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Uncovering turbulent plasma dynamics via deep learning from partial observations

One of the most intensely studied aspects of magnetic confinement fusion is edge plasma turbulence which is critical to reactor performance and operation. Drift-reduced Braginskii two-fluid theory has for decades been widely applied to model boundary plasmas with varying success. Towards better understanding edge turbulence in both theory and experiment, we demonstrate that a novel multi-network physics-informed deep learning framework constrained by partial differential equations can accurately learn turbulent fields consistent with the two-fluid theory from partial observations of electron pressure which is not otherwise possible using conventional equilibrium models. This technique presents a novel paradigm for the advanced design of plasma diagnostics and validation of magnetized plasma turbulence theories in challenging thermonuclear environments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NSTX-U National Research Program: White Paper in Response to Call from FESAC Sub-Committee

Both scientific and technical innovation is needed for the realization of an attractive engineering solution for a timely and cost-effective Pilot Plant, the design and construction of which is the overarching recommendation of the FESAC Long Range Plan, and the 2021 NASEM Pilot Plant reports, which underpin the Bold Decadal Vision. The two most significant plasma physics gaps to close for a Compact Pilot Plant (CPP) are core confinement improvement and heat flux mitigation, neither of which have been closed in an integrated fashion for any planned fusion power production device. High core confinement and stability are essential for producing majority self-driven plasmas in CPPs with reduced size and auxiliary heating power requirements, with an improvement in confinement being the major driver for cost reduction of a CPP. The National Spherical Tokamak Experiment - Upgrade (NSTX-U) is a unique low aspect ratio research facility that will address the fundamental challenge of developing the science and technology basis for a CPP design that integrates high core and edge confinement with the ability to mitigate very high incident heat fluxes. NSTX-U capabilities will enable the high performance, already achieved on NSTX, to extend into physics regimes much closer to those anticipated in Spherical Tokamak (ST)-based CPPs. These confinement and stability properties will be assessed by a full complement of diagnostics and analysis tools, which will also aid in the development of the underlying theory and predictive models needed for further optimization. Both conventional and transformative heat flux mitigation methods, such as liquid lithium plasma-facing components, will be developed and tested in-situ in NSTX-U at incident heat fluxes of ~100 MW/m 2 , and will inform plans and reduce risk for a subsequent major upgrade to the device to fully heated, high-Z wall and full liquid lithium divertor capability, a technology that potentially could then be implemented on any magnetic confinement device at any aspect ratio. NSTX-U research is fully complementary to programs performed on other STs, nationally and internationally. Furthermore, NSTX-U research has a direct connection to the private sector by informing design choices for future power production facilities being developed by these companies. The NSTX-U program will operate as a national User Facility, with collaborating researchers, engineers, and graduate students from 19 outside institutions, and open to participation and experiments led by researchers from both public and private entities. The research program will advance workforce development through training of young scientists, engineers, and technicians, and it will also serve for further diagnostic innovation, especially for high heat flux and high-Z wall environments, and implementation of advanced artificial intelligence (AI) for plasma and heat flux control.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

CRADA Final Report: CRADA Number NFE-22-09330 with General Fusion

General Fusion is developing a magnetized target fusion (MTF) approach that involves compressing an initial magnetically confined plasma inside a cavity formed in liquid metal. This approach builds from concepts initially developed under the Linus program at the U.S. Naval Research Laboratory and combines it with advances from compact toroid experiment (CTX) and sustained spheromak plasma experiment (SSPX) in compact toroid plasmas and coaxial Marshall gun systems. Modeling the tokamak during compression is central to designing a successful MTF device. The plasma is formed by coaxial helicity injection in the General Fusion device. Immediately after formation, the plasma has a diverted tokamak configuration with a single null. As the wall moves inwards, the plasma is repelled from the conducting surface and driven inwards by currents induced by its magnetic field in the liquid metal wall. As the liquid metal closes (or bridges) the opening of the coaxial plasma injector, the magnetic field topology alters to remove the null. Due to this, the plasma moves from a diverted to a wall-limited configuration. The liquid metal liner continues to close in and change shape, reducing in radius by a factor of ten at the peak of plasma compression. A model of the MTF plasma must be able to handle this continually varying geometry, and to be predictive, it must faithfully include the real imperfections arising in the process. In this project, we pursued a Monte Carlo approach to closures for MHD by computing kinetic electron trajectories in an MHD plasma background from simulations of GF devices. This requires enhancing the capabilities of the KORC-T code for running large ensembles of kinetic trajectories by porting it to GPU architectures and enabling workflows for large ensembles on OLCF machines. With these capabilities, it is possible to produce a large library of kinetic calculations of electron orbits evolving in plasma configurations spanning the magnetic configurations and plasma density profiles, including non-axisymmetry, arising in the General Fusion’s existing PI3 spherical tokamak device. Using ensembles will capture particles passing a single point in space in a given magnetic configuration, and the entire dataset will cover a range of global magnetic field geometries. By sampling around many starting points, this dataset will capture the spatial dependence of the plasma parameters. From this large dataset, it is possible to produce a reduced model for the kinetic effects not captured in MHD.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Mitigation of ICRF—edge plasma interaction in Alcator C-Mod

The parasitic interaction between ion cyclotron range of frequencies (ICRF) waves and the edge plasma has long limited high-power ICRF utilization in magnetically confined fusion plasmas. In this paper, we report on the successful mitigation of this interaction by power tapering a four-strap field-aligned (FA) antenna in the Alcator C-Mod tokamak. With the antenna operated in dipole phasing ($0\pi0\pi$), the ratio of the power coupled by the central two straps ($P_\mathrm {cent}$) to the power coupled by the outer two straps was varied at fixed total coupled ICRF power ($P_\mathrm {tot}$). With $P_\mathrm {cent}$/$P_\mathrm {tot} \approx 0.8-0.9$, no enhancement of the plasma potential was measured despite 1 MW of coupled ICRF power. When the antenna is powered, energy deposition increases on its four corners and on neighboring limiter tiles magnetically connected to some of those corners. The energy deposited on the antenna and limiter is minimized together with near-field plasma potentials. Additionally, we show that deviation from $P_\mathrm {cent}$/$P_\mathrm {tot} \approx 0.8$ enhances wave-plasma interactions in places not magnetically connected to the antenna. These far-field effects are correlated with changes in the antenna spectrum. Hence, on C-Mod, near-field and far-field interactions were minimized for about the same range of $P_\mathrm {cent}$/$P_\mathrm {tot}$. Optimal power tapering was also found to improve ICRF heating efficiency and facilitate H-mode access. Finally, we show that the heat flux pattern on the toroidally aligned antennas reverses with the direction of the RF-induced E×B flow in front of the antenna, a correlation not observed for the FA antenna. We argue that the RF-induced E×B flow, which carries high-density plasma from the near-SOL, is aligned with the FA antenna and does not intercept its corners, where the plasma potential is large. This could explain the previously reported smaller impurity generation by the FA antenna (Wukitch et al 2013 Phys. Plasmas 20 056117).

Alcator C-Mod↗

The magnetic gradient scale length explains why certain plasmas require close external magnetic coils

Abstract The separation between the last closed flux surface of a plasma and the external coils that magnetically confine it is a limiting factor in the construction of fusion-capable plasma devices. This plasma-coil separation must be large enough so that components such as a breeding blanket and neutron shielding can fit between the plasma and the coils. Plasma-coil separation affects reactor size, engineering complexity, and particle loss due to field ripple. For some plasmas it can be difficult to produce the desired flux surface shaping with distant coils, and for other plasmas it is infeasible altogether. Here, we seek to understand the underlying physics that limits plasma-coil separation and explain why some configurations require close external coils. In this paper, we explore the hypothesis that the limiting plasma-coil separation is set by the shortest scale length of the magnetic field as expressed by the ∇ B tensor. We tested this hypothesis on a database of > 40 stellarator and tokamak configurations. Within this database, the coil-to-plasma distance compared to the minor radius varies by over an order of magnitude. The magnetic scale length is well correlated to the coil-to-plasma distance of actual coil designs generated using the REGCOIL method (Landreman 2017 Nucl. Fusion 57 046003). Additionally, this correlation reveals a general trend that larger plasma-coil separation is possible with a small number of field periods.

Physics↗

Multi-delay coherence imaging spectroscopy optimized for ion temperature measurements in the divertor plasma of the Wendelstein 7-X stellarator

A new coherence imaging spectroscopy (CIS) diagnostic optimized to measure the C 2+ impurity ion temperature T i spatial distribution in the divertor plasma of the W7-X stellarator is designed, tested, and validated. Using CIS to obtain T i in the edge of magnetically confined plasmas has historically been challenging because Doppler broadening and Zeeman splitting have comparable effects on the shape of spectral emission lines. To distinguish between these two mechanisms, a novel approach to birefringent crystal design is employed to minimize the diagnostic’s sensitivity to Zeeman splitting. The recently developed pixelated multi-delay CIS approach is also used to obtain four times as much spectral information as traditional CIS approaches. The T i -optimized CIS diagnostic is validated in a long-pulse W7-X plasma by comparison with a high-resolution spectrometer whose sightlines overlap with the CIS field of view. The CIS and spectrometer T i profiles have the same shape and agree to within 10% on average and 25% in the worst case. Images of the T i distribution near the divertor show toroidally elongated bands aligned with the magnetic field, with T i ranging between 10 and 40 eV.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Nested Pebble Bed Blanket (NesPeB)

Recent advances in magnetic confinement fusion technology have attracted billions of dollars of investments in startups from venture capitals and corporations, resulting in the development of devices aiming to demonstrate net energy gain in a self-heated burning plasma, such as SPARC (under construction) and others. However, future fusion power plants must operate in regimes that will require technologies far beyond current experience. According to a National Academies of Science, Engineering, and Medicine report, to have nuclear fusion power plants contributing in a timely manner to the planned reduction of atmospheric carbon dioxide, a pilot plant should be built by 2035, and it should demonstrate fusion power production and the performance of the tritium fuel system (requiring a high enough tritium breeding) by 2040. A recognized key technology gap by [26] is the fusion first wall and blanket since no current blanket concept is considered satisfactory or has been built and proven. The first wall and blanket in magnetic fusion reactors form a vital and complex system, as it must satisfy different functions such as power extraction, tritium breeding, plasma containment, radiation shielding, and safety. The list of design requirements is even longer: high enough tritium production for fusion self-sufficiency, low material activation, decay heat and shutdown dose rates, high thermal efficiency, high-capacity factor, high magnets-divertor-vacuum vessel-first wall life, low corrosion, low cost, and intrinsically safe (requiring minimal licensing). Despite fifty-plus years of research, the first wall and blanket concepts proposed suffer from fundamental technical problems and immaturity (TRL=2-3) that jeopardize the timely delivery of a commercial fusion power plant. A fusion first-wall blanket has never been built nor tested, and a "winning", practical functioning design requires enough engineering margins (high enough tritium breeding considering the uncertainty, etc.), manufacturing simplicity, ease of continuous operation, maintenance, and low cost. A new, groundbreaking blanket concept called "Nested Pebble Bed Blanket" (NesPeB) was developed at ORNL under the successful ARPA-E GAMOW FERMI project (patent application allowed by the USPTO). The NesPeB blanket concept addresses current blanket concepts' shortcomings and technical immaturity, paving the way for accelerated delivery of fusion power plants. NesPeB is based on nested pebbles, which are binary-sized lithium-ceramic pebbles enclosed in "Beryllide" perforated and coated spherical shells, which are also binary-sized, stacked on top of each other, forming a "bed" and cooled by Nitrogen gas also "sweeping" the Helium and Tritium generated by the neutron irradiation of Lithium; the vacuum vessel plasma facing material is Molybdenum-96 and -97 with the first wall cooled by Helium while the divertor armor is made of Tungsten. The simulations of the NesPeB blanket using Fusion Reactors Models Integrator (FERMI) are encouraging as they estimate a tritium breeding ratio (TBR) greater than 1.2 using natural Lithium, acceptable pressure drop, and excellent heat transfer properties. Furthermore, the NesPeB blanket is not limited by magneto-hydro-dynamics (MHD) effects, is designed for online refueling, relies on existing tritium extraction technologies, has a simple construction, and limits the corrosion and chemical reactivity problems. NesPeB has the potential to be transformational and disruptive since it can solve all the main, challenging technical problems of fusion device blankets and accelerate a pilot plant delivery for 10 or more years.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A Fast Algebraic Multigrid Solver and Accurate Discretization for Highly Anisotropic Heat Flux I: Open Field Lines

We present a novel solver technique for the anisotropic heat flux equation, aimed at the high level of anisotropy seen in magnetic confinement fusion plasmas. Such problems pose two major challenges: (i) discretization accuracy and (ii) efficient implicit linear solvers. We simultaneously address each of these challenges by constructing a new finite element discretization with excellent accuracy properties, tailored to a novel solver approach based on algebraic multigrid (AMG) methods designed for advective operators. We pose the problem in a mixed formulation, introducing the directional temperature gradient as an auxiliary variable. The temperature and auxiliary fields are discretized in a scalar discontinuous Galerkin space with upwinding principles used for discretizations of advection. We demonstrate the proposed discretization’s superior accuracy over other discretizations of anisotropic heat flux, achieving error 1000x smaller for anisotropy ratio of 10 9 , for closed field lines. The block matrix system is reordered and solved in an approach where the two advection operators are inverted using AMG solvers based on approximate ideal restriction, which is particularly efficient for upwind discontinuous Galerkin discretizations of advection. To ensure that the advection operators are nonsingular, in this paper we restrict ourselves to considering open (acyclic) magnetic field lines for the linear solvers. We demonstrate fast convergence of the proposed iterative solver in highly anisotropic regimes where other diffusion-based AMG methods fail.

97 MATHEMATICS AND COMPUTING↗

Two Photon Absorption Laser Induced Fluorescence for Neutral Hydrogen Profile Measurements

The magnitude and spatial dependence of neutral density in magnetic confinement fusion experiments is a key physical parameter, particularly in the plasma edge. Modeling codes require precise measurements of the neutral density to calculate charge-exchange power losses and drag forces on rotating plasmas. However, direct measurements of the neutral density are problematic. In this work, we proposed to construct a laser-based diagnostic capable of providing spatially resolved measurements of the neutral density in the edge of plasma in the DIII-D tokamak. The diagnostic concept is based on two-photon absorption laser induced fluorescence (TALIF). By injecting two beams of 205 nm light (co or counter propagating), ground state hydrogen (or deuterium or tritium) can be excited from the n = 1 level to the n = 3 level at the location where the two beams intersect. Individually, the beams experience no absorption, and therefore have no difficulty penetrating even dense plasmas. After excitation, a fraction of the hydrogen atoms decay from the n = 3 level to the n = 2 level and emit photons at 656 nm (the H α line). Calculations based on the results of previous TALIF experiments in magnetic fusion devices indicated that a laser pulse energy of approximately 3 mJ delivered in 5 ns would provide sufficient signal-to-noise for detection of the fluorescence. In collaboration with the DIII-D engineering staff and experts in plasma edge diagnostics for DIII-D from Oak Ridge National Laboratory (ORNL), WVU researchers designed a TALIF system capable of providing spatially resolved measurements of neutral deuterium densities in the DIII-D edge plasma. The laser systems were specified, purchased, and assembled at WVU. The TALIF system was tested on a low-power hydrogen discharge at WVU and the plan was to move the instrument to DIII-D for installation in collaboration with ORNL researchers. After budget cuts at DIII-D, the DIII-D facility declined to support installation on their tokamak. Instead, after a no-cost extension, the apparatus was moved to the University of Washington-Seattle and successfully tested on the HIT-SI3 spheromak experiment. As a result of this project, TALIF measurements of the absolutely calibrated neutral density hydrogen and deuterium were obtained in a helicon source and in a spheromak, designs were developed for installation of a TALIF system on a tokamak, and a new, xenon-based calibration scheme was proposed and demonstrated. The xenon-calibration scheme eliminates significant problems that were identified with the standard krypton calibration scheme.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Understanding Plasma Divertor Detachment in Fusion Power Reactors

Key LLNL spectroscopic and modeling capabilities have been successfully applied to a range of ionizing and recombining plasmas in a magnetically confined fusion device to elucidate the roles of physical processes relevant to the ‘detached divertor’ regime essential for operation of future fusion power reactors. The primary goal of this work was improving theoretical models and the interpretability of plasmas near the ionizing/recombining balance, in order to improve predictive capability for divertor performance in state-of-the-art fluid-based modeling codes. To do so, contributors to a universal shortfall in predicted radiation, the underestimated impact of convective plasma drifts/flows, and the role of molecules in cold plasmas were identified in the DIII-D National Fusion Facility using newly installed multispectral extreme ultraviolet and visible spectroscopy, and advanced boundary modeling developed by LLNL. As a result of this LDRD, a powerful array of spectroscopic diagnostics that are each unique worldwide have been added to the DIII-D device for continued use in coming operational campaigns including research in boundary and core-edge integration to further expand operational space. Experiments scanning the detached regime have resulted in application of essential missing physics with plasma-boundary codes and a transformation in the recognition among international magnetic fusion programs of the formidable influence of convective plasma transport due to drifts in regimes including conditions necessary for future fusion power reactors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Suppression of first-wall interaction in negative triangularity plasmas on TCV

Magnetically confined fusion plasmas with negative triangularity (δ) exhibit greater L-mode confinement than with positive δ. Recent experiments in the TCV and DIII-D tokamaks have correlated the confinement improvement to a reduction of fluctuations within the plasma core. We report on fluctuation measurements in the scrape-off layer (SOL) for -0.61 < δ < +0.64 in limited and diverted ohmic L-mode plasmas; these reveal a strong reduction in SOL fluctuation amplitudes at δ < -0.25, and, surprisingly, an almost full suppression of plasma interaction with the main-chamber first-wall, which could have important implications for the prospects of using negative δ plasmas as a reactor solution. An exploration of several physical mechanisms suggests that a reduced connection length—intrinsic to negative δ plasmas—plays a critical role in the origin of this phenomenon.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Electromagnetic torque measurements in DIII-D using internal/external magnetic field decomposition

Given spatially resolved measurements of normal and tangential components of the magnetic field just outside the surface of a magnetically confined plasma, the field at the measurement location can be uniquely decomposed into contributions from the plasma and from external sources. This principle allows direct measurement of the electromagnetic torque on the plasma without knowledge of the distribution of the internal and external currents, similar to the more well-known formalism using the Maxwell stress tensor. The internal/external field decomposition also enables a mixed approach that incorporates any explicitly known current distributions (e.g., from non-axisymmetric coils). We discuss the requirements and limitations of such an approach to torque measurements. Experimental measurements of the torque evolution as a rotating tearing mode locks to the wall in the DIII-D tokamak are consistent with a simple model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Ulysses observations of double ion beams associated with coronal mass ejections

Coronal mass ejections (CME's) are thought to result from the loss of stability within a magnetically confined coronal structure leading to its radial expansion into interplanetary space. As the CME expands into the corona current sheets will form between the expanding CME and surrounding field lines in the ambient wind. This configuration may lead to reconnection between the CME and adjacemt field lines. Such reconnection may produce double ion beams as has been observed in the terrrestrial magnetosphere. We examine all 24 distinct signatures of CME's observed by Ulysses during the in-ecliptic portion of the mission. In 5 of these 24 cases the ion spectra were not clear and thus the presence of double ion beams could not be determined. In 13 of the remaining 19 CME's double ion beams were found on the leading and/or trailing edge of the CME but not in the interior of the CME. In 3 of the CME's double ion beams were found throughout the CME while in the remaining 3 CME's double ion beams were not present near or just inside of the CME. In contrast in a control sample of 19 randomly chosen intervals, double ion beams were present at the leading and/or trailing edges of the random intervals in only 3 of the 19 cases. There appears to be no correlation between probability of occurrence of double ion beams and a magnetic cloud or non-cloud configuration of the CME and no correlation between the presence of the double ion beams at the edges of the CME and the CME being a fast or slow CME.

Hammond, C. M.↗

Features of near and far scrape-off layer heat fluxes on the Wendelstein 7-X inboard limiters

The power fall-off length is used as a characteristic dimension to describe the power exhaust in the scrape-off layer (SOL) in magnetic confinement fusion devices. Measurements from the limiter campaign of the stellarator Wendelstein 7-X with inboard limiters are presented with the first-time characterization of the limiter heat loads. Two fall-off regimes are found with a narrow near SOL with power fall-off length in millimeters and a wider far SOL with fall-off lengths of several centimeters. An attempt is made to describe both regimes with a scaling law for plasma with different heating powers and densities. Finally, the results confirm the major geometry effects of the connection length on the heat transport predicted by 3D modeling.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Magnetospheric Multiscale Overview and Science Objectives

Magnetospheric Multiscale (MMS), a NASA four-spacecraft constellation mission launched on March 12, 2015, will investigate magnetic reconnection in the boundary regions of the Earth's magnetosphere, particularly along its dayside boundary with the solar wind and the neutral sheet in the magnetic tail. The most important goal of MMS is to conduct a definitive experiment to determine what causes magnetic field lines to reconnect in a collisionless plasma. The significance of the MMS results will extend far beyond the Earth's magnetosphere because reconnection is known to occur in interplanetary space and in the solar corona where it is responsible for solar flares and the disconnection events known as coronal mass ejections. Active research is also being conducted on reconnection in the laboratory and specifically in magnetic-confinement fusion devices in which it is a limiting factor in achieving and maintaining electron temperatures high enough to initiate fusion. Finally, reconnection is proposed as the cause of numerous phenomena throughout the universe such as comet-tail disconnection events, magnetar flares, supernova ejections, and dynamics of neutron-star accretion disks. The MMS mission design is focused on answering specific questions about reconnection at the Earth's magnetosphere. The prime focus of the mission is on determining the kinetic processes occurring in the electron diffusion region that are responsible for reconnection and that determine how it is initiated; but the mission will also place that physics into the context of the broad spectrum of physical processes associated with reconnection. Connections to other disciplines such as solar physics, astrophysics, and laboratory plasma physics are expected to be made through theory and modeling as informed by the MMS results.

Space plasma physics↗

FIREFLY: heat load and particle exhaust approximations for rapid evaluation of divertor designs

The divertor in a magnetic confinement fusion reactor is an essential component for power dissipation and particle removal. The FIREFLY package for rapid evaluation of divertor designs is presented as an extension of the FLARE code for field line reconstruction from a flux tube mesh. First, divertor loads are approximated with a simplified heat transport model. Neutralized particles are then sampled from the resulting load distribution, and the EIRENE code is used to track molecules and atoms in a plasma background while accounting for dissociation, charge exchange and ionization. Particles are removed on pumping surfaces in order to estimate the exhaust efficiency for a given divertor geometry. Optimization of the divertor geometry for more efficient particle exhaust is explored by using W7-X as an example, and the sensitivity to model parameters for the plasma background in the proxy calculations is evaluated.

mesh generation, magnetic field lines, scrape-off ↗

Collaboration with NSTX in Calculations of Radiofrequency and Neutral Beam Heating and Current Drive

The overall objective of this project was to advance the understanding of heating and current drive necessary for toroidal magnetic confinement fusion energy reactors, and to provide accurate models for these sources to aid in understanding magneto-hydrodynamic, transport and boundary physics issues. Increased understanding is provided by computer simulation using the underlying physics laws, and will lead to greater reliability and increased efficiency of a power producing fusion reactor. The proposed work entailed applications of existing CompX Fokker-Planck, ray tracing, full-wave microwave, and particle diffusion calculator codes to the National Spherical Torus Experiment at Princeton Plasma Physics Laboratory. Special features of NSTX include that large ion orbits are emphasized in its geometry and thus offer a major opportunity within fusion research for focused exploration of their ubiquitous effects, including comparison with simulation codes. The CompX CQL3D Fokker-Planck code was be further adapted to the finite-orbit-width physics. Comparison with experiment ensured that the computer codes have sufficient accuracy to accurately model the experiments. Nonthermal distributions of energetic ions are produced in experiments-- and modeled with the codes-- exhibiting the signatures of auxiliary heating, transport, and radiation processes within the plasma. Using physics-based modeling, in conjunction with experimental data, nonthermal distributions can provide keys to validation and quantification of auxiliary heating physics. Nonthermal distributions also hold particular information on radial transport processes, not obscured by the smoothing Maxwellization effects of Coulomb collisions. Generally, radial transport is not well understood but is a key to efficient fusion energy production. By comparison with Fokker-Planck modeling, the velocity dependence of radial transport coefficients becomes experimentally accessible, particularly in cases of well-modeled sources such as neutral beams, fast wave power, or the toroidal electric field. It is clear from modeling of fast-wave interactions with ions that finite-orbit-width effects play a significant role. For example, a different set of ions is computed to intersect a given cyclotron resonance depending on whether or not radial orbit drifts are taken into account. Also, radial transport, associated bootstrap current, and alpha channeling depend on radial drifts. Ion cyclotron heating above the first harmonic interacts preferentially with higher velocity ions, giving large radial drifts. The CQL3D Fokker-Planck code, maintained by the proposers, is a physics based model used extensively within the US fusion community to compare with and interpret experimental observations. At the beginning of this grant, bounce-averages of the rf quasilinear and other operators have been performed neglecting the radial drifts which give finite orbit widths to the particle orbits. The proposed work included a major upgrade to CQL3D to include finite-orbit-width effects be accounted for by performing the bounce-averages of rf and neutral beam fast ions along guiding center orbits. This CQL3D enhancement provided microwave and neutral beam contributions to neoclassical radial transport coefficients for nonthermal distributions, and substantially increased the comprehensiveness of the ion model. Additional work validated Fokker-Planck and ray tracing modeling of neutral beam and high harmonic fast wave absorption and current drive against the NSTX experiment, as had been very successful for electron cyclotron current drive in the DIII-D tokamak at General Atomics and lower hybrid waves on C-Mod at MIT. The validation work was in conjunction with staff and graduate students at Princeton Plasma Physics Laboratory. This DOE grant supported fusion energy research, a potential long-term solution to the world's energy needs. The research grant under consideration, DE-SC0006614, provided research support at the 0.3 Full-Time-Equivalent level for application of computer models to aid in understanding and projecting efficacy of heating and current drive sources in the National Spherical Torus Experiment, a tokamak variant, at the Princeton Plasma Physics Laboratory. The NSTX experiment explores the physics of very tight aspect ratio, almost spherical tokamaks, aiming at producing steady-state fusion plasmas. The current drive is an integral part of the steady-state concept, maintaining the magnetic geometry in the steady-state tokamak.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Transport Barriers in Symplectic Maps

Chaotic transport is a subject of paramount importance in a variety of problems in plasma physics, specially those related to anomalous transport and turbulence. On the other hand, a great deal of information on chaotic transport can be obtained from simple dynamical systems like two-dimensional area-preserving (symplectic) maps, where powerful mathematical results like KAM theory are available. In this work we review recent works on transport barriers in area-preserving maps, focusing on systems which do not obey the so-called twist property. For such systems KAM theory no longer holds everywhere and novel dynamical features show up as nonresistive reconnection, shearless curves and shearless bifurcations. After presenting some general features using a standard nontwist mapping, we consider magnetic field line maps for magnetically confined plasmas in tokamaks.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗