and cannot be ignored. Kinetic simulations with the new collision operator show an upward shift of the critical electric field value compared to previous results. These results can help us better understand the runaway electron momentum space structure, and give insights into quiescent runaway electron (QRE) experiments and runaway electron mitigation in disruptions. This research is supported by the US Department of Energy.
    [1] Chang Liu, Dylan P. Brennan et al., Phys. Plasmas 23, 010702 (2016)
    [2] A. Stahl, E. Hirvijoki et al., Phys. Rev. Lett. 114, 115002 (2015)
    [3] Pavel Aleynikov & Boris N. Breizman, Phys. Rev. Lett. 114, 155001 (2015)
  • 2016 International Sherwood Fusion Theory Conference
    First realistic characterizations of chirping instabilities in tokamaks
    Vinícius Duarte, abstract, slides
    [#s73, 06 Apr 2016]
    In tokamak plasmas, the dynamics of phase-space structures with their associated frequency chirping is a topic of major interest in connection with mechanisms for fast ion losses. The onset of phase-space holes and clumps which produce chirping phenomena, has been theoretically shown to be related to the emergence of an explosive solution of an integro-differential, nonlocal cubic equation (IDNC) [1,2] that governs the early mode amplitude evolution in the nonlinear regime near marginal stability. We have extended the analysis of the IDNC model to quantitatively account for multiple resonance surfaces of a given mode in the presence of drag and diffusion (due to collisions and microturbulence) operators. Then a more realistic criterion is found, that takes into account the details of the mode structure and the variation of transport coefficients in phase space, to determine whether steady state solutions can or cannot exist. Stable steady state solutions indicate that chirping oscillations do not arise, while the lack of steady solutions due to the predominance of drag, is indicative that a frequency chirping response is likely in a plasma. Waves measured in experiments have been analyzed using NOVA and NOVA-K codes, with which we can realistically account for the mode structure and varying resonance responses spread over phase space. In the experiments presently analyzed, compatibility has been found between the theoretical predictions for whether chirping should or should not arise and the experimental observation or lack of observation of toroidicity-induced Alfvén eigenmodes in NSTX, DIII-D and TFTR. We have found that stochastic diffusion due to wave microturbulence is the dominant energetic particle transport mechanism in many plasma experiments, and its strength is the key as to whether chirping solutions are likely to arise.
    [1] H.L. Berk, B.N. Breizman & M. Pekker, Phys. Rev. Lett. 76, 1256 (1996)
    [2] M.K. Lilley, B.N. Breizman & S.E. Sharapov, Phys. Rev. Lett. 102, 195003 (2009)
  • 2016 International Sherwood Fusion Theory Conference
    Penetration and amplification of resonant perturbations in 3D ideal-MHD equilibria
    S.R. Hudson, abstract, slides
    [#s70, 04 Apr 2016]
    Understanding 3D ideal-MHD equilibria, as described by the ideal force-balance equation, $\nabla p = {\bf j} \times {\bf B}$, is fundamentally important for understanding both tokamaks & stellarators. Edge-localized modes are believed to be ideal, peeling-ballooning modes; and a ‘hot-topic’ of current research is to suppress these modes using resonant magnetic perturbations (RMPs). However, the nature of ideal-MHD equilibria in 3D geometry is profoundly affected by resonant surfaces, which beget a non-analytic dependence on the boundary. And, in order to preserve quasi-neutrality, non-physical infinite currents arise in equilibria with continuously-nested magnetic surfaces and smooth pressure & transform profiles. These difficulties are not fundamental flaws in ideal-MHD, which remains perhaps the most successful, relevant yet simplest model of plasma dynamics. It is just that, until recently, self-consistent tractable solutions to the ideal-MHD equilibrium equation for arbitrary 3D geometry had not been discovered. Recently, for the first time, we computed the $1/x$ and $\delta$-function current-densities, and we realized that self-consistent solutions demand locally-infinite shear at the resonant surfaces. We introduced a new class of solutions that admit additional delta-function current-densities that produce a discontinuity in the rotational-transform that removes the singularities. Our equilibrium solutions can be computed both perturbatively and using fully-nonlinear equilibrium calculations (with the SPEC code), and we present precise verification calculations. Most importantly, our solutions yield predictions that are in sharp contrast to previous predictions, with direct implications for understanding the penetration of RMPs: in ideal-MHD, a resonant perturbation penetrates past the rational surface and into the core of the plasma; and the perturbation is magnified by pressure inside the resonant surface, increasingly so as stability limits are approached.
  • 57th Annual Meeting of the APS Division of Plasma Physics
    A new class of three-dimensional ideal-MHD equilibria with current sheets
    J. Loizu, abstract, slides
    [#s82, 20 Nov 2015]
    Ideal MHD predicts singular current densities in 3D equilibria with nested flux surfaces: a pressure-driven $1/x$ current density that arises around resonant rational surfaces, and a Dirac $\delta$-function current that develops at those surfaces. Only recently have these currents been computed numerically [1], and we provide details of the calculation. We show that locally-infinite shear (i.e. discontinuous rotational-transform) at the resonant surfaces ensures well-defined solutions. Singularities in the current density are allowed in ideal-MHD, but the current passing through any surface must be finite for any physically-acceptable equilibrium model. While the integral of the $\delta$-current density is finite, the $1/x$ current diverges over certain surfaces. This led to the conclusion that pressure gradients cannot exist in the vicinity of rational surfaces and thus that the possible pressure profiles are either fractal [2] or discontinuous [3]. In this talk, we present a new class of 3D, globally-ideal, MHD equilibria with (i) continuously nested surfaces, (ii) arbitrary, continuous and smooth pressure profiles, (iii) arbitrary, 3D boundaries, (iv) without unphysical currents, and which are (v) analytic functions of the boundary [4]. Examples of such equilibria, computed with the SPEC code [5], are shown and verified against generalized solutions to Newcomb equation, showing excellent convergence. The results imply that a resonant magnetic perturbation can penetrate all the way into the centre of a tokamak without being shielded at the resonant surface, even within ideal MHD.
    [1] J. Loizu, S.R. Hudson et al., Phys. Plasmas 22, 022501 (2015)
    [2] Harold Grad, Phys. Fluids 10, 137 (1967)
    [3] Oscar Bruno & Peter Laurence, Commun. Pure Appl. Math. 49, 717 (1996)
    [4] J. Loizu, S.R. Hudson et al., Phys. Plasmas 22, 090704 (2015)
    [5] S.R. Hudson, R.L. Dewar et al., Phys. Plasmas 19, 112502 (2012)
  • 57th Annual Meeting of the APS Division of Plasma Physics
    Acceleration of plasma electrons by intense nonrelativistic ion beams propagating in background plasma due to two-stream instability
    I.D. Kaganovich, abstract, slides
    [#s75, 19 Nov 2015]
    In this paper we study the effects of the two-stream instability on the propagation of intense nonrelativistic ion and electron beams in background plasma. Development of the two-stream instability between the beam ions and plasma electrons leads to beam breakup, a slowing down of the beam particles, acceleration of the plasma particles, and transfer of the beam energy to the plasma particles and wave excitations. Making use of the particle-in-cell codes EDIPIC and LSP, and analytic theory we have simulated the effects of the two-stream instability on beam propagation over a wide range of beam and plasma parameters. Because of the two-stream instability, the plasma electrons can be accelerated to velocities as high as twice the beam velocity. The resulting return current of the accelerated electrons may completely change the structure of the beam self-magnetic field, thereby changing its effect on the beam from focusing to de-focusing. Therefore, previous theories of beam self-electromagnetic fields that did not take into account the effects of the two-stream instability must be significantly modified. This effect can be observed on the National Drift Compression Experiment-II (NDCX-II) facility by measuring the spot size of the extracted beamlet propagating through several meters of plasma. Particle-in-cell, fluid simulations, and analytical theory also reveal the rich complexity of beam-plasma interaction phenomena: intermittency and multiple regimes of the two-stream instability in dc discharges; band structure of the growth rate of the two-stream instability of an electron beam propagating in a bounded plasma and repeated acceleration of electrons in a finite system. In collaboration with E. Tokluoglu, D. Sydorenko, E. A. Startsev, J. Carlsson, and R. C. Davidson. Research supported by the U.S. Department of Energy.
  • 57th Annual Meeting of the APS Division of Plasma Physics
    Free-Boundary 3D Equilibria and Resistive Wall Instabilities with Extended-MHD
    N. Ferraro, abstract, slides
    [#s76, 19 Nov 2015]
    The interaction of the plasma with external currents, either imposed or induced, is a critical element of a wide range of important tokamak phenomena, including resistive wall mode (RWM) stability and feedback control, island penetration and locking, and disruptions. A model of these currents may be included within the domain of extended-MHD codes in a way that preserves the self-consistency, scalability, and implicitness of their numerical methods. Such a model of the resistive wall and non-axisymmetric coils is demonstrated using the M3D-C1 code for a variety of applications, including RWMs, perturbed non-axisymmetric equilibria, and a vertical displacement event (VDE) disruption. The calculated free-boundary equilibria, which include Spitzer resistivity, rotation, and two-fluid effects, are compared to external magnetic and internal thermal measurements for several DIII-D discharges. In calculations of the perturbed equilibria in ELM suppressed discharges, the tearing response at the top of the pedestal is found to correlate with the onset of ELM suppression. Nonlinear VDE calculations, initialized using a vertically unstable DIII-D equilibrium, resolve in both space and time the currents induced in the wall and on the plasma surface, and also the currents flowing between the plasma and the wall. The relative magnitude of these contributions and the total impulse to the wall depend on the resistive wall time, although the maximum axisymmetric force on the wall over the course of the VDE is found to be essentially independent of the wall conductivity. This research was supported by US DOE contracts DE-FG02-95ER54309, DE-FC02-04ER54698 and DE-AC52-07NA27344.
  • 57th Annual Meeting of the APS Division of Plasma Physics
    Magnetic self-organization in Tokamaks
    S.C. Jardin, abstract, slides
    [#s74, 17 Nov 2015]
    We report here on a nonlinear mechanism that forms and maintains a self-organized stationary (sawtooth free) state in tokamaks. This process was discovered by way of extensive long-time simulations using the M3D-C1 3D extended MHD code in which new physics diagnostics have been added. It is well known that most high-performance modes of tokamak operation undergo “sawtooth” cycles, in which the peaking of the toroidal current density triggers a periodic core instability which redistributes the current density. However, certain modes of operation are known, such as the “hybrid” mode in DIII-D, ASDEX-U, JT-60U and JET, and the long-lived modes in NSTX and MAST, which do not experience this cycle of instability. Empirically, it is observed that these modes maintain a non-axisymmetric equilibrium which somehow limits the peaking of the toroidal current density. The physical mechanism responsible for this has not previously been understood, but is often referred to as “flux-pumping”, in which poloidal flux is redistributed in order to maintain $q_0 > 1$. In this talk, we show that in long-time simulations of inductively driven plasmas, a steady-state magnetic equilibrium may be obtained in which the condition $q_0 > 1$ is maintained by a dynamo driven by a stationary marginal core interchange mode. This interchange mode, unstable because of the pressure gradient in the ultra-low shear region in the center region, causes a $(1,1)$ perturbation in both the electrostatic potential and the magnetic field, which nonlinearly cause a $(0,0)$ component in the loop voltage that acts to sustain the configuration. This hybrid mode may be a preferred mode of operation for ITER. We present parameter scans that indicate when this sawtooth-free operation can be expected.
  • International Conference on Numerical Simulation of Plasmas, Colorado
    Fully non-linear multi-species Fokker-Planck-Landau collision operator for kinetic simulation of magnetized plasma
    Robert Hager, abstract, slides
    [#s290, 12 Aug 2015]
    We describe computational and mathematical sciences techniques in improving and implementing a time-dependent, fully non-linear multi-species Fokker-Planck-Landau collision operator based on the single species description of Yoon and Chang [Phys. Plasmas 21, 032503 (2014)] in the full-function gyrokinetic particle-in-cell codes XGC1 [Ku et al., Nucl. Fusion 49, 115021 (2009)] and XGCa. XGC simulations include pedestal and scrape-off layer regions, where steep gradients and large fluctuations can cause significant deviations of the particle distribution function from a Maxwellian. Therefore, the use of a non-linear collision operator is necessary. For XGC simulations including gyrokinetic ions and drift-kinetic electrons, we generalized the single-species non-linear Fokker-Planck-Landau collision operator by Yoon and Chang to a multiple-species operator. This operator is based on a finite volume method using distribution functions mapped from the marker particles to 2D velocity space. The relative errors of mass, momentum, and energy conservation can be required to be negligible through the convergence criterion of the implicit time stepping method used in the collision operator. For a typical simulation, we limited to error to be 10-6. After a collision operation, the updated distribution function is interpolated back to the particles. Due to the large number of configuration space grid points on which the collision operator is evaluated (XGCa: ~104, XGC1: ~106), the workload due to collisions can be comparable or larger than the workload due to particle motion. In order to keep the added computing time at a tolerable level we have implemented 1) a nested OpenMP parallelism that allows to evaluate the collision operator on several grid points at the same time in the outer thread level and accelerates the calculation for every single grid point in the inner thread level, and 2) a completely new load balancing algorithm that constantly adjusts particle and mesh decomposition to minimize runtime. In addition, Nested OpenMP threading also helps to meet memory constraints on low-memory computers such as Mira that offers as little as 256 MB of memory per thread. With the computational and algorithmic improvements, the fully-nonlinear multispecies collision operator is now used routinely at extreme scale in XGC simulations on leadership class supercomputers such as Titan, Mira, and Edison.
  • 2015 International Sherwood Fusion Theory Conference
    Computation of singular currents at rational surfaces in non-axisymmetric MHD equilibria
    J. Loizu, abstract, slides
    [#s81, 17 Mar 2015]
    Ideal MHD predicts the existence of singular current densities forming at rational surfaces in three-dimensional equilibria with nested flux surfaces. These current singularities consist of a Pfirsch-Schlüter, $1/x$ current that arises around rational surfaces as a result of finite pressure gradient and a Dirac $\delta$-function current that develops at rational surfaces and presumably prevents the formation of islands that would otherwise develop in a non-ideal plasma. These currents play a crucial role in describing (1) the plasma response to non-axisymmetric boundary perturbations, (2) the equilibrium and stability of non-axisymmetric, toroidally confined plasmas, and (3) the triggering of reconnection phenomena such as tokamak sawteeth. While analytical formulations have been developed to describe such currents in simplified geometries, a numerical proof of their existence has been hampered by the assumption of smooth functions made in conventional MHD equilibrium models such as VMEC. Recently, a theory based on a generalized energy principle, referred to as multi-region, relaxed MHD (MRxMHD), was developed and incorporates the possibility of non-smooth solutions to the MHD equilibrium problem. Using SPEC [1], a nonlinear implementation of MRxMHD, we provide the first numerical proof of their mutual existence and a novel theoretical guideline for the numerical computation of three-dimensional ideal MHD equilibria with singular currents [2]. Examples of such kind of equilibria are shown for both slab and cylindrical geometries, and the numerical results are thoroughly verified against analytical predictions from linearly perturbed ideal MHD equilibria. Based on these results, we present the hypothesis that non-axisymmetric ideal MHD equilibria only exist for discontinuous rotational transform profiles [3].
    [1] S.R. Hudson, R.L. Dewar et al., Phys. Plasmas 19, 112502 (2012)
    [2] J. Loizu, S.R. Hudson et al., Phys. Plasmas 22, 022501 (2015)
    [3] J. Loizu, S.R. Hudson et al., Phys. Plasmas 22, 090704 (2015)
  • 56th Annual Meeting of the APS Division of Plasma Physics
    X-Point-Position-Dependent Intrinsic Rotation in the Edge of TCV
    T. Stoltzfus-Dueck, abstract, slides
    [#s97, 28 Oct 2014]
    A simple transport-based theoretical model predicts that intrinsic toroidal rotation in the tokamak edge should depend strongly on $R_X$, the major-radial position of the X-point, including a sign change to counter-current rotation for adequately outboard X-point. To test the prediction, an $R_X$ scan was conducted in Ohmic L-mode shots on TCV, in both USN and LSN configurations. The strong linear dependence on $R_X$ was experimentally observed, with quantitative magnitude corresponding to a realistic value for the theory’s corresponding input parameter. Although peaked rotation profiles complicate the comparison of absolute rotation values, the data is consistent with the predicted sign change. The core rotation profile shifted fairly rigidly with the edge rotation value, maintaining a relatively constant core rotation gradient. Core rotation reversals, triggered accidentally in a few shots, had little effect on the edge rotation velocity. Edge rotation was modestly more counter-current in USN than LSN discharges.
  • Joint 19th ISHW and 16th IEA-RFP workshop
    Minimally constrained model of self-organised helical states in RFX
    G.R. Dennis, abstract, slides
    [#s83, 17 Sep 2013]
    We show that the self-organized single-helical-axis (SHAx) and double-helical-axis (DAx) states [1, 2] in reversed field pinches can be reproduced in a minimally constrained equilibrium model using only five parameters [3] (see Figure 1). This is a significant reduction on previous representations of the SHAx which have required an infinite number of constraints [4]. The DAx state, which has a non-trivial topology, has not been previously reproduced using an equilibrium model that preserves this topological structure. We show that both states are a consequence of transport barrier formation in the plasma core, in agreement with experimental results.

    Figure 1: Comparison of the ideal MHD representation of the SHAx state in RFX-mod and the minimal model (MRXMHD) of this state presented in this work. Figures (a)–(d) show the (poloidal) magnetic flux contours of the ideal MHD plasma equilibrium at equally spaced toroidal angles covering one period of the helical solution. Figures (e)–(h) show Poincaré plots of the minimal model at the same toroidal locations as (a)–(d). The thick black lines mark the location of the transport barrier separating the two plasma volumes.
    [1] D.F. Escande, P. Martin et al., Phys. Rev. Lett. 85, 1662 (2000)
    [2] P. Martin, L. Marrelli et al., Nucl. Fusion 43, 1855 (2003)
    [3] G.R. Dennis, S.R. Hudson et al., Phys. Rev. Lett. 111, 055003 (2013)
    [4] D. Terranova, D. Bonfiglio et al., Plasma Phys. Controlled Fusion 52, 124023 (2010)
  • 2013 International Sherwood Fusion Theory Conference
    A minimally constrained model of self-organised helical states in reversed-field pinches
    G.R. Dennis, abstract, slides
    [#s96, 17 Apr 2013]
    We show that the self-organized single-helical-axis (SHAx) and double-helical-axis (DAx) states [1, 2] in reversed field pinches can be reproduced in a minimally constrained equilibrium model using only five parameters [3] (see Figure 1). This is a significant reduction on previous representations of the SHAx which have required an infinite number of constraints [4]. The DAx state, which has a non-trivial topology, has not been previously reproduced using an equilibrium model that preserves this topological structure. We show that both states are a consequence of transport barrier formation in the plasma core, in agreement with experimental results.

    Figure 1: Comparison of the ideal MHD representation of the SHAx state in RFX-mod and the minimal model (MRXMHD) of this state presented in this work. Figures (a)–(d) show the (poloidal) magnetic flux contours of the ideal MHD plasma equilibrium at equally spaced toroidal angles covering one period of the helical solution. Figures (e)–(h) show Poincaré plots of the minimal model at the same toroidal locations as (a)–(d). The thick black lines mark the location of the transport barrier separating the two plasma volumes.
    [1] D.F. Escande, P. Martin et al., Phys. Rev. Lett. 85, 1662 (2000)
    [2] P. Martin, L. Marrelli et al., Nucl. Fusion 43, 1855 (2003)
    [3] G.R. Dennis, S.R. Hudson et al., Phys. Rev. Lett. 111, 055003 (2013)
    [4] D. Terranova, D. Bonfiglio et al., Plasma Phys. Controlled Fusion 52, 124023 (2010)
  • 38th EPS Conference on Plasma Physics
    Partially-relaxed, partially-constrained MHD equilibria
    S.R. Hudson, abstract, slides
    [#s87, 01 Jul 2011]
    The commonly used equation of ideal force balance, $\nabla p = {\bf j} \times {\bf B}$, is pathological when the magnetic field, ${\bf B}$, is chaotic. Any continuous, non-trivial pressure that satisfies ${\bf B}\cdot\nabla p = 0$ with a chaotic field will have an infinity of discontinuities in the pressure gradient. The perpendicular current ${\bf j}_\perp = {\bf B} \times \nabla p/B^2$ is either zero or discontinuous, and $\nabla \cdot {\bf j}_\perp$ is zero or not defined. This pathological structure causes problems for the so-called “Spitzer” iterative approach, which is fundamentally ill-posed as it depends on inverting magnetic differential equations, e.g. ${\bf B} \cdot \nabla (j_\parallel/B) = −\nabla \cdot {\bf j}_\perp$, and such equations have a dense set of singularities. We suggest instead a well-posed equilibrium construction based on an extension of Taylor relaxation: a weakly-resistive plasma will relax to minimize the plasma energy subject to the constraint of conserved helicity. To obtain non-trivial pressure profiles we add additional topological constraints on a selection of KAM surfaces on which the constraints of ideal MHD are imposed. Consider a plasma region comprised of a set of $N$ nested annular regions which are separated by a discrete set of toroidal interfaces, ${\cal I}_l$. In each volume, ${\cal V}_l$, bounded by the ${\cal I}_{l-1}$ and ${\cal I}_l$ interfaces, the plasma energy, $U_l$, the global-helicity, $H_l$, and the “mass”, $M_l$, are given by the integrals: \begin{eqnarray} U_l \equiv \int_{{\cal V}_l} \left( \frac{p}{\gamma-1} + \frac{B^2}{2} \right)dv, \;\; H_l \equiv \int_{{\cal V}_l} {\bf A}\cdot{\bf B}\;dv, \;\; M_l \equiv \int_{{\cal V}_l} p^{1/\gamma}\;dv, \end{eqnarray} where ${\bf A}$ is the vector potential, ${\bf B} = \nabla \times {\bf A}$. The equilibrium states that we seek minimize the total plasma energy, subject to the constraints of conserved helicity and mass in each annulus. Arbitrary variations in both the magnetic field in each annulus and the geometry of the interfaces are allowed, except that we assume the magnetic field remains tangential to the interfaces which act as “ideal barriers” and coincide with pressure gradients. The Euler-Lagrange equations show that in each annulus the magnetic field satisfies $\nabla \times {\bf B} = \mu_l {\bf B}$, and across each interface the total pressure is continuous, $[[p + B^2/2]] = 0$. We have implemented this model in a code, the Stepped Pressure Equilibrium Code (SPEC), which uses a mixed Fourier, finite-element representation for the vector potential. Quintic polynomial basis functions give rapid convergence in the radial discretization, and the freedom in the poloidal angle is exploited to minimize a “spectral-width”. For given interface geometries the Beltrami fields in each annulus are constructed in parallel, and a Newton method (with quadratic-convergence) is implemented to adjust the interface geometry to satisfy force-balance. Convergence studies and three-dimensional equilibrium solutions with non-trivial pressure and islands and chaotic fields will be presented.
  • 17th International Stellarator / Heliotron Workshop
    Cantori, chaotic coordinates and temperature gradients in chaotic fields
    S.R. Hudson, abstract, slides
    [#s86, 12 Oct 2009]
    Toroidal magnetic field line flow is a $1\frac{1}{2}$dimensional Hamiltonian system and, in the absence of symmetry, such systems are generally chaotic. The existence of local regions of irregular trajectories has profound implications for a variety of problems in plasma confinement: here we consider anisotropic heat transport. The study of heat transport in chaotic fields has a long history [1], but conventional approaches effectively treat chaotic fields as random, and thus overlook some important properties of chaotic fields, namely the hierachy of invariant dynamics comprised of regular, irrational trajectories. The invariant irrational sets, known as “cantori”, that persist after the destruction of the “KAM” surfaces can form effective partial barriers to anisotropic transport. We demonstrate using a model of heat transport with separate parallel and perpendicular thermal diffusion coefficients, $\kappa_\parallel$ and $\kappa_\perp$. For fusion plasmas the ratio $\kappa_\parallel / \kappa_\perp$ may exceed $10^{10}$, and the temperature adapts to the fractal structure of the magnetic field. This paper will show that temperature gradients coincide with the cantori. We develop chaotic-magnetic coordinates [2]: coordinates adapted to the invariant structures of the field line flow. By adapting the coordinate surfaces to the partial barriers formed by the cantori, the coordinate surfaces coincide with isotherms. The temperature written in chaotic coordinates is well approximated by $T = T(s)$, where $s$ is a radial coordinate, and an expression for the temperature gradient is derived: \begin{eqnarray}\frac{dT}{ds} = \frac{c}{\kappa_\parallel \varphi + \kappa_\perp G}, \end{eqnarray} where $\varphi \equiv \int \int d\theta d\phi \sqrt g B^2_n$ is the squared field-line flux across a coordinate surface, and $G \equiv \int \int d\theta d\phi \sqrt g g^{ss}$ is an averaged metric quantity.
    [1] A.B. Rechester & M.N. Rosenbluth, Phys. Rev. Lett. 40, 38 (1978)
    [2] S.R. Hudson & J. Breslau, Phys. Rev. Lett. 100, 095001 (2008)
  • 22nd IAEA Fusion Energy Conference
    Temperature Gradients are supported by Cantori in Chaotic Magnetic Fields
    S.R. Hudson, abstract, slides
    [#s85, 13 Oct 2008]
    With the tantalizing prospect that localized regions of chaotic magnetic field can be used to suppress ideal instabilities in fusion devices, as suggested by the resonant magnetic perturbation (RMP) experiments on DIIID, it becomes necessary to understand the impact of chaotic fields on confinement, particularly so considering that RMP fields are being considered as an ELM mitigation strategy for ITER. Using a model of heat transport for illustration, this paper will show that chaotic fields can support significant temperature gradients, despite the fact that flux surfaces may be destroyed by applied error fields. The remnants of the irrational flux surfaces, the cantori, present extremely effective partial-barriers to field-line transport, and thus present effective barriers to any transport process that is dominantly parallel to the field. We extend the concept of magnetic coordinates to chaotic fields [1], and show that the temperature, generally a function of three-dimensional space, takes the simple form $T(s)$, where $s$ labels the chaotic-coordinate surfaces.
    [1] S.R. Hudson & J. Breslau, Phys. Rev. Lett. 100, 095001 (2008)