R&R Seminars

The Research & Review seminars are intended to:

• to prepare for the upcoming review of the five-year research plan of the Theory Department
• to update and inform the PPPL Theory Department on progress of individual research and future plans
• to disseminate this information broadly throughout the community

R&R seminars are usually held Tuesdays, @10:45 am, in the Theory Conference Room, T169.

Upcoming

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  TBA
  Weixing Wang, Princeton Plasma Physics Laboratory
  #s1110, Tuesday, 23 Jun 2020, 10:45am

Past

• Click here to join the zoom meeting:
  Stellarator Coil Design: Past, Present and Future
  Stuart Hudson, Princeton Plasma Physics Laboratory , abstract, slides
  [#s1108, 02 Jun 2020]
  The magnetic field required to confine a plasma must be provided externally, provided (historically) by a set of external current-carrying “coils”. Very early coil design algorithms were simplistic; but, advanced stellarators were constructed, e.g. LHD. The idea of “optimized stellarators” was a conceptual breakthrough. In this talk, the mathematics of modern coil-design algorithms & trends shall be described.
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  Machine learning and serving of discrete field theories — when artificial intelligence meets the discrete universe
  Hong Qin, Princeton Plasma Physics Laboratory, Princeton University, abstract, slides
  [#s1107, 26 May 2020]
  In 1601, Kepler inherited the observational data of planetary orbits meticulously collected by his mentor Tycho Brahe. It took Kepler 5 years to discover his first and second laws of planetary motion, and another 78 years before Newton solved the Kepler problem using his laws of motion and universal gravitation.* In this talk, I will develop a machine learning and serving algorithm for discrete field theories that solves the Kepler problem without learning or knowing Newton’s laws of motion and universal gravitation. The learning algorithm learns a discrete field theory from a set of data of planetary orbits similar to what Kepler inherited, and the serving algorithm correctly predicts other planetary orbits, including parabolic and hyperbolic escaping orbits, of the solar system. The proposed algorithm is also applicable when the effects of special relativity and general relativity are important without knowing or learning Einstein’s theory. The illustrated advantages of discrete field theories relative to continuous theories in terms of machine learning compatibility are consistent with Bostrom’s simulation hypothesis. I will also show how this algorithm can help to achieve the goal of fusion energy. *Newton discovered his laws of gravitation and motion while in quarantine from the Great Plague of London in 1665. Physics has not changed much for almost a century and we are in quarantine from the COVID-19……
• Chirp Simulation with Orbit
  Roscoe White, PPPL, abstract, slides
  [#s1106, 18 May 2020]
  In tokamak discharges, toroidal Alfv ́en eigenmodes often experience complex semi-periodic frequency modulation known as chirping. These events modify the local high energy particle distribution and are expected to occur in many future fusion devices which include energetic beams or fusion products. This work presents a study of simulations of mode chirping made in order to better understand its phase-space properties in a realistic tokamak configuration. We find a mechanism which permits rapid repeated chirping with strong amplitude variation in each chirp. Each chirp is associated with an amplitude crash to low magnitude and local manipulation of the density gradients through a shift of mode phase through π. The chirping produces high density clumps which propagate down the fast ion density gradient and low-density holes that propagate up the density gradient away from the resonance. This flow of particles across the resonance provides the energy source and local gradients for repeated chirping.
• Roles of Plasmoid Instability in Magnetic Reconnection and Magnetohydrodynamic Turbulence
  Yi-Min Yuang, Princeton University, abstract, slides
  [#s1063, 24 May 2019]
  The ubiquitous thin current sheets in high-Lundquist-number space and astrophysical plasmas are known to be unstable to the plasmoid instability, which disrupts current sheets to form smaller structures such as flux ropes and secondary current sheets. The plasmoid instability thus plays a significant role in magnetic reconnection and magnetohydrodynamic (MHD) turbulence. In this talk, I will present recent theoretical and numerical advances in plasmoid-mediated current sheet disruption and the onset of fast magnetic reconnection. Then I will discuss the effects of plasmoid instability in steepening MHD turbulence spectrum. In addition to these theoretical and numerical developments, I will also present evidence of the plasmoid instability in solar observations.
• Kinetic Modeling of Non-Equilibrium Plasmas for Modern Applications
  Igor D. Kaganovich, PPPL, abstract, slides
  [#s1026, 02 May 2019]
  We have studied several non-equilibrium plasma devices where kinetic effects determine plasma self-organization: neutralization of ion beams and electron cloud effects in accelerators, negative hydrogen Ion Sources, ExB discharges (plasma switch and Penning discharge), thermoelectric converters. Neutralization of positive ion beam space-charge by electrons is important for many accelerator applications, i.e., heavy ion inertial fusion, and ion beam-based surface engineering. Past experimental studies showed poorer ion beam neutralization by electron-emitting filaments, compared with neutralization by plasmas. Now researchers have found that reduced neutralization may be related to the generation of electrostatic solitary waves (ESWs) during the neutralization process, as the ion beam passes through the electron-emitting filaments. Use of 2D Particle-in-Cell simulations shows that the process of electron capture by the ion beam pulse can cause two-stream instability of electrons, which quickly evolve into the formation of stable nonlinear ESWs. The ESWs with longitudinal size reaching several centimeters can reflect back-and-forth between the two ends of the ion beam pulse and last far longer than the duration of the pulse. As a result, the degree of neutralization of the ion beam pulse is reduced when compared to the case without ESWs. These results provide new insight into the physics of ion beam neutralization and present a new example of the importance of taking into account the presence of multi-dimensional solitons in plasmas [1]. We have also developed a Global Model Code for Negative Hydrogen Ion Sources, GMNIS [2]. The codes ultimate goal is to aid developing optimized negative ion beams for ITER. The code solves volume-averaged equations: continuity for plasma species and electron energy equation for the electron temperature, and include more than 1000 volumetric and surface reactions for interactions of electrons, ground-state atomic and molecular hydrogen, molecular ions and atomic ions, negative ions, 14 vibrationally-excited states of molecular hydrogen, and excited atoms. Results of the code are benchmarked against another code [2]. Convenient analytical solution for vibrational spectrum of H2 was also derived. We have studied the low-pressure (left-hand) branch of the Paschen curve at very high voltage when electrons are in the runaway regime and charge exchange/ionization avalanche by ions and fast neutral atoms becomes important for plasma switch application, which operates at 100-500KV range. For these voltages, a multi valued Pashen curve was observed. We performed particle-in-cell simulations and developed analytical model that can explain experimentally observed Pashen curve .[3] We have also preformed studies of rotating spoke in a Penning discharge and proposed analytical scaling law for its frequency [4]. Efficient thermal electric converter is proposed in Ref.[5]. References [1] C. Lan and I. D. Kaganovich, “Electrostatic solitary waves in ion beam neutralization”, arXiv:1810.04655 and accepted Phys. Plasmas (2019) - feature article. [2] W. Yang, S. N. Averkin, A. V. Khrabrov, I. D. Kaganovich, Y.-N. Wang, S. Aleiferis, and P. Svarnas, "Benchmarking of global model code for negative hydrogen ion sources", Phys. Plasmas 25, 113509 (2018). [3] Liang Xu, Alexander V Khrabrov, Igor D Kaganovich and Timothy J Sommerer, "“Analytical model of high-voltage breakdown in helium with cold cathode”, Plasma Sources Sci. Technol. 27, 104004 (2018). [4] Andrew T. Powis, Johan A. Carlsson, Igor D. Kaganovich, Yevgeny Raitses, and Andrei Smolyakov, "Scaling of spoke rotation frequency within a Penning discharge", Physics of Plasmas 25, 072110 (2018). [5] A. S. Mustafaev, V. I. Yarygin, V. S. Soukhomlinov, A. B. Tsyganov, and I. D. Kaganovich, "Nano-size effects in graphite/graphene structure exposed to cesium vapor", Journal of Applied Physics 124, 123304 (2018).
• Constructing “chaotic coordinates” for non-integrable dynamical system
  Stuart Hudson, abstract, slides
  [#s969, 18 Jan 2019]
  Action-angle coordinates can be constructed for so-called integrable Hamiltonian dynamical systems, for which there exists a foliation of phase space by surfaces that are invariant under the dynamical flow. Perturbations generally destroy integrability. However, we know that periodic orbits will survive, as will cantori, as will the “KAM” surfaces that have sufficiently irrational frequency, depending on the perturbation. There will also be irregular “chaotic” trajectories. By “fitting” the coordinates to the invariant structures that are robust to perturbation, action-angle coordinates may be generalized to non-integrable dynamical systems. These coordinates “capture” the invariant dynamics and neatly partition the chaotic regions. These so-called chaotic coordinates are based on a construction of almost-invariant surfaces known as ghost surfaces. The theoretical definition and numerical construction of ghost surfaces and chaotic coordinates will be described and illustrated.
• Kelvin-Helmholtz instability is the result of spontaneous parity-time symmetry breaking*
  Hong Qin, PPPL, abstract, slides
  [#s941, 13 Dec 2018]
  Parity-Time (PT)-symmetry is being actively investigated as a fundamental property of observables in quantum physics. We show that the governing equations of the classical two-fluid interaction and the incompressible fluid system are PT-symmetric, and the well-known Kelvin-Helmholtz instability is the result of spontaneous PT-symmetry breaking. It is expected that all classical conservative systems governed by Newton's law admit PT-symmetry, and the spontaneous breaking thereof is a generic mechanism for classical instabilities. Discovering the PT-symmetry of systems in plasma physics and fluid dynamics and identifying the spontaneous PT-symmetry breaking responsible for instabilities enable new techniques to classical physics and enrich the physics of PT-symmetry.
  [1] Hong Qin, et. al, arxiv: 1810.11460
• Quasi-linear resonance broadened model for fast ion relaxation in the presence of Alfvénic instabilities
  N. N. Gorelenkov, PPPL, abstract, slides
  [#s890, 19 Oct 2018]
  The resonance broadened quasi-linear (RBQ) model is developed for the problem of relaxing the fast energetic particle distribution function in constant-of-motion (COM) 3D space [N.N. Gorelenkov et al., Nucl. Fusion 58 (2018) 082016]. The model is generalized by using the QL theory [H. Berk et al., Nucl. Fusion 35 (1995) 1661] and carefully examining the wave particle interaction (WPI) in the presence of realistic Alfvén eigenmode (AE) structures and pitch angle scattering with the help of the guiding center code ORBIT. The RBQ model for realistic plasma conditions is adapted by going beyond the perturbative-pendulum-like approximation for the wave particle dynamics near the resonance. An iterative procedure [White, PoP'18] is introduced in order to account for eigenstructures varying within the resonances. It is found that radially-localized mode structure implies a saturation level 2-3 times smaller than predicted by an earlier bump-on-tail QL model that employed uniform mode structures. In addition, the resonance broadening includes the Coulomb collisional pitch angle scattering. The RBQ code takes into account the beam ion diffusion in the direction of the canonical toroidal momentum. The wave particle interaction is reduced to one-dimensional dynamics where for low-frequency Alfvénic modes typically the particle kinetic energy is nearly constant. The diffusion equation is solved simultaneously for all particles together with the evolution equation for the mode amplitudes. We apply the RBQ code to a DIII-D plasma with elevated q -profile where the beam ion profiles show stiff transport properties [C.S. Collins et al., Phys. Rev. Lett. 116 (2016) 095001]. The sources and sinks are included via the pitch-angle scattering operator. The properties of AE driven fast ion distribution relaxation are studied for validations of the applied QL model to DIII-D discharges. Initial results show that the model is robust, numerically efficient, and can predict intermittent fast ion relaxation in present and future burning plasmas.
• Pressure balance in a low collisionality tokamak scrape-off layer
  Michael Churchill, PPPL, abstract, slides
  [#s888, 12 Oct 2018]
  An understanding of the physics at play in the tokamak scrape-off layer is key to planning fusion machines which can achieve the necessary fusion performance while avoiding damaging material walls. The gyrokinetic neoclassical code XGCa finds that the parallel pressure balance in the diverted scrape-off layer does not follow that from a fluid description based on CGL theory [1]. To understand the missing physics, a gyrofluid equation for pressure balance in a low-collisionality tokamak SOL is derived. The new pressure balance equation allows determining physical processes which dominate the setting of pressure in the divertor, utilizing closure information directly from a kinetic code which reduces the number of assumptions going into a fluid code. This pressure balance equation is used with results from an XGCa simulation of a DIII-D H-mode discharge, and it is found that the total pressure balance is much better matched using the gyrofluid equation. Electrons are shown to be dominantly adiabatic, while ions have multiple contributions to pressure balance, including radial fluxes due to parallel energy flow and E x B motion.
  
  [1] R.M. Churchill, et. al., Nucl. Fusion 57 (2017) 046029.
• How do things become unstable*?
  Hong Qin, PPPL, abstract, slides
  [#s878, 28 Sep 2018]

  Stability, or instability, is the central theme for plasma physics. In this talk, I will prove and demonstrate using examples from plasma physics the following facts. 1) The only route for a conservative system to become unstable is through the resonance between a positive-action mode and a negative-action mode. It is not the “free energy” that drives the system unstable. 2) For most stable systems, stability is a consequence of being symplectic (or G-unitary for complex systems), instead of the existence of dissipation or damping. 3) Dissipation can destabilize a system by breaking the symplectic (or G-unitary) condition. 4) By not preserving the symplecticity, numerical and analytical models for conservative systems diverge quickly from the true dynamics.
  [1] R. Zhang, H. Qin et al., arxiv:1801.01676 (2018)
  [2] R. Zhang, H. Qin et al., Phys. Plasmas 23, 072111 (2016)
  [3] J. Xiao, H. Qin & J. Liu, Plasma Sci. Tech. 20, 110501 (2018)
  *Things in this context include conservative systems, numerical and analytical models thereof.

• Quantumlike approach to drift-wave turbulence
  Ilya Dodin, abstract, slides
  [#s858, 21 Sep 2018]
  Inhomogeneous wave turbulence with zonal flows (ZFs) can be modeled as an effective quantum plasma where the ZF velocity serves as a collective field [1, 2]. This effective plasma can be described by a Wigner-Moyal kinetic equation, whose geometrical-optics limit is also an improvement of the traditional wave kinetic equation. We report the first application of the Wigner--Moyal formalism to analytical and numerical modeling of ZF physics [3, 4] within the generalized Hasegawa-Mima model. "Full-wave" effects are found to be essential and can qualitatively affect the formation of ZFs and their stability [3, 5]. Some recent results [yet to be published] are also discussed regarding the theory of predator-prey oscillations and localized propagating coherent structures seen in simulations of drift-wave turbulence.
  [1] D. E. Ruiz, J. B. Parker et al., Phys. Plasmas 23, 122304 (2016)
  [2] D. E. Ruiz, M. E. Glinsky & I. Y. Dodin, arXiv:1803.10817
  [3] H. Zhu, Y. Zhou et al., Phys. Rev. E 97, 053210 (2018)
  [4] H. Zhu, Y. Zhou & I. Y. Dodin, Phys. Plasmas 25, 072121 (2018)
  [5] H. Zhu, Y. Zhou & I. Y. Dodin, Phys. Plasmas 25, 082121 (2018)
• Nonlocal transport in toroidal confinement devices
  Roscoe White, PPPL, abstract, slides
  [#s811, 14 Sep 2018]
  Collisional particle transport is examined in several toroidal plasma devices in the presence of perturbations typical of modes leading up to a disruption, of saturated tearing modes, or of unstable Alfven modes. The existence of subdiffusive transport for electrons is found to occur in some cases at very low mode amplitudes and to also exist even for ions of high energy. Orbit resonances can produce long time correlations and traps for particle trajectories at perturbation amplitudes much too small for the orbits to be represented as uniformly chaotic. The existence and nature of subdiffusive transport is found to depend on the nature of the mode spectrum and frequency as well as the mode amplitudes.
• SciDAC ISEP: Integrated Simulation of Energetic Particles
  Zhihong Lin, University of California, Irvine, abstract, slides
  [#s796, 13 Jul 2018]
  The goals of SciDAC ISEP project are to improve physics understanding of EP confinement and EP interactions with burning thermal plasmas through exascale simulations, and to develop a multiscale and multiphysics ISEP framework with predictive capability as an EP module in the future whole device modeling (WDM) project. I will discuss recent ISEP progress in physics understanding, simulation models, verification and validation. Regarding simulation models, a conservative scheme of drift kinetic electrons has been formulated and verified for gyrokinetic simulations of multiple kinetic-MHD processes responsible for plasma transport including drift-Alfvénic microturbulence and collisionless tearing mode, meso-scale Alfvén eigenmodes, and macroscopic MHD instabilities. I will highlight the physics understanding of toroidal Alfvén eigenmode (TAE) nonlinear saturation via self-generated zonal fields, the key process that determines the fluctuation amplitude and EP transport level. I will also elucidate the excitation of low frequency beta-induced Alfvén-acoustic eigenmode (BAAE), which may provide a strong coupling between EP and thermal plasmas.
• An overview of recent results from the SCREAM SciDAC project
  Dylan P. Brennan, PPPL, abstract, slides
  [#s742, 15 Jun 2018]
  An overview of recent results is presented, including theoretical developments and simulation results that have advanced our understanding of runaway electron physics. Experimental observations of runaway electron phenomena have been explained by this effort, including wave particle interaction and radiative emission, and how they appear in the experimental measurements. These effects are primarily studied through the development of synchrotron and ECE synthetic diagnostics in the modeling and simulation. Highlights of recent results and publications are presented along with a brief summary of future plans for the project, indicating how the efforts contribute toward the development of runaway electron avoidance and mitigation techniques in ITER.
• Designing Stellarator Coils
  Stuart Hudson, abstract, slides
  [#s705, 04 May 2018]
  ​Designing the current-carrying coils required to confine plasmas in non-axisymmetric geometry, i.e., in stellarators, is a challenging mathematical problem. Furthermore, cheap coils that are easy to build are required.
  This talk will describe some approaches for designing coils that are presently used in the stellarator community. These methods seek to minimize an error function, namely the surface integral of the squared normal component of the magnetic field ​to a given target surface, i.e. the quadratic flux. Expressions describing how the quadratic flux varies with both (i) variations in the coil geometry, and (ii) variations in the geometry of the target surface can be derived. An expression that describes how the coil geometry varies as the geometry of the target surface is varied can be derived.
• Magnetized High-Energy-Density Plasmas from Astrophysics to Fusion
  Will Fox, abstract
  [#s687, 20 Apr 2018]
  The recent generation of laboratory high-energy-density physics facilities has opened significant physics opportunities for experimentally modeling astrophysical plasmas. Several challenge problems are being tackled, including magnetic reconnection, laboratory generation of magnetized collisionless shocks, magnetic field generation by Biermann battery and Weibel instability, and astrophysical particle energization processes. The research program connects experiments using national laser facilities including NIF and OMEGA, with large-scale particle-in-cell simulations using the PSC code, supported by INCITE. Finally, I review some future opportunities of these topics, in particular where PPPL can make a significant impact on the broader NNSA mission, including understanding the physics of hohlraums, and studying anomalous transport processes in magnetized, pulsed-power-driven ICF platforms such as MagLIF.
• Plasma simulations using real-time lattice scalar-QED
  Yuan Shi, abstract, slides
  [#s637, 06 Apr 2018]
  When dense plasmas are exposed to intense fields, intrinsically relativistic-quantum effects such as pair production can happen. To faithfully capture such phenomena, plasma models based on quantum electrodynamics (QED) become necessary. As a toy model, we develop a variational algorithm for solving the Klein-Gordon-Maxwell (KGM) equations, which describe tree-level scalar-QED effects in bosonic plasmas. The variational algorithm is developed by discretizing the scalar-QED action on a space-time lattice. On this lattice, the complex scalar fields, which describe charged bosons, naturally live on vertices as discrete functions, while the gauge field, which describes electromagnetic fields, naturally lives on edges as discrete 1-form. This discretization respects structures of discrete exterior calculus (DEC) and U(1)-gauge symmetry, thereby guarantees local conservation laws. Upon minimizing the discrete action, the resultant finite difference equations are used to advance initial conditions in time. Our real-time lattice simulation scheme is fully explicit and can be parallelized using domain decomposition and quantum parallelism. To demonstrate how this scheme can be used in plasma applications, we apply it to two example problems. The first example is the propagation of linear waves, whose numerical spectrum recovers the analytic wave dispersion relations. The second example is pair production when intense x-ray lasers interact with plasma targets. Using this example, we demonstrate that our algorithm naturally allows pair production when laser intensity exceeds the Schwinger threshold.
• From Gyrokinetics to MHD
  Wei-li Lee, abstract, slides
  [#s661, 30 Mar 2018]
  This talk consists two parts: 1) Discussion of the special issue of Physics of Plasmas for the recent gyrokinetic particle simulation symposium [1], which includes papers ranging from derivation of fundamental gyrokinetic equations and various numerical algorithms to their applications to tokamak physics; and 2) Presentation of the recently derived MHD equations based on gyrokinetic theory and its use for studying MHD equilibria in the presence of magnetic islands [2].
  [1] Z. Lin, Phys. Plasmas 24, 081101 (2017)
  [2] W. W. Lee, S. R. Hudson & C. M. Ma, Phys. Plasmas 24, 124508 (2017)
  
• Plasmoid Instability Mediated Current Sheet Disruption and Onset of Fast Reconnection
  Yi-Min Huang, abstract, slides
  [#s638, 02 Mar 2018]
  Magnetic reconnection is a physical process that breaks the frozen-in constraint imposed by the ideal Ohm's law, thereby enabling the conversion of magnetic energy to plasma energy. Magnetic reconnection events are often preceded by an extended quiescent period, during which the magnetic energy gradually accumulates, followed by an impulsive “onset” phase when the magnetic energy is suddenly released. Therefore, a successful theory of reconnection must account for not only the fast reconnection rate but also the impulsive onset. Recent studies suggest that current sheet disruption mediated by the plasmoid instability, which takes place when the sizes of plasmoids become comparable to the inner layer width of the tearing mode, may provide the trigger for the impulsive onset. In this talk, I will give an overview of recent results on the condition for current sheet disruption, obtained from direct numerical simulations and a theoretical model. The linear growth rate, current sheet width, and dominant wavenumber at current sheet disruption depend on not only the Lundquist number but also the noise amplitude of the environment. The scalings obtained from simulations are consistent with the predictions of the theoretical model, which incorporates the effects of the linear growth of the tearing instability, as well as mode-stretching and advective losses due to reconnection outflow. Our theoretical model also predicts a critical Lundquist number below which disruption does not occur. The critical Lundquist number is not a constant value but has a weak dependence on the noise amplitude.
• Control of secondary electron emission flux through surface geometry
  Charles Swanson, abstract, slides
  [#s624, 09 Feb 2018]
  Secondary electron emission (SEE) is an important process to be taken into account in plasma-material interface models. But what happens if the material surface is not flat? Can SEE be suppressed by changing the surface geometry? Applications such as electric propulsion, particle accelerators, RF amplifiers, and materials processing would all like to apply greater control over SEE. It was shown that SEE can be heavily suppressed by changing the material surface into complex, fibrous structures like velvet, foam, dendritic structures, etc. The effect is easy to understand as the re-absorption of secondary electrons when they hit a fiber. Analytical modeling, verified by Monte-Carlo simulations, predicts degree of SEE reduction for such complex modeling.
• Energetic Particle-driven Fishbone Instability: Theory and Simulation
  G-Y. Fu, abstract
  [#s621, 26 Jan 2018]
  Energetic particle-driven fishbone instability is commonly observed in tokamak and stellarator plasmas with NBI and/or RF heating after its discovery in the PDX tokamak [1]. The fishbone instability can be either driven by trapped energetic particles through precessional drift resonance [2,3] or passing energetic particles via parallel wave particle resonance [4,5]. In this talk we report recent results from two studies of fishbone instability. In the first study [6,7], an analytic theory of passing particle-driven low frequency fishbone of EPM branch is derived. The analytic results have been verified by numerical calculation and are consistent with the recent observation of low frequency fishbone instability in the HL-2A tokamak. In the second study [8], hybrid simulations with the global kinetic-MHD hybrid code M3D-K have been carried out to investigate the linear stability and nonlinear dynamics of beam-driven fishbone in the EAST experiment. Linear simulations show that a low frequency fishbone instability is excited at experimental value of beam ion pressure. The mode is driven by trapped beam ions via precessional resonance. The results are consistent with the experimental measurement with respect to mode frequency and mode structure. When the beam ion pressure is increased to exceed a critical value, the low frequency mode transits to a high frequency branch identified as BAE. Nonlinear simulations show that the frequency of the low frequency fishbone chirps up and down with corresponding hole-clump structures in phase space.
  [1] K. McGuire, R. Goldston et al., Phys. Rev. Lett. 50, 891 (1983)
  [2] Liu Chen, R. B. White & M. N. Rosenbluth, Phys. Rev. Lett. 52, 1122 (1984)
  [3] B. Coppi & F. Porcelli, Phys. Rev. Lett. 57, 2272 (1986)
  [4] R. Betti & J. P. Freidberg, Phys. Rev. Lett. 70, 3428 (1993)
  [5] Shaojie Wang, Phys. Rev. Lett. 86, 5286 (2001)
  [6] L.M. Yu, F. Wang, G.Y. Fu, in preparation
  [7] Feng Wang, L.M. Yu et al., Nucl. Fusion 57, 056013 (2017)
  [8] W. Shen, G. Y. Fu et al., Nucl. Fusion, in press (2017)
  
• Metriplectic dynamics -- a framework for plasma kinetic theory and numerics
  Eero Hirvijoki, abstract, slides
  [#s612, 12 Jan 2018]
  In dissipationless systems, Hamiltonian mechanics, culminating in an antisymmetric Poisson bracket and a Hamiltonian, provides a convenient framework for both theoretical and numerical studies. In systems that obey both the First and the Second Law of Thermodynamics, the dissipationless dynamics can often be extended with a symmetric bracket and an entropy functional to account for the dissipation. The resulting, so-called metriplectic framework captures many interesting models, including the Navier-Stokes equations, non-isothermal kinetic polymer models, and the Vlasov-Maxwell-Landau model used in plasma physics. In this seminar, we review the basic principles of metriplectic dynamics, focusing on the Vlasov-Maxwell-Landau model due to its relevance for plasma physics. For a numerical example, we provide a recipe for constructing a metriplectic spatial and temporal discretization of the Landau collision operator which preserves the invariants and guarantees positive-semidefinite entropy production. If time permits, we shall also present a metriplectic formulation of collisional full-f electrostatic gyrokinetics with energy and momentum conservation laws.
  [1] Philip J. Morrison, Physica D 18, 410 (1986)
  [2] M. Kraus & E. Hirvijoki, Phys. Plasmas 24, 102311 (2017)
  [3] E. Hirvijoki & J. W. Burby, arxiv.org/abs/1706.09519 (2017)
  
• Quasioptics with mode conversion: theory and applications
  Ilya Dodin, abstract, slides
  [#s504, 20 Oct 2017]
  In magnetically confined fusion plasmas, ray tracing is commonly considered to be a reasonably accurate method of modeling wave dynamics in the electron-cyclotron frequency range. However, ray tracing is inapplicable in helical plasmas with a strongly sheared magnetic field, where mode conversion between the two electromagnetic cold-plasma modes can occur in the plasma edge. In collaboration with the LHD team (NIFS, Japan), a new theory is proposed that captures both mode conversion and transverse diffraction of wave beams [yet to be published]. Unlike in beam tracing, a specific beam structure is not assumed. The new theory builds on “extended geometrical optics” (XGO) that was recently developed at PPPL [1-4]. Also using XGO, a tractable analytical three-dimensional model is proposed for the O-X mode conversion in edge plasma with a sheared magnetic field [5]. This problem does not fit into the Landau-Zener paradigm that is almost always adopted (under various names) at modeling mode conversion of other types. Nevertheless, this problem is made tractable by using an analogy between the coupled-mode dynamics and the adiabatic precession of the spin of a quantum particle in a time-dependent magnetic field. In particular, a simple recipe is proposed to ensure the suppression of the parasitic X mode in the plasma core.
  [1] D.E. Ruiz, “Geometric theory of waves and its applications to plasma physics”, PhD thesis (2017)
  [2] D.E. Ruiz & I.Y. Dodin, Phys. Plasmas 24, 055704 (2017)
  [3] D.E. Ruiz & I.Y. Dodin, Phys. Rev. A 92, 043805 (2015)
  [4] D.E. Ruiz & I.Y. Dodin, Phys. Lett. A 379, 2337 (2015)
  [5] I.Y. Dodin, D.E. Ruiz & S. Kubo, arXiv:1709.02841
  
• Alfvénic Aurora: An overview
  Peter Damiano, abstract, slides
  [#s448, 08 Sep 2017]
  Aurora are the most visible manifestation of the interaction between the magnetosphere and ionosphere and occur in several different classes. Alfvénic (or broadband) aurora are generally associated with dispersive scale Alfvén waves; Alfvén waves with perpendicular scale lengths on the order of the electron inertial or ion gyroradius scale lengths. We present an overview of these aurora, including their morphology and the characteristics of the electron energization. Satellite observations will be discussed in the context of simulation and recent laboratory experimental results.
• Centrifugal particle confinement in Mirror Geometry
  Roscoe White & Adil Hassam, abstract, slides
  [#s203, 30 Jun 2017]
  The use of supersonic rotation of a plasma in mirror geometry has distinct advantages for thermonuclear fusion. The device is steady state, there are no disruptions, the loss cone is almost closed, sheared rotation stabilizes magnetohydrodynamic instabilities as well as plasma turbulence, and the coil configuration is simple. We report on the experiments done at the University of Maryland and examine the effect of rotation on mirror confinement using a full cyclotron orbit code. Both collisionless loss as a function of rotation and the effect of collisions are investigated.
• Plasmoid instability as a tearing instability in time-evolving current sheets
  Luca Comisso, PPPL, abstract, slides
  [#s178, 23 Jun 2017]
  Abstract: 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 [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 comprises of a relatively long period of quiescence followed by rapid growth over a shorter timescale.
  [1] L. Comisso, M. Lingam et al., Phys. Plasmas 23, 100702 (2016)
  [2] L. Comisso, M. Lingam et al., to be submitted (2017)
  
• Disruption modeling with M3D-C1
  Nate Ferraro, PPPL, abstract, slides
  [#s175, 09 Jun 2017]
  A successful tokamak reactor will require robust methods for avoiding and withstanding disruptions. Achieving this will require considerable progress in understanding both the causes and dynamics of disruptions. Here we describe present research and future directions in extended-MHD modeling, in particular with the M3D-C1 code, to address these issues. Nonlinear MHD modeling is necessary to understand how some linearly unstable modes develop into disruptions while others saturate or cycle without causing disruptions. For example, the nonlinear evolution of the tearing mode may result in locking—one of the most common causes of disruptions—or may saturate benignly, as in “hybrid” operation. Macroscopic linear instability is therefore not a sufficient condition for disruption prediction and avoidance schemes. We present results of M3D-C1 modeling of mode locking and Resistive Wall Tearing Mode stability as a step towards understanding how linearly unstable modes may develop into disruptions. In order to characterize the dynamics of a disruption, we also present M3D-C1 simulations of vertically unstable plasmas in toroidal geometry. In these simulations, the plasma drifts toward the wall and the plasma current quenches, leading to large halo currents and eddy currents in the surrounding conducting structures. We consider the effect of breaks in the resistive wall on the evolution of the current quench and the wall currents.
• Hybrid simulations in application to NSTX, FRCs, and basic plasma physics
  Elena Belova, PPPL, abstract, slides
  [#s136, 07 Apr 2017]
  The HYM code is used to study the excitation of high-frequency Alfvén eigenmodes by energetic beam ions in NSTX/NSTX-U. Numerical results support an energy channeling mechanism for $T_e$ flattening [1], in which beam-driven CAE dissipates its energy at the resonance location close to the edge of the beam, therefore significantly modifying the energy deposition 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. Initial NSTX-U simulations of GAE stabilization have been performed showing that off-axis neutral beam injection reliably and strongly suppresses GAEs. Numerically calculated most unstable toroidal mode numbers, polarization, and Doppler-shift corrected frequencies are in a good agreement with experiments. HYM shows suppression of all unstable counter-rotating GAEs by the additional beam injection. 2D and 3D hybrid simulations of counter-helicity spheromak merging have been performed using the HYM code. Hybrid simulations results show that even in the MHD-like regime, there are significant differences between hybrid and fluid simulations of global reconnection, and demonstrate the need for a full kinetic description of plasma. These findings are in a sharp contrast with generally accepted paradigm that the inclusion of the Hall effects is sufficient to reproduce realistic reconnection rates of kinetic plasmas. Results of this study are also consistent with 2D full PIC and hybrid simulations of island coalescence, where it was found that fluid description including the Hall term does not describe reconnection in large systems correctly [2,3,4].
  [1] E.V. Belova, N.N. Gorelenkov et al., Phys. Rev. Lett. 115, 015001 (2015)
  [2] H. Karimabadi, J. Dorelli et al., Phys. Rev. Lett. 107, 025002 (2011)
  [3] A. Stanier, W. Daughton et al., Phys. Rev. Lett. 115, 175004 (2015)
  [4] Jonathan Ng, Yi-Min Huang et al., Phys. Plasmas 22, 112104 (2015)
• Resonant Pressure Driven Equilibrium Currents In and Near Magnetic Islands
  Allan Reiman, PPPL, abstract, slides
  [#s128, 20 Jan 2017]
  In toroidal MHD equilibria, pressure can generally be regarded as constant on the flux surfaces. The regions near small magnetic islands, and those near the $X$-lines of larger islands, are exceptions. We show that the variation of the pressure within the flux surfaces in those regions has significant consequences for the pressure driven current. We further show that the consequences are strongly affected by the symmetry of the magnetic field if the field is invariant under combined reflection in the poloidal and toroidal angles (“stellarator symmetry”). In non-stellarator-symmetric equilibria, the pressure-driven currents have logarithmic singularities at the $X$-lines. In stellarator-symmetric MHD equilibria, the singular components of the pressure-driven currents vanish. In contrast, in equilibria having $p$ constant on the flux surfaces the singular components of the pressure-driven currents vanish regardless of the symmetry. In 3D MHD equilibria having simply nested flux surfaces, the pressure-driven current goes like $1/x$ near a rational surface, where $x$ is the distance from the rational surface. To calculate the pressure-driven current near a magnetic island, we work with a closed subset of the MHD equilibrium equations that involves only perpendicular force balance, and is decoupled from parallel force balance. Two approaches are pursued to solve our equations for the pressure driven currents. First, the equilibrium equations are applied to an analytically tractable magnetic field with an island, obtaining explicit expressions for the rotational transform and magnetic coordinates, and for the pressure-driven current and its limiting behavior near the $X$-line. The second approach utilizes an expansion about the $X$-line to provide a more general calculation of the pressure-driven current near an $X$-line and of the rotational transform near a separatrix.
• Report of the Panel on Frontiers of Plasma Science
  Igor Kaganovich, PPPL, abstract, slides
  [#s108, 09 Sep 2016]
  I will present technical details of Report of the Panel on Frontiers of Plasma Science [1] and discuss what directions panel put forward as most promising research frontiers.
  [1] U.S. DoE, Office of Fusion Energy Sciences, Report of the Panel on Frontiers of Plasma Science, 2016
  
• Report of the Panel on Frontiers of Plasma Science
  Michael Mauel, Columbia U., abstract, slides
  [#s104, 26 Aug 2016]
  The report is intended to inform Fusion Energy Sciences (FES) in planning and executing its strategic vision for the FES stewardship of the Plasma Science Frontiers activities. The preliminary draft of “Report of the Panel on Frontiers of Plasma Science” is now available [1]. Fundamental plasma physics has never had the benefit of a research-needs workshop, and we believe that the community of researchers would greatly benefit from a survey of the current state of the art, as well as from formulating a cohesive vision of the future horizons we can aim towards. Our goal is that the Plasma Science Frontiers report will be of benefit to both the community and all funding agencies interested in plasma science, not just the Department of Energy. Furthermore, our report will serve as a starting point for the next NRC decadal survey of plasma science (Plasma 2020).
  [1] U.S. DoE, Office of Fusion Energy Sciences, Report of the Panel on Frontiers of Plasma Science, 2016
  
• Is there a fundamental principle for energy partitioning in a proto-typical reconnection layer?
  Masaaki Yamada, PPPL, abstract, slides
  [#s60, 24 Jun 2016]
  Recently, a quantitative inventory of magnetic energy conversion during magnetic reconnection was carried out in the MRX reconnection layer with a well-defined boundary. This study concluded that about half the inflowing magnetic energy is converted to particle energy, $2/3$ of which is ultimately transferred to ions and $1/3$ to electrons. This observation was found to be consistent with numerical simulation results based on VPIC codes. It was also found that features of energy conversion and partitioning do not strongly depend on the size of the analysis region over the tested range of scales. So a question arises: is a fundamental principle in the energy partitioning in a proto-typical reconnection layer? This talk describes my physics understanding of the energy conversion processes in the magnetic reconnection layer of two-fluid physics regime and leads to a general quantitative evaluation of energy partitioning.
• Opportunities and challenges for integrated tokamak modeling
  Francesca Poli, PPPL, abstract, slides
  [#s52, 10 Jun 2016]

  The DOE workshop on “Integrated Simulations” has identified a number of critical aspects in the integration of physics modules in a whole device model for tokamak simulations. Challenge includes not only the need for physics description, but also a need for hardware infrastructure, software integration and difficulties in integrating multi-scale coupling.

  This seminar summarizes the conclusions from the integrated simulations workshop on MHD stability and disruptions, boundary physics and core transport, as well as a need for research on innovative workflows that enable the integration.

• Opportunities highlighted by the 2015 FES PMI workshop report
  Rajesh Maingi, PPPL , abstract, slides
  [#s23, 06 May 2016]
  The 2015 FES PMI Workshop identified five priority research directions (PRDs), updating the community discussions that were held during ReNeW. In shorthand notation, these PRDs include (i)Identify the present limits on power and particle handling of present candidate PFCs (ii)Develop innovative dissipative/detached divertor solutions for power exhaust and particle control (iii)Develop innovative boundary plasma solutions for main chamber wall components (iv)Understand the science of evolving materials at reactor-relevant plasma conditions (v)Understand the mechanisms by which boundary solutions and plasma facing materials influence pedestal and core performance
  In addition, four cross-cutting research opportunities, i.e. activities that contributed to each of the PRDs, were identified. This talk will discuss the science elements in these PRDs and cross-cutting areas. The goal is to identify the areas appropriate for expanded theory involvement, e.g. liquid metal research as a cross-cutting opportunity.
• Modeling Stability and Control of Tokamaks with Resistive Walls
  D. Brennan, PPPL, abstract, slides
  [#s47, 22 Apr 2016]
  In a collaborative effort covering several areas within MHD stability theory, we employ a theoretical and computational framework to analyze and understand experimental discharge stability. Reduced MHD modeling is developed to interpret simulations and computational analyses, where we alternately include several essential ingredients to study global mode stability: toroidal field line curvature to couple modes in a cylindrical model, trapped energetic ions, differential flow between surfaces, a resistive wall, and a model for feedback control from external coils. Asymptotic matching methods are used to determine the non-ideal MHD stability, where toroidal effects can also enter into the resistive layers, causing finite frequency responses and altering the stability. We briefly review a few research projects where extended MHD simulations and computational analyses of experiments including some of these ingredients are interpreted using reduced models.
  
  We then further focus on one of these projects, the effects of trapped energetic ions on resistive MHD instabilities. In simulation analyses modeling the DIII-D tokamak, the $2/1$ tearing mode was found to be damped or stabilized by energetic ions with monotonic safety factor profile extending to the core, while the mode was found to be driven unstable with weakly sheared or reversed core safety factor profile. Using a reduced analytic model, we add in the effect of a slowing down distribution of energetic ions integrated to a scalar modification to the perturbed pressure. We find that with positive magnetic shear $(s = 1/q \, dq/dr)$ and a pressure gradient, the particles contribute a stabilizing effect to the $2/1$ tearing mode, while for $s \le 0$, the particles drive the mode unstable. This finding agrees with the drift-kinetic PIC / extended MHD simulations, and indicates that the core shear and pressure gradient combination can determine if energetic ions stabilize or drive the $2/1$ mode unstable.
• Waves in the ion cyclotron frequency range at Earth and Mercury
  Eun-Hwa Kim, PPPL, slides
  [#s6, 06 Mar 2016]
• Numerical implementation of the fully non-linear Fokker-Planck-Landau operator
  R. Hager, PPPL, abstract, slides
  [#s46, 05 Feb 2016]
  This talk describes the implementation of a fully non-linear, Fokker-Planck-Landau (FPL) collision operator in the gyrokinetic neoclassical particle-in-cell code XGCa. This work is the multi-species generalization of the work by Yoon and Chang [1] applied to a total-$\delta f$ particle code. The accuracy of the ion-electron version of this FPL operator has been verified in various tests that are described in this talk. The favorable conservation properties of the discretized FPL operator and its computational efficiency and scalability, which is achieved by efficient MPI-OpenMP parallelization, are discussed. This FPL operator is now used routinely at extreme scale in XGC simulations on leadership class supercomputers such as Titan, Mira, and Edison. While this talk discusses the implementation of the FPL operator in a particle code, the collision operator itself is a continuum operator and can be applied in continuum codes as well.
  [1] E. S. Yoon & C.S. Chang, Phys. Plasmas 21, 032503 (2014)
• Selected topics in Energetic Particle Research in Preparations for Burning Plasmas
  Nikolai Gorelenkov, PPPL, abstract
  [#s48, 08 Jan 2016]
  The area of energetic particle (EP) physics in fusion research has been actively studied in recent decades. The progress understanding physics in this area is substantial since the last comprehensive review on this topic by Heidbrink & Sadler [1]. Recently another comprehensive review was published in the same journal in preparations for burning plasmas by Gorelenkov, Pinches & Toi [2]. It selects important topics of the field which will be covered in this talk. Some of them are critical for the success of ITER mission being built in France. The topics range from the ‘sea’ of Alfvénic eigenmodes (AEs) to high frequency cyclotron instabilities responsible for Ion Cyclotron Emission (ICE). Some other problems are also highlighted such as the plasma equilibrium in the presence of fast ions. Another important problem of interest for ST devices is the transport of the background plasma in the presence of EP driven instabilities. Many of these problems can be advanced using the expertise of PPPL theory department such as ICE which is being proposed to diagnose alphas in burning plasmas.
  [1] W.W. Heidbrink & G.J. Sadler, Nucl. Fusion 34, 535 (1994)
  [2] N.N. Gorelenkov, S.D. Pinches & K. Toi, Nucl. Fusion 54, 125001 (2014)
  
• MHD Modes in NSTX
  Roscoe White, PPPL
  [#s7, 01 Jan 2016]
• Acceleration of plasma electrons by intense nonrelativistic ion beams propagating in background plasma due to two-stream instability
  I.D. Kaganovich, PPPL, abstract, slides
  [#s45, 04 Dec 2015]
  In this paper we study the effects of the two-stream instability on the propagation of intense non-relativistic 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 excitation. 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 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. We show, through simulations and analytical estimates, that a beamlet produced from an ion beam that has passed through an aperture can be used as a diagnostic tool to identify the presence of the two-stream instability and quantify its de-focusing effects. 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.
• High-order energy conserving, (discontinuous) finite-element algorithms for (gyro) kinetic simulations of plasmas
  Ammar H. Hakim, PPPL, slides
  [#s28, 04 Sep 2015]
• A new hybrid Lagrangian numerical scheme utilizing phase space grid for XGC1 edge gyrokinetic code
  S. Ku, PPPL, slides
  [#s40, 28 Aug 2015]
• Midplane Neutral Density Profiles in NSTX
  D.P. Stotler, PPPL, slides
  [#s35, 24 Jul 2015]
• Simulation of Reflectometry in Toroidal Plasmas
  E. Valeo, PPPL, slides
  [#s42, 12 Jun 2015]
• Edge Intrinsic Rotation: Theory and Experiment"
  Timothy Stoltzfus-Dueck, Princeton Plasma Physics Laboratory , abstract, slides
  [#s1109, 29 May 2015]
  Plasma near the last closed flux surface of a tokamak often rotates at Mach numbers of several tenths, even in the absence of applied torque. The relative magnitudes of various quantities in the tokamak edge lead to a physical model where the edge rotation is caused by the interaction of drift orbit excursions of passing ions with the amplitude of transport-causing turbulent potential fluctuations. Analysis of the model reveals that the major-radial position of the X-point adjusts the relative orbits of co- and counter-current passing ions in a way that should strongly modify the edge rotation, changing it from strongly co-current for an inboard X-point to zero or weakly counter-current for an outboard X-point. Motivated by these theoretical predictions, recent dedicated experiments on the Swiss Tokamak à Configuration Variable (TCV) have indeed directly observed the predicted X-point position dependence of the edge intrinsic rotation, in qualitative and even reasonable quantitative agreement with the theoretical predictions. Other popular heuristic models of edge intrinsic rotation, in particular ion orbit loss and transport-driven scrape-off-layer flows, fail to reproduce the observations.
• Spline Representations for More Efficient Stellarator Coil Design
  Joshua Breslau, PPPL, slides
  [#s32, 22 May 2015]
• Turbulent optimization of stellarators & tokamaks
  H.E. Mynick, PPPL, slides
  [#s10, 08 May 2015]
• A Cross-Benchmarking and Validation Initiative for Tokamak 3D Equilibrium Calculations
  A. Reiman, PPPL, slides
  [#s9, 01 May 2015]
• Particle Simulation, Gyrokinetics, Turbulence and Beyond
  W.W. Lee, PPPL, slides
  [#s8, 17 Apr 2015]
• Electron acceleration by Alfvén waves in the magnetosphere
  Peter Damiano, PPPL, slides
  [#s43, 23 Jan 2015]
• Edge Turbulence in Tokamaks
  S.J. Zweben, PPPL, slides
  [#s41, 09 Jan 2015]
• From Chirikov's island overlap criterion to cantori and ghost-surfaces
  S.R. Hudson, PPPL, slides
  [#s30, 02 Jan 2015]
• Plasma Instabilities in Post-Eruption Solar Corona, Formation of Plasmoids and Supra-Arcade Downflows
  Yi-Min Huang, PPPL, slides
  [#s29, 21 Nov 2014]
• Numerical optimization of tokamak and stellarator equilibrium
  Samuel A. Lazerson, PPPL, slides
  [#s44, 17 Oct 2014]
• The origins of tokamak density limit scalings
  D.A. Gates, PPPL, slides
  [#s34, 10 Oct 2014]
• Using the HYM code for numerical simulations of NSTX and FRC
  Elena Belova, PPPL, slides
  [#s31, 20 Jun 2014]
• High-energy-density physics and laboratory astrophysics with laser-produced plasmas
  W. Fox, PPPL, slides
  [#s36, 23 May 2014]
• Extended MHD Studies with the M3D-C1 Code
  S.C. Jardin, PPPL, slides
  [#s39, 18 Apr 2014]
• Full-f/Total-f XGC1: Present Status and Future Plans
  C.S. Chang, PPPL, slides
  [#s33, 21 Mar 2014]
• Studies of energetic particle-driven modes and energetic particle transport via kinetic-MHD hybrid simulation
  Guo-Yong Fu, PPPL, slides
  [#s27, 14 Feb 2014]
• Predictive modelling in Energetic Particle Research
  N.N. Gorelenkov, PPPL, slides
  [#s37, 07 Feb 2014]
• Plasma-surface interactions
  I.D. Kaganovich, PPPL, slides
  [#s38, 31 Jan 2014]