Session PP10: Poster Session VI: Posters for Mini-conference: Turbulence, Reconnection, Shocks, and Particle Acceleration. Basic Plasmas: Laboratory Techniques, Plasma Production, Plasma Dynamics. Magnetic Fusion: Energetic Particles, Disruption, MHD, Turbulence and Transport (2:00pm-5:00pm)

Transition from weakly to strongly anisotropic dynamics in magnetohydrodynamic turbulence

Magnetohydrodynamic (MHD) turbulence is an essential aspect of a wide range of astrophysical systems, among them convection in stellar interiors, mixing of accreted material into stars, and the dynamics of stellar winds. In each of these astrophysical settings, large-scale structuring of the magnetic field has been observed or is predicted. A large-scale magnetic field produces an anisotropy in the turbulent dynamics of the plasma. We investigate the structure of anisotropic MHD turbulence from the Lagrangian viewpoint based on the trajectories of Lagrangian tracer particles, the natural point of view to study mixing and diffusion. We produce standard Lagrangian statistics such as single-particle diffusion curves, two-particle dispersion curves, and velocity autocorrelation functions. We also demonstrate new Lagrangian statistics developed to understand anisotropic turbulence, including the convex hull and the turning time. Simulation results will be presented that are performed using grid sizes up to 2048^3.   

Novel Processes to Produce High Energy Particles in Plasma Surrounding Compact Binaries

The existence of plasmas around black holes was proposed as early as 1968 and in fact the first identification of galactic black holes was through the radiation mission of the plasmas associated with them. When a binary of two neutron stars or two black holes is relatively close to collapse, magneto gravitational modes [1] can be sustained by the oscillations of the surrounding plasma density having frequencies related to the orbiting frequency of the binary components. The plasma modes introduced for this are of the ballooning type (in the vertical direction) and have the frequencies of corresponding compressional Alf$\'e$n waves. Anew form of ``damping'' associated with the relevant mode particle resonances is identified [1]. \\ $[1]$ B. Coppi, Plasma Physics Reports, 45, 5, (2019).   

Formation of Shocks in Pulsed-Power Driven Magnetized Plasma Jets

Plasma jets, turbulence and shocks are of great interest to many research areas in physics due to their abundant presence throughout the universe. Supersonic, magnetized plasma jets formed using pulsed power facilities [1] provide interesting opportunities for studies of the interaction of magnetized flows with various obstacles. In our experiments the jets are created using the MAGPIE pulsed power generator at Imperial College, London by ablation of an Al foil driven by a 1 MA, 250 ns current pulse [2,3]. The \textit{JxB }force from the current flow across the foil re-directs the ablated plasma onto the central axis, forming a collimated jet with electron density of 10$^{\mathrm{18}}$-10$^{\mathrm{19}}$ cm$^{\mathrm{-3}}$ and propagating with velocity of 100km/s. Modification of the geometry and material of the obstacles positioned in the jet path allows observation of reverse shocks and magnetic field pile-up at planar obstacles, as well as bow shocks formed at compact obstacles. The set-up allows investigations of temporal variability (oscillations) of the radiatively cooled shocks and the development of shear-flow instabilities. Plasma interactions were characterized using Thomson scattering, laser interferometry, Faraday imaging and schlieren imaging diagnostics. [1] S.V. Lebedev, \textit{et al.}, RMP, \textbf{91}, 025002 (2019) [2] F. Suzuki-Vidal \textit{et al.,} Astrophys. Space Sci. \textbf{322}, 19 (2009) [3] F. Suzuki-Vidal \textit{et al.,} PoP, \textbf{19}, 022708 (2012).   

Magnetized plasma flow interactions in pulsed-power driven experiments

The interactions of fast-streaming, magnetized plasmas can result in a wide range of fundamental plasma physics processes such as the formation of MHD shocks, magnetic turbulence, reconnection and wave-particle interactions. We present experiments from a versatile platform, where supersonic plasma flows generated by the ablation of pulsed-power driven wire arrays are used to study a wide range of magnetized plasma interactions [1,2]. The setup allows a control over the global system parameters, including the drive strength, magnetization, magnetic field topology and interaction geometry. The plasma composition (wire material) can also be chosen to vary the collisionality of the plasma and introduce dynamically significant radiative cooling. The detailed structure of the interactions is measured using optical Thomson scattering, multi-color laser interferometry and Faraday rotation diagnostics, providing measurements of the flow velocities, plasma temperature, electron density and magnetic field distributions of the plasma. [1] Suttle et al., PRL 116, 225001 (2016) [2] Burdiak et al., PoP 24, 072713 (2017)   

Laboratory high density high Mach number plasmas to study particle acceleration relevant to astrophysical collisionless shocks

High velocity, low density, interpenetrating plasma flows are studied on the Omega and National Ignition Facility (NIF) lasers. These interpenetrating flows exhibited strong filamentation via the Weibel instability, which in turn generated microscale magnetic fields that were observed with proton radiography and optical Thomson scattering [1]. On the (NIF), the interpenetrating plasmas extended over much larger time intervals and interaction volumes. Under these conditions on NIF, we observed the evidence of collisionless shock formation, as demonstrated by an abrupt increase in density, with significant increase in temperature [2]. In addition, the electron spectrometer observes non-thermal high-energy enhancement of electron spectrum. This paper will present the recent results from Omega and NIF. [1] C. M. Huntington et al., Nature Physics, 11, 173 (2015). [2] F. Fiuza et al., in preparation (2019).   

A Newly Discovered Source of Turbulence in the Solar Chromosphere

Above the Sun's luminous photosphere lies the solar chromosphere where the temperature increases from below 4000 K to over 1 million K. Though solar researchers do not understand the origin of these increases, they know it powers the solar wind with enormous consequences for the solar system. This talk describes an analytical theory and a set of massively parallel simulations showing that conditions in the coolest parts of the solar chromosphere. The conditions there have some similarities with the lower Earth's ionosphere where plasma collisions with neutral atmosphere play a crucial role. Our simulsations have shown that neutral motions in the chromosphere may easily drive a previously unidentified thermal plasma instability that rapidly develops into turbulence. This meter-scale turbulence will modify the conductivity, temperatures, and energy flows through the chromosphere. Additionally, it provides a mechanism to convert energy from neutral flows into plasma turbulence and electron heating. This research demonstrates the importance of small-scale plasma wave physics on the larger scale solar atmosphere.   

Laboratory Magnetic Turbulence Studies at the Bryn Mawr Plasma Laboratory

The Bryn Mawr Experiment (BMX) at the Bryn Mawr Plasma Laboratory (BMPL) aims to study magnetic turbulence in a laboratory plasma wind-tunnel with the purpose of making comparisons to heliospheric, magnetospheric, and astrophysical turbulent systems. The magnetic turbulence is generated using a magnetized coaxial gun source to inject magnetic helicity into a 24cm by 2.7m long cylindrical flux-conserving chamber. The diagnostic section of the chamber includes an axial array of single-loop magnetic pickup coils at 1.3cm cadence along the axial direction. For a ~180us window of stationary broadband magnetic, two-point correlations functions are computed from various pairs of probes to determine time-delay estimated velocity measurements as well as spatial decorrelation. From these decorrelation measurements and energy spectra, basic magnetic turbulence parameters of the plasma can be determined including magnetic spectral indices and the magnetic Reynolds number. Early density measurements using ion saturation current from a double Langmuir probe will also be shown. Effort is underway to model this experiment using a resistive MHD model within the Dedalus framework.   

Particle acceleration due to mildly relativistic reconnection in a proton-electron plasma

In astrophysical environments such as AGN jets the energy density in the magnetic field can exceed all other contributions, including the energy density contributed by the rest mass of particle. If magnetic reconnection can free a fraction of this energy by changing the magnetic topology it is the dominant source of free energy. Some of it will heat the plasma and drive bulk flows, but a significant fraction of the energy will go to energetic particles. These particles typically form a hard power law distribution (spectral indices up to -1, harder than shock acceleration) that extend to very high cut-off energies. We performed self-consistent kinetic simulations of relativistic reconnection in hydrogen plasma without resorting to a modified mass radio using VPIC. Based on those simulations we study the relevant mechanism for the acceleration of both protons and electrons and the resulting spectra. Understanding those allows to include particle acceleration in large scale simulations that are inaccessible to fully kinetic simulations and to predict observable signatures in real systems.   

On the fast magnetic reconnection rate

The magnitude of the reconnection electric field parallel to the reconnection x-line not only determines how fast reconnection processes magnetic flux, but can also be crucial for generating super-thermal particles. Observations and numerical simulations have revealed that collisionless magnetic reconnection in the steady state tends to proceed with a normalized reconnection rate of an order of 0.1 in disparate systems. However, the explanation of this value has remained mysterious for decades. We propose that this value 0.1 is essentially an upper bound value constrained by the force balance at the upstream and downstream regions [1], independent of the dissipation-scale physics, independent of the mechanism that localizes the x-line [2]. The prediction from this model compares favorably to particle-in-cell simulations of magnetic reconnection in both the non-relativistic and extremely relativistic limits, from symmetric to asymmetric reconnection [3]. These results may be significant for solar, magnetospheric, astrophysical and fusion plasmas. [1] Liu et al., Phys. Rev. Lett. 118, 085101 (2017). [2] Liu et al., Phys. Plasmas, 25, 080701 (2018). [3] Liu et al., Geophys. Rev. Lett. 45, 3311-3318 (2018).   

Volumetric Measurements of Spontaneously Generated Magnetic Fields at High Repetition Rate

The Biermann battery effect describes the spontaneous generation of magnetic fields by non-parallel temperature and density gradients, and is an important source of magnetic fields in astrophysical and high density laboratory plasmas. In particular, Biermann fields are generated in the corona of an expanding laser-produced plasma (LPP). A new high repetition rate (HRR) experimental platform has been commissioned at the University of California Los Angeles to study the three-dimensional spatial structure and parameter dependence of these fields. A HRR laser is incident on a plastic target, which may be placed in an ambient gas or magnetic field. The ablated laser-produced plasma (LPP) is collisional and characterized by the dimensionless ratio $L/d_e \approx 10$, where $d_e$ is the electron inertial length and L is the LPP length scale. Density and temperature gradients in the LPP spontaneously generate magnetic fields via the Biermann battery effect, which are measured by a magnetic flux probe. We present volumetric measurements collected by moving the probe between shots to collect datasets comprised of several thousands of points. Results are compared to resistive MHD (FLASH) simulations.   

Optical Ion Velocity Diagnostics in the Interaction of a Laser Produced Plasma and an Ambient Magnetized Plasma

Measuring particle velocities is crucial to understanding plasma dynamics in the study of diamagnetic cavity formation, anomalous magnetic diffusion, plasma instabilities, and collisionless shock formation. We present two methods of measuring super-Alfv\'{e}nic particles in a laser-produced plasma (LPP). The first uses a high spectral resolution monochromator to measure fluorescence from beam ions to determine velocity distributions by charge state. Fluorescence traces were time-integrated to conduct a low resolution spectroscopic survey. The resulting spectra can be compared to NIST and collisional-radiative model data in order to evaluate the population densities and temperatures. Additionally, we propose an innovative application of laser induced fluorescence (LIF) on an expanding, super-Alfv\'{e}nic LPP. LIF is a widely used, noninvasive optical technique that can determine ion distributions, velocities, and qualitative concentrations with a high degree of spatial and temporal resolution. By using collisional-radiative simulations, we have identified the configurations with the best signal to noise ratio SNR. Hybrid simulation results are displayed to help visualize the expected results.   

Mass Ratio Dependence of Collisionless Reconnection Under Strong Guide Field

Magnetic reconnection under a strong guide field BG/B0\textgreater \textgreater 1, as in laboratory plasmas, is investigated using the gyrokinetic electron and fully-kinetic ion (GeFi) particle simulation model, where BG and B0 are the guide and the anti-parallel component of magnetic field, respectively. The simulation is carried out for a two-dimensional (2D) force free current sheet. Cases with various ion-to-electron mass ratio mi/me and guide field BG are presented in order to understand the effects of the mass ratio and guide field on the rate and structures of reconnection. Results are shown for mi/me $=$100-1836. The simulation results are compared with the linear eigenmode analysis. 3-D magnetic reconnection with a strong guide field BG is also discussed using our GeFi simulation model.   

The Ideal Evolution Equation and Fast Magnetic Reconnection

The ideal evolution equation, $\partial \vec{B}/\partial t = \vec{\nabla}\times(\vec{u}_\bot\times \vec{B})$, implies magnetic field lines move with a velocity $\vec{u}_\bot$ and cannot change their connections. Nevertheless, for an electric field that is arbitrarily close to the ideal form, $\vec{E}+\vec{u}_\bot\times \vec{B}=-\vec{\nabla}\Phi$, magnetic connections will in general break on a time scale $\tau \ln R_m$, where $1/\tau\approx |\vec{\nabla}\vec{u}_\bot|$ is the Lyapunov exponent for neighboring streamlines of $\vec{u}_\bot$. The magnetic Reynolds number $R_m\equiv |\vec{u}_\bot\times \vec{B}|/|\mathcal{E}_{ni}|$, where $\mathcal{E}_{ni}$ is the deviation of the parallel electric field from the ideal form. This mathematical theorem is proven in Phys. Plasmas \textbf{26}, 042104 (2019) using Lagrangian coordinates, $\partial\vec{x}(\vec{x}_0,t)/\partial t =\vec{u}_\bot(\vec{x},t)$. Though true in two dimensions, the assumption that the part of the magnetic flux that is reconnecting $\psi_p$ must be dissipated by the parallel electric field $\partial\psi_p/\partial t= \int E_{||}d\ell$ is not correct in three. Then, $\psi_p$ can be mixed not destroyed conserving magnetic helicity. Two dimensional theories also effectively exclude exponentiation.   

Magnetic reconnection observation in the Earth's bow shock transition region

We investigate magnetic reconnection in the Earth's bow shock transition region using space observations by the Magnetospheric Multiscale (MMS) mission. A reconnecting current sheet with a thickness comparable to the ion inertial length is identified to exhibit electron outflow jets, Hall field and current patterns, and energy conversion, while no ion response is observed. In the same shock transition region, a reconnecting current sheet with an ion exhaust also exists, and the parallel heating of ions and electrons therein is similar to that in the standard reconnection exhaust. We will further discuss features for reconnection at the shock, how reconnecting current sheets are formed, and compare the contribution to energy conversion by reconnection with that by non-reconnecting current sheets and waves.   

Characterization of Phase Space Energy Transfer in 2-D Collisionless Magnetic Reconnection using Field-Particle Correlations

Magnetic reconnection plays an important role in the energization of particles in collisionless plasmas. We apply a new field-particle correlation technique to explore the energization of ions and electrons in collisionless magnetic reconnection simulations. The goal is to determine the characteristic velocity-space signatures of magnetic reconnection using single-point measurements of the electromagnetic fields and particle velocity distributions. We compare wave-particle energization to energy in bulk flows at specific spatial locations. This work extends a diagnostic suite allowing examination of the phase space energy budget of 2-D Gyrokinetic magnetic reconnection simulations. Understanding the entire phase space energy budget in single point measurements may provide novel insight leading to spacecraft measurement techniques to identify particle energization due to magnetic reconnection.   

Particle acceleration in relativistic unmagnetized collisionless plasma shocks: the emergence of Fermi Acceleration and energy bifurcation

We numerically study collisionless shocks generated by two colliding electron-positron plasma shells by using 2D first principle PIC code. Shocks are mediated by Weibel instability (WI), and initial kinetic energy (KE) of particles $mc^{2}\gamma_{0}$ changes via WI induced electric fields. We have found two groups of particles: having moderate ($\gamma \sim \gamma_{0}$) and large kinetic energies ($\gamma >> \gamma_{0}$). To get insight of the acceleration/deceleration mechanism, KE of the particles in these groups has been decomposed into the works done by the transverse and longitudinal electric fields. It is found that in the first group the KE takes equal contribution from both components of the electric field, while in the second group the KE takes most of the energy from the transverse electric field: the ratio of work done by the transverse and longitudinal electric field is found out to be $ \sim 5$. The position of the separation point between these two groups is found to be $\gamma/\gamma_{0} \sim 2$. An analytical model has been developed to explain the work decomposition and separation point.   

Pulsar magnetospheres and their radiation: a multi-scale challenge

In this talk I will review recent advances in modeling pulsar magnetospheres using a combination of global and local first-principles kinetic plasma simulations. This numerical approach allowed to shed light on several long-standing questions in pulsar astrophysics, including the behavior of pair discharges, the nature of magnetic dissipation and production of high-energy emission. Unexpectedly, simulations showed that effects of general relativity play a crucial role in pulsar activity. Finally, I will discuss strategies that would allow to answer the most fundamental question about pulsars, e.g. how do they produce their remarkable coherent radio emission.   

Kinetic-Alfven plasma turbulence mediated by magnetic reconnection

Recent measurements of plasma turbulence at scales smaller than the ion gyroscale in the earth magnetosheath by NASA's MMS mission, discovered small-scale reconnection events where only the electrons take part. We propose an explanation of this phenomenon. We investigate low-electron-beta plasma turbulence at sub-proton scales, the so-called inertial kinetic-Alfven turbulence. We argue [1] that the nonlinear dynamics tends to organize turbulent eddies into thin current sheets, consistent with the existence of two conserved integrals of the ideal equations, energy and helicity. The formation of strongly anisotropic structures triggers the tearing instability. We argue that the instability, in turn, governs the energy cascade and affects the statistical properties (energy spectrum, anisotropy) of small-scale kinetic-Alfven turbulence. \\ $[1]$ S. Boldyrev, N.F.Loureiro, Phys. Rev. Res. (2019) to appear.   

The two-time energy spectrum of weak magnetohydrodynamic turbulence

The two-time energy spectrum is a fundamental quantity in turbulence theory from which relevant statistical properties of a homogeneous turbulent system can be derived. A closely related quantity, obtained via a spatial Fourier transform, is the two-point, two-time correlation function that describes the space-time correlations arising from the underlying dynamics of the turbulent fluctuations. Both quantities are central in fundamental turbulence theories as well as in the analysis of turbulence experiments and simulations. The recent launch of the Parker Solar Probe (PSP), whose goal is to explore the near-Sun region where the solar wind is born, has renewed the interest in understanding the structure, and possible universal properties, of space-time correlations. The main hurdle affecting statistical turbulence theories is the well know closure problem, which requires ad-hoc assumptions about the high-order statistics of the space-time correlations. In this work, a wave-turbulence closure is used to obtain the structure of the two-time power spectrum of weak magnetohydrodynamic (MHD) turbulence from the nonlinear equations describing the dynamics. A wave-kinetic equation for the two-time power spectrum is derived for incompressible Alfvenic fluctuations whose nonlinear dynamics is described by the Reduced MHD equations.   

Confocal LIF Measurements of the Plasma Meniscus Boundary

The extraction of ion beams from plasmas has found many applications over the years; from neutral beam heating in tokamaks to ion engines on spacecraft. One major application is in semiconductor manufacturing where it is used in ion implantation and the etching of silicon wafers. The characteristics of these ion beams are strongly dependent on the plasma-vacuum boundary, i.e., the plasma meniscus. The meniscus controls the beam emittance, a key parameter that determines manufacturing rates and efficiency. To this end we used WVU's confocal system to perform laser induced fluorescence (LIF) measurements of the plasma boundary. The confocal system is unique in that it allows for the injection and collection of light along the same axis and can probe into the optically restricted area inside the reactor. With this optical system, we scan single points inside and outside the reactor to create a meniscus depth profile at different source parameters. Here we present measurements of the ion temperature and bulk flow at and around the meniscus boundary as a function of meniscus shape. Armed with knowledge of ion properties in the meniscus, it should be possible to tailor ion beams for a wide range of applications and industries.   

Observation of keV X-ray emitted from laser produced Au plasmas by using a crystal spectrometer

X-ray emitted by a laser generated plasma has various applications. Serious issue to be solved is that the energy conversion efficiency from the laser to X-ray is quite low. Recently, it was found that the X-ray emitted by the laser produced Au plasma increases under nitrogen atmospheres. In particular, the intensity of the water window soft X-ray (2.4-4.4 nm) increases approximately ten times. In order to elucidate this enhancement mechanism of X-ray, we have measured soft X-ray spectra from Au plasma in the wavelength of 1-7 nm so far. Recently, we fabricated a TAP crystal spectrometer to observe the photons over 1 keV region (1.0-1.9 eV), which provides useful information of plasma temperature. As a detector, an imaging plate(IP) was used. Titanium filters was also used to block out-of-band emission. As a result, continuum spectra attributed unresolved transition arrays (UTAs) was observed from the Au laser plasma. This spectral profile was compared with the Star2D hydrodynamic code.   

Characteristics of soft x-ray emissions from Au plasmas generated with various driving laser pulse durations

X-ray microscope using water window X-rays (2.3-4.4 nm) emitted from laser plasmas enables us to observe nanoscale structures of living cells. For higher spatial resolution without blurring, we need bright X-ray source with a pulse duration of less than a few nanosecond. As a promising X-ray source, we have focused on laser produced gold plasmas that emit continuum radiation in water-window wavelengths. In this study, by using Nd-YAG laser systems (1064 nm) with pulse durations of 7 ns, 400 ps and 10 ps, characteristics of the laser plasmas were investigated. The target with a thickness of 0.3 mm was irradiated by the laser beams focused using a convex lens (100 mm). For spatial resolved X-ray measurement, a grazing incidence spectrometer (flat field grating, 2400 grooves/mm) with a toroidal mirror was used. A pinhole camera with an aperture of 10 $\mu $m observed 2D plasma emission image. Two photodetectors were installed to measure the X-ray pulse duration and its energy with respect to the laser incident angle. Compared with these measurements, dependence of the plasma properties on laser pulse duration was examined. We also evaluated the conversion efficiency from laser to water-window X-rays.   

Zeeman Spectroscopic Determination of Magnetic Field in Magnetized Plasma Expanding into Vacuum

By passing a current through two wires perpendicular to a conducting surface a B-field that is largely parallel to the surface is created. UV light produced by the exploding wires creates a surface plasma on the conductor. Visible plasma emission is collected parallel to the magnetic field from along the surface to about 5 mm above the surface as the plasma expands. The light is split into left and right hand circularly polarized components, focused into two linear fiber bundles and delivered to a 750 mm spectrometer. The Zeeman components can resolve the peaks of the two polarizations even though the peaks show Stark Broadening. With this method, the magnetic field measures about 2.2 T 2-3 mm from the conductor surface, which is substantially lower than the estimated field at that distance. This method was developed for z-pinch experiments at the Weizmann Institute of Science (a Cornell Center collaborator) by G. Rosenzweig, E. Kroupp, A. Fisher and Y. Maron, ``Measurements of the spatial magnetic field distribution in a z-pinch plasma throughout the stagnation process'' JINST 12, P09004 (2017)   

PIN Diode and Amplifier Array for Imaging Transient X-ray Bursts from the Caltech MHD Jet Experiment

Transient 6 keV x-ray bursts having a duration of about one microsecond are detected in association with the breaking off of an MHD-driven plasma jet in the Caltech MHD jet experiment [1]. The detection of x-rays is surprising because the plasma is both cold (2 eV) and highly collisional (mean free path about one micron in a plasma having a spatial scale of 10's of cm).~ The X-rays were observed using detectors that provide temporal but no spatial information. In order to locate the x-ray source, a PIN diode detector array is being developed for use in a coded-aperture imaging system. A prototype channel consisting of a PIN diode and an amplifier has been demonstrated to be sensitive to single 6 keV photons from a Fe-55 radioactive source. This prototype also detects the transient x-rays from the jet experiment and the detected signal is simultaneous with the signal from the previously-used photomultiplier-based detector. The signal-to-noise ratio of the prototype is comparable but may need to be improved in order to attain imaging capability. [1] R. S.~Marshall,~M. J.~Flynn~and~P. M.~Bellan,~Physics of Plasmas 25 (2018)~Art. No. 112101   

HIDRA-MAT Development for HIDRA Plasma Exposure and \textit{In-situ }Material Characterization

The Hybrid Illinois Device for Research and Applications (HIDRA) at the University of Illinois Urbana Champaign (UIUC) is a hybrid fusion device that enables PMI testing for both stellarator and tokamak plasmas. HIDRA's long-pulse stellarator plasmas provide a platform for long exposures of PFCs. HIDRA-MAT is a material characterization module attached to HIDRA that is being designed and fabricated to include TDS and Raman systems for \textit{in-situ }characterization of materials that liquid metals have been introduced to. A specialized rotatable sample holder positions the sample for liquid metal droplet application from a lithium droplet injector on HIDRA-MAT. Early experiments look to investigate the effect of liquid lithium on porous tungsten samples regarding the retention of H, D, and He after plasma exposure. Preliminary results from RGA calibrations show the ability to differentiate D and He with TDS characterization of W samples after glow discharges to soon follow. Lastly, a systematic study of Li-H and Li-D bonds is being carried out to create a Raman spectra database to explore the effectiveness of Raman spectroscopy in references to liquid metal PFCs.   

Time-resolved dispersion interferometry for measuring low density air plasmas.

Many electrical phenomena in the atmosphere result in either full or partial local ionization of air. Such plasmas are unique from many laboratory plasmas due to the large concentration of neutral particles that can strongly affect the dynamics. One interesting active area of research is that of laser filamentation in air. Here, a laser beam with power above the critical power for Kerr self-focusing tends to collapse until it is arrested by generation of free electrons through field-ionization. A dynamic balance between Kerr self-focusing and plasma defocusing allows for guiding of an intense laser beam over multiple Rayleigh lengths. We have recently shown that a picosecond, terawatt CO$_{\mathrm{2}}$ laser self-guided through air forms a centimeter-scale diameter channel with a very low density plasma in the range of 10$^{\mathrm{13}}$ -- 10$^{\mathrm{16}}$ cm$^{\mathrm{-3}}$ [1]. The measured laser intensity in the channel of 10$^{\mathrm{12}}$ W/cm$^{\mathrm{2}}$ is significantly below the tunnel ionization threshold for oxygen and nitrogen. Simulations show that free electrons are generated by a combination of many-body Coulombic interactions and avalanche ionization. To experimentally measure such a low density, we tested a dispersion interferometer on a 1 cm long plasma produced by 10 \textmu m optical breakdown. Results suggest that we can measure 10$^{\mathrm{13}}$ cm$^{\mathrm{-3}}$ plasma density in a channel by probing nearly collinearly over \textasciitilde 50 cm. The diagnostic design and initial measurements will be presented. \begin{enumerate} \item S. Tochitsky et al, Nature Photonics 13, 41-46 (2019). \end{enumerate}   

Plasma Impedance Tomography for Imaging Plasma Dynamics

Plasma impedance probes measuring the self-impedance of the antenna-plasma system have been shown to provide accurate measurements of electron plasma density for space and laboratory plasmas. Plasma impedance probes measuring the mutual impedance between two antennas and a plasma dielectric have been successfully flown on sounding rockets and satellites. At the US Naval Research Laboratory, we have recently developed a novel plasma impedance tomography system consisting of an array of mutual impedance probes that uses the broadband impedance spectrum of the plasma to image electron density structures. The goal is to develop a system capable of providing tomographic reconstructions at a rate of a tenth of the peak plasma frequency of the system. Recent numerical and experimental results will be presented.   

New Results in Impedance Probe Applications and Antenna Coupling in the NRL Space Physics Simulation Chamber

We will present recent progress in plasma impedance probe experiments and antenna coupling calculations at NRL's Space Physics Simulation Chamber. The experiments are performed under a variety of conditions with magnetized and unmagnetized collisionless, cold plasmas in density ranges of $10^5-10^{10} cm^{-3}$. A range of low frequency measurements less than the ion plasma frequency will be compared with revised impedance probe models. Additionally, we will present new computational results on antenna coupling in a magnetized plasma.   

High bandwidth DT reaction history measurements in inertial confinement fusion

Simulations of high-yield DT ice layered shots at the National Ignition Facility (NIF) are matching key measured parameters such as bang time and ion temperature. However, the DT burn width measured by the diagnostic Gamma Reaction History (GRH) are wider by \textasciitilde 40{\%} compared to simulations. The new Gas Cherenkov Detector GCD-3 with the new Pulse Dilation -- Photo Multiplier Tube (PDPMT) provides increased temporal resolution compared to GRH of 10ps and gives results matching measurements by GRH. The high band width of the new detector allows for resolving the shape of the DT fusion reaction history for the first time and therefore yield a deeper understanding of evolution of the implosion experiments. The shape of the DT fusion reaction history can inform about which features are captured by simulation and where they results differ. The discrepancies between measurements and simulations need to be resolved, the physics involved understood to give a more complete picture of Inertial Confinement Fusion, and to aid in the quest for ignition.   

Sensor Multivariate Analysis for measuring X-ray radiation drive using the DANTE Diagnostic towards Inertial Confinement Fusion experiments

DANTE is a diagnostic used to measure x-radiation drive from hohlraums initiated by laser produced plasmas. It records the spectrally and temporally resolved radiation flux from various targets e.g., hohlraums, etc. at x-ray energies between 50 eV and 20 keV. Each sensor configuration on DANTE is composed of filters, mirrors and x-ray diodes to define 18 different x-ray channels whose output is voltage as a function of time. The absolute flux is then determined from the photometric calibration of the sensor configuration and a spectral reconstructing algorithm. The reconstruction of the spectra vs time from the measured voltages and known response of each channel has presented challenges. We demonstrate a novel approach here for quantifying the uncertainties on the determined flux and therefore, radiation temperature using A Partial Least Squares Regression (PLSR) calibration model. This technique uses the variances in both the spectral reconstruction and the error associated with the absolute calibration of each channel. Individual source spectra are created using an unfold algorithm where one channel response as a leave-out-one (LOO) model validation is performed on a test source spectrum and the radiation temperature and fluxes are predicted.   

Measuring current distributions with a probe that interrupts the current

Current distributions inside plasmas have been measured for nearly as long as probes have been used in plasmas. The distribution is typically derived from magnetic field measurements using B-dot probes, and computing the curl of B. The B-dot probes used are typically compact and enclosed. The general assumption is that current flows around such a probe, so that the overall current distribution is relatively undisturbed and the measurements can be reasonably accurate. Other authors contradict the validity of such a measurement, asserting that the only workable measurement involves as minimal interruption as possible. In either case the sensor is mounted on a shaft of finite extent. The current work attempts to measure the degree to which the finite interruption of the current flow by both the probe itself and the shaft affects the overall measurement. We find that the compact enclosed B-dot measurement of the current profile works well so long as the probe is not too large. We will attempt to quantify the meaning of ``too large''. Methods for taking the curl will be discussed, for example how accurate is a 4 point measurement?   

Relative Electric Field Measurements within the Striation Pattern of a Steady-State Microwave Driven Plasma

Using a focused continuous microwave beam to generate a plasma in a vacuum chamber the Air Force Research Lab (AFRL) is studying free-space plasmas. These plasmas are generated in a gas mixture of argon, oxygen, and nitrogen at pressures ranging from 100 mTorr to 200 mTorr. Previous studies from the AFRL reported that plasma in a stable mode exhibits periodic variations to electron temperature and density at intervals approximately half the free-space wavelength of the driving microwave beam. Using simulations the AFRL had hypothesized that this pattern was due to standing waves from the driving beam reflecting within the plasma. In this study, a coaxial probe has been used to measure the relative electric field strength in the striation pattern of the plasma. Changes in the electric field were interpreted against the variations in electron density and temperature. Gas composition and driving power of the beam were varied to see what impact these parameters would have on the electric field strength. Results from these relative electric field measurements and corresponding analysis will be presented.   

Monitoring of linear transformer driver switches through photodetection

To achieve a high peak current by producing the best overlap of currents, LTD switches must fire simultaneously. The nanosecond time scale on which an LTD operates can make it difficult to diagnose misfiring switches. Development of a circuit that generates a programmable signal delay from each switch allowed for diagnostic capabilities. In each switch, a fiber optic cable transmitted light from the switch firing and relayed it to a photodetector in the circuit. The input pulses from the switches were separated in time with programmed delay width, which were then combined into a single signal that was measured by an oscilloscope. Comparing the Boolean output signal to the initial firing signal time and expected delay detected pre-firing or misfiring from individual switches. The high-speed nature and signal recombination made this circuit an accurate way to compare the firing of switches that number in hundreds with a single measurable output. We present our circuit board and experimental results.   

Development of a compact cascade arc discharge apparatus and its application to generation of a sheet plasma

Plasma window has a high potential as novel vacuum interface, which can separate vacuum from atmosphere without solid materials. Electron beam welding under an atmospheric condition is one of the applications of the plasma window. Cascade arc discharge device having a channel diameter of 3 mm, therefore, has been developed and characterized by visible and vacuum UV emission spectroscopy. On the other hand, the sheet plasma with a thickness of \textless 1 mm and a width of \textgreater 10 mm is also attractive as the vacuum interface to isolate between upper and lower region. To this end, we applied the magnetic field on the cylindrical plasma expanding from the arc discharge channel. Here, the magnetic field was formed by the combination of two opposing permanent magnets and an external solenoid coil, resulting in the creation of sheet-shaped plasma. Dependence of the thickness and width of the sheet plasma on the geometry and strength of the magnetic field was investigated.   

Effect of non-uniform magnetic field on helicon plasma generation.

Helicon plasmas are very efficient sources for high-density plasma generation. The original efficiency of helicon plasma source can be further raised, if this source operated in non-uniform magnetic field. In present work experiments are carried out with different non-uniformity of magnetic field near the antenna keeping the magnetic field at the center of antenna \textless 100 G. It has been observed that antenna plasma coupling and plasma production efficiencies increase with magnetic field non-uniformity. It is found that density obtain by introducing non-uniform magnetic field results in higher density than conventional helicon. The effect results from the alternation in wave performance rather than in particle confinement. Observation of beat wave in the axial variation of axial wave magnetic field suggests the presence of different radial wavemode. Wavelength is measured for nonuniform magnetic field near the antenna when the magnetic field is kept at 25 G and 50 G at the antenna center. For the 25 G case, measured axial wavelength is found to be twice the length of the antenna. This suggests that half wavelength antenna excites full wavelength helicon wave. However, in the 50 G case, the measured wavelength is shown to be approximately equal to the antenna length.   

Research of ICRF heating in simple mirror cell on GAMMA 10/PDX with TASK/WF code

Ion Cyclotron Range of Frequency (ICRF) heating make it possible to produce plasma with the ion temperature of more than 100 eV at end region of GAMMA 10/PDX and the end-loss plasma is utilized for the divertor simulation experiments. However, electron density of end-loss plasma is $10^{16}$ m$^{-3}$ order, so more than tenfold increase of density is demanded. The heating experiments in plug/barrier cell, which has simple mirror configuration, implied improvement of heating efficiency when the ion cyclotron frequency at midplane was applied to an antenna near the midplane. These results are reproduced at the same density to the experiments by calculations of heating efficiencies using a full-wave code TASK/WF. In addition, for heating ions in higher density plasmas, calculations of ICRF heating efficiency in higher density plasmas are carried out and will be shown and discussed in this presentation. Using these knowledge of ICRF heating in GAMMA 10/PDX, a new device with the simple magnetic field configuration is developed in order to produce plasmas with ion temperature of up to 100 eV and electron density of 10$^{19}$ m$^{-3}$.   

Effects of ICRF waves on the axial transport of mirror confined ions in GAMMA 10/PDX

In the GAMMA 10/PDX tandem mirror, end-loss ions are used in the studies on divertor physics. Plasmas are produced with Ion Cyclotron Range of Frequency (ICRF) waves at the central cell, which has a simple mirror configuration. The peaked profiles near the loss-cone boundary in the pitch angle distribution of the end-loss ions are clearly observed. This implies the main source of the end-loss ions is the pitch angle diffusion due to ion-ion collisions in the mirror confined region. In order to control the temperature of the end-loss ions, additional ICRF waves are applied in the central cell and the other cells. When the ICRF waves, which have resonance layers in the central cell are applied, the end-loss ions with pitch angle near the 0 degree are increased. This will indicate that the ions are dropped into the loss-cone by the large pitch angle scattering due to wave-particle interactions. In addition, the interaction with Alfv\'{e}n-Ion-Cyclotron (AIC) waves, which are excited spontaneously due to strong anisotropy of ion temperature is observed.   

Plasma flow in the magnetic nozzle

The flow of plasmas through the magnetic nozzle is an important element of the physics of some open mirror systems and is a defining feature of some electric propulsion devices. Here, the acceleration of quasineutral magnetized plasma via the magnetic nozzle is considered assuming anisotropic ion pressure in the Chew-Goldberger -Low (CGL) approximation while electrons are considered isothermal. Ions are accelerated by the electric field as well as by the ion pressure gradient forces (including the force due to the pressure anisotropy in the inhomogeneous magnetic field). Paraxial approximation is adopted so the problem is one-dimensional. Acceleration is considered from the plasma source producing ions with isotropic pressure and low (subsonic) ion velocity. Ion velocity undergoes sonic transition near the magnetic field maximum in converging-diverging magnetic nozzle configuration. The stationary solutions are obtained requesting the non-singular transition at the sonic point. The effects of the ionization and charge -exchange collisions on resulting profiles of the ion velocity, ion pressure, plasma density and potential are analyzed.   

Transport and radiation of charged particles in chaotic, time dependent, force-free magnetic fields

In regions of low plasma pressure and large currents, such as in solar corona, interstellar space, and gaseous nebulae, the magnetic fields are force-free as the Lorentz force vanishes. The three-dimensional, time-independent, Arnold-Beltrami-Childress (ABC) field is an example of a force-free, helical, magnetic field that is a mix of chaotic and regular field lines. The characteristic motion of particles in the chaotic field lines is chaotic and their transport is super-diffusive in space [1]. Charged particles in the ABC field emit electromagnetic radiation as well. We compare and contrast the radiation emitted by particles exhibiting regular motion with those having chaotic dynamics. For a time-dependent force-free magnetic field, Maxwell’s equations require that there be an associated electric field. Consequently, charged particles not only experience spatial transport but also energy transport. For a time-dependent ABC field, we find that the maximum energy a particle can gain is bounded from above. We will present results on the cross-field diffusion and energization of charged particles, and on the emission of radiation by these particles.. [1] A.K. Ram \textit{et al.}, \textit{Phys. Plasmas} \textbf{21}, 072309 (2014).   

Magnetic flux amplification via the Hall effect high-$\beta$ plasmas

A global flow drive scheme implemented in the Plasma Couette Experiment (PCX) under Hall conditions is shown to increase or decrease the magnetic flux in the plasma volume based on electrode placement. The flow scheme relies on electrodes driving current radially outward (increase in flux) or inward (decrease in flux) across a weak (~1G) externally applied magnetic field. Under PCX plasma conditions, $n\sim10^{17}-10^{18}$ m$^{-3}$; $T_{e}\sim5$ eV and $T_{i}\sim 0.2-0.6$ eV, argon ions are unmagnetized ($\Omega_{ci}\ll\nu_{i}$) while the electrons are magnetized. The electrons undergo a $V\times B$ drift, while the ions do not, resulting in an azimuthal current that can act to increase or decrease the magnetic flux. Previous experiments run on the Big Red Ball (BRB) show a similar mechanism as well as NIMROD simulations performed with the BRB geometry.   

Experimental evaluation of complexity of ions interacted with high-frequency waves in a mirror field

A hot plasma confined in a mirror magnetic field is used for the study of complexity of ion dynamics in a magnetized plasma. The main concentration of this study is on discrimination of the complexity caused by interaction with waves of frequencies up to ion cyclotron range of frequencies (ICRF). The data was taken from a hot collisionless plasma with good separated measurement of ions. Since ions with enough energy seldomly meet collisions with plasma, dynamics of such ions would have better sign of interacted waves. In addition, open-field system like a mirror field offers better environment for ion measurement than closed system. Our experimental observation is as follows. When ion pressure perpendicular to a field line was significantly increased by the application of ICRF wave, an unstable Alfven wave called as AIC wave appeared to relax the excessive ion pressure anisotropy. At the same time, high flux of high--energy ions was measured at the machine end by several ion detectors, indicating pitch-angle scattering of trapped ions owing to interactions with the waves. The complexity of ion dynamics in this case was dominated by interactions with the externally applied ICRF wave and the AIC waves. Jensen-Shannon complexity and normalized permutation entropy showed some unique change against varied plasma parameters and different ion--energy band. The observed complexity will be reported in relation to interaction with the waves.   

\textbf{Filamentation in Capacitively Coupled Magnetized Plasmas}

Recent experiments at the Magnetized Dusty Plasma Experiment (MDPX) at Auburn University have observed the formation of filamentary structures in capacitively-coupled, rf generated plasmas at high magnetic field (B $\ge $ 0.5 T). These plasma filaments, when viewed from the side, appear as bright vertical columns aligned parallel to the magnetic field that can either be stable or mobile structures, depending upon the experimental conditions in the plasma. In this work, the MDPX device is used to study the threshold conditions for filamentation formation under a variety of RF power, pressure, and applied magnetic field conditions. The formation of various spatial patterns of filaments, from individual filaments to spiral and ring-like structures, will be analyzed to determine how their physical properties (size distribution, number, etc.) vary with the plasma parameters. This presentation will focus on how those properties of the filaments compare with fundamental length scales in the plasmas (ion/electron gyroradii, collision mean free path, Debye length, etc.).   

Progress on understanding electron-beam driven plasma chemistry at the US Naval Research Laboratory

There has recently been a renewed interest at the US Naval Research Laboratory (NRL) in better understanding the physics of the breakdown of air by a high-current, fast, pulsed electron beam. This poster describes recent progress in experiments and modeling that are underway at NRL. An electron beam is produced in vacuum using a Febetron pulsed-power generator modified to produce a peak voltage of 80 kV, a peak current of 4 kA, and a pulse width of 100 ns. The beam then passes through thin anode and pressure barrier foils into a cavity filled with low-pressure dry air. Visible and near-ultraviolet spectral lines are used to diagnose the presence of excited and ionized states induced as the beam transits the air. The time dependence of these excited states at different pressures is compared with the electron density and current within the cavity, as well as framing camera images of the visible emission. Experimental results are compared to several simplified models of the plasma breakdown, demonstrating regions of drive-current/gas-density parameter space in which these models can be accurately applied.   

Modeling Collisional Ionization Using a Modified Binary-Encounter-Bethe Model in the Particle-in-Cell Code OSIRIS

Collisions, and subsequently collisional ionization, have become necessary to a proper understanding of plasma dynamics in a variety of situations. For example, collisional ionization must be used to properly model electron bunch propagation over long distances (up to several meters or more) outside vacuum. To correctly simulate these problems, it is important to develop and implement computational models that accurately depict the complex atomic physics of these interactions. However, difficulties can arise when the atomic structure and electron configuration of an atom greatly alters the binding energy and cross sections to be used in these formulations. We have implemented a collisional ionization routine in the particle-in-cell code OSIRIS that draws on examples and advancements from other particle-in-cell codes. We use a modified binary-encounter-Bethe model to calculate atomic cross-sections along with the Monte Carlo collisional scheme in order to model inter- and intra-species collisional ionization in both relativistic and non-relativistic regimes. We present details of the implementation and results from running OSIRIS using this new collisional ionization module.   

Low-frequency electromagnetic pulse radiation from metal targets irradiated by a short pulse laser

A theoretical study of low-frequency radiation from a short laser pulse (\textless 1 ps) normally incident on metal targets is presented and applied to experiments at NRL. The laser field drives large time-varying currents (MA/cm$^{\mathrm{2}})$ in the skin layer of the metal, which emit radiation that peaks in the THz range, but have a significant component in the microwave band. A one-dimensional electrostatic model for Cu is coupled to a radiation model for an infinitely thin flat disc (thickness -- one skin depth, diameter -- laser focal spot size). The salient characteristics of the emitted radiation are calculated, which include radiated power, energy, and spectra as a function of laser energy and angle of observation. Work supported by the NRL Base Program.   

Reduced model of runaway electrons in NIMROD

Disruption poses a serious threat to the continuous operation of tokamaks. The thermal quench cools the plasma quickly, and the resulting change in resistivity can transfer current to a runaway electrons (RE) population. The REs can drive or suppress MHD instabilities during the current quench phase, which in turn may improve or deteriorate the confinement. Studying the interaction of REs with low-frequency MHD modes via full-scale explicit PIC simulation will be computationally expensive because of the CFL time-step constraint when solving the equations of motion of REs, which travel at relativistic speeds. However, approximating the RE distribution in velocity space as a delta function leads to a passive convective-like equation for RE density, which governs the evolution of their spatial distribution, subject to high parallel speed and perpendicular drift motion. The equation for RE density is solved by using the least-squares finite element method in the framework of NIMROD. The implicit implementation relaxes the time-step constraint, although the convection speed is as large as the speed of light. The REs contribute a resistance-free current in the momentum equation and in the MHD Ohm's law, which is used during the advance of magnetic field.   

Modeling and Simulation of Runaway Electron Dissipation by Impurity Injection Using KORC

Runaway electrons (REs) generated during a disruption pose an existential threat to ITER and future high current tokamaks. The most mature technique for mitigating the effects of REs is the injection of high-Z impurities into the post-disruption RE beam via shattered pellet injection (SPI). The impurities provide additional free and bound electrons that scatter REs through Coulomb collisions, where both elastic pitch angle scattering and inelastic slowing down play an essential role in the evolution and decay of the RE current and energy. In this work, we study this problem using the Kinetic Orbit Runaway electrons Code (KORC). KORC evolves a general initial distribution of REs along full and guiding-center orbits in a toroidal geometry with Monte-Carlo collisions, electric field acceleration, and radiation damping. Calculations are performed using analytical and experimentally reconstructed electromagnetic fields and plasma profiles in the post-disruption, RE plateau phase. We present a comparative study of different RE collisional dissipation models along with an assessment of the role played by spatially-dependent orbit effects and the self-consistent evolution of the electric field. Preliminary comparisons with SPI dissipation experiments will also be discussed.   

Radiation emission measurements during mitigated disruptions on ASDEX Upgrade

Disruption mitigation remains a critical, unresolved, issue for ITER and accurate quantification of possible mitigation efficiency is proving difficult. Insufficient diagnostic coverage and analyses can generate false trends with unacceptably large uncertainties. ASDEX Upgrade (AUG) is uniquely equipped with massive gas injection valves in several toroidal and poloidal locations. From the high resolution bolometer and AXUV diode arrays, the radiation emission profile was inferred at varying toroidal distances from several injection locations. A single fan of sensors was chosen, to mimic systems used on other tokamaks equipped with a shattered pellet injector, and then compared to measurements from the complete set of sensors available. The resulting radiated energy fraction calculated from several inversion techniques varied by up to a factor of two with no constant ratio between the methods found. In contrast to JET observations, an increase in mitigation efficiency was observed for higher stored thermal energy fractions by all measurement techniques applied. Whilst massive gas injection is currently not considered for ITER mitigation, this study is applicable and pertinent to diagnostics and analysis techniques for the qualification of any disruption mitigation system.   

\textbf{Kinetic Equilibrium Reconstruction Validation and Stability Analysis of KSTAR Plasmas supporting Disruption Event Characterization and Forecasting}

Validated kinetic equilibrium reconstructions are an essential requirement for accurate stability and disruption prediction analyses to support continuous operation of high beta KSTAR tokamak plasmas. Present analysis significantly expands prior reconstruction capability. [1] Pressure profiles are created from Thomson scattering and charge exchange spectroscopy data, and allowance for fast particle pressure. This supplements external magnetics and shaping field current data, and includes vacuum vessel and passive plate currents following an approach used in NSTX. [2] Up to 25 channels of MSE data, including tests of the new background polychrometer diagnostic, are used to constrain the magnetic field pitch angle to reconstruct the safety factor, q, profile. Comparison with MHD activity shows that m/n $=$ 2/1 and 3/2 mode positions from ECE data compare well to rational surface positions. Approaches are taken to minimize variation of the equilibria within data error to reduce uncertainty in stability analysis used for disruption event characterization and forecasting (DECAF). [1] Y.S. Park, S.A. Sabbagh, J.W. Berkery, et al., Nucl. Fusion 51 (2011) 053001. [2] S.A. Sabbagh, A.C. Sontag, J.M . Bialek, et al., Nucl. Fusion 46 (2006) 635.   

\textbf{Rotating MHD torque balance analysis and island width measurement in support of disruption event characterization and forecasting}

Effective disruption forecasting and mitigation tools will be critical to the lifetime and successful operation of reactor-scale tokamaks such as ITER. A forecaster has been built based on the automated and validated characterization of events relevant to the plasma evolution towards a disruption. This includes an automated characterization of born-rotating non-ideal MHD modes employing a toroidal array of Mirnov coils to measure the toroidal mode number and frequency that has been developed. A toroidal torque balance model initially assuming a ``no-slip'' electromagnetic drag of the mode is introduced for forecasting. A set of criteria based on the measured mode and relevant plasma parameters (e.g. plasma rotation profile data, equilibrium quantities including normalized beta and internal inductance) are used to determine warning levels to a disruption. Preliminary couplings of the bulk single-solid torque model to cylindrical approximations of the tearing mode island width (the evolution of which is indicative of the mode stability) are generated to further validate and improve the characterization. Wide aspect ratio ranges and differences in amplitude of error fields are examined using this model for NSTX/U, MAST, and KSTAR plasmas supporting disruption forecasting (DECAF code).   

\textbf{Progress on Disruption Event Characterization and Forecasting in Tokamaks}

Disruption prediction and avoidance is critical in ITER and reactor-scale tokamaks. Results from the disruption event characterization and forecasting (DECAF) research effort are shown for multiple tokamaks. Analysis of KSTAR, MAST, and NSTX databases shows low disruptivity paths to high beta operation. DECAF analysis of a \textasciitilde 10$^{\mathrm{4}}$ plasma database with only 5 DECAF events predicts disruptions with 91.2{\%} true positives and 8.7{\%} false negatives. Automated analysis of rotating MHD modes allows identification of disruption event chains including coupling, bifurcation, locking, and potential triggering by other events. DECAF can provide an early disruption forecast (on transport timescales) allowing disruption avoidance through profile control. New hardware to evaluate this analysis in real-time is now being configured for installation on KSTAR. TRANSP predictive analyses with as few as 4 (of 6) NBI sources computes plasmas at $\beta_{N}$ \textgreater 3.5 with 100{\%} non-inductive current drive - a novel operating regime for KSTAR disruption prediction studies. Analysis of MAST has uncovered resistive wall modes at high $\beta _{\mathrm{N}}$. Mode shape and growth rate are significantly altered by conducting structure differences compared to NSTX. Wall stabilization is computed to increase in MAST-U due to new divertor plates.   

\textbf{Equilibrium and Stability Calculations of MAST Spherical Torus Plasmas in Preparation for MAST-U, Supporting DECAF}

Research examining the stability of plasmas in the MAST database utilizing new kinetic equilibrium reconstructions and comparisons to models in the Disruption Event Characterization and Forecasting code (DECAF) is crucial to illuminating relevant physics and enabling long-pulse operation in MAST-U. Progress towards producing kinetic equilibrium reconstructions for the MAST database, and for MAST-U operations, is ongoing. A DECAF model for $\beta _{N}^{no-wall}$ tested for NSTX is now being utilized for MAST. Machine learning (ML) techniques, including neural networks and random forests have been used to improve the model. Additionally, ideal MHD stability analysis with DCON has begun for the MAST database, enabling these ML techniques to be used for cross-machine comparison. MAST-U projected equilibrium beta scans examined with DCON indicate a no-wall limit around $\beta_{N} \quad =$ 4. The VALEN code, containing a 3D model of the MAST-U conducting structure projects an ideal with-wall limit ($\beta_{N} $\textasciitilde 5-6), higher than for MAST, due to enhanced conducting structure. Automated analysis of rotating MHD modes that processes the spectral decomposition of magnetic probe signals for mode discrimination has also been implemented for MAST.   

Quasilinear critical gradient model for the intermittency of Alfven eigenmode transport of energetic particles}$^{\mathrm{1}}$

The critical gradient model (CGM) for the time-average transport of energetic particles (EP) by Alfven eigenmodes (AEs) has been verified by local nonlinear GYRO gyrokinetic simulations [1], validated by DIII-D experiments [2], and used to predict ITER EP confinement loss [3]. High intermittency of even low time-average EP transport loses at the edge of ITER could cause significant wall erosion. Here we explore the nature of intermittent AE-EP transport with a simplified quasilinear critical gradient model (QLCGM) using the time dependent EP density transport code ALPHA [3]. In agreement with DIII-D experiments [4] the intermittency is found to increase with the EP source strength. \\ \\ $[1]$ E. M. Bass and R. E. Waltz, \textit{Phys. Plasmas} \textbf{17}, 112319 (2010)\\ \\ $[2]$ R.E. Waltz, E.M. Bass, W.W. Heidbrink, and M.A. VanZeeland, \textit{Nucl. Fusion} \textbf{55} 123012 (2015)\\ \\ $[3]$ R. E. Waltz and E. M. Bass, \textit{Nucl. Fusion} \textbf{54}, 104006 (2014)\\ \\ $[4]$ C. S. Collins et al, \textit{Phys. Rev. Lett.} \textbf{116}, 095001 (2016)   

Theory of collective energy transfer from neutral beam-injected ions to fusion-born alpha-particles on cyclotron timescales

Fast collective relaxation of neutral beam-injected (NBI) ion populations at the edge of magnetically confined fusion (MCF) plasmas has been inferred from recent observations of suprathermal ion cyclotron emission (ICE). Studies of ICE from NBI plasmas in the KSTAR tokamak (B Chapman et al, Nucl Fusion, submitted) and LHD stellarator (B Reman et al, Nucl Fusion, submitted), using particle-in-cell (PIC) codes, confirm that this ICE arises from the magnetoacoustic cyclotron instability (MCI) due to population inversion in velocity-space of the NBI ions at spatial locations close to their injection point. Here we report PIC studies addressing future scenarios where a minority population of fusion-born alpha-particles (either energetic, or Helium ash) is also present at this location. We identify a novel form of the MCI in which the dominant collective energy flow is from NBI deuterons to the alpha-particles, on cyclotron timescales. This energy flow is partly mediated by ICE-type electromagnetic fields which can also be excited, but whose amplitude is lower than when alpha-particles are absent. Physically, this new effect appears to arise from cyclotron resonant coupling enabled by the finite gyroradius, and identical gyrofrequency, of NBI deuterons and alpha-particles.   

Long-term Alfv\'{e}n instability nonlinear simulations and high-bandwidth linear eigenmode surveys

Fast ion driven Alfv\'{e}n instabilities are often observed to persist at sustained/steady amplitudes in experiments for 10$^{\mathrm{5}}$ to 10$^{\mathrm{6}}$ Alfv\'{e}n times ($\tau_{\mathrm{Alfv\mbox{\'{e}}n}}$ $=$ R$_{\mathrm{0}}$/v$_{\mathrm{A}})$. Nonlinear saturation effects that lead to self-organized states are important since they influence the mode intermittency and associated fast ion transport levels. Gyro Landau fluid models (TAEFL/FAR3D) have achieved very long simulation times for these instabilities (up to 50,000 Alfv\'{e}n times). The sustained nonlinear state requires a balance between transport of the fast ion component into the resonance regions and transport out by nonlinear flattening of the distribution function; also, zonal flows (with neoclassical damping) and currents aid in regulating the amplitudes. Time series frequency analysis (spectrograms) of the evolving modes indicate that the zonal flows/currents are associated with transitory low frequency activity; this can provide a clue for diagnosis of such effects. In the linear regime, the eigenmode solver option facilitates mode surveys over wide frequency ranges and parameter variations. Such techniques are useful in understanding nonlinear dynamics and mode couplings.   

Predator-prey paradigm for Alfvén instability dynamics in realisitc RBQ simulations

To understand the dynamics of multiple Alfvén Eigenmode (AE) instabilities excited simultaneously by energetic beam ions we developed a heuristic Predator-Pray (PP) model where two PP systems each consisting of a predator (AE) and a prey (resonant ions) are coupled together. The first PP system works as a source of particles for the second system which in its turn plays a role of a sink of those particles. Our model helps to understand multiscale intermittencies observed in Resonance Broadened Quasi-linear (RBQ) simulations [Gorelenkov, NF'18, PoP'19]. An interplay between the growth, damping rates and the effective scattering frequency in RBQ simulations is found in the presence of a single and multiple RSAEs. RBQ model adapts the quasi-linear (QL) approach (Berk et al.,PLA 1996) and generalizes it for a realistic problem near marginal state of unstable AEs. The diffusion equation is solved simultaneously for all particles together with the evolution equation for mode amplitudes by going beyond the perturbative-pendulum-like approximation for the wave particle dynamics. We apply the RBQ code to DIII-D plasma with elevated q-profile where the fast beam ions show stiff transport properties [Collins, PRL'16].   

Verification and Validation of Integrated Simulation of Energetic Particles in Toroidal Plasmas

As the first step in developing the predictive capability, verification and validation of linear simulations of Alfven eigenmodes in the current ramp phase of DIII-D L-mode discharge #159243 have been carried out by eight gyrokinetic, gyrokinetic-MHD hybrid, and eigenvalue codes from US, EU, and Japan. The simulated most unstable reversed shear Alfven eigenmode(RSAE) frequencies agree with experimental measurements if the minimum safety factor qmin is adjusted within experimental errors. A toroidal Alfven eigenmode(TAE) is found to be unstable in the outer edge, consistent with the experimental observations. Electron temperature fluctuations and radial phase shifts from simulations using synthetic diagnostics show no significant differences with the experimental data for the strong RSAE, but significant differences for the weak TAE. Furthermore, gyrokinetic toroidal code(GTC) simulations find that the most unstable ion temperature gradient(ITG)-like mode has an amplitude peaking in the core, but large fluctuations nonlinearly spread to the whole radial domain. These results indicate that RSAE and TAE in this DIII-D experiment could interact nonlinearly with each other and with the microturbulence. Finally, GTC simulations of TAE have also been validated in JET, HL-2A and KSTAR.   

Neoclassical Transport of Energetic Alpha Particle

A simulation of neoclassical transport for energetic alpha particle is carried out using the gyrokinetic particle code GTC. A linearized Coulomb collision operator is implemented, including slowing down, pitch angel scattering and energy scattering term. In addition, source and sink are carefully treated in the simulation to ensure conservation properties. Simulation results show good agreement with analytic results on radial particle and heat diffusivity, as well as bootstrap current.   

Modeling of suprathermal electron radial flux and toroidal torque by ECH in non-axisymmetric toroidal plasmas

A drastic change of the toroidal velocity profile has been observed when we applied the ECH to the NBI heated plasma. We assume that the radial flux of supra-thermal electron would play an essential role in causing a toroidal flow by the JxB torque, We have evaluated the toroidal torque by ECH applying the GNET code and have found significant net toroidal torques by ECH due to the radial flux of supra-thermal electrons in LHD. In this study, We, first, estimate the radial flux of suprathermal electrons assuming a drift convection model and estimate the radial profile of the JxB toroidal torque by ECH in a rippled tokamak. We find that the maximum toroidal torque which is proportional to $\delta^{3/2}/n$, where $\delta$ and $n$ are the ripple amplitude and plasma density, respectively. We find that the obtained model fluxes show relatively good agreements with the numerical results by GNET code. Also, we extend this drift convection model in the case of LHD and HSX. We find that the larger JxB toroidal torques are obtained in helical plasmas than that in the rippled tokamak due to the large fraction of trapped electrons. The drift convection model results are compared with the numerical results by GNET code.   

Runaway Generation in Tokamak Plasmas for Large Disruption Relevant Electric Fields

The generation of relativistic electrons in tokamak plasmas has been the subject of extensive research due to their intrinsic interest as well as the threat they pose to reactor-scale tokamak devices. Runaway electron generation becomes particularly robust for the very large inductive electric fields that are often present during tokamak disruptions. In this work we show that when such large inductive electric fields are present, the physics of how tokamak geometry impacts runaway generation processes is qualitatively modified compared to the more commonly studied limit of weak inductive electric field strengths. In particular, for the large electric fields which may be present during a disruption, the efficiency of Dreicer production is found to increase as a function of minor radius, rather than undergo a sharp decrease, as is characteristic of the weak inductive electric field limit. In addition, the rate of avalanche amplification of a runaway population is found to be largely insensitive to the minor radius for the large electric fields characteristic of a disrupting tokamak plasma. Ongoing work is devoted toward applying these results to the self-consistent description of a disrupting plasma.   

Influence of error field on resistive tearing mode in Tokamak

The influence of error field on the m/n $=$ 2/1 resistive tearing mode is studied numerically using the three-dimensional toroidal code (CLT) based on a set of full magnetohydrodynamics equations. It is found that there is a threshold of the error field to achieve mode penetration, which depends on the plasma rotation. The saturated magnetic island width increases with the increasing strength of the error field once the mode penetration occurs, but stays almost the same when the error field is under the threshold of mode penetraion. Moreover, the magnetic island can be locked to the error field in the nonlinear stage by a large amplitude of error field. The locking threshold significantly increases with the increasing mode frequency. The onset time of mode locking is negtively related to the amplitude of the error field for the same plasma rotation frequency. It is also found that there is an unlocking threshold, which is lower than the locking threshold and determined by the width of magnetic island and the mode frequency.   

Progress on a Laser Inverse Compton Scattering Runaway Electron Diagnostic Design for DIII-D

We report on progress in the design and component testing of a Laser Inverse Compton Scattering diagnostic (i) to measure runaway electrons in the range of 3-30 MeV in the DIII-D tokamak during triggered disruptions. An 80 picosecond, 2-3 Joule, rep-rated Nd:Yag laser is being developed at Voss Scientific. This short-pulse high energy laser is required due to the large background soft x-ray levels and low density of runaway electrons being diagnosed. A 4-channel gated soft x-ray imager (based on ones used at NIF) has been tested on the synchrotron Advanced Photon Source at Argonne National Laboratory. A synthetic diagnostic model is being developed at Woodruff Scientific to optimize design issues, with regards to geometry and choice of filters. Finally, a suitable (tentative) tangential port has been identified on the DIII-D tokamak, and a diagnostic design package is being completed. (i) G. A. Wurden, J. A. Oertel, T. E. Evans, Rev Sci. Instr. 85(11), 11E111, (2014)   

CQL3D Time-Dependent Runaway Electron Discharge Dynamics, Including Self-Consistent Ampere-Faraday Equation, Radial Transport, and RF QL Diffusion

CQL3D [1,2] provides a relativistic, finite-difference, bounce-averaged Fokker-Planck solution for the electron distribution $f$(v$_{\mathrm{0}}$,theta$_{\mathrm{0}}$,rho$_{\mathrm{0}}$,t) under the influence of density/temperature variations induced, in this case, by a parameterized model for impurity stream from gas or pellet injection simulating plasma disruption or RE mitigation, and the toroidal electric field. For CQL3D, 6D phase-space is reduced to 3D by averaging over gyro-phase, bounce-phase, and toroidal angle in toroidal axisymmetric geometry. The solution is found self-consistently with the time-dependent Ampere-Faraday equations. We vary parameters controlling the amount and velocity of the impurity source, the rate of T$_{\mathrm{e}}$-reduction, and the lowest T$_{\mathrm{e}}$ achieved, in order to clarify the role of these parameters for RE minimization. Effects of RF wave injection and internal excitation are considered, as a mechanism for enhanced pitch-angle scattering of electrons. [1] R.W. Harvey and M.G. McCoy, ``The CQL3D Fokker Planck Code,'' \underline {www.compxco.com/cql3d.html}. [2] R.W. Harvey, V.S. Chan, S.C. Chiu et al., Phys. Plasmas 7, 4590 (2000).   

Modeling and simulation of synchrotron emission by relativistic runaway electrons

High-energy relativistic runaway electrons (RE) can be produced during magnetic disruptions due to the strong electric fields generated during the thermal and current quench of the plasma. Understanding this problem is key for the safe operation of ITER because, if not avoided or mitigated, RE can severely damage the plasma facing components. The accurate modeling and simulation of the synchrotron emission (SE) by RE is critical because it provides a limiting mechanism for the maximum energy that RE can reach, and also because it can be used as an experimental diagnostic to infer RE parameters including energy and pitch-angle distributions. Here we report recent results on SE taking into account full-orbit effects and the details of the camera geometry using KORC (Kinetic Orbit Runaway electrons Code). Of particular interest is to study the dependence of the SE spatial distribution and power spectrum on different models of the RE energy and pitch angle distributions. The study is done for both ``visible'' and infrared emission.   

Development of coupled DTRAN/CQL3D codes for runaway electron quench studies

Generation and kinetic transport of runaway electrons (RE) in disruption and disruption mitigation events depend strongly on the rapid change in the plasma parameters, impure plasma ion composition, and electro-magnetics, whereas the RE in turn have crucial impact on plasma current, plasma conductivity and heating. For self-consistent plasma/RE studies, we are developing DTRAN/CQL3D package, in which kinetic Fokker-Planck code CQL3D is coupled to macroscopic plasma transport code DTRAN. This is a multi-element, multispecies, 1-D (radially), magnetic flux surface averaged parameters, diffusive-convective transport code. The code solves a system of strongly coupled equations reproducing the dynamics of plasma electrons, ions, parallel electric field, ionization states of various intrinsic and extrinsic impurity species, neutral atoms and molecules. Capability of DTRAN to simulate low-temperate (down to sub-eV in afterglow phase) partially-ionized plasmas including molecular effects (MAR), interchange ion reactions, increasing ion conversion) and plasma radiation opacity of many lines will be highlighted. Results of DTRAN benchmark against DIII-D experimental data for disruption mitigation with Argon and D2 gas puffs will be presented   

Nanoparticle Injection for Disruption Diagnostics and Mitigation

Diagnostics/mitigation of runaway electrons (REs) and thermal quench (TQ) can benefit from maximized assimilation fraction. Nanoparticles (NPs) have large specific surface area, up to hundreds of m$^{\mathrm{2}}$/g. NPs may be injected into tokamak via plasma jet (NPPJ) or by dispersive shell pellet (NPDSP). Once injected into tokamak plasma, NPs undergo fragmentation or ablative sublimation, depending on the species. We developed models for these processes and implemented them into the in-house Hybrid Electro-Magnetic code HEM-2D. We currently investigate the following NPs: 1) C$_{\mathrm{60}}$ (suited for CFC tokamaks), including multiply charged C$_{\mathrm{60}}$ ions by high intensity UV/EUV flux photoionization, and 2) ITER-compatible boron nitride (BN) NPs. We report simulation results for NPPJ penetration and mass delivery from fragmenting C$_{\mathrm{60}}$ and sublimating BN NPs.   

Interpretation of Machine Learning Disruption Predictions on DIII-D

Chains of precursors leading to disruptive events on hundreds of DIII-D discharges are compared with predictions from the Disruption Prediction using Random Forests (DPRF) algorithm embedded in the DIII-D plasma control system. Using a feature contribution method developed for random forest algorithms, the input features driving each prediction are identified and shown to correlate with the occurrence of relevant physics precursors. In contrast to other ‘black-box’ approaches, this lends an element of interpretability to the application of a machine-learning based disruption predictor. This introduces the possibility of pairing predictions with appropriate actuator responses in order to avoid disruptions. Disruptions initiated by locked modes and radiative events, for example, are shown to be prevalent in DIII-D but could be preventable using relevant actuators if properly identified with sufficient warning time. These examples are compared with similar cases on JET in order to motivate the development of an interpretable, cross-device predictor that can satisfy constraints for next generation tokamaks.   

Poloidal currents in COMPASS vacuum vessel during disruptions: diamagnetic measurements and comparison with CarMa0NL modeling

For the first time signal from diamagnetic loop is used to deduce poloidal eddy current in the tokamak vacuum vessel during thermal and current quenches as was recently proposed in [1]. The results are in good quantitative agreement with values deduced from toroidal Mirnov coil signal, analytical predictions [2] and numerical modeling with CarMa0NL code. The COMPASS tokamak has a unique set of diagnostics for measurements of poloidal distribution of poloidal current, specifically, 3x24 sensors for the toroidal magnetic field. This feature allows to distinguish between poloidal eddy and halo currents, and to perform comparison with the diamagnetic measurements. Eddy and halo current evolution, and the related electromagnetic forces on the vacuum vessel are calculated using CarMa0NL. [1] Pustovitov V D 2019 Fusion Eng. Des. 138 53-58 [2] Pustovitov V D 2017 Fusion Eng. Des. 117 1-7   

Internal/External Magnetic Field Decomposition: Application to Disruption Warning

Combined analysis of magnetic field measurements normal and tangential to a closed surface such as a tokamak vacuum vessel wall allows a decomposition of the field into contributions from sources internal and external to the measurement surface [R.M. Sweeney {\&} E.J. Strait, Phys. Plasmas 26, 012509 (2019)]. This technique is a potentially powerful tool for detection of tearing modes and other low-n instabilities, avoiding some of the drawbacks of conventional B-dot and locked-mode detectors. The analysis provides a clean separation of signals from the plasma versus those from external sources such as induced wall currents, and is independent of whether the mode is rotating or locked. The separation of internally and externally sourced fields also enables a straightforward calculation of the electromagnetic torque on the plasma. The accuracy and advance warning time of a disruption predictor based on such analysis of DIII-D data will be discussed.   

Overview of two new tokamak disruption research projects on DIII-D and MST

Two new projects have been initiated on DIII-D and MST to further the understanding of disruptions in tokamak plasmas. Both projects focus on internal measurement of the magnetic fluctuations that play a key role in disrupting plasmas. The project on DIII-D encompasses the physics of the tearing mode trigger, thermal and current quenches, and post-quench runaway electrons. The project on MST, which has relatively recently begun operating as a tokamak, has a singular focus on the physics of the thermal quench. Internal measurement of magnetic fluctuations is made possible by advanced diagnostics including Faraday-effect polarimetry, cross-polarization scattering, and a rugged, multi-point insertible magnetic probe. Measurements with these diagnostics can reveal dynamics not detectable by sensing coils at the plasma boundary. A primary goal of these projects is comparison of the measurements to the results of 3D nonlinear MHD computation. That is with the goals of validating the modeling and improving predictive capability for ITER. Here we will present an overview of and initial results from these new projects. Work supported by U.S.D.O.E.   

Internal measurement of magnetic fluctuations in disrupting plasmas in DIII-D

We present preliminary results from a new project that aims to utilize advanced diagnostics such as Faraday-effect polarimetry for internal measurement of magnetic fluctuations during disrupting plasmas. Such a measurement can reveal dynamics not detectable by sensing coils at the plasma boundary, and we aim to better understand the physics of tearing mode onset, the thermal and current quenches, and the runaway electron plateau that sometimes follows the current quench. Our initial analysis targeted data gathered in 2018 with the Radial Interferometer Polarimeter (RIP), consisting of three horizontal chords with impact parameters relative to the equatorial midplane of -13.5, 0, and $+$13.5 cm. In a discharge where injection of an Ar pellet causes a disruption followed by a runaway electron plateau, RIP detects density and/or magnetic fluctuations following the current quench, but with a chordal asymmetry. The largest fluctuations are measured along the chord at -13.5 cm, which may be due to the temporary, roughly 25 cm downward shift of the plasma. This shift is tracked by external magnetics, but also by RIP, based on the fact that the equilibrium Faraday effect is zero along a chord passing through the magnetic axis. During the runaway plateau, RIP detects a steady band of low-frequency (\textless 20 kHz) fluctuations which for the most part are not detected by the edge sensing coils. Work supported by the US DoE under DE-FC02-04ER54698 and DE-SC0019003.   

Vertical Force during Vertical Displacement Events in an ITER Plasma and the Role of Halo Currents

Vertical displacement events (VDEs) can occur in elongated tokamaks causing large currents to flow in the vessel and other adjacent metallic structures. Any new device must be designed to withstand the associated forces. Due to the importance of these events, many calculations have been performed using different approximations in order to include the forces due to the poloidal (halo) currents flowing to the vessel. To better understand the potential magnitude of these forces and the role of halo currents in producing them, we have used the M3D-C1 code to simulate potential VDEs in ITER. In a first for an initial-value MHD code simulation of VDEs in ITER, we used actual values for the vessel resistivity and pre-quench temperatures. The halo region is naturally formed by triggering the thermal quench with an increase in the plasma thermal conductivity. We used the 2D non-linear version of the code and varied the post-thermal quench thermal conductivity profile as well as the boundary temperature in order to generate a wide range of possible cases that could occur in the experiment. We also show that, for similar conditions, increasing the halo current does not increase the total force on the wall since it is offset by a decrease in the toroidal contribution.   

Thermal quench and asymmetric wall force in ITER disruptions

The thermal quench (TQ) time and asymmetric wall force in disruptions can depend on the resistive wall penetration time $\tau_{wall}$, as shown by simulations with M3D [1]. In ITER, $\tau_{wall}$ will be much longer than in present experiments. This might cause the TQ time to be much longer, because parallel thermal transport can be affected by resistive wall tearing modes [2], scaling with a fractional power of $\tau_{wall}$. The asymmetric wall force depends on whether disruptions are cold or hot. In cold disruptions, such as locked mode disruptions, the TQ precedes a vertical displacement event (VDE). In ITER, cold disruptions might produce an asymmetric wall force of only about 5 MN [3]. In hot disruptions, a VDE precedes the TQ. The maximum asymmetric wall force can be quite large [4], but should be small for ITER relevant $\tau_{wall}$. \break [1] W. Park et al, Phys. Plasmas 6, 1796 (1999). \hfill\break [2] J. A. Finn, Phys. Plasmas 2, 3782 (1995) \hfill\break [3] H. Strauss, Phys. Plasmas 25, 020702 (2018) \hfill\break [4] H. Strauss et al, Nucl. Fusion 53, 073018 (2013).   

3D Disruption Mitigation Modeling with M3D-C1

Future tokamaks will require robust disruption-mitigation techniques, the most promising of which use impurity injection to radiate stored energy. We simulate pellet mitigation using the M3D-C1 extended-MHD code coupled to the KPRAD ionization/radiation code. Three-dimensional, nonlinear modeling shows that, with an axisymmetric, on-axis impurity source, the plasma remains stable throughout the thermal quench. Increased resistivity on-axis causes plasma current to diffuse into a thin shell. This shell eventually goes unstable, resulting in a pronounced current spike, the first seen of its magnitude in 3D MHD disruption modeling. Results of a 3D, nonlinear benchmark with NIMROD simulations will be presented. Simulations with a moving, ablating pellet will also be presented, with particular focus on the effect of increased toroidal localization of the deposited impurities. Results will be validated against DIII-D shattered-pellet-injection (SPI) experiments. Finally, we will present progress on using more-sophisticated pellet models, including multiple impurity sources (for multiple toroidal injection and/or SPI modeling) and coupling to a Lagrangian particle code for pellet ablation.   

Modeling Fast Thermal Quenches Due to MHD Instabilities During Disruptions

Simulations of disruptive instabilities, including vertical displacement events and radiative collapse due to impurities, tend to exhibit a common sequence of events, beginning with the contraction of the current channel due to the enhancement of resistivity in the edge. This contraction of the current channel leads to secondary instabilities, which further results in the stochastization of the magnetic field and a rapid thermal quench due to parallel heat conduction to the vessel walls. We present simulations of these events using M3D-C1, an extended-MHD code that now includes a model for the ionization, recombination, radiation, and transport of impurities. This model uses realistic values of resistivity in both the plasma and in the conducting wall, and is able to self-consistently treat the thermal quench, current quench, and resistive wall timescales. These simulations suggest that highly core-localized impurity injection might be necessary to avoid large conductive thermal losses to the wall. We describe ongoing activities to include additional physical effects, including models for runaway electrons and pellet injection for disruption mitigation.   

Lagrangian Particle Simulation of Neon Pellets and SPI for Plasma Disruption Mitigation in Tokamaks

Numerical studies of the ablation of neon pellets and shuttered pellet injection (SPI) fragments in tokamaks in the plasma disruption mitigation parameter space have been performed using the time-dependent pellet ablation model based on the Lagrangian Particle (LP) code. The code implements kinetic models for the electronic heat deposition, pellet surface ablation model, equations of state with multiple ionization support, radiation in optically thin limit, and a model for grad B drift of the ablated material across the magnetic field. The Lagrangian particle algorithm is highly adaptive, capable of simulating a large number of fragments in 3D while eliminating numerical difficulties of dealing with the tokamak background plasma. The code achieved good agreement with theory for spherically symmetric ablation flows in terms of ablation rates and their scaling laws as well as the properties of the ablated cloud at the sonic radius. The LP pellet ablation model has been validated using experimental data for deuterium fueling pellets. Simulation prediction of the dependence of single pellet ablation rates on background plasma parameters and the magnetic field will be presented. We will also present simulations of SPI fragments at conditions relevant to DIII-D injection experimen   

Recent progress on tokamak disruption simulations for mitigation design

Tokamak Disruption Simulation (TDS) SciDAC project aims to understand the transport physics that govern the thermal quench and current quench of a major disruption, which can hopefully inform experimental design for effective mitigation. Two primary design targets for mitigation are to (1) bring down the plasma power load to divertors during thermal quench, and (2) avoid runaway electrons or control their energy during current quench. Approaches that are effective for one objective can induce negative consequence for the other, an example is radiative cooling by high-Z impurities that spreads the power load onto the first wall, but which can drive more robust runaway formation. Here we give an overview on the recent progress made by the TDS SciDAC team on (1) magnetic dynamics that trigger thermal quench and current profile relaxation, (2) Ohmic-to-runaway current transfer, (3) radiative cooling in the presence of a runaway population, (4) interaction between runaways and externally injected waves, and (5) current-carrying plasma scrape-off. An emphasis will be placed on the options and physics constraints for potential disruption mitigation approaches.   

Plasma response and flow relaxation induced by resonant magnetic perturbation in the Rutherford regime

Externally applied non-axisymmetric magnetic fields such as error field and resonant magnetic perturbation (RMP) can influence the plasma momentum dynamics through plasma response in a tokamak, whereas the plasma response itself strongly depends on the plasma flow as well. Such a nonlinear interaction between the two has been modeled in an extended error field theory for a coupled system of toroidal and poloidal torque balance and magnetic island evolution equations in the Rutherford regime. For a more complete and self-consistent account, we solve for the nonlinear plasma response and the associated flow relaxation induced by a single-helicity RMP to a tokamak equilibrium with an initial uniform toroidal flow, using the full resistive MHD model in the NIMROD code. Simulations show that the time evolution of the parallel flow or ``slip frequency" and its asymptotic relaxation to steady state are different from the island rotation frequency on resonant surface, which invalidates the ``no-slip" condition often assumed for the Rutherford regime. The difference between theory and simulation also suggests nontrivial contributions from the non-resonant response.   

An analytic model of plasma response to external magnetic perturbation in absence of no-slip condition

Recent simulation and experimental results suggest that the magnetic island and flow on resonant surface often do not satisfy the ``no-slip" condition even in the Rutherford regime. A new theory model on nonlinear plasma response to external magnetic perturbation in absence of ``no-slip" condition is proposed. The model is composed of the evolution equations for both island size and phase due to forced reconnection driven by the external magnetic perturbation, and the force-balance equation for the plasma flow. When the island width is much less than the resistive layer width, the island growth is governed by the linear Hahm-Kulsrud-Taylor solution in presence of plasma flow. In the other regime when the island width is much larger than the resistive layer width, both island width and phase evolutions are described using the Rutherford theory. The corresponding quasi-linear electromagnetic force and viscous torque determine the force balance for plasma flow. The no-slip condition assumed in the conventional error field theory is not imposed here, where the island oscillating frequency depends on but does not necessarily equal to the plasma flow frequency at the rational surface.   

Steady State Toroidal Rotation in Tokamak Edge Pedestal Induced by Resonant Magnetic Perturbations

Neoclassical toroidal viscosity (NTV) torque induced by resonant magnetic perturbation (RMP) has been found significant in tokamak edge pedestal [1]. In this work, we investigate how the edge toroidal rotation may be influenced by RMP through NTV torque, based on a coupling scheme developed between the NIMROD and the NTVTOK codes. In presence of the NTV torque alone, toroidal rotation eventually relaxes to the neoclassical offset rotation in steady state. For any radial location, multiple branches of neoclassical offset rotation may exist, particularly in the low collisionality regime and the edge pedestal region where the temperature gradient is large. The actual steady state of toroidal rotation therefore depends on the initial conditions and is potentially subject to bifurcation. In general, other toroidal momentum sources in addition to NTV torque would pull the rotation away from the neoclassical offset rotation. However, as the RMP amplitude increases, the steady state rotation should evolve towards the neoclassical offset rotation, which is qualitatively consistent with recent KSTAR experimental observations.\\ $[1]$ X.-T. Yan, P. Zhu, and Y.-W. Sun, Phys. Plasmas 24, 082510 (2017).   

Analytic solutions of the Grad-Shafranov equation using Solov'ev profiles for different configurations and aspect ratios

The purpose of this paper is to test the approach followed in Refs 1 and 2 to provide analytic solutions for the Grad-Shafranov equation for different configurations, and clarify some of the details not mentioned in them. While the toroidal current profile is necessarily limited, and cannot be realistic, some of the main features of the magnetic fields can be obtained. Going beyond the calculation of averaged poloidal $\beta $ and safety factor \textit{q\textsuperscript {*}}, we examine the magnetic fields, the effect of the choice of the Solov'ev profiles on the Shafranov shift, and the safety factor for four tokamak configurations: ST-40, SPARK and ITER, as well as a small tokamak attempted design, where inverse triangularity could be studied. We expect this study to be provide useful reference solutions for numerical codes. \\\relax [1] S.B. Zheng, A.J.Wootton and E. Solano, \textit{Physics of Plasmas }\textbf{3} (1996) 1176. \\\relax [2] A.J. Cerfon y J.P. Freidberg, \textit{Physics of Plasmas} \textbf{17} (2010) 032502.   

Role of electric field in transition from two- to single-fluid equilibrium

Two-fluid equilibrium with small but non-zero two-fluid parameter $\varepsilon $ is identified as a singular perturbation of single-fluid (MHD) equilibrium. It is important to understand the relationship between the two-fluid equilibrium and the single-fluid one, since the single-fluid equilibrium is widely used in the stability analyses of various plasma confinements. However, the formulation for the transition of the two-fluid equilibrium to the single-fluid one was an open problem for several years [1]. Recently, Hameiri has solved this problem by variational formulation [2]. We have formally derived in a different way from Hameiri's one. The two-fluid equilibrium equations are normalized by employing three basic reference scales: global length $L_{R}$, magnetic field $B_{R}$, and density $n_{R}$. From these, the reference scales of electric field $E_{R}$ and electrostatic potential $V_{ER}$ should be treated as $u_{R}B_{R}$ and $u_{R}B_{R}L_{R}$, respectively, where $u_{R}$ is Alfven velocity expressed by the above basic scales. This treatment can be regarded as a strong electric field (MHD) ordering, since the inertia and pressure terms in motion equation for ion become $O(\varepsilon )$. When calculating the reduction of the two-fluid equilibrium, all terms of $O(\varepsilon )$ can be ignored, except the total enthalpies related to the electrostatic potential appeared in the generalized Bernoulli equations. It is found that such treatments make the smooth transition from the two-fluid equilibrium to the single-fluid one. $^{\mathrm{1}}$L.C. Steinhauer and A. Ishida, Phys. Plasmas \textbf{13}, 052513 (2006). $^{\mathrm{2}}$E. Hameiri, Phys. Plasmas \textbf{20}, 092503 (2013).   

Effect of Two-Fluid Equilibrium Flow on Tearing Linear Stability

Tearing modes have been studied extensively. Much attention has been devoted to two-fluid effects (i.e.~on the effect of distinguishing ion and electron dynamics) on their behavior. However, the effect of equilibrium flow on tearing stability, in particular when the equilibrium is described with a two-fluid model, has not been examined in detail. In two-fluid equilibrium ions and electrons are frozen into different surfaces: a flow surface for ions and the magnetic surface for (massless) electrons. Thus in toroidal systems plasma poloidal flow is not aligned with magnetic surfaces and there is a $\theta$-dependent component of the velocity $v_\psi \sim \sin \theta$ normal to the magnetic surfaces. Using a slab model we highlight the differences introduced to the standard tearing mode problem by the presence of a finite $v_\psi$. In particular, it is found that a single-mode analysis is not possible, even if all the effects of toroidicity other than $v_\psi$ are neglected. Moreover, a finite $v_\psi$ introduces a higher-order derivative for the perturbed velocity than in the single-fluid version of the problem. We report on our progress in building a solution for the slab model problem including a sinusoidal component of the equilibrium velocity normal to the magnetic surfaces.   

Near-Axis framework for stellarator equilibrium: elimination of magnetic resonances to all orders

We systematize the near-axis expansion formalism developed by Mercier, Solov’ev-Shafranov through an extension of the framework developed by Weitzner. We use Mercier’s orthogonal coordinates and the Frenet-Serret framing of the magnetic axis that allows arbitrary curvature and torsion. Our formalism enables us to carry out the axis expansion systematically to all orders for vacuum, force-free as well as MHD equilibrium magnetic fields. We present a closed-form expression for the on-axis magnetic shear and point out the geometrical and physical interpretations of the various terms. Mercier and Solov’ev-Shafranov showed that in general, there are singularities near rational surfaces where the rotation transform is rational. Assumption of a highly irrational rotation transform still leads to small-divisors in higher orders of the expansion. Fortunately, the magnetic axis being a closed spatial curve allows us to exploit powerful analytical tools such as Floquet theory and Calugareanu-White-Fuller theorem. With the help of these, we show that it is possible to eliminate the magnetic resonances systematically order by order through the inclusion of resonant fields, provided the on-axis rotation transform is close to a rational number, and magnetic shear is weak.   

Non-symmetric closed line vacuum magnetic fields and MHD equilibria in a topological torus

Non-symmetric vacuum magnetic fields with closed magnetic field lines are of interest in the development of stellarator equilibria. After the early results of D.Lortz [1], there have been few advances. This work presents a closed form expression for a class of vacuum magnetic fields with closed magnetic lines in a topological torus. For one particular simple example for this class, we find the field invariants, and we show that an extension of the Lortz analysis allows the construction of ideal MHD equilibria by a convergent expansion in plasma beta. [1] Lortz, D. (1970) ZAMP, 21(2), 196-211.   

Recent progress in the developments of the free-boundary version of the SIESTA 3D MHD equilibirum code

SIESTA [Hirshman, Sanchez and Cook, Phys.Plasmas {\bf 18}, 062504 (2011)] is a 3D MHD equilibrium code designed to perform fast and accurate calculations of ideal MHD equilibria for three-dimensional magnetic configurations. It is an iterative code that uses the solution previously obtained by the VMEC code [Hirshman and Whitson, Phys. Fluids {\bf 26}, 3553 (1983)] for the same problem to provide an Eulerian background coordinate system and an initial guess of the equilibrium solution. In contrast to VMEC, SIESTA does not assume closed magnetic surfaces and, as a result, the final equilibrium solution can include magnetic islands and stochastic regions. Recently, the SIESTA code was successfully extended to address the solution of free-boundary problems specific to the geometry of the W7-X stellarator [Peraza-Rodriguez, Reynolds-Barredo, Sanchez, Tribaldos and Gieger, Phys. Plasmas {\bf 24} 082516 (2017)]. The way vacuum field and coil information was fed to SIESTA was however adapted to specific formats/software from that device. In this contribution we describe current efforts to facilitate the input of this information via the more general and widely used MAKEGRID code in order to extend the applicability of free-boundary SIESTA to arbitrary magnetic configurations.   

Analysis of Interrelationship between Stability and End Effect in the Magnetohydrodynamic Flow of Annular Linear Induction Electromagnetic Pump

One of the most important parts in the development of generation IV nuclear reactors is safety. In the research on generation IV sodium-cooled fast reactors, Annular Linear Induction electromagnetic Pump (ALIP) have received attention for the stable transport of coolants. In this study, the stability of an ALIP was evaluated using a mathematical approach to obtain the critical value of the developed pressure. The critical developed pressure equation is a function of the flow rate and dimensionless parameters, which were derived from the theoretical model of the ALIP with a dimensionless scaled velocity, flow rate, and pressure. Also, influence of end effect which is caused by distortion of magnetic field on stability in the magnetohydrodynamic flow is analyzed. The influence is estimated expressed using the critical value of the developed pressure and dimensionless parameters.   

Sausage to kink instability transition-induced fast magnetic reconnection resulting in a magnetized plasma disruption

We present observations and a model of a sausage-kink sequence that causes a fast magnetic reconnection which results in plasma jet disruption and breaking off from the originating electrode at the Caltech laboratory experiment. The sausage instability occurs first and pinches a fat, short magnetized jet to become a thin, long magnetized jet. The thin, long jet then becomes kink unstable. The incompressible kink further lengthens and thins the jet. When the jet radius becomes comparable to the ion-skin depth and so satisfies the condition for magnetic reconnection, the jet disrupts. The observed sausage-kink sequence is consistent with the theoretical stability criteria predicted by the MHD energy principle. X-ray bursts and waves are observed when the plasma jet breaks off from the electrode. The results of a three-dimensional ideal MHD numerical simulation are consistent with both the experiment and the analytic model. The observations and associated analytic and numerical models provide not only a multi-scale cascade path for fast magnetic reconnection but also a plausible underlying mechanism for impulsive natural phenomena such as quasi-periodic pulsations and solar X-ray jet eruptions and for fusion relevant phenomena such as spheromak formation and tokamak instabilities.   

Quasi-interchange Modes and the Sawtooth Crash

Quasi-interchange (QI) modes over a central region with safety factor $q\sim 1$ and sufficiently low magnetic shear are shown numerically with the M3D code to be able to cause nearly ideal MHD sawtooth crashes with complete flattening of the central temperature and current density. The current density flattens more slowly than temperature. Major differences with early analytical and numerical work, which predicted saturation short of a full crash, include elliptical flux surface shape near $q=1$, higher central beta, and low shear at $q=1$ that contribute to instability. Also, unlike the $m/n=1/1$ internal kink mode, a QI instability can have multiple coherently growing toroidal harmonics, where over $q\le 1$ the higher $m=n$ components align to reinforce the displacement due to the 1/1 mode. If the sawtooth is stabilized, quasi-steady 1/1 and 2/2 QI modes can sustain a crescent shaped region inside $q=1$ with higher temperature. The results agree with experimental sawtooth observations in DIII-D\footnote{E. Lazarus, et al., Phys. Plasmas 14, 055701 (2007)}, JET, and other tokamaks and with central $m=n$ modes driven by local ECH/ECCD in KSTAR.   

External kink modes for a tokamak plasma with diffuse pressure and toroidal rotation profiles

External kink modes constitute one of the most serious MHD instabilities in tokamaks due to the fact that they impose plasma beta (the ratio between the kinetic pressure and the magnetic pressure) limits. There is a tradition of analytical and numerical MHD studies that aims at determining how beta stability limits are modified in the presence of toroidal flows. The present work considers the stability of a high-aspect-ratio, circular plasma with diffuse profiles in the safety factor, pressure, and angular toroidal rotation. Pressure gradient mode coupling across the plasma column and a global shear-flow drive are both captured by the model. By employing a simple analytic form for the diffuse equilibrium state, it has been possible to reduce the stability problem to an eigenvalue linear system of ordinary differential equations for the coupled poloidal harmonics. A sharp-boundary model with a rigid angular toroidal rotation [1] serves as a reference case to understand the effect of diffuse profiles on stability boundaries. [1] R. Betti, Phys. Plasmas \textbf{5}, 3615 (1998).   

Inclusion of predictive modeling in NTM control algorithms towards advanced integrated control of long-pulse tokamaks

Present-day experiments on neoclassical tearing mode (NTM) control have shown that, if sufficient electron cyclotron current drive can be positioned on the target rational surface, NTMs can be stabilized or preempted. However, in future devices like ITER, it is necessary to carry out NTM control tasks simultaneously with other tasks, sharing a limited set of actuators. For this purpose it is advantageous to have a real-time (RT) module that is able to compute the amount of power required to stabilize or preempt an NTM in RT, facilitating actuator allocations. The RT prediction of NTM width and frequency will contribute to disruption prediction and avoidance tasks that are essential for devices like ITER. We will present the first example of such predictive capabilities in the NTM control algorithms for TCV and ASDEX Upgrade, based on RT-capable evaluation of the Modified Rutherford Equation (MRE). The proposed RT-MRE module is tested with extensive simulations in preparation of its experimental applications. Relevant results and the implications for the overall integrated control strategy will be discussed.   

Core magnetic shear effects on tearing mode stability in the presence of energetic ions

Simulations of the onset of resistive MHD instabilities are presented where a slowing down distribution of energetic ions can either stabilize or destabilize disruptive tearing modes depending on the magnetic shear in the core. Two cases are compared, one with monotonic shear throughout the profile ($q_{\textrm{min}}=1.1$) and one with reversed shear in the core ($q_{\textrm{min}}=1.3$). Outside of the reversal surface the equilibrium profiles are nearly identical between the two cases. The drive from energetic ions is stabilizing in monotonic shear and destabilizing in reversed shear, consistent with previous theory. In the reversed shear case without energetic ions a 3/2 mode is unstable, while with ions both a 2/1 and 3/2 mode are driven unstable. Comparison of the simulated beta limits are made against a reduced MHD model with a tearing layer, resistive wall, and energetic ion pressure included, showing qualitative agreement. Nonlinear simulations with energetic ions are also explored, and analyzed in terms of the linear results and a reduced model of the energetic ion effect on the resistive mode.   

Two fluid stability of rotating tokamak plasmas using machine learning

The stability boundaries of two fluid resistive instabilities in a tokamak with a resistive wall, are examined as a function of omega vs beta, the toroidal rotation frequency vs the ratio of thermal to magnetic energy. ~A numerical solver for the two fluid layer response is presented, which is valid across various two fluid regimes. ~The equilibria are stable for low beta, and the marginal stability values in beta and rotation are computed. ~The results show the Semi-Collisional regime to be most relevant to large tokamak experiments such as ITER. ~The stability boundary extends to lower beta as the frequency of the plasma response approaches that of the rotation. ~At high rotation, the plasma response has strong variation across the layer, breaking the constant-psi assumptions typically made in reduced models. ~Here the stability boundary is again found to move to lower beta, indicating that accurate treatment of two fluid layer responses is critical to quantitatively predicting the stability boundaries of disruptive modes. ~To facilitate a more fluid workflow in exploring these effects, regression models are trained on the numerical layer data to return the complex layer response given equilibrium quantities, rapidly producing new results as the equilibrium and outer region structure are varied.~   

Nonlinear simulations of locking for finite $\beta$ and favorable average curvature

We present NIMROD simulations of error field locking in plasmas with weakly damped linear tearing modes (TM's) stabilized by pressure gradient and favorable curvature. Linear theory shows that the Glasser effect, the stabilization of TM's due to favorable average curvature and positive $\Delta'$, occurs in the visco-resistive as well as the resistive-inertial regime, and more generally, in any tearing regime having real frequencies. A periodic cylinder with a hollow pressure profile is used to model the favorable curvature. Linear simulations with rotation and an error field of magnitude $\psi_{w}$ show the peak reconnected flux occurs near the TM phase velocity where the (quasilinear) Maxwell torque is zero. In nonlinear simulations, the real frequency and stabilization by favorable average curvature are masked by the pressure flattening near the mode rational surface due to sound wave propagation. This flattening can destabilize the mode, and the interaction of the field due to both $\psi_{w}$ and the destabilized TM can lead to oscillations in the Maxwell torque and rotating islands. We describe the interplay of three effects on TM behavior: I) pressure flattening, II) nonlinear saturation due to current flattening, III) and locking by the Maxwell torque.   

Improved Inner Region Matching Conditions for Resistive MHD

In a recent publication, [A. H. Glasser, Z. R. Wang, and J.-K. Park, Phys. Plasmas \textbf{23}. 112506 (2016); doi 10.1063/1.4967862], a procedure was presented to construct a global growth rate and eigenfunction for resistive instabilities in axisymmetric toroidal plasmas, using the method of matched asymptotic expansions. Verification against the straight-through MARS code [Y. Liu, A. Bondeson, C. Fransson, B. Lennartson, and C. Breitholtz, Phys. Plasmas 7, 3681 (2000)] was presented for a limited range of cases. More extensive comparisons reveal serious discrepancies. Further studies show that the inner region solutions are too broad to match to the outer region solutions. The problem has been identified as an error in the asymptotic large-$x$ power series solutions for the inner region. A new method is presented that corrects this error. More extensive benchmarks show that the new solutions are in much better agreement. Results will be presented. While the inner region equations contain only resistive MHD, the new mathematical methods should be applicable to more general plasma dynamics.   

Modeling Peeling-ballooning Stability in 3D Pedestals Using PB3D

Local 3D magnetic geometry can impact the stability of localized MHD ballooning instabilities in the presence of 3d magnetic perturbations. To better understand the changes in MHD stability due to 3d geometry, it is necessary to describe the stability properties of intermediate wavelength global peeling-ballooning modes in 3d pedestals. In this work, we provide an overview for a new tool being developed for studying these peeling-ballooning modes in 3d: pb3d. We make connections between 3d peeling-ballooning theory, infinite-n ballooning theory, and local 3d magnetic geometry to predict the 3d stability behavior of the peeling-ballooning modes. Finally, preliminary results are presented making use of experimentally-derived VMEC equilibria for both ASDEX upgrade and DIII-d. Work supported in part by the US DOE under contracts DE-86ER53218, DE-AC05-00OR22725, and DE-FC02-04ER54698.   

Current and pressure gradient triggering and nonlinear saturation of low-$n$ edge harmonic oscillations in tokamaks

It is shown that non-axisymmetric free-boundary equilibrium computations represent nonlinearly saturated external kink modes and external kink-like sidebands coupled to pressure-driven infernal modes. In this study, two different driving mechanisms for external kink type-modes are identified. It is found that standard current-driven external kinks are linearly unstable, and nonlinearly stable in a wide parameter range, especially where $q_{edge} < m/n$. But, where standard current-driven kinks are linearly stable coupling of pressure-driven infernal modes can cause instability, and their upper sideband drives edge corrugations that appear to have external kink features. Both types of modes are identified with the VMEC equilibrium code, and the spectra are compared favorably with those of linear numerical approaches and analytic methods. Pressure-driven external infernal modes are shown to robustly occur in sophisticated modeling where the separatrix effect on the $q$ profile is accounted for.   

Formation and evolution of localized pressure gradients from force-free magnetic fields

We develop a theoretical framework that quantifies the conditions under which the evolution of a tokamak-relevant plasma can be approximated by a sequence of instantaneous equilibria and, as an illustrative example, apply this principle to model the onset of a 3D helical core in tokamak-like equilibria. We then consider the evolution of a 1D cylindrical initial state which resembles a (possibly nonlinear) force-free magnetic field ‘seeded’ with localized pressure gradients. Using the M3D-C1 extended MHD code we explore the validity of the proposed framework and identify circumstances in which pressure gradients diffuse via ohmic dissipation, persist or accumulate. Gradual accumulation, followed by rapid collapse, of localized pressure gradients is commonly associated with phenomena which play an important role in magnetically confined fusion devices, including internal transport barriers, edge-localized modes and sawtooth cycles. Modelling temporally extended phases of relatively slow (e.g. quasi-steady state) plasma evolution as a sequence of equilibria would circumvent the need to evolve the full set of extended or resistive MHD equations over large time domains, yielding clear benefits for time and computational resources, particularly in complex, 3D geometries.   

Simulation of MHD Instabilities with Runaway Electron Current using M3D-C1

Runaway electrons can be generated in a tokamak during a plasma disruption and can be accelerated to high energies, potentially damaging the first wall. To predict the consequences of runaway generation during a disruption, it is necessary to consider resonant interactions of runaways with the bulk plasma. Here we consider the interactions of runaways on low mode-number tearing modes. For this study, we have developed a fluid runaway electron model for the 3D MHD code $M3D-C^1$[Jardin et al., 2012]. The code employs high-order $C^1$ continuous finite elements in 3 dimensions. It can be switched into reduced MHD or full MHD, linear or non-linear, cylindrical or toroidal geometry. The code allows localized mesh adaptation around certain rational surfaces so that it can better resolve the near-singular behavior of the runaway electron current. To benchmark, we have reproduced the reduced-MHD linear tearing mode results (with runaway electrons) in a circular cylinder presented in previous studies [Matsuyama et al., 2017]. This work is being extended in several ways including generalization to full MHD, nonlinear evolution, and generalizing the kinetic runaway electron model. This work is supported by US DOE grant DE-AC02-09CH11466.and the SciDAC SCREAM and CTTS centers.   

Investigations of stationary tokamak states in MHD using NIMROD

Using the extended-MHD code NIMROD, we perform linear and nonlinear simulations of zero- and finite-beta MHD in toroidal geometry oriented toward stationary tokamak states. A previous study by Jardin, Ferraro, and Krebs (PRL 2015) utilizing the MHD code M3D-C1 identified a class of such states, maintained by continuous dynamo action corresponding to a saturated interchange mode, such that the safety factor $q$ was held slightly above 1 and sawteeth were absent. Our NIMROD simulations begin with linear stability tests of tokamak equilibria with on-axis $q(0)$ values slightly below 1. Initial comparisons of unstable $n=1$ modes show noticeably different mode structures for zero and finite beta (of a few percent), reminiscent of an earlier comparison by Krebs et al.\ (POP 2017). We have begun nonlinear simulations starting from similar equilibrium cases, aiming to explore the conditional boundaries between sawtoothing and non-sawtoothing tokamaks.   

Numerical study of pressure-gradient driven dynamics in a cylindrical pinch

Computational modeling of Reversed-Field Pinch (RFP) dynamics is a challenging multi-scale problem. Most past efforts towards modeling RFPs have focused on studying macro-scale evolution of fluctuations and dynamo effects, without pressure-gradient driven dynamics. Recent NIMROD studies on RFPs with uniform background pressure have, however, shown that thermal effects play a significant role in RFP relaxation dynamics. We therefore seek to understand how thermal transport develops self-consistently with pressure-gradient dynamics and magnetic relaxation. In order to account for the absence of micro-scale effects in NIMROD, we initiate our model with a cylindrical Z-pinch equilibrium with a strong guide field, centrally peaked pressure and uniform temperature. Such a configuration forms a symmetric Ohmic steady state that is in classical particle-transport balance while being highly unstable to interchange. Nonlinear 3D evolution from this state develops tearing and interchange dynamics, where energy transport in quasi-steady state involves fluctuating parallel conduction and convection. Future goals include studying the dynamics of how this steady state is sustained self-consistently by the interplay between tearing, interchange and thermal transport.   

New Stability Analysis Methods Developed for Tokamaks and Stellarators and Physics Insights Gain with These Methods

Two new methods to calculation of ideal and resistive stability of tokamaks and stellarators and physical insights are presented. Ideal and resistive stability of tokamaks are found using Riccati method. We show how the resistive stability and Deltaprime is a storage of the unstabilizing energy at the surface on a singular surface using Riccati formalism and how this insight can be used to stabilize plasma. For stellarators, we converted the equilibrium calculation into finding a fixed point of a map. Then the stability can be found from first order perturbation analysis around this equilbria. We show initial results of this method of stability analysis and try to make connections to dW analysis.   

Toroidal modelling of core plasma flow damping induced by RMP fields in ASDEX Upgrade

Resistive plasma response to the n$=$1 RMP field is systematically investigated for a high-beta hybrid discharge in ASDEX Upgrade. Both linear and quasi-linear response are modelled using the MARS-F and MARS-Q codes, respectively. Linear response computations show a large internal kink response when the plasma central safety factor q$_{\mathrm{0}}$ is just above 1. This internal kink response induces core neoclassical toroidal viscous (NTV) torque, which is significantly enhanced by the precessional drift resonance of thermal particles in the super-banana regime. Quasi-linear simulation results reveal a core plasma flow damping by about 25{\%}, agreeing well with experimental observations, with the NTV torque playing the dominant role. Sensitivity studies indicate that the internal kink response and the resulting core flow damping critically depend on the plasma equilibrium pressure, the initial flow speed, the coil phasing and the proximity of q$_{\mathrm{0}}$ to 1. No appreciable flow damping is found for a low $\beta_{\mathrm{N}}$ plasma. A relatively slower initial toroidal flow results in a stronger core flow damping, due to the enhanced NTV torque. Weaker flow damping is achieved as q$_{\mathrm{0}}$ is assumed to be farther away from 1. Finally, a systematic coil phasing scan finds the strongest (weakest) flow damping occurring at the coil phasing of approximately 20 (200) degrees, again quantitatively agreeing with experiments.   

Characteristic Analysis of Lab Scale Magnetohydrodynamic Generator with Bi-plant Method

A magnetohydrodynamic (MHD) generator with an electric output of 10 kW was analyzed for the application of bi-plant method electricity generation. The MHD generator was considered to increase total efficiency of fossil power plant by adopting bi-plant method which generates electricity by both turbine and MHD generation. The flue gas with the high temperature of around 2000 K from the fossil power plant was used for the generation of electricity from its flow in the magnetic field, where electricity is produced directly without turbine facility from such an MHD generator. The magnetic flux density of a magnet, conductivity of plasma state of flue gas and velocity of gas were considered to analyze MHD generator with electric output of 10 kW. The velocity profile of fluid on the change of geometrical variables of the generator was analyzed by using finite element method. The magnetic flux density and velocity profile in the MHD generator calculated solving MHD equations by finite element method code simulation were used for calculation of electrical output.   

Analysis of high temperature combustion and plasma characteristics for magnetohydrodynamic power generation

Magnetohydrodynamic (MHD) based electric power generation is an eco-friendly generation system that uses heat from thermal power plants by formatting a plasma. To operate MHD generation, temperatures of more than 2,000 °C are needed. Atmospheric pressure and oxygen concentration of 20 {\%} combustion creates a combustion temperature of around 2015 °C. At a pressure of 3 bar, the combustion temperature of more than 3000 ° C can be formed in oxygen enriched combustion. The study estimated the plasma generation rates based on temperature and seeding (K, Cs) to enhance electrical conductivity and confirmed that the corresponding temperature was applicable to create a plasma for exhaust gases.   

Deep Learning Studies Linking Tokamak Disruption to Neoclassical Tearing Modes (NTM's)~

Disruptive instabilities are extreme amplitude plasma~perturbations that cause abrupt termination of discharges in fusion-grade experiments such as ITER. The Fusion Recurrent Neural Network (FRNN)~code is a recently developed AI/deep learning software to predict the onset of disruptions~with high accuracy and speed [J. K. Harbeck, Nature (2019)]. FRNN uses measured time series from experiments~as input, and can perform training on deep learning architectures such as RNNs.~~Here we study the effect of adding as input signals physics-based models of NTM's -- which feature magnetic islands from positive feedback between tearing magnetic perturbations and bootstrap current. As a first step, we add simple signals such as the pressure gradient profiles and rational surface locations. Preliminary results show these signals improve general model performance, suggesting links between disruptions and NTM's. We also implement a new deep learning architecture based on temporal convolutions. This new algorithm has various benefits in computational and predictive performance, especially~when high frequency profile data are introduced (such as the ECEI data), as targeted in our next-step investigations.   

Validation Study of Turbulent Transport Models for DIII-D H-mode Parameters

We report the results of a validation study in which turbulent transport predictions are tested against measurements from a series of DIII-D H-mode discharges. Three discharge conditions are considered, in which neutral beam heating and torque levels are separately varied between 3 to 7 MW, and 1.4 to 6 N-m. Both nonlinear gyrokinetic and quasilinear gyrofluid model predictions are tested, using the CGYRO and TGLF codes, respectively. We find that both models predict ion temperature gradient modes are the dominant long-wavelength instability in all cases, and generally able to simultaneously drive the observed levels of particle, energy, and momentum transport, as well as density fluctuation amplitudes. Significant scatter is found in model performance across case and radius, but no systematic trend is observed, and observations are often reproduced within uncertainties. In general, the gyrokinetic predictions exhibit fidelity equal to or better than the gyrofluid model. Both models predict the low power case lies close to the linear critical gradient, while the high power cases are well above it. Clear differences in predicted critical gradients and transport scaling above these gradients is observed. Synthesis of these results using composite validation metrics is presented.   

Particle simulations in a global toroidal geometry

The gyrokinetic toroidal code (GTC) has been upgraded for global simulations by coupling the core and scrape-off layer (SOL) regions across the separatrix with field-aligned particle-grid interpolations. A fully kinetic particle pusher for high frequency waves (ion cyclotron frequency and beyond) and a guiding center pusher for low frequency waves have been implemented using cylindrical coordinates in a global toroidal geometry. The two integrators correctly capture the particle orbits and agree well with each other, conserving energy and canonical angular momentum. As a verification and application of this new capability, ion guiding center simulations have been carried out to study ion orbit losses at the edge of the DIII-D tokamak for single null magnetic separatrix discharges. The ion loss conditions are examined as a function of the pitch angle for cases without and with a radial electric field. Finally, as a further verification of the capability of the new code, self-consistent simulations of zonal flows in the core region of the DIII-D tokamak were carried out.   

Global simulations of Ion Temperature Gradient instability with JOREK

Ion Temperature Gradient (ITG) turbulence is known as a dominant contributor to anomalous ion energy transport in tokamaks. Here, we report the results of global simulations of ITG modes with the JOREK, which uses Fourier decomposition in the toroidal direction and finite elements in the poloidal plane. The emphasis is on the global equilibrium profile effects (temperature and magnetic shear). Linear and nonlinear simulations have been performed. The linear simulations demonstrate the development of typical asymmetrical ballooning mode structure with an amplitude maximum off the low field side mid-plane. With lower magnetic shear, the ballooning structure is lost and the mode transitions into the narrowly localized (isolated) mode. The radial structure and poloidal composition of Reynolds stress is investigated for these two types of modes. It is shown that the Reynolds stress has significant finite m (poloidal) harmonics that can lead to the generation of the connective cells.   

Study of Core and Edge Gradients in Positive and Negative Triangularity Shaped Discharges in DIII-D

Plasma shaping, in particular triangularity ($\delta$), has been shown to influence turbulence levels and energy confinement in experimental tokamak plasmas. The effects of triangularity on gradients and edge transport in DIII-D have been studied using precise equilibrium reconstructions created with the EFIT code with constraints from ONETWO modeling. It has been observed that, in matched negative (NT) and positive triangularity (PT) L-mode discharges, NT plasmas have on average similar $a/L_{Te}$ and 65\% higher $a/L_{Ti}$ in the region $0.6 < \rho < 1.0$. For L-mode NT compared to H-mode PT discharges with comparable heating input, NT plasmas have on average 40\% higher $a/L_{Te}$ and 85\% higher $a/L_{Ti}$ in the same region, which may indicate a higher critical gradient and gives the same $T_e$ and $T_i$ values at the core. Instead of the exponential profile shape expected for stiff transport models with $a/L_{Te}$ independent of radius, we observe regions at the edge of L-mode plasma with a linear dependence of $T_e$ on $\rho$ that have been characterized as depicting non-stiff transport.\footnote{Sauter O., et al., \textbf{Phys. Plasmas} 21, 055906 (2014)} Consequently, these results offer an insight to the improved confinement obtained in NT discharges.   

Effects of Triangularity on Ion Temperature Gradient Turbulence Saturation

In this work, we model how changing the triangularity (both positive and negative) of an axisymmetric flux surface affects ion temperature gradient (ITG) turbulence saturation. Emphasis is placed on understanding quantitative difference between predictions from both quasilinear estimates and nonlinear gyrokinetic simulations of ion heat fluxes. A fluid model is used to study the saturation mechanisms of unstable modes through coupling to stables via three-wave interactions [1]. Using the gyrokinetics code GENE, linear and nonlinear behavior of ITG turbulence were compared among each geometry. Quasilinear and nonlinear heat fluxes qualitatively differed, but both methods of heat flux estimation revealed a decrease in heat flux with both enhanced positive or negative triangularity. [1] Hegna et al. PoP, 25, 022511 (2018)   

Gyrokinetic Simulations of Multi-scale Mircoturbulence in Tokamak Plasmas

Microturbulence driven by drift-wave instabilities is expected to be a dominant contributor to the anomalous transport processes. The coherent treatment of multi-scale nonlinear dynamics of coupled ITG-CTEM-ETG microturbulence is presently a challenging open issue, especially for the real ion-electron mass ratio. This study aims to apply the $\delta f$ particle-in-cell gyrokinetic simulation code GEM to investigate the coupled ITG-CTEM-ETG microturbulence in tokamak plasmas. Optimization of GEM code will be carried out to reduce the numerical cost, then we focus on the multi-scale interplay of microturbulence and zonal structures, and the associated turbulent transport at different scales.   

Self-heating Role for Triggering and Control of ITBS in Fusion Burning Plasmas

In a commercial fusion reactor, self-heating is expected to be main the source of plasma heating. Auxiliary heating sources are mainly for initiation of the reaction and control of the profiles.~Internal Transport Barriers(ITBs) provide one good route to developing a Steady State Tokamak Reactor(SSTR). The ability to control ITBs leads to the ability to achieve fusion criteria to get fusion energy and also the ability to clean the device by moving out the impurities accumulated at the core. Here ITBs refers to those regimes at which maximum linear growth rates are exceeded by local E X B velocity shear suppression rates and hence reduce the transport of particle and energy from core to edge. These are characterized by local reduction of transport coefficients. These barriers have a positive feedback loop in which they are created or sustained by the pressure gradient while at the same time they create or enhance those gradients in the temperature and density or pressure profiles. In this work we focus on the control of internal transport barriers in ITER parameter scenarios with auxiliary heating and proper q-profile. Then we replace much of the auxiliary heating with self-heating and fueling to control those ITBs. Some distinctions between dynamics of electron and ion ITBs are also explored.   

Evidence for Electron Heat Flux - Temperature Gradient Hysteresis During Modulated ECRH Experiments on the HL-2A Tokamak

Here we report observation of hysteresis between perturbed electron heat flux and electron temperature gradient in modulated ECRH experiments on the HL-2A tokamak, which clearly show that the classical view that heat flux is determined by local plasma variables is violated. In the experiments, hysteresis is found to exist in L-mode plasmas under quite a few plasma conditions, including different plasma density and ECRH/NBI heating power. The electron heat flux is determined from a heat balance analysis of the core plasma using data from the multi-channel ECE, FMCW reflectometry, FIR interferometer and bolometer diagnostics, while the multi-channel ECE gives the spatially and temporally resolved electron temperature gradients. We noticed that similar phenomenon had been reported on LHD, but to our knowledge this is the first time that such hysteresis is reported in tokamaks. The behavior of density fluctuations is diagnosed by a 2D BES system as well, and some results concerning the relationship between turbulence intensity, temperature gradient and heat flux will also be presented.   

RMPs, Zonal Flows, and Microturbulence in the DIII-D L-mode

Recent measurements using Beam Emission Spectroscopy on DIII-D tokamak L-mode plasmas report a dependence of microturbulent amplitude on the strength of an externally applied Resonant Magnetic Perturbation (RMP). Density fluctuations in the range of $50-100$ kHz increase as the amplitude of an $n=3$ I-coil RMP is raised incrementally. This behavior is suggestive of the presence of magnetic-flutter-induced zonal-flow erosion, a phenomenon previously documented on the Reversed-Field Pinch (RFP). Gyrokinetic simulations of the RFP reveal that small tearing mode fluctuations serve to degrade zonal flow structures, resulting in an increase in microturbulence levels. These DIII-D discharges are studied using gyrokinetics to determine if RMPs in tokamaks play an analogous role to tearing modes in the RFP. An increase in microturbulent activity occurs in the simulations over a range of externally applied RMP amplitudes, in qualitative agreement with the experiment. The effect requires flux-surface-breaking magnetic perturbations. Discrepancies in microturbulent amplitude scaling are addressed via profile corrugations.   

Large moment simulations of plasma dynamics with exact conservation

Understanding edge turbulent phenomena in tokamaks requires global, transport-timescale simulations with sub-millimeter resolution, which must handle large amplitude fluctuations, large gradients, and strong non-linearity. ALMA (Accelerated, Large-Moment, Anti-symmetric) is being developed to address such scenarios using high-order fluid hierarchies based on Gaussian Radial Basis Functions. We employ the anti-symmetry formalism, which results in exact conservation of mass, momentum, and energy independently of the chosen numerical scheme, preserving the Hamiltonian structure of fluid models. First simulations of drift-ordered high-order fluid hierarchies will be demonstrated. Benchmark simulations are also presented, including flow instabilities in neutral fluids, the Tang-Orszag vortex problem in MHD, and plasma filament motion in two fluid plasma models.   

Turbulence and Transport in Strong Interchange-Type Turbulence

The Helimak is an approximation to the infinite cylindrical slab with a size large compared with turbulence transverse scale lengths, but with open field lines of finite length. A pressure gradient in unfavorable magnetic curvature is unstable to interchange-type modes, leading to large amplitude nonlinear fluctuations similar to those in a tokamak SOL. A novel magnetically-baffled probe cluster permits full characterization of the turbulence, including density, temperature and plasma potential fluctuations as well as particle and thermal radial transport rates across the full plasma profile. Turbulence varies in a complex way with plasma parameters, but it can be most strongly modified by the application of bias to alter the transverse (poloidal, orthogonal to B and R) flow patterns. Despite the short coherence lengths, the level of saturated turbulence cannot be inferred from local parameters. The transport is mediated by two, often independent, mechanisms. The flows change the amplitudes of the fluctuating fields responsible for the transport. The flows also change the coherence between the fields (seen in either time or frequency domains), leading to changed net transport. The Helimak is moving to Shenzhen University.   

Turbulence and transport in mirror geometries in the LAPD

Measurements of turbulence and transport in varying magnetic mirror ratios, including multi-celled configurations, have been performed using the flexible magnetic geometry of the Large Plasma Device (LAPD).~Fluctuations in density (ion saturation current), floating potential, and magnetic field were recorded, with amplitudes peaking, as expected, on the edge pressure gradient. Planar correlation functions of single-celled mirror cases were also recorded. In a single-celled mirror, density and magnetic field fluctuation amplitudes decreased with increasing mirror ratio, while potential fluctuation amplitudes remained similar. The cross-phase between potential and density fluctuations varies with increasing mirror ratio, suggesting a shift in the underlying linear instability as the mirror ratio is increased and magnetic curvature is introduced. Differences in the~spectra and cross-phases of~floating potential and ion saturation current were also observed with increased cell count.~Swept Langmuir probe measurements, analyzed using neural-network-based machine learning techniques, will also be presented.   

Interaction between velocity shear and turbulent fluctuations in Texas Helimak

Efforts to identify mechanism by which turbulence is suppressed in Helimak when radial electric field is externally applied are described. Candidate mechanisms include linear and nonlinear coupling between fluctuations and flows as in a Lotka-Volterra predator-prey model, mode coupling with a stable or damped mode (fluctuation-amplitude reduction [Terry et al, Phys. Plasmas 2006]), and changes in phase relationship between density and potential fluctuations as in the velocity shear decorrelation of turbulence models (fluctuation-amplitude reduction [Biglari et al, Phys. Fluids B, 1990]). We compare experimental results obtained from magnetically insulated baffled probe cluster [Koepke et al, Contrib. Plasma Phys., 2006] with existing models of candidate mechanisms. Already-completed spectral analysis of suppressed and turbulent states of Helimak plasma leads us to anticipate that the state of suppressed turbulence is the result of an unstable mode being stabilized or being coupled to a stable/damped mode via its interaction with enhanced velocity shear.   

Electromagnetic gyrokinetic simulation in GTS

We report on the recent developments in the electromagnetic simulation capability for general toroidal geometry based on the global particle-in-cell gyrokinetic code GTS. Due to the cancellation problem, gyrokinetic simulations with electromagnetic perturbations run into numerical difficulties in the MHD limit where the plasma beta is larger than the mass ratio. We utilize a modified $p_\parallel$ formulation with a time integral of $E_\parallel$ in place of $A_\parallel$ [Mishchenko, PoP (2014)]. The time integral of $E_\parallel$ is solved directly using Ampere's Law. Since the original Mishchenko scheme can suffer from the effects of numerical noise due to particle discreteness, we have devised a new noise correcting scheme that removes particle noise from both the electron density and electron current. This is essentially a higher order extension of Chen’s noise reduction scheme [Chen, JCP (2003)]. With the new scheme our simulations correctly reproduce the finite beta stabilization effect of ITG and the onset of KBM for the Cyclone Base Case parameters. Our algorithm is extended for nonlinear simulation. Preliminary nonlinear simulation results will also be presented.   

Differential Heating to Control the Cross-phase: A Mechanism for Controlling I-modes and Other Enhanced Confinement Regimes?

The I-mode and similar new transport regimes offer good confinement properties with reduced density limit issues and better control. While a number of different mechanisms have been identified for the formation and maintenance of enhanced confinement regimes few if any allow enhanced confinement in one channel but not another which is seen in the I-mode. We propose differential cross-phase modification as a possible mechanism for different transport in different channels and investigate control tools. Simple dynamical models have been able to capture a remarkable amount of the dynamics of the core and edge transport barriers found in many devices. By including in this rich though simple dynamic transport model a simple model for cross phase effects, due to multiple instabilities, between the transported fields such as density and temperature, we can investigate whether the dynamics of more continuous transitions such as the I-mode can be captured and understood. If this mechanism is valid, what can the model tell us about control knobs for these promising regimes? Can we use differential electron and ion heating to control the I-mode regime going both into and out?   

The Spatial Core-edge Coupling of Particle-in-cell Gyrokinetic Codes GEM and XGC

Within the Exascale Computing Program (ECP), the High-Fidelity Whole Device Modeling (WDM) project aims at delivering a first-principle-based computational tool that simulates the plasma neoclassical and turbulence dynamics from the core to edge of Tokamak. To permit such simulations, different gyrokinetic codes need to be coupled, which will take advantage of the complementary nature of different applications to build the most advanced and efficient whole volume kinetic transport kernel for WDM. Here we present that the two existing particle-in-cell (PIC) gyrokinetic codes GEM and XGC have been successfully coupled, where GEM is optimized for the core and XGC is optimized for the edge plasma. The current GEM-XGC coupling adopts a coupling scheme, which is initially developed using XGCcore-XGCedge coupled simulations [1]. In this scheme, the time-stepping of the global core and edge distribution functions is achieved by pushing the composite distribution function independently in each code, but using the common global potential field solution for the whole domain. Due to the different grids, an interpolation scheme is used for transferring data back and forth between GEM's structured grid and XGC's unstructured grid. Meanwhile, the whole coupling framework is based on the high-performance ADIOS library with its state-of-the-art dataspaces in file/memory coupling capability. [1] J. Dominski, et al. Physics of Plasmas 25 (7), 072308   

Reduced model (nSOLT) turbulence simulations of neutral-plasma interaction in the SOL

The 2D scrape-off-layer turbulence code (nSOLT) includes neutral-plasma interactions; a Boltzmann equation describes the evolution of the bi-normally (y) averaged neutral distribution function, G(x,v$_{\mathrm{x}}$,t), in the radial dimension, and neutral-plasma interactions are mediated by charge-exchange and ionization rates based on poloidally-averaged plasma density and temperature. The code has been verified in comparisons with the Monte Carlo neutral transport code DEGAS 2 [1]. Recent modifications of nSOLT will be described, including (i) an updated convective transport algorithm and (ii) the addition of a spatially distributed source of neutrals for modeling diverter recycling. For MAST-U-like parameters, equilibrium and turbulence simulations with self-consistent neutral and plasma profiles will be discussed. [1] D.A. Russell, J.R. Myra and D.P. Stotler, Phys. Plasmas \textbf{26}, 022304 (2019).   

Application of gyrokinetic "fingerprints" in identifying microinstabilities in DIII-D pedestals

Advances in gyrokinetic codes, along with analytic techniques for mode identification based on a "fingerprints" method have found the significance of Micro-Tearing Modes (MTM) and electron temperature gradient (ETG) modes in driving the energy losses within the Edge Transport Barriers (ETB) of fusion experiments operating in the ELMy H-mode regime. Gyrokinetic simulations using the GENE code [1] are performed using equilibrium EFIT profiles constructed from experimental data. Nonlinear local simulations of DIII-D shots 174082 and 174092 have shown that electron heat flux has only minor contributions from ETG turbulence, allowing for the presence of MTM's and neoclassical effects to account for observed energy losses. The increased particle sources in shot 174092 leads to additional transport mechanisms. The MTM instabilities found in simulations of shot 174082 are consistent with an observed magnetic fluctuation, having a frequency in the electron diamagnetic direction and range. Simulation results have also shown that kinetic-ballooning modes (KBM) can contribute to particle losses in pedestals. Fluctuations linked to KBM's and MTM's provides a useful "fingerprint" in distinguishing these two modes, and can be used in a quasilinear prediction of transport channels.   

Indirect evidence for a hybrid ITG/TEM scenario in nonlinear simulations of a DIII-D near-edge L-mode plasma

The near-edge of L-mode plasmas is an important testing ground for our understanding of microturbulence. We present recent results from gyrokinetic simulations of DIII-D near-edge L-mode plasmas with the gyrokinetic turbulence code GENE. Nonlinear simulations at $\rho=0.90$ previously matched the experimental heat flux by increasing the electron temperature gradient by $23\%$ and including $\mathbf{E}\times \mathbf{B}$ shear effects (arXiv:1808.06607). We present similar simulations at a larger radial position of $\rho=0.95$ that match the experimental heat flux by including $\mathbf{E}\times \mathbf{B}$ shear effects and leaving the electron temperature gradient unchanged. We also revisit simulations at $\rho=0.90$, since they show an unexpected sensitivity of the total heat flux to small changes in electron temperature gradient. We present indirect evidence that this behavior may be caused by a hybrid ion temperature gradient (ITG)/ trapped electron mode (TEM) scenario, which was unexpected due to linear stability of ITG modes. This tentatively suggests that TEM modes may be nonlinearly exciting the linearly stable ITG modes. This result may also be important for spherical tokamaks, where ITG modes are more often linearly stable than in conventional tokamaks.   

Mode identification using “fingerprint method” on DIII-D

Comparisons between gyrokinetic simulations and experimental data from a new diagnostic tool: Faraday-effect Radial Interferometer-Polarimeter (RIP)[1] and Beam emission spectroscopy (BES)[2], are utilized for verification of micro-tearing instabilities (MTM) in DIII-D. Instability identification in simulations is achieved by using a variety of transport coefficients and their ratios to provide gyrokinetic “fingerprints”[3]. RIP will provide the $\frac{\int \delta (n_eB_r) dR}{\int n_e dR}$ with information of frequency, which can be compared with simulation results that provide strong indication that MTM are present in the pedestal region based on large $\frac{\delta B/B}{\delta n/n}$. BES measurements provide a location of density fluctuation with its amplitude at the outboard midplane. Global and local simulations using Gyrokinetic Electromagnetic Numerical Experiment (GENE) will be compared with experimental measurements. $^1$ J. Chen, W. X. Ding, D. L. Brower, et al., (2017) \url{http://dx.doi.org/10.1063/1.4960056.} $^2$ G. McKee et al., (1999) \url{https://doi.org/10.1063/1.1149416.} $^3$ M. Kotschenreuther et al., 5–6 (2019). \url{https : / /iopscience.iop.org/article/10.1088/1741-4326/ab1fa2}   

Global gyrokinetic simulation study of micro-turbulence in the presence of magnetic islands

It is essential to take into account the effects of magnetic islands on micro-turbulence to understand the physics associated with magnetic perturbations in tokamak plasmas, such as RMP and thermal quench. The nonlinear dynamics of electrostatic turbulence under the magnetic perturbations is simulated with global gyrokinetic GTS code by systematically considering additional particle transports and forces along the perturbed magnetic fields. We applied a magnetic perturbation of (m,n)$=$(3,2) mode on the cyclone base equilibrium to investigate how the magnetic island influences the temporal evolution of the micro-turbulence. At the very initial stage, the fast electron streaming rapidly flattens the electron temperature inside the magnetic island. As the ITG turbulence grows, the ExB transport correlated with the magnetic island plays an essential role in the nonlinearly saturated phase. We observe that the magnetic island size determines plasma transport behavior around the island. While a small island shows a weak influence on the plasma transport and ITG turbulence, a large island can generate strong ExB shear flows around its separatrix that can effectively mitigate or even suppress the ITG turbulence in the island region.   

Implementation of the electromagnetic ``pullback transformation scheme" in the gyrokinetic code XGC

The ``pullback transformation scheme"\footnote{A. Mishchenko et al., Phys. Plasmas 21, 092110 (2014)} for electromagnetic gyrokinetic simulations is being implemented as an option in the total-f gyrokinetic code XGC.\footnote{S. Ku et al., Phys. Plasmas 25, 056107 (2018)} This scheme significantly improves upon the conventional $p_\|$-formulation of electromagnetic gyrokinetics. At present, XGC uses a fully implicit $v_\|$-based electromagnetic scheme.\footnote{G. Chen, L. Chac\'{o}n, Comput. Phys. Commun. 197, 73-87 (2015)} We describe the details of the new electromagnetic scheme being implemented. We present the necessary adaption of this scheme to XGC's particular numerical design, such as its unstructured mesh that allows simulation across the magnetic separatrix and X-point. One of the first verification tests being performed is the reproduction of the kinetic-ballooning-mode linear growth-rate threshold that is observed for finite $\beta$.\footnote{T. G\"{o}rler et al., Phys. Plasmas 23, 072503 (2016)} Progress on this and other verification tests will be reported, and performance comparisons between $p_\|$-based schemes and the implicit $v_\|$-based scheme will be detailed.   

Analysis of Tungsten Ion Transport in Rotating Tokamak Plasmas by Orbit Calculation

To explain the increase in the accumulation of tungsten in case of the toroidal rotation opposite to the plasma current, which was observed in the JT-60U experiment, analytical models of the PHZ (inward pinch of high-Z impurity due to atomic processes) and the pinch due to the radial electric field Er through Coulomb collision were proposed. In the analysis of the JT-60U experiment, it was found that the experimental conditions did not satisfy assumptions of the original Er pinch. Furthermore, trapped particles were not considered in the original models. In order to overcome these shortcomings of the models, we developed a code to calculate the guiding center orbit of an impurity ion and evaluate the PHZ pinch and the Er pinch in rotating tokamak plasma. In the analysis of the JT-60U experiment, a positive dependence of the tungsten accumulation on the counter toroidal rotation was obtained. The tungsten accumulation was larger compared to the previous analysis using analytical pinch models for the large toroidal rotation cases.   

Effects of Impurity Injection for Divertor Heat Load Reduction in Tokamak Reactors

For DEMO and the commercial fusion plant, the argon Ar impurity injection in the divertor region is planned as a candidate in order to reduce the heat load to divertor, while its contamination in the core plasma is concerned in particular for peaked density profiles. We examined the plasma response for Ar injection, under the condition of the fixed fusion power P$_{\mathrm{fus}}$ maintained by the feedback control of injection frequency of DT pellets (3mm radius, 4mm height, injected at 1 km/s), using TOTAL code. The plasma parameters are referred to JA DEMO. We assumed Mixed Bohm / Gyro-Bohm model for the heat and particle transport. We changed the dimensionless coefficient C$_{\mathrm{P}}$ in the pinch velocity, V$^{\mathrm{AN}}=$-C$_{\mathrm{P}}$D$^{\mathrm{AN}}$(2r/a$^{\mathrm{2}})$, for the particle flux to vary the electron density n$_{\mathrm{e}}$ profile. The alpha heating power and RF power are used for heating. The Ar injection rate was adjusted to fix the ratio of the Ar density to the n$_{\mathrm{e}}$ at 0.23 percent (the expected value in ITER), at the plasma surface, in each C$_{\mathrm{P}}$. We found that the radiation loss of the core plasma can be increased while reducing the volume-averaged n$_{\mathrm{e\thinspace }}$for fixed P$_{\mathrm{fus}}$, by making the n$_{\mathrm{e}}$ profile moderately peaked one.   

Gyrokinetic Simulations of Pellet Perturbed Plasma Relaxation in Tokamak Geometry

Pellet injection is one of the methods for controlling edge localized modes (ELMs) that has been adopted for ITER. There remain some uncertainties over how the localized pellet density is distributed through the ablation process, how it interacts with the plasma modes and instabilities, and how it relaxes, which are important factors in optimizing the characteristics of the pellet injection such as the pellet size, injection geometry and velocity. One of the immediate plasma modes and instabilities that could be excited by the pellet-produced (PP) plasma perturbation is the geodesic acoustic mode (GAM) oscillations, which could play a dominant role in the redistribution of the PP plasma poloidally, toroidally and radially. The plasma redistribution across the steep plasma gradient (SPG) needs to be studied kinetically. Ions with nonlocal orbit excursion across SPG may relax and interact with GAMs differently from electrons, and affect the edge radial electric field structure. The PP GAMs could also be responsible for instigating the small-scale ELMs desired in the ITER H-mode operation and observed in the existing tokamak experiments. As the first step in the kinetic study of these processes, the total-f gyrokinetic code XGC will be utilized. A simple pellet ablation model based upon the neutral gas shielding model is implemented in XGC allowing self-consistent simulations of the interaction of pellets with a background plasma.   

Development of a Use Cases for Validation and Predictive Modeling in the AToM SciDAC Project.

We report on the development of the joint ``use cases'' database as part of the AToM (Advanced Tokamak Modeling) integrated modeling SciDAC project [1] to facilitate inter-SciDAC collaboration with the Center for Integrated Simulation of Fusion Relevant RF Actuators [2]. The cases presented here focus on an Alcator C-mod H-mode discharges with different off and on/off axis ICRF heating profiles resulting in different bulk confinement and core impurity contents. The ICRF heating results in no momentum input and the discharges only have intrinsic rotation that is low. We use the existing TGYRO and EPED workflows to predict thermal transport and infer impurity transport coefficients in each case. The goal is to identify impurity edge source rates via impurity transport modeling that best match experimental core radiation. As part of this effort, we also use the developed FASTRAN workflow to benchmark it using these low rotation C-mod cases and DIII-D H-mode discharges with high toroidal rotation. [1] https://scidac.github.io/atom/ [2] https://sites.google.com/view/rfscidac4   

Implementation of compressional magnetic field fluctuations in global GENE

The gyrokinetic framework has been successful in simulating a variety of phenomena in fusion and astrophysical plasmas. Past research has mostly focused on electrostatic and shear-magnetic fluctuations, neglecting compressional magnetic fluctuations. This is particularly true in the cases of global gyrokinetics, for which a self consistent treatment of parallel magnetic fluctuations had not been derived until now. The effects of compressional magnetic fluctuations could be significant in several systems that require global treatment, for example, tokamak pedestals, magnetic reconnection in solar coronas, and LAPD high-$\beta$ experiments. [Pueschel et al., PoP 22, 062105 (2015)] The radially global gyrokinetic framework including compressional fluctuations is derived. Benchmarked with well-established local field-aligned simulations, we present an initial implementation of these equations in the gyrokinetic turbulence code \textsc{Gene}.   

On deterministic nature of intermittent geodesic acoustic mode observed in tokamaks

Through a carefully designed numerical experiment, we demonstrate that a transition between two distinct phases of energy concentration in a zonal flow-drift wave system (caviton and instanton) may play a key role in the intermittent excitation of geodesic acoustic mode (GAM) that are observed in tokamaks. The two energy structures - the caviton, a slowly breathing spatial local structure of `negative' energy, and the instanton, a fine radial structure of short lifetime in rapid propagation, were recently identified in [Zhang Y. Z., Liu Z. Y., Xie T., Mahajan S. M., and Liu J. 2017 Physics of Plasmas \textbf{24}, 122304] (now extended to include GAM). The transition (decay) from the former to the latter is triggered by a rapid zero-crossing of radial group velocity of drift wave and is found to be strongly correlated with the GAM onset. Many features peculiar to intermittent GAMs, observed in real machines, are identified in the numerical experiment; the results will be displayed in figures and in a movie.   

Neoclassical and turbulence-driven ExB flow and macroscopic current structures in magnetic island

Global gyrokinetic simulations with self-consistent coupling of neoclassical and turbulent effects show turbulence can significantly reduce plasma self-driven current generation in collisionless regime, generate current profile corrugation near rational magnetic surface and nonlocally drive current in the linearly stable region -- all these are expected to have broad impact on tokamak confinement and global stability. The magnetic island is found to strongly change ExB shear flow and self-driven current structures in the island region. A charge separation due to electron parallel transport induced finite electron density flattening in the O-point generates a strong radially localized ExB shear layer, which may facilitate the formation of a transport barrier near the resonant magnetic surface by decoupling plasma inside the shear layer from the outside. On the other hand, turbulence self-generated zonal flow shows a helical structure akin to the island in large island case, namely, a poloidal ExB shear flow on the perturbed magnetic surface, which may prevent the turbulence developed in the outside of the island from spreading into the O-point. The parallel mean current is also largely modified in the island region by both neoclassical and turbulent effects.   

Study of Thermal Transport in Magnetized Laser-Produced Plasmas

Experiments at the Omega Laser Facility are measuring the heat-wave propagation in plasmas where an external magnetic field is scaled to 100 T. Collective Thomson scattering was used to temporally and spatially resolve the plasma conditions within a 2-mm-diam gas-jet plasma. At the highest fields, the magnetic-field pressure is significantly larger than the plasma pressure (B \textless 1). Classical thermal transport models break down when the magnetic field is turned off and the mean free path of the electrons is much larger than the temperature scale length. Initial experimental and simulation results will be presented.   

Micro/macro-scale ion heating and transport process of magnetic reconnection during merging plasma startup of TS-6 spherical tokamak

Micro/macro-scale ion heating and its transport process of magnetic reconnection have been investigated using 96CH/320CH ultra-high resolution ion Doppler tomography diagnostics which resolve both fine structure around X-point and global heat transport process in the TS-6 merging ST (Spherical Tokamak) formation experiment. As micro-scale characteristics around X-point, ions are heated around diffusion region as well as downstream of outflow jet. In synchronization with current sheet dynamics, ion temperature initially forms peaked structure around X-point but then gets split and ejected toward downstream. In guide field reconnection, it was also observed that ion temperature profile forms poloidally tilted structure which is related to the polarity of Hall-effect. Higher temperature typically appears in the negative potential region and it becomes clearer when ion/electron mass ratio is increased. While as macro-scale characteristics, the high temperature region in the downstream is affected by global heat transport process. Under the influence of high guide field which strongly suppresses perpendicular heat conduction, ion heat flux clearly propagates on field lines and high temperature region finally forms characteristic poloidally-ring-like structure at the end of merging.   

Simulation of a Nonlinear Model for Strong Electrostatic Plasma Turbulence

This work simulates a nonlinear model for the dissipation of strong turbulence in unmagnetized plasma, a process arising from the separated-scale interaction of large acoustic fluctuations and small Langmuir waves. The model consists of two fluid equations coupled, through ponderomotive pressure, to a kinetic equation for the plasma wave spectral energy density. The fluid equations are representative of macroscopic motions and are thought of as moments taken from a time-and-space averaged microscopically turbulent distribution. The plasma wave kinetic equation represents the spectrum of microscopic fluctuation energy with sources from solution of a dielectric function and sinks from Landau damping. The small-scale waves are taken to be non-self-interacting. The simulations presented focus on one-dimensional current driven turbulence.