# 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 Fridays, @10:45 am, in the Theory Conference Room, T169.

### Past

• 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?
[#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]
• 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]