Session CP11: Poster Session II: Basic Plasma Physics; Boundary, PMI, Proto-MPEX; International Tokamaks; Turbulence and Transport; Other Configurations; Z-pinch, Dense Plasma Focus and MagLIF (2:00pm-5:00pm)

Electron collision term due to reflections in electron-electron collisions in a magnetized plasma

For a electron-electron (e-e) collision with impact parameter p between the electron thermal gyro-radius ρ_th and the Debye length λ_D, ρ_th<p<λ_D, when the initial relative parallel kinetic energy is smaller than the Coulomb repulsive potential e²/(4πε₀p), reflection will occur with interchange of the parallel velocities of the two electrons after the collision. The Fokker-Planck approach is employed to derive the electron collision term C_R due to the reflection. The electron parallel velocity friction and diffusion coefficients <Δv_z>_R, <Δv_zΔv_z>_R are calculated which depend insensitively on the electron perpendicular velocity v_perp. For Maxwellian background electrons, when v_z<<v_th, <Δv_z>_R and <Δv_zΔv_z>_R are found to be, respectively, three times the corresponding results of the no magnetic field case with v<<v_th, where v, v_z, and v_th are the electron speed, parallel velocity, and the background electron thermal velocity, respectively. When v_z>>v_th, <Δv_z>_R and <Δv_zΔv_z>_R are exponentially small as the number of e-e collisions with reflections is exponentially small in this case. Through studying the time evolution of the  quantity H under the effect of C_R, it is surprising to find that C_R finally makes the electron distribution f_e(v) relax to the form f_e(v)=F_e(v_perp)G_e(v_z).   

Overview of Experiments at the Wisconsin Plasma Physics Laboratory

During the past year, the Wisconsin Plasma Physics Laboratory has been formed to operate several devices asa a DoE User Facility for Frontier Plasma Physics. The devices include the Madison Symmtric Torus, constructed and supported by the DoE for many years for fusion research and the Big Red Ball device constructed with support from the NSF.  This poster will present an overview of the transition to a User Facility and an introduction to how users can become engaged. It will also provide highlights of scientific progress, including recent results on reconnection, dynamos, turbulence, and particle acceleration from both devices.   

Strong magnetic field amplification in quasi-Keplerian high-β plasma flows

Quasi-Keplerian flows in the Big Red Ball (BRB) develop a peaked axial magnetic field approximately an order of magnitude larger than the applied field. The method of stirring, volumetric flow drive (VFD), consists of forcing current injected by biased cathodes to cross a weak (ν_ii » Ω_ci) externally applied field using a Helmholtz coil set. Flows can reach a Mach number of M∼0.3 with β∼100 and δ_i/L∼1. The magnetic field amplification is observed in spherical NIMROD simulations only when including the Hall term in Ohm’s law and when the injected current is directed radially outwards at the equator.  The magnetic flux increase results from conversion of toroidal flux from the injected current into poloidal flux by the Hall effect. In the experiment there are also significant pressure gradients due to losses along open field lines in the core that cause poloidal flux to peak in the core via the diamagnetic effect. These observations suggest mechanisms important to magnetic induction beyond MHD in unmagnetized plasmas.   

Theta Pinch Collisionless Shock Experiment on the Big Red Ball

A high-beta theta pinch collisionless shock experiment was performed on the big red ball. Cylindrical VPIC simulations were used to interpret experimental results. Hall-MHD in this cylindrical geometry mostly succeeds in explaining results via the following mechanism: the fast theta-pinch field affects the magnetized electron fluid, creating an ExB drift inward. The resultant charge separation serves to pull ions inward, with ion inertia slowing the current layer. Reflected ions that move at twice the piston speed are observed, as are resonant ions that ‘surf’ the compressing wave inward. The experiment and simulation were repeated in the strongly magnetized regime and compared with pure MHD. Whether the reflected ions could lead to a collisionless shock through Buneman, Weibel, or other instabilities is explored.   

Measuring Plasma Viscosity with a Fabry-Perot Spectrometer

A Fabry-Perot spectrometer has been developed for measuring ion temperature and inferring the Braginskii viscosity of flowing, unmagnetized plasmas at WiPPL. Ion viscosity is important in coupling the momentum from JxB edge-driven flows throughout the plasma to generate large-scale shear flow. In a Fabry-Perot spectrometer, collimated light is dispersed by an etalon to provide high-throughput,  compact, and simple optical design with high resolving-power. The precision needed to measure the fixed etalon plate separation for an absolute wavelength calibration at high order motivates an analysis using multi-modal nested sampling. An experiment has been designed to measure the ion viscosity and the momentum diffusion length of JxB edge-driven flows on the PCX-U using the Fabry-Perot spectrometer and to compare against Mach-probe velocity profiles and Braginskii viscosity.   

Experimental platforms for plasma turbulence studies at WiPPL

Both the spherical BRB device and the toroidal MST device provide opportunities for plasma turbulence experiments at the Wisconsin Plasma Physics Laboratory (WiPPL) to both internal and external users of the facility.  Plasma gun arrays and compact-toroid (CT) injectors are being developed as sources to enable a variety of turbulence scenarios.  In BRB, electrostatically biased plasma gun arrays produce rotating helical flux ropes along an axial magnetic field, driving magnetic relaxation and energizing what appear to be Alfvenic and ion cyclotron fluctuations observed up to frequencies of order 100 kHz.  Colliding CTs with stationary grids may allow control of the injection scale for studies of magnetized plasma turbulent cascades.  Colliding CTs with each other may produce shocks and turbulent structures which could generate magnetic energy or accelerate particles up to suprathermal energies.  In MST, the energy input by colliding CTs or flux ropes might interact with the strong turbulent cascade produced by reversed-field pinch current relaxation.   

The FLARE Device and Its First Plasma Operation

The FLARE device (Facility for LAboratory Reconnection Experiments; http://flare.pppl.gov) is a new laboratory experiment constructed at Princeton for the studies of magnetic reconnection in the multiple X-line regimes directly relevant to space, solar, astrophysical, and fusion plasmas, as guided by a reconnection phase diagram [Ji \& Daughton, Phys. Plasmas 18, 111207 (2011)]. The first plasma operation was successfully conducted to validate its engineering design and to demonstrate its experimental access to the parameter space of Lundquist number and normalized system size beyond its predecessor, MRX (Magnetic Reconnection eXperiment; http://mrx.pppl.gov). Details on construction completion and first plasma results will be presented; future operation plans - possibly as a user facility - and research plans will be discussed. In addition to the names listed above, The FLARE Team includes A. Bhattacharjee and S. Prager (Princeton Univ.), W. Daughton (LANL), W. Fox, M. Kalish, C. Meyers, Y. Ren, M. Yamada (PPPL), S.D. Bale (UC-Berkeley), T. Carter and S. Dorfman (UCLA), J. Drake (U. Maryland), J. Egedal, J. Sarff, and J. Wallace (UW-Madison).

Results from Preliminary FLARE Operation and Development of Tomographic Ion Doppler Spectroscopy Diagnostic

The Facility for Laboratory Reconnection Experiments (FLARE) has been constructed with the aim of answering many longstanding problems in magnetic reconnection research. Many of these problems relate to the conversion of magnetic energy to particle energy. One of the most important diagnostics for studying the energy flow on FLARE is a measurement of spatial profiles of ion temperature. Expected ion temperatures between 5-30eV on FLARE make in-situ measurement possible, such as those made on FLARE’s predecessor, MRX. This technique however, relies on reconstructing 2-D profiles by averaging over many shots. This method is cost prohibitive and restricts studies to a single case. For this purpose, a 2-D Doppler spectroscopy diagnostic is being designed that will utilize tomographic inversion to reconstruct Ion temperature profiles from measured broadening of emission lines. This presentation covers the design, numerical tests, early construction, and possible applications of the aforementioned probe as well as a brief overview of early results from first FLARE operation.   

3-D Particle Simulation of Electromagnetic Instabilities in Harris Current Sheet under Realistic Mass ratio and Finite Guide Field

Previously we studied 3-D instabilities in the electrostatic limit in a Harris current sheet with a finite guide magnetic field $B_G$ and a realistic mass ratio $m_i/m_e$=1836. In this work, fully electromagnetic instabilities in the Harris sheet are systematically studied by employing the gyrokinetic electron and fully kinetic ion (GeFi) particle code. Our studies show that lower-hybrid drift instability (LHDI) with $k\sqrt{\rho_i\rho_e} \sim 1$ and drift kink instability (DKI) and drift sausage instability (DSI) with $k\rho_i \sim 1$ are excited in the current sheet. The most unstable DKI is away from $\mathbf{k} \cdot \mathbf{B}=0$, and the most unstable DSI is at $\mathbf{k} \cdot \mathbf{B}=0$, where $\mathbf{k} \equiv (k_x, k_y)$, with $k_x$ being along the anti-parallel field direction and $k_y$ is along the current direction. The DSI from GeFi code is consistent with fully kinetic particle simulation. On the other hand, an instability with a compressional magnetic field perturbation located at the center of current sheet is also excited under a relatively large $B_G$, and its maximum growth rate is at $\mathbf{k} \times \mathbf{B} = 0$. The presence and structure of these instabilities as a function of $B_G$ is presented.   

Three-dimensional hybrid simulations of spheromak merging

Hybrid simulations with full kinetic ions and fluid electrons of counter-helicity spheromak merging have been performed using the HYM code and compared with 3D MHD simulations. The ion heating and the effects on FRC pressure profiles have been studied. In hybrid simulations the resulting FRC has larger elongation and flatter pressure profile compared to the MHD; smaller ion flow velocities before and during the reconnection have also been observed. In both cases the resulting FRC was unstable to the n=1 tilt mode, as expected for these parameters (small FLR, MHD-like regime, and small elongation). One of the unexpected results in 3D simulations was behavior of the n=1 Fourier harmonic of the ion kinetic energy, growing faster than linear, right before the reconnection. Additional simulations with varying initial separation between spheromaks have demonstrated that this behavior is related to the tilting instability of the spheromaks prior to reconnection. At closer initial separations, the growth of the tilting mode was strongly nonlinear. It has been shown that in hybrid simulations in contrast to the MHD, the reconnection rate is also very sensitive to the initial separation of two spheromaks.   

The Particle-in-Cell and Kinetic Simulation Software Center

The UCLA Particle-in-Cell and Kinetic Simulation Software Center (PICKSC) aims to support an international community of PIC and plasma kinetic software developers, users, and educators; to increase the use of this software for accelerating the rate of scientific discovery; and to be a repository of knowledge and history for PIC.  We discuss progress towards making available and documenting illustrative open-source software programs and distinct production programs; developing and comparing different PIC algorithms; coordinating the development of resources for the educational use of kinetic software; and the outcomes of our first sponsored OSIRIS users workshop.  We also welcome input and discussion from anyone interested in using or developing kinetic software, in obtaining access to our codes, in collaborating, in sharing their own software, or in commenting on how PICKSC can better serve the community.   

Gyrointegrated kinetic theory for arbitrary gradient scale lengths, Larmor radii and distribution functions

We present a 5D electromagnetic gyrointegrated kinetic theory (GI) valid for non-Maxwellian distribution functions in magnetized plasmas with arbitrary gradient scale lengths, Larmor radii and 3D magnetic geometry. GI theory describes collective full-orbit effects and yet differs fundamentally from gyrokinetic (GK) theory in the mathematical approach to the treatment of the kinetic physics. The fundamental difference in GI is the introduction of a new "gyrointegration" that is operated on the perpendicular velocity direction of all particles at the same 5D phase-space coordinate. This gyrointegration leads to the local definition of slower 5D macro-particles without requiring any ordering on gradient scale lengths or Larmor radii.  Basis sets for complete representation of the distribution function with respect to the instantaneous gyroangle are chosen to allow for the exact analytic computation of gyrointegrals of the Boltzmann equation. We then show how GI can be applied to non-Maxwellians and include arbitrary 3D magnetic geometry, and discuss how GI avoids many of the GK challenges such as the cancellation problem and the evaluation of the Ampère's law. Evaluation of conservation laws, Hamiltonian structure, and dispersion relations are discussed within the GI theory.   

Spectrally Accurate Methods for Computing Kinetic Electron Plasma Wave Dynamics

We present two numerical methods for computing solutions of the Vlasov-Fokker-Planck-Poisson equations that are spectrally accurate in all three variables; time, space and velocity.  The first is a Chebyshev collocation method for solving the Volterra equation for the space-time evolution of the plasma density for the linearized, collisionless case. This is then used to construct the velocity distribution function in Case-van Kampen normal modes, building on the work of Li and Spies, for example. The second is an arbitrary-order exponential time differencing scheme that makes use of the Duhamel principle to fold in the effects of collisions and nonlinearity. We investigate the emergence of a continuous spectrum in the collisionless limit and the embedding of Landau's poles in this general setting. We simultaneously resolve the effects of filamentation, phase mixing, and  Landau and collisional damping to arbitrary order of accuracy. We will ultimately incorporate echoes and trapping phenomena in three dimensions by generalizing the latter method as presented here in a simpler setting.   

A domain-decomposed multi-model plasma simulation of collisionless magnetic reconnection

Plasmas exhibit different properties depending on their degree of magnetization, charge separation, and collisionality.  This implies a requirement for modeling different physics within different regimes.  Work on simulation of collisionless magnetic reconnection in the past has shown that in some areas of the domain, a fluid model may provide sufficient physical accuracy while in others a kinetic model may be required, though at higher computational expense.  This motivates an investigation of the collisionless magnetic reconnection phenomenon using a hybrid approach incorporating multiple models, including Hall-MHD, multi-fluid 5N-moment, and multi-species continuum kinetics on a domain-decomposed grid in physical space.  The investigations are performed using the WARPXM code developed at the University of Washington, which uses a discontinuous Galerkin Runge-Kutta finite element algorithm on an unstructured mesh, implementing boundary conditions between models at subdomain interfaces to couple between each model's variables.  The goal of this work is to determine the parameter regimes most appropriate for each model to maintain sufficient physical fidelity over the whole domain while minimizing computational expense.

Hybrid plasma model simulations of a plasma opening switch

Plasma models have regimes of validity that depend on local parameters.  In some problems a computationally-expensive, high-fidelity model is required in a small subset of the domain while lower-cost reduced models can adequately describe the plasma behavior everywhere else.  Partitioning the domain and using the simplest plasma model that is locally valid can maintain global physical fidelity while improving computational efficiency.  This research investigates the coupling between MHD and two-fluid plasma models using a physics-based domain-decomposition.  Comparisons are made on the accuracy and performance of using a hybrid plasma model versus a single conventional plasma model on the planar plasma opening switch. The models used are allowed to change to lower or higher fidelity models to adjust to the shifting regions of local validity as the plasma evolves.  The setup consists of a low density background and a high density bulk plasma with a large density gradient, leading to instabilities which are not captured by MHD models. Elsewhere however, MHD models provide sufficient accuracy. A perpendicular magnetic field is then added to investigate changes in the plasma propagation and stability properties.   

Langevin-based Coulomb collision algorithm extended for arbitrary momentum distribution in particle-in-cell simulations

Two kinds of Coulomb collision algorithms, binary collision and Langevin-based algorithms, have been actively studied, still each of them has its own advantages and disadvantages. Binary collision algorithms can handle any particle distribution functions, which is important because the fully kinetic nature is a crucial advantage of particle-in-cell simulations. However, Langevin-based algorithms need assumptions to distribution functions or other physical quantities. This is to remove the complexity in calculating drag and diffusion coefficients of Langevin equation that states motion of particles. Theoretical background of Langevin-based algorithms has been well-established owing to mathematical theory of stochastic differential equations (SDE). Ordinary discretization of Langevin equation gives first-order approximation of particle distribution. Binary collision algorithms had taken decades to be given its not-so-straightforward formal proof and convergence order being 0.5 to 1.0, which is worse than Langevin-based algorithms. In this study, we developed a new Langevin-based algorithm that can handle arbitrary distribution function. Discretization technique of Langevin equation will be presented for energy and momentum conservation with the help of theory of SDE.   

PlasmaPy: an open source community-developed Python package for plasma physics

PlasmaPy is a community-developed and community-driven open source core Python package for plasma physics. This package is being developed to provide the core functionality that is needed to support a fully open source Python ecosystem for plasma physics. PlasmaPy prioritizes code readability, consistency, and maintainability while using best practices for scientific computing such as version control, continuous integration testing, embedding documentation in code, and code review. PlasmaPy has a code of conduct and is available under a BSD 3-clause license with explicit protections against software patents. PlasmaPy includes functional and object-oriented interfaces to particle data; tools to calculate plasma parameters, dielectric tensor components, and transport coefficients; mathematical functions commonly needed in plasma physics; and tools to analyze diagnostic data including Langmuir probes. Work is underway to develop PlasmaPy's base data structures. PlasmaPy's first development releases serve as an invitation to plasma students and scientists to collaboratively develop a community-wide shared software package for our field.   

Comparison of VPIC Performance on Several Modern Architectures

VPIC [ K. J. Bowers, B. J. Albright, L. Yin, B. Bergen, and T. J. T. Kwan, Phys. Plasmas 15, 055703 (2008) ] is being ported and optimized on several modern architectures. These include KNL
processors available on Trinity, Cori and Stampede2, Skylake processors available on Mare Nostrum and Stampede2, IBM Power 9 processors and Volta GPUs available on Summit and Sierra and ARM ThunderX2 processors, soon to be available on Astra at Sandia. VPIC
is in production on several of these systems. These architectures vary in many ways including available memory bandwidth, vector length, threads per core, clock frequency and overall node architecture.  This work is focused on single node performance. Current efforts to optimize single node performance are exploring changes to data layout of key data structures and performance profiling with a variety of performance analysis tools. Results will be presented
which compare the performance of VPIC on these different architectures.   

Particle Method for the Vlasov-Poisson System

We present a semi-Lagrangian particle method (SLPM) for the Vlasov-Poisson system in which the electric field is obtained by summing pairwise particle interactions rather than the usual particle-in-cell (PIC) approach. The aim is to achieve higher accuracy and less noise than PIC, while still providing an efficient representation of phase space using an adaptive particle distribution and treecode acceleration. We compare SLPM with a standard PIC code and an Eulerian Vlasov code for several test cases.   

High Fidelity Geometry and Meshing for RF Fusion Systems Simulations

Accurate RF simulations of fusion systems like ITER require the definition of high fidelity analysis geometries that include detailed antenna and reactor wall representations. The analysis domains must also include the boundaries of coupling meshes (e.g., core plasma models). The ability to effectively control the mesh generation process is enhanced by the inclusion of specific physics geometry (e.g., the SOL) into the analysis geometry. This poster will describe a set of tools being developed to support the construction and subsequent meshing of the needed analysis geometry. The steps in the process include (i) fast defeaturing of un-needed details (e.g., mounting bolts) from antenna CAD models, (ii) defining desired physics model features using input data like EFIT, (iii) combining the antenna, reactor wall, physics and any coupling meshes into a single analysis model geometry, (iv) applying simple high level mesh control to topological entities in the analysis model, and (v) executing a fully automatic mesh generator that will construct well controlled curved meshes for use in high-order finite element simulations.   

Saturation Mechanisms of Magnetic Field Growth in a Two-Stream Mediated Weibel Instability

We present 2X2V continuum Vlasov-Maxwell simulations of colliding electron populations to study the non-linear saturation of magnetic field growth resulting from competition between Two-Stream, Oblique, and Weibel modes in non-relativistic and weakly relativistic regimes. Understanding the robustness of the Wiebel instability to other modes present is important for estimating its role in generating magnetic fields in many astrophysical scenarios with interpenetrating plasma flows. In the isotropic temperature case, we find that for hotter temperatures non-linear saturation leads to magnetic fields with 1e-2 to 1e-1 of the equipartition energy density. However, for colder temperatures the non-linear state of the Weibel instability is significantly disturbed and results in energy conversion efficiencies much lower than 1e-2, an effect not observed in 1X2V simulations. Simulations of non-relativistic counter streaming velocities with large initial anisotropic temperatures relevant to cosmological scenarios are also presented.
  

Generation of THz radiation by parametric coupling of Laser and Trivelpiece–Gould mode

A scheme to study powerful source of radiations at Terahertz band (THz) is proposed, wherein the high power extraordinary (X-mode) laser pump parametrically decays into Trivelpiece-Gould (TG) mode and Kinetic Alfven Wave (KAW) in a magnetized plasma system. In this process, the nonlinear coupling between X-mode laser (ω₀) and TG mode produces KAW with frequency in terahertz range (THz). The X-mode laser beam exerts a ponderomotive force on the electrons, and imparts a nonlinear oscillatory velocity at beat frequency. A strong transient current is generated by the nonlinear coupling of laser velocity and TG density perturbation. The requisite phase matching condition is shown by modeling the parallelogram. High dependency upon the applied transverse magnetic field is exhibited by the efficiency, power, beam quality, and the tunability of the present scheme. At the laser intensity of 10¹⁶ W/cm² and magnetic field of 30 MG, the evaluated power flux, P_THz comes out at the Terawatt level. With the optimization of various plasma parameters, the power conversion efficiency ~   is achieved   

The modified Zakharov equations for time-space envelope in magnetoactive plasma

Considering the presence of an external magnetic field, the modified Zakharov equations are obtained with the help of two-component fluid mechanics and the two-scale method. Based on the nonlinear equations, the effect of the magnetic field on the modulational instability is studied. The numerical results show that the growth rate increases with the intensity of the magnetic field, which means that the magnetic field could enhance the collapse of the Langmuir field.   

Two-fluid and kinetic study of sheared flow instabilities in non-uniform collisionless plasmas in ExB configurations

The transport properties of low-density non-uniform ExB plasmas have important consequences in pulsed power systems such as the Z facility, where current is delivered to the load via magnetically insulated transmission lines.  Formation of low-density plasmas within these ExB configuration transmission lines is known to give rise to parasitic currents, which interfere with load dynamics and prevent scaling of pulsed power experiments to higher energy densities.  To understand the mechanisms that lead to current loss and plasma transport, the ExB environment is investigated using two-fluid plasma theory and high-order continuum kinetic Vlasov-Poisson simulations in (x,y,vx,vy) phase space.  The computational study is facilitated in part through the initialization of self-consistent kinetic equilibria.  Sheared flows are found to be present and density gradients are found to strongly influence dynamics and transport.  The kinetic Kelvin-Helmholtz instability, induced by ExB sheared flow, is studied in detail as a candidate transport mechanism.  This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.  LLNL-ABS-753410   

Experimental Investigation of Wave Generation by a Relativistic Electron Beam in Magnetized Plasma

The interaction between relativistic electron beams and a magnetized plasma is a fundamental and practical problem that is relevant to many challenging issues in space physics and astrophysics.  For example, compact high-energy electron beam sources may be used on future spacecraft to generate waves that would remove the energetic particles from the radiation belt region.  Similar classes of waves (whistler, Langmuir, etc.) may also be generated by naturally occurring relativistic electron beams, possibly explaining type II/III solar radio emissions.  Proposed experiments on the Large Plasma Device (LAPD) and UCLA and supporting simulations will investigate in detail the generation of waves produced by such beams, beam stability, and applicability to space-based beams and type II/III radio bursts. Initial experiments using a 20 keV electron gun, the proposed 1 MeV experimental setup, and ongoing simulation feasibility studies will be discussed.   

Two species continuum kinetic simulation of electrostatic plasma instabilities

Several classic problems in collisionless plasma kinetics are treated by solving the one-dimensional multi-species Vlasov-Poisson system. Calculations are done using a second order discontinuous Galerkin algorithm on a high resolution structured 1D1V grid with speed and efficiency enabled by GPU parallelization. Subjects of simulation and analysis include: Landau damping and excitation of single and multi-species plasma waves, evolution of 1D plasma wave turbulence, ion interaction with electron holes, plasma streaming instabilities, collisional interaction with Landau damping, and plasma sheath kinetic effects. Some results of interest entail wave-trapped particle mixing in 1D wave turbulence and ion acoustic wave excitation by electron streaming instability. Discussion is in terms of spectral analysis and collisionless kinetic theory through the paradigms of linearized Landau damping theory, electrostatic stability, mechanical resonance in a system with mean field interaction, and the phase mixing principle. General takeaways of electrostatic plasma instability are explored such as the ideas of collisionless heating, current drive, and anomalous heat fluxes.   

First results from the Bryn Mawr Magnetohydrodynamic Experiment (BMX) at the Bryn Mawr Plasma Laboratory.

The first measurements from the Bryn Mawr Magnetohydrodynamic Experiment (BMX) are presented. BMX is a magnetic turbulence experiment at the Bryn Mawr Plasma Laboratory (BMPL) consisting of an ~300us long coaxial plasma gun discharge that injects magnetic helicity into a 24cm by 2m flux-conserving chamber in a process akin to sustained slow-formation of spheromaks. Broadband temporal fluctuation measurements using a low-inductance magnetic pickup coil and fast Langmuir probe are reported. Mapping of gas flow using a fast ionization gauge as well as measurements of the plasma gun magnetic field structure are also reported   

Magnetic Structure and Gas Dynamics Measurements of the Bryn Mawr Magnetohydrodynamic Experiment Coaxial Plasma Source

Measurements of the magnetic structure and gas dynamics of the coaxial plasma source on the Bryn Mawr Magnetohydrodynamic Experiment (BMX) are reported. The gun consists of three pulsed magnetic coils, two outer and one inner. The coils are oriented such to generate a radial magnetic field at the mouth of the gun in order to provide a stiff, but brittle stuffing field for the ejected plasma which is necessary for sustained injection of plasma helicity. Four Parker puff valves inject pure hydrogen gas into the chamber. A fast ionization gauge is used to measure gas flow and distribution using time of flight.   

Experiments and Modeling of Turbulence, Transport, and Flows in a Magnetized Linear Plasma Using a Global Two-Fluid Braginskii Solver

Experiments and numerical modeling of the dynamics of turbulence in the presence of flow shear are being conducted in helicon plasmas in the linear HelCat device. Modeling is being done using GBS, a 3D, global two-fluid Braginskii code that solves for plasma equilibrium as well as fluctuations. Past flow measurements have been difficult to reconcile with expectations, such as azimuthal flows being dominated by Er x Bz rotation. Therefore, recent measurements have focused on understanding plasma flows, and the role of neutral dynamics. In the model, a set of drift-reduced Braginskii equations are evolved using the GBS code. For low-field Ar plasmas a cross-field thermal collisional term must be added to shift the electric potential in the ion momentum and vorticity equations, as the ions are unmagnetized. Significant radially and axially dependent neutral profiles are also included in the simulations to try and match those observed in HelCat. Simulations show a dependence on the axial magnetic field and strong axial variations that suggest drift waves may be important in the low-field case. Recent LIF neutral profiles and off-axis plasma sourcing have been incorporated to the simulations, consistent with observations.   

Status of Dual-Laser Digital Holography for Surface Characterization at ORNL

A dual-laser differential digital holography system is under development at Oak Ridge National Laboratory (ORNL) for 3D measurement of surface erosion of plasma facing component (PFC) materials.  Digital holography produces topological data of a target from IR laser interferometry.  The system is capable of a depth resolution range perpendicular to the surface of 100 nm to 4.5 μm (single-laser holography) and up to 2 mm for dual-laser differential holography.  Transverse resolution of the measurements is limited by diffraction effects, covering an area of 7x7 mm² with a 1X magnification lens.  Holograms produced “on the bench” of test targets have shown that the system can produce measurements from <1 μm to ~2 mm total depth, demonstrating good progress towards deployment in the field.  Measurements of Proto-MPEX plasma-exposed targets, including a SiC target, have been made.  Status of the dual-laser system and progress in single- and dual-laser measurements will be presented.   

Tungsten sputtering by simultaneous deuterium and nitrogen irradiation

In magnetic fusion devices, extrinsic impurities like nitrogen (N) are introduced in hydrogen plasmas to reduce the power load onto tungsten (W) plasma facing components. Evaluating the sputter characteristics of W under simultaneous irradiation of hydrogen isotopes and nitrogen species is required to quantify the effects of W-contamination on plasma confinement. Due to the rich chemistry involving hydrogen- and nitrogen- species, the W surface is expected to evolve in a complex manner with significant influence on the W sputtering. In this study, we report on systematic W sputtering experiments as a function of incident ion energy (300-1000 eV) and sample temperature (400-700 K) for fixed D/N ratio (3.5% N). Experimental W-sputtering yields are compared to the results of a dynamic BCA code (TRIDYN). In the energy range between 700-1000 eV, experiments and simulation results agree within 20% as a function of incident ion energy, with very weak dependence on temperature. However, in the energy range between 300-500 eV, sputtering yields show stronger temperature dependence. Therefore, we conclude that physical sputtering is the dominant mechanism at incident energy greater than 700 eV, while deposited nitrogen is desorbed by chemical sputtering at incident energy less than 500 eV.   

Density Estimation Techniques for Multiscale Coupling of Kinetic Models of the Plasma Material Interface

We analyze two classes of Density-Estimation techniques which can be used to consistently couple kinetic models of the plasma-material interface, intended as the region of plasma immediately interacting with the first surface layers of a material wall. In particular, we handle the general problem of interfacing a continuum multi-species Vlasov-Poisson-BGK plasma model to discrete surface erosion models. The continuum model solves for the energy-angle distributions of the particles striking the surface, which are then driving surface response. A modification to the classical Binary-Collision Approximation method is utilized as a prototype discrete model of the surface, to provide boundary conditions and impurity distributions representative of the material behavior during plasma irradiation. The numerical tests revealed superior convergence properties of Kernel Density Estimation methods over Gaussian Mixture Models, with Epanechnikov-KDEs being up to two orders of magnitude faster than Gaussian-KDEs. The methodology presented allows a self-consistent treatment of the dynamic response of the surface including effects such as sputtering, back-scattering, and ion implantation.   

Flow Collisionality Effects in Plasma Guns for Simulating Fusion Wall Response to Disruption Events

In this work, the suitability of a pulsed coaxial deflagration accelerator to simulate the interaction of edge-localized modes with plasma first wall materials is investigated. Suites of experimental diagnostics are used to characterize plume conditions in the Stanford plasma gun facility to quantify both the incident plasma heat flux and estimate the mean free path in the vicinity of stagnating surfaces. The process by which plasma jets stagnate on tungsten tokens is visualized using an ultra-high frame rate CMOS camera coupled to a Z-type laser Schlieren apparatus. Results indicate the formation of a strong extended bow shock that acts to redirect the flow away from the surface of the material. Measurements show that while sufficiently high plasma heat fluxes are achievable with gun devices (in excess of 10 GW m-2), significant differences in plasma density and temperature cause the formation of collisional fluid shocks that are not expected at similar timescales during ELM events in fusion conditions. Finally, MHD simulations are employed to quantify the shock shielding effect within the flow and how the strength of the diversion varies as the energy of impeding plasma jet changes.   

Comparative Study of Explicit vs. Implicit Particle-in-Cell schemes for Plasma Sheath Simulations

In this work we present a comparative study of explicit vs. implicit fully-kinetic full-orbit Particle-in-Cell schemes, using: (1) the explicit Vlasov-Poisson scheme of the hPIC[1] code, and (2) the implicit Maxwell-Vlasov scheme of Chacon et al.[2]. Implicit schemes remain stable at much longer time steps than traditional, explicit schemes, but at greater computational cost. The Maxwell-Vlasov formulation avoids the use of a Poisson solver by directly evolving the electric field in time based on the particle fluxes. We report simulation results of asymmetric phase-spaces (e.g. bump-on-tail instability) and finite-size domains (non-periodic) facing an absorbing wall, where a plasma sheath is formed.  [1] Khaziev, Curreli, Comput. Phys. Commun. 229, 87, 2018; [2] Chacon, Chen, Barnes, J. Comp. Phys. 233, 1–9, 2013.   

Multi-timescale coupling simulation between turbulence and transport codes using BOUT++ framework

A new coupling model has been developed to integrate multi-scale turbulence and transport simulations, such as ELM bursts and pedestal recovery. As a proof of principle, we first start from a set of three-field two-fluid model equations which includes the pressure, current, and vorticity. The equations are separated into the slowly evolving part of the axisymmetric component by taking a time average of the axisymmetric component. The time-averaged fluxes, which are quadratic in fluctuating quantities, act as drive terms for the time-averaged axisymmetric quantities that determine the plasma transport, and therefore the large-scale evolution of the plasma profiles. Good agreement has been achieved for the solutions obtained by the coupled simulation to direct numerical simulation of the unseparated equations. Multiple ELM cycles have been simulated using the coupling technique in the circular geometry. The axisymmetric component evolution tracks the pedestal pressure profile collapsing in the fast component and the profile recovery between ELMs with additional sources in the slow component. The same coupling technique is applied to a set of six-field two-fluid model equations and results will presented.
  

A gyrokinetic model for the tokamak periphery

Despite significant development over the last decades, a model able to describe the tokamak periphery region extending from the edge to the far scrape-off layer is still missing. In this work, we present a new gyrokinetic model that retains the fundamental elements of the plasma dynamics at the tokamak periphery, namely electromagnetic fluctuations at all scales, comparable amplitudes of background and fluctuating components, and a large range of collisionality regimes. Such model is derived within a gyrokinetic full-F approach, describing distribution functions arbitrarily far from equilibrium, and projecting the gyrokinetic equation onto a Hermite-Laguerre velocity space polynomial basis, obtaining a gyrokinetic moment hierarchy. This extends a previously derived electrostatic drift-kinetic moment hierarchy to the electromagnetic gyrokinetic regime. The treatment of arbitrary colisionalities is performed by expressing the full Coulomb collision operator in gyrocentre phase space coordinates, and providing a closed formula for its gyroaverage in terms of the gyrokinetic moments. In the electrostatic high collisionality regime, the novel hierarchy reduces to an improved set of drift-reduced Braginskii equations which have been widely used in scrape-off layer simulations.   

Physics Designs for a Lithium Vapor Box Test at PPPL and a Lithium Vapor Detachment Experiment at Magnum-PSI

The lithium vapor box [1] is under study as a candidate divertor. Prior to implementation in a tokamak, the concept should be tested with lab-scale experiments and in linear plasma devices. Key physics issues to be evaluated include the efflux of Li vapor (1a) without and (1b) with plasma, (2) the required density of vapor to induce detachment and volumetric recombination, (3) power spreading away from the target during volumetric recombination, (4) transport of Li ions in the plasma, and (5) pumping of H (and potentially He) emitted by a detaching plasma, using co-deposition onto liquid Li surfaces. An experiment at PPPL to test (1a) is being constructed, and the physics design for an experiment at the linear plasma device Magnum-PSI is being developed with the primary goals of measuring (1b), (2), (3), and potentially (4). We will present the physics designs of these experiments, including both practical aspects [see also Butler et al, this conference] as well as a simplified plasma model that can be adjusted to study the implications of a range of assumptions.

[1] Goldston, R.J., et al, Nucl. Mat. and Energy 12 (2017): 1118–21. https://doi.org/10.1016/j.nme.2017.03.020.   

Turbulence Characteristics from XGC1 simulations of Tokamak Edge.

Strong turbulence near the separatrix is believed to produce filamentary structures (blobs) whose detachment from the bulk impacts the heat flux width and, as a result, the total power deposited at the divertor. Although considerable progress has been made in core research, studies of the edge so far have been mostly confined to reduced models and simplified geometries. 

Here, we analyze the results of simulations performed with the full-f, gyrokinetic code XGC1 which includes both turbulence and neoclassical effects in realistic divertor geometries. More specifically, we study the characteristics of turbulence from simulations of two different machines (DIII-D and CMOD): We examine the spatial pattern of turbulent fluxes and the cross-phases between various turbulent quantities. In addition, we perform linear simulations using the gyrokinetic code GENE in order to investigate the effect of  driving gradients and the growth rates of dominant modes. Lastly, we identify blobs, measure some of their properties and compare the results with theoretical predictions.     

Disruptivity and Density Limits in MAST and other Tokamaks

The Disruption Event Characterization and Forecasting (DECAF) code was written to automate analysis of tokamak data for disruptivity characterization of existing databases and related testing of specific physics analyses for disruption forecasting, such as density limits. DECAF analysis has been performed on the MAST, KSTAR, NSTX, NSTX-U, and TCV devices. DECAF is equipped to produce event probability plots of events leading to the disruption identified by DECAF physics models, such as MHD modes, no-wall beta limits, or the current quench itself. It was found that low q₉₅ was especially disruptive for MAST, as was density above the Greenwald limit. Recently a local island power balance limit theory, developed to explain the observed density limit in tokamaks, has been implemented in DECAF and tested on a set of NSTX discharges with long periods of rising density, eventual onset of low frequency n = 1 MHD activity, and disruption. Both the local island and global Greenwald limit criteria were found to rise towards, or surpass theoretical limits associated with the termination of the discharges. Both criteria are being evaluated for their utility as disruption predictors for the MAST-U device.
  

Investigation of MHD Stability and Active Mode Control Supporting Disruption Avoidance on KSTAR

H-mode plasma operation in KSTAR has surpassed the computed n = 1 ideal no-wall stability limit for several seconds in duration. High normalized beta operation was limited by resistive tearing instabilities rather than RWMs. Kinetic equilibrium reconstructions including MSE data have been developed for accurate stability and transport analysis. The reconstructed high performance equilibria can exhibit significant variation of the q-profile dependent upon the broadness of the bootstrap current profile as computed by TRANSP code. The stability of the observed m/n = 2/1 tearing mode is computed by using the resistive DCON code and the M3D-C¹ code. MISK code analysis examining global MHD stability modified by kinetic effects shows significant passive kinetic stabilization of RWMs. To accurately measure the dynamics of unstable RWMs expected to onset at higher beta by utilizing the newly installed second NBI system, real-time mode identification and active control has been developed in the KSTAR PCS including magnetic sensor compensation of the prompt applied field and the field from the induced current in the passive conductors. This analysis provides the foundation for disruption prediction and avoidance research on KSTAR.    

Non-Inductive Vertical Position Measurement by Faraday-Effect Polarimetry on EAST Tokamak

The vertical position for elongated, long-pulse tokamak plasmas has to be precisely controlled to optimize performance and prevent disruptions. For a steady-state tokamak reactor, integration of voltage signals arising from flux change is extremely challenging due to zero-offset drift as the measurement is intrinsically inductive. The vertical position of the plasma core current density is defined as the position where radial magnetic field is zero, making this parameter critical to investigating vertical instability. A Faraday-effect POlarimeter-INTerferometer system has been developed for measuring the internal radial magnetic field in EAST. Horizontally-viewing chords at/near the midplane allow us to determine plasma vertical position non-inductively with sub-centimeter spatial resolution and 1 ms time response. The polarimeter-based position measurement, which does not require equilibrium reconstruction, is benchmarked against conventional flux loop measurements for EAST discharges.  Non-inductive vertical position measurements are very promising for future steady-state plasmas and fast time response allows for direct feedback on plasma vertical displacement instabilities.    

Fast vertical control in superconducting tokamaks

For superconducting tokamaks like KSTAR, EAST and ITER the use of normal conducting coils internal to the vacuum vessel have been chosen as the actuator for fast vertical control.  Modelling by the General Atomics control group and others have specified coil locations and power supplies for the internal vertical control (IVC) coils needed necessary for fast vertical control.  Both EAST and KSTAR have used their IVC coils for vertical control since early in their operation.  The control achieved early in their campaigns was limited by experimental realities.  Conducting passsive plates used for stability control slow the response of the plasma to the IVC coils and the response of sensor coils to the plasma. Recent progress on identifying which sensors in KSTAR have both the sensitivity and fast response needed for feedback control is being extended to EAST.  Both devices have implemented a separation of the time response to use the IVC coil for only fast deviations from the plasma vertical position determined by the plasma control system, primarily determined by the superconducting coils.  The results of vertical control using the newly selected sensors for each machine will be discussed along with implications for ITER.
  

First experimental result of disruption mitigation by shattered pellet injection on J-TEXT tokamak

The mitigation of disruption damage is essential for the safe operation of a large-scale tokamak. Disruption mitigation by shattered pellet injection (SPI) has been proposed to achieve safe operation of ITER. A dedicated argon SPI system that focuses on disruption mitigation and runaway current dissipation has been designed for the J-TEXT tokamak. The pellet can be injected with speed of 200-300 m/s. The performance of disruption mitigation by Ar SPI has been compared with identical Ar massive gas injection (MGI). The cooling process observed from the ECE indicates that the SPI has deeper deposition. The current quench rate of SPI induced disruption is more than 100 MA/s. The increase of plasma density during fast shutdown is higher than that with identical Ar MGI. The dissipation of runaway current by Ar SPI is about 12 MA/s, which is lower than that with Ar MGI.    

Beta induced Alfven Eigenmode Driven by Fast Ions in HL-2A plasma

Researches on beta induced Alfven eigenmodes (BAEs) driven by fast ions have been carried out in HL-2A plasma. The mode frequencies are around 35-95kHz. The poloidal/toroidal mode numbers are m/n = 3/2 or m/n = 2/2 when the q_min is higher or lower than unit, respectively. They localize at the core region and their radial mode structures have been detected by the multi-channel microwave reflectometer. The BAEs are confirmed by the theoretical calculations given by the general fishbone-like dispersion relation (GFLDR) and Alfven mode code (AMC). Both the mode frequency and location are found to agree with each other between experimental measurements and theoretical calculations. There is a density threshold for the excitation of BAEs. The modes are excited more easily in low electron density discharges and suffer stronger ion Landau damping in high density cases. The BAEs can coexist with reversed shear Alfven eigenmodes (RSAEs), which performs the MHD spectroscopy well. Finally, the amplitude and growth rate of the frequency chirping BAEs will provide inputs for simulations of potential ion and alpha particle losses due to energetic particle driven modes.
  

Implementation and Testing of Model-based Optimal Control Strategies for q-profile Feedback Regulation in EAST

Regulation of the q-profile via feedback control has been demonstrated experimentally in EAST for the first time ever. Extensive studies have shown that the q-profile, which is closely related to poloidal magnetic flux profile, is a key factor to achieving advanced tokamak operating scenarios that are characterized by improved confinement and possible steady-state operation. A general framework for real-time feedforward + feedback control of magnetic and kinetic plasma profiles has been implemented in the EAST Plasma Control System (PCS). Moreover, a first-principles-driven, control-oriented model of the poloidal magnetic flux profile evolution has been used to design a linear quadratic integral (LQI) controller for q-profile regulation in EAST. The proposed controller has been tested successfully in reference tracking and disturbance rejection experiments. These experiments constitute the first time ever a model-based, closed-loop, q-profile controller has been successfully implemented and tested in EAST.   

First measurements of edge impurity flow across the L-H transition in TCV

Recent upgrades of the CXRS diagnostic, together with a low power diagnostic neutral beam injector, have, for the first time, enabled accurate measurement of the changes in the impurity intrinsic flow across the transition to ELM-free H-mode on TCV. Photon statistics limited the time resolution to 12 ms, for a 30 Hz measurement frequency.
A narrow (≈5.5 mm) and deep (|u_θ| ≥ 20 km/s) poloidal rotation well develops at the last closed flux surface, together with a pedestal in the density profile < 15 mm wide. The impurity temperature profile shows after the transition a uniform increase of about 100 eV, with no evident pedestal. The radial electric field E_r, computed from the impurity kinetic profiles, revealed the development of the E_r-well characteristic of H-mode as observed in other devices, whose width agrees with previous inter-machine scaling [McDermott, Phys. Plasmas 16 (2009)]. Estimates of the main ion flow suggests that the E_r well main contributor after the transition is the main ion density gradient term.
The measured impurity flows are in reasonable agreement with neoclassical analytical [Kim, Phys. Fluids B Plasma Phys. 3, 1991] and numerical NEO [E.A. Belli and J. Candy, Plasma Phys. Control. Fusion, 50:095010, 2008] predictions.

  

Modeling of AUG pellet discharges

Particle transport in tokamaks has been widely investigated both experimentally and
theoretically over the last 2 decades, advancing our physics understanding, in particular
for the density peaking. The density perturbation by pellet injection allows to decouple
particle diffusion and convection, while only their ratio matters to determine the peaking
at steady-state.  In this paper we analyze a pellet frequency scan in ASDEX Upgrade, at fixed pellet mass . and velocity. At lower frequency the density profile has time to relax to the state before . the injection, at higher frequency there is a secular increase of the plasma density as the . profile remains hollow. This suggests a critical transport time scale, thus providing a
constraining test for transport models.  The profile evolution is first simulated with ad-hoc models of region-wise uniform particle . diffusivity, constant in time. In this way we characterize the transport level inside and . outside the pellet deposition region. The effect of a particle pinch is also investigated.  Then the TGLF model is used for the predictive study, with both saturation rules.  The modeling results are presented and the eventual shortcomings are discussed.   

First result of edge impurity transport with EMC3-EIRENE code in HL-2A plasmas

Understanding of edge impurity transport is essentially important for impurity control and detached divertor operation, which are the key points to realize high-performance plasma. The EMC3-EIRENE simulation code is focused on the edge plasma transport and successfully applied to many machines to resolve the transport with 3-dimentional magnetic structure. The RMP coils have been installed in HL-2A, therefore it is necessary to apply the EMC3-EIRENE code to HL-2A plasmas. The computational grid is firstly generated for each magnetic configuration of interest as the input of EMC3-EIRENE. The edge temperature and density profiles measured by probe system are used for adjusting the transport coefficients of background plasmas. Good agreement in ohmic phase is obtained with D_⊥= 0.3m²s⁻¹ and χ_⊥ = 1.5m²s⁻¹. The profile of CIV line emission (312.4Å: 1s²2s - 1s²3p) obtained from simulation is compared with experimental result measured by the space-resolved extreme ultraviolet spectrometer. Analysis shows that the thermal force is dominated in ECRH heating plasma instead of the dominant friction force in ohmic heating plasma, resulting the enhancement of CIV intensity in ECRH heating phase. The detailed analysis on carbon impurity transport based on EMC3-EIRENE code will be presented.   

Turbulent Plasma transport in the PKU Plasma Test (PPT) device

Turbulent plasma transport causes the loss of particle and energy in magnetized plasma, which decrease the confinement of Tokamak plasma. Recently, a series of experiments have been carried out in the PPT device, to study turbulence transport including particle and energy transport. Combining both the high-speed camera and probe analysis, some problems of turbulence transport have been studied preliminarily. A lot of modes, such as drift wave turbulences, high frequency eigen modes, low frequency coherent structures, etc., are all observed. The interchange of energy and momentum between these modes are also identified. The interaction of multi-modes may play an important role on the radial plasma transport of particle and momentum.   

A Large-Aspect-Ratio Multiscale Pedestal

Understanding of the behaviour of tokamak pedestals is critical to forging a path towards efficient fusion reactors. Existing models [1] of the pedestal region are focused on modelling experiment. These models have achieved great success but some of the underlying physics remains obscure. 
Hence, in this work a first-principles approach to the problem is taken. We start from the equations of [2], and construct solutions in the large-aspect-ratio limit. We  approximate the fluxes within the pedestal as strongly-driven, critically-balanced turbulence similar to [3].  We support this with nonlinear simulations of the inter-ELM turbulence equations of [2] using GS2 [4]. This results in an inter-ELM equilibrium including in-out asymmetry, poloidal flows, and finite radial electric fields.
We explore the linear theory of such equilibria - both stability to ELM-like perturbations and the theory of slower oscillations.

[1] Snyder, P.B. et. al. Nucl. Fusion 51, 103016.
[1] Abel, I. G. & Hallenbert, A. J. Plasma Phys. vol. 84, 745840202
[2] Barnes, M., et. al.   Phys. Rev. Lett. 107, 115003
[3] Wilkie, G., Highcock, E. and Dorland, W. Private Communications   

Simulation study of toroidal flow generation by ECH in non-axisymmetric toroidal plasmas

   Spontaneous flows have been observed during ECH with no direct momentum input in tokamak and helical plasmas. In LHD, when we applied ECH to the NBI heated plasma, the toroidal velocity profile changed drastically. We assume that the radial flux of supra-thermal electron enhances the bulk ion cancelling current. This current generates the JxB torque, which would play an essential role in causing a toroidal flow. 
   In this study, we study the JxB torque due to the radial current of supra-thermal electrons and the collisional torque by the supra-thermal electrons in the LHD using GNET code, which can solve the 5D drift kinetic equation for supra-thermal electrons. As a result, we find that the JxB torque generated by ECH is several times larger than the collisional torque of the supra-thermal electrons and the total torque by ECH is the same order as the NBI torque. Also, its direction is opposite (same) direction to NBI torque in the inner (outer) region, those are consistent with the experimental observations.
   Also, we evaluate the torque by ECH in the non-axisymmetric tokamaks (finite toroidal field ripples and magnetic perturbations). We find that the significant torque by ECH is obtained in the case the toroidal field ripple > 0.2%.   

Role of Toroidal Rotation in ITB Formation in Tokamaks

A set of tokamak discharges with internal transport barriers (ITBs) are studied using the TRANSP code in order to investigate the role of toroidal rotation in triggering of ITBs. The toroidal momentum transport is predicted using theory-based Multi-Mode and TGLF anomalous transport models to compute the toroidal rotation profiles and  the effects of turbulence quenching as a result of associated sheared flows.  The effect of co- versus counter injected beams on the location and strength of ITBs is studied. Results are presented for existing discharges in order to illustrate the extent to which the Multi-Mode and TGLF models in TRANSP code yield toroidal rotation profiles that are consistent with experimental data. The comparison is quantified by calculating the RMS deviations and Offsets. The self-consistent evolution of the equilibrium is computed using the TEQ module.  Neoclassical transport is calculated using the Chang-Hinton model. NBI and ICRF heating and current drive are obtained using the NUBEAM and TORIC modules.   

Simulating magnetic fusion experiments with initial value codes

Fusion laboratory experiments are characterized by large gradients as is needed to confine plasmas hotter than the sun in laboratory devices.  These large gradients result in a wide-range of instabilities.  In toroidally-confined plasmas these linear instabilities (e.g., $1/1$, TM, ITG) evolve nonlinearly to produce phenomenological events (e.g., sawtooth, MARFE, transport).  The phenomenological events are generally of three types: violent relaxation (or transients), coherent saturated steady state, and turbulent steady state. How to formulate the simulation of experiments with an initial value code requires understanding the phenomenological type, and appreciating the subtle implications of the solution technique.  These subtle implications are discussed generally, and then specifically in the context of simulating QH-mode, ELM-free regimes.   

Data-driven approach to plasma profile evolution for plasma control

High-current disruptions must be avoided in ITER to prevent prohibitively expensive damage. Most modern Plasma Control Systems partially solve this problem by predicting disruptions in real time and shutting down the experiment altogether when necessary. However, a more useful system would automatically vary controllable parameters (such as ECH and neutral beam systems) to guide the shot along a path that circumvents instabilities before disruptions are imminent. This study tackles the first step toward such a system: predicting the future evolution of a shot based on the history of the shot up to the current moment. Using first principles simulations for this task is notoriously slow and unreliable, so our approach is instead data-driven. A statistical / machine learning algorithm takes in the history of the pressure profile, current profile, plasma rotation, and a few other parameters at a time t. It then outputs the prediction for the profile at time t+1. By repeating this process iteratively on predicted steps with various options for the controllable parameters at each step, a Plasma Control System could set the controllable parameters to maintain safety with optimized performance.   

From Lawson to Burning Plasmas: a Multi-Fluid Approach

The Lawson criterion gives the value for the triple product of density, temperature and energy confinement time needed for the plasma to ignite. Lawson's work was improved, adding 1D geometry and multi-fluid (ions, electrons and alphas) physics to the model. Physical equilibration times and different energy confinement times between species were accounted for in steady-state (Lawson-like) and time-dependent calculations. At this time it is more meaningful to consider a finite gain factor Q. The plasma conditions needed to achieve any desired value of Q both in the 0D and the 1D multi-fluid plasma description can be evaluated through freely-available versatile Mathematica notebooks. Arbitrary density and temperature profiles can be assigned from input. Results are related with experimental pure-deuterium discharges defining a no-alpha pressure. Given the multi-fluid Lawson product needed for a desired Q the alpha heating is subtracted from the energy balance and the no-alpha equilibrium pressure is obtained. The model easily allows to introduce scalings for energy confinement times. Including the τ_E dependence on power only one thermal equilibrium point exists for a given heating power instead of the two predicted by Lawson-like calculations.   

Resistive MHD Evolution of Shaped RFP Equilibria

Computational modeling of the resistive MHD evolution of reverse-field-pinch (RFP) plasmas with boundary shaping is undertaken. The VMEC code obtains equilibria that are similar to quasi-single helicity (QSH) states in an RFP with a helical axis and a symmetric boundary [J.D. Hanson, et al., Nuclear Fusion 53, 083016 (2013)]. Previous work has shown that axisymmetric boundary shaping affects whether an axisymmetric or QSH equilibrium is obtained in VMEC. In this work these equilibria are used as initial conditions for the NIMROD code [C.R. Sovinec, et al., Phys. Plasmas 10, 1727 (20030]. Particular attention will be paid to the evolution of global tearing modes in both axisymmetric and helical equilibria.   

Operation of the Lockheed Martin T4B experiment

The T4B experiment is a linear, encapsulated ring cusp confinement device. The mission of the T4B experiment is to develop a physics and technology basis for a follow-on high beta (beta ~1) machine, T5. The T4B experiment consists of 13 magnetic field coils (11 external, 2 internal), to produce a series of on-axis field nulls surrounded by modest magnetic fields of up to 0.3 T. A series of physics investigations were performed to retire risk from the T5 heating experiment, presently under construction. Following an initial test campaign used for machine check-out and diagnostic validation, a thorough investigation of plasma sources was completed. In addition, a series of Neutral Beam Injection (NBI) coupling tests were conducted to investigate fast-ion confinement and plasma source / NBI interaction. Finally, magnetic shielding experiments were performed to study the effect of local magnetic perturbations on particle losses to the internal coil support structures. Detailed results from these studies will be presented.
© 2018 Lockheed Martin Corporation. All Rights Reserved.
  

Plasma Source Development for Lockheed Martin’s Compact Fusion Reactor Program

A multipronged plasma source development effort is underway for the Lockheed Martin Compact Fusion Reactor (CFR) program. The objective of the plasma source development effort is to build a plasma source that can provide a sufficiently dense plasma target for neutral beam heating in the CFR geometry (a linear encapsulated ring cusp). An ideal source would allow for high mirror ratios in the expansion regions (divertors) of the device, have a very high ionization fraction, have very low impurity levels, and create sufficiently dense plasma (>5 x 1019 m-3).  In addition to the arc-reflex thermionic source currently employed on the T4B linear encapsulated ring cusp experiment, we are developing three alternative technologies: a high power (>2 MW) MagnetoPlasmaDynamic source (MPD), a cross-field (ExB) homopolar type source, and a high power (>400 kW), high field (>4 kG) RF source.  We present the performance of these high power plasma sources.
© 2018 Lockheed Martin Corporation. All Rights Reserved. 

An Overview of Laser Diagnostics Developed for the Compact Fusion Reactor

The T4B experiment is a linear, encapsulated ring cusp confinement device, designed to develop a physics and technology basis for a follow-on high beta machine as part of the compact fusion reactor program. Toward this end, a pair of non-invasive laser diagnostics have been developed to investigate confinement, neutral beam heating, and source behavior on the T4B device. These diagnostics include: (1) a Thomson scattering system employing a 532 nm Nd:YAG laser and high throughput spectrometer to measure electron density and temperature and (2) a dispersion interferometer utilizing a continuous-wave CO2 laser (𝝀 = 10.6 μm) to measure time resolved, line-integrated electron density. An overview of laser systems, detection schemes, and data analysis techniques for both systems is presented, including up to date results obtained from the T4B experimental campaign.
© 2018 Lockheed Martin Corporation. All Rights Reserved.

  

Ion Cyclotron Resonant Heating in the Central Cell of the Keda Mirror with AXisymmetricity (KMAX)

We report the results of ion cyclotron resonance heating (ICRH) in the central cell of a fully axisymmetric tandem mirror. With a total power of 100 kW radiated by double half-turn (DHT) and half-turn (HT) antennas, the plasma diamagnetism increases by 15-fold, with a corresponding peak  beta ~2%, density ~ 2*10^18 m^-3 , and total temperature ~60 eV. The effects of the magnetic configuration on resonance heating and wave emission are studied by varying the magnetic fields at the midplane and at the location of the antennas, respectively; the results confirm that the magnetic beach configuration is key to successful ICRF heating. The axial phase speed measurements suggest that the excited wave is a slow wave in the plasma core and a fast wave at the edge.
  

Investigation of magnetic mirror configurations at the WiPPL facility and their applications

The Wisconsin Plasma Physics Lab (WiPPL) has a unique flexibility to experimentally study various magnetic mirror geometries. Recently, two distinct types of mirror plasmas were made: one with axial current and one without. The former allows for confinement and stability properties to be explored and, further, may serve as a viable, cheap, simple fusion neutron source design. The latter allows for the creation of flux rope turbulence important for studying coronal loop heating. Axial current can additionally provide a mirror plasma with high beta turbulence or one that can serve as a plasma target for reconnection experiments. Initial data gives mirror plasmas as dense as 2x10^{19} m^{-3} with 8eV electrons/ions and betas ranging from 0.1 to 10. WiPPL has also performed a number of numerical calculations for plasma stability in mirrors. Specifically, non-paraxial (spherical) mirrors are predicted to stabilize the m = 1 flute mode due to their favorable curvature. Further analysis in the ballooning approximation has shown stability with respect to high-m modes. Future non-paraxial mirror experiments at WiPPL will hope to confirm these stability properties. Magnetic mirrors improve confinement and provide a great base plasma for studying reconnection, turbulence, and stability.   

FuZE Compact Fusion Device - Outlook for Scaling up to Reactor Conditions

The University of Washington and Lawrence Livermore National Laboratory have partnered to advance the sheared-flow stabilized (SFS) Z-pinch concept and assess its potential for scaling to fusion conditions. The Fusion Z-pinch Experiment (FuZE) expands on UW's ZaP and ZaP-HD SFS devices by employing higher power-handling electrodes along with flexible gas injection and power systems that tailor the discharge current and distribution of gas to establish the required plasma flow and pinch current. An extensive set of diagnostics provide key measurements. We are executing experimental campaigns to increase the pinch current, duration of pinch stability, and DD fusion neutron production guided by both fully-kinetic and fluid based computer simulations. These efforts aim to scale this concept to high current, plasma density, and temperature with a goal of demonstrating a practical path to a compact, low-cost fusion reactor.   

Implementation of an eight-cord equal path length, heterodyne interferometer on the Fusion Z-pinch Experiment FuZE

The Fusion Z-Pinch Experiment (FuZE) project uses a radial-sheared axial flow stabilized Z-pinch to develop a compact fusion device. The machine is able to drive ~ 200 kA of pinch current, compressing the pinch to a radius of ~ 3 mm. By seeding the hydrogen Z-pinch with a minority concentration of deuterium, thermal fusion neutrons are produced. An extensive set of diagnostics provide key measurements, including an eight-cord equal path, heterodyne, quadrature phase differential interferometer. Three chords are located at acceleration region to investigate the snowplow and deflagration processes for long-lived Z-pinch structures. Five chords are located at the midplane of the 50 cm Z-pinch assembly region with 1 cm vertical spacing to measure the evolution of plasma density profile. Assuming cylindrical symmetry, Abel-inverted radial density profiles are reconstructed from these five-chord line-integrated electron density data. Furthermore, assuming a constant drift speed, the temperature profile is calculated and compared with ion Doppler spectroscopy measurement. The design of the interferometer and detailed data analysis will be presented.   

Design of a Megajoule-Class Dense Plasma Focus as a Flash Neutron Source At LLNL

The MegaJOuLe Neutron Imaging Radiography (MJOLNIR) experiment is an approximately 3MA (upgradable to 4.5MA) dense plasma focus (DPF) that has been designed and is currently being constructed at LLNL.  The goal of the device is to produce an intense, flash source of neutrons for radiography applications.  The device will leverage recent results from both LSP hybrid fluid/kinetic simulations and smaller scale DPF’s at LLNL.  These modifications include improvements to conventional DPF designs such as advanced anode geometries, modified insulator geometry vacuum chamber/electrodes removable as a sealed unit, and an improved diagnostic package.  Here, we present an overview of the current device design, including progress made in prototyping and constructing the device. We also report on status of first plasmas.   

Improvements in Pinch Formation Using Tapered, Hollowed Anodes in a MJ-Class Dense Plasma Focus

A dense plasma focus (DPF) device drives current through a set of coaxial electrodes to assemble plasma inside the device and implode the plasma on axis to form a Z-pinch. The implosion drives instabilities to generate strong electric fields, which produce short intense pulses of x-rays, high-energy (>100 keV) electrons and ions, and if using fusion-reactant ions (e.g. D, T), will generate neutrons. As well as being dependent on the high-energy ion “beam”, neutron production relies on the formation of a long, high-density, “plasma target” that the ions will pass through. Using the particle-in-cell code Chicago in 2D-3V, we simulate the plasma target formation in a multi-mega-amp DPF device. We find that adding a taper and a hollow to the inner electrode (anode) improves the formation of the plasma target on axis by creating a more uniform implosion. The taper is most helpful for large radius anodes and is a potential method for mitigating yield roll-off at high currents (3+ MA). We investigate the importance of the electron temperature of the plasma target on the ion stopping power to understand the optimization of the anode shape. We also describe how to achieve a given neutron yield based on estimates of the ion beam & plasma target.   

Optimizing Dense Plasma Focus Neutron Yields with Fast Gas Jets

We report on a study using the particle-in-cell code Chicago to perform fully kinetic simulations of dense plasma focus (DPF) devices with patterned gas loads created via supersonic gas jets on axis. The supersonic jets are modeled in the large-eddy Navier-Stokes code CharlesX, which is suitable for modeling both sub-sonic and supersonic gas flow. The gas pattern, which is essentially static on z-pinch time scales, is imported from CharlesX to Chicago for neutron yield predictions. Fast gas jets allow for manipulating the mass on axis while maintaining the optimal background pressure for the DPF. The conditions favorable for producing neutrons are found to be more consistently met when a jet is present on axis. Perturbations in the jet density introduced via super-sonic flow (known as Mach diamonds) allow for consistent seeding of the m=0 instability, producing a better ion beam, and consistent target formation leading to more consistent ion acceleration and higher neutron yields with less variability. The optimal jet configuration for increasing neutron yield and reducing shot-to-shot yield variability is explored.   

Density and Temperature Measurements on the Microsecond X-Pinch

Several comprehensive experimental measurements have been conducted on the microsecond x-pinch. First, a two-frame Mach-Zehnder interferometer has been implemented for electron density measurements via a frequency doubled, pulsed Nd:YAG laser. The second frame is delayed from the first by 61 ns, which allows for same-shot time evolution dynamics to be observed. The measurements presented on the axial plasma jets complement previous schlieren imaging results. Secondly, time-integrated x-ray spectroscopy has been conducted with a flat crystal spectrometer and x-ray sensitive film. Results from aluminum x-pinches have demonstrated the presence of He- and H-like ionic states, allowing a determination of the electron temperature of the hot spots. Further results on the spectroscopy of other wire materials will also be presented. Lastly, a study of load optimization for x-ray yield on the microsecond pinch will also be presented.
  

Simulations of Gas-Puff Z-Pinch Implosions with comparison to Magnetic Fields measurements at the Weizmann Z-Pinch.

Measurements of magnetic field in gas-puff implosions on the generator at the Weizmann Institute of Science (WIS) have been recently shown to be in contradiction to a snowplow model using the current of the pulsed-power generator and the pinch radius. Simulations of magnetic field evolution using the 2D radiation-magneto-hydrodynamic code, MACH2-TCRE are presented in two steps as follows. In the first step, simulations of the initial density profile by modeling the neutral gas-flow of subsonic oxygen through De-Laval nozzles are made and compared to measurements. In the second step, the density profiles from the previous step are used as initial conditions for investigating the distribution evolution of the magnetic field during the gas-puff implosions. Comparisons are made with the measured data of magnetic field and radius. It is shown that simulating the nozzle geometry and outflow significantly improves the comparison between the measurements and the pinch simulations.   

Staged Z-pinch experiments at the 1MA Zebra pulsed power generator using Kr-liner and Cu-W nozzle and cathode

In these experiments a krypton liner is compressing deuterium target while the plasma column is stabilized with external axial magnetic field B_z = 0.5-1.5 kG. The cathode and the gas injection nozzle erosion is minimized by using copper-tungsten alloy. Multi-spoke and honeycomb cathodes are used, with the later providing more consistent pinches. The pinch stability is monitored with two quad X-ray pinhole cameras. The fusion neutrons are diagnosed with silver activation diagnostics, neutron bubble detectors and four time of flight detectors (nTOF). Consistently high neutron yields in the ~5-10 x10⁹ range are measured and their thermonuclear origin is suggested by data from a pair of horizontally and vertically placed  nTOFs. The eight frame X-ray pinhole camera images confirm the staged Z-pinch stability.   

Experiments and Simulations of staged Z-Pinch on 1MA ZEBRA facility

Experiments at ZEBRA show uniform compression of a deuterium plasma target compressed by a high-Z gas-puffed liner like Ar or Kr. Pinch stability is improved by seeding the implosion with 0.05-0.15T of B_Z.  Implosion dynamics are also studied computationally with MACH2 & HYDRA codes. Simulations show that magnetic field diffuses through the outer shell and piles up at the interface providing narrow profile of high intensity current that preheats the target.   This secondary piston launches shock waves in target plasma that heats the target to several hundred eV and this preheated target plasma is adiabatically compressed to densities up to 5x10²⁰ cm^-3 and temperature of 5-10KeV. Simulations show more pronounced pre-heating with Kr than Ar. Axial magnetic field is compressed only in the shocked target and in the liner plasma, providing greater MRT mitigation. For Ar liner on D target experiments we measured neutron yield of 2-5x10⁹ and for Kr liner 5-12x10⁹.  Experimental observations like plasma current, visible streak images, gated-XUV pinhole images, and laser shadowgraphs are compared with simulations, and show general agreement. The experimentally measured neutron yield is also in good agreement with simulations.   

HEDP experiments on a 0.8 MA LTD generator at UCSD

Linear Transformer Drivers (LTDs) are the most promising high-current pulse generators, as they offer several advantages over Marx bank based systems: small footprint, more efficient energy coupling to the load, possible multi-stage modularity, and potential for higher repetition rate. 
Here, we present the first results from the operation of a 0.8 MA, 150 ns LTD generator recently installed at UCSD, coupled to a conical transmission line to drive a variety of loads. 
Initial experiments are performed using gas puff Z-pinch loads. A variety of diagnostics including multi-frame laser interferometry, XUV and optical gated imaging, Thomson scattering, X-ray spectroscopy, and time-resolved visible spectroscopy are used. Experimental data and relevant simulations will be presented.    

Planar Shock Wave Propagation in Multi-Species Gas with a 200-kA Pulsed Power Driver

Shock waves in multi-species gases are relevant in a variety of topics in high energy density physics including astrophysical plasma physics and inertial confinement fusion (ICF) especially in liner-on-target implosion schemes. Results from planar foil shock experiments on a 200-kA pulsed power driver, GenASIS, are presented. In this experimental setup, a 5×5 mm² foil load of 1-10 μm thickness is heated and ablated by a high current pulse. The material is then accelerated normal to the foil plane via a magnetic pressure gradient set up by the anode-cathode gap. The characteristics of foil expansion and motion are initially studied by diagnosing the accelerating material in vacuum to determine the effect of foil load parameters on performance. Ablated material motion, as well as shock velocity, is determined using a four-frame schlieren imaging system with 30 ns inter-frame delay on an Nd:YAG laser. The relative motion of gas species is measured using spatially resolved visible spectroscopy coupled to a two-frame gated ICCD camera with 1 μs inter-frame interval.    

At ignition scale experiments on NIF of next generation MagLIF laser preheat

Development of a cryogenic and magnetized gas pipe platform is underway at NIF. Experiments have been done into unmagnetized, room temperature, hydrocarbon and cryogenic D2 gases of densities that span 1.6 mg/cc to 4.8 mg/cc (5% to 16% critical electron density). 30 kJ of energy from one quad have been delivered into a oval spot of 1580 micron mean diameter over a time of about 11 ns with a power 2 TW and an intensity of 2x10¹⁴ W/cm². A large fraction of the laser energy has been absorbed by Inverse Bremsstrahlung absorption over the 1 cm length of the gas pipe. Temperatures of up to about 1300 eV have been reached in the core. Raman and Brillouin backscatter were measured to be "low" on all shots. Experiments in FY19 are planned that will apply a magnetic field of up to 30 Tesla along the axis of the laser deposition for warm hydrocarbons. Applying a magnetic field to the cryogenic D2 gas is possible in future years. These experiments are focused on doing "to ignition scale"  Magnetized Liner Inertial Fusion (MagLIF) laser preheat experiments for the next generation pulse power machine.   

Favorable Collisional Demixing of Ash and Fuel in Magnetized Inertial Fusion

Magnetized inertial fusion experiments are approaching regimes where the radial transport is dominated by collisions between magnetized ions, providing an opportunity to exploit effects usually associated with steady-state magnetic fusion. In particular, the low-density hotspot characteristic of magnetized liner inertial fusion (MagLIF) results in diamagnetic and thermal frictions which can demix thermalized ash from fuel, accelerating the fusion reaction. A simple diffusion model shows that increases in the fusion energy yield on the order of 5-10% are in fact possible. Our results could also be relevant for magnetic target fusion. Effects due to pressure anisotropy may also be discussed.   

Extended MHD in the Ares multiphysics code

The Ares multiphysics code models a variety of processes relevant to high-energy-density systems, including radiation hydrodynamics, laser energy deposition, thermal conduction, atomic physics, themonuclear burn, and magnetohydrodynamics (MHD). Pulsed power experiments provide a demanding setting for multiphysics codes, requiring accurate models for solid-density, room-temperature materials and low-density, high-temperature plasmas. To improve the fidelity of the low-density plasma treatment, Hall MHD has been implemented in the 2D MHD package in Ares. The algorithm and implementation have been benchmarked using a Hall drift wave problem [J. D. Huba, Space Plasma Simulation, Springer (2003)]. The Hall term introduces short-timescale oscillations that can drastically limit the numerical timestep when modeling pulsed power experiments. To mitigate these impacts, a combination of algorithmic modifications and subcycling have been implemented. This presentation will focus on these and other improvements to the treatment of low-density plasmas in the context of pulsed power systems.
LLNL-ABS-753700   

Modeling Highly Unsteady Current-driven Liquid Metal Free-Surface MHD Flows

The flow of electrically conducting liquids in response to a highly unsteady applied current (or magnetic field) is of practical interest in nuclear fusion, and metallurgy. Analytical and semi-numerical methods have been used to model such flows for a number of years, but suffer from serious model limitations when there are large and rapid deformations of the free surface, and in complex geometries. We present a candidate time-accurate simulation method which uses a magnetic vector potential and a scalar electric potential in a general purpose high performance computing software. Variants of this method are often seen in eddy current analysis, but applications in free surface MHD appear limited and rather restrictive. The model permits the flow of current into the conducting elements, and can resolve highly unsteady phenomena and the skin effect. We will present the method with verification, and apply it to the mini-SLiC experiment at General Fusion, where a pool of liquid lithium in a steel vessel is rapidly propelled by an electric current pulse (about 1ms) and exhibits interesting dynamics. We will compare numerical results with observed experimental data.   

Tomographic density profile measurements of spheromak plasma targets for MTF applications

A method of plasma sustainment, imposed-dynamo current drive (IDCD), could improve the performance of compact, magnetized plasma targets of interest to ARPA-E’s ALPHA fusion portfolio. A new tomography system has been built and installed on the HIT-SI3 spheromak experiment at the University of Washington. Several hundred chords of light from three poloidal planes and the toroidal mid plane are simultaneously collected by 13 wide-angle lenses and imaged onto custom fiber optic bundles. The plasma light travels through a beam splitter after which each leg is filtered to a different He I emission line (668 nm and 728 nm) and collected by a single Phantom v1212 high-speed camera. The plasma density is calculated from the ratio of the lines. This diagnostic is used to assess the effect of imposed electron velocity shear symmetrizing and stabilizing compact, spheromak plasma targets. An improvement in the symmetry of compact plasma targets while preserving gross plasma stability may lead to high energy confinement quality, thereby enabling higher temperature magnetized plasma targets.