Session JP1: Poster Session IV: Ed. and Outreach, HS and Undergrad Research; Divertors and Edge Physics, Elementary Processes, Chaos, Low Temp Plasmas; Plasma Sim

Educational Outreach at the MIT Plasma Science and Fusion Center

At the MIT PSFC, student and staff volunteers work together to increase the public's knowledge of fusion science and plasma technology. Seeking to generate excitement in young people about science and engineering, the PSFC hosts a number of educational outreach activities throughout the year, including Middle and High School Outreach Days. The PSFC also has an in-school science demonstration program on the theme of magnetism. The Mr. Magnet Program, headed by Mr. Paul Thomas, has been bringing lively demonstrations on magnetism into local elementary and middle schools for 15 years. This year Mr. Magnet presented the program to nearly 30,000 students at over 67 schools and other events, reaching kindergartners through college freshmen. In addition to his program on magnetism, he is offering an interactive lecture about plasma to high schools. The "Traveling Plasma Lab" encourages students to learn more about plasma science while having fun investigating plasma properties using actual laboratory techniques and equipment. Beyond the classroom, Paul Thomas has provided technical training for Boston Museum of Science staff in preparation for the opening of a Star Wars exhibit. His hands-on demos have also been filmed by the History Channel for a one-hour program about Magnetism, which aired in June 2006.   

Science Education Collaborations at PPPL

PPPL's Science Education Program (SEP) collaborates with a variety of institutions in order to expand its K-12 programs. The Plasma Camp professional development workshop now includes middle and high school teachers from the same school district in order to vertically integrate new plasma-based curricula from grades 6 - 12. A collaboration with a “learning different” school includes new energy- centered curricula while an entire elementary school creates a model renewable-energy city. Finally, a new program with a local science museums that will include remote video conferencing from the NSTX control room, a table-top plasma experiment, and new plasma displays for the general public will debut this Fall. Along with education programs, student research continues on an ECR sputter source and transport measurements in a dusty plasma.   

Promoting Science Education Using an Energetic Multi-faceted Program

The Fusion Education Program at General Atomics is beginning its 13$^{th}$ year of interaction with teachers and students and continues to be a fundamental source of information and activities covering states of matter, fusion science and technology, and classroom demonstrations. DIII-D facility field trips by students and classroom visits by scientists offer students close interaction with professional scientists and engineers and hands-on demonstrations. Educator workshops allow teachers to build items for their classroom that allow clear demonstration of specific science concepts found in basic plasma science and science measurements using devices such as DVMs, compasses, and pressure gauges. Materials for teaching plasma and fusion science in the class are readily available and formats include notebook, videotape, CD, and DVD. In recent summer `Build-it Day' workshops teachers built a 300 turn coil used in magnetic field mapping exercises and a 200 turn coil used in a magnetic levitation demonstration. Teachers also harvested a small coil from a standard relay to make a magnetic field pickup coil for making quantitative field measurements. Demonstration equipment will be present for review and interaction.   

Optical Filters for Use in a Plethora of Applications

Nova Photonics has invented a new kind of optical filter that has many exciting prospects. This filter is capable of allowing only a very narrow range of light through it while also allowing this light to be incident upon it from a wide range of angles. Although this sort of filter has been studied and worked on for many years, nothing has ever been able to come close to having as high a transmission rate or incident angle range as this one does. This filter also incorporates several novel ideas into it. As of now, it is already in use on NSTX (the Princeton Plasma Physics Lab's Tokamak). In this application of the versatile device it is filtering light around the red end of the spectrum. Currently the filter is also being adapted to transmit light at $\sim$532~nm so the Navy can use it on their submarines. The product being made for the Navy is still in the early stages of its testing, but it is looking promising.   

MiniCNT - A Tabletop Stellarator

MiniCNT is a scaled down version of the Columbia Non-Neutral Torus, a stellarator built to study confinement of non-neutral plasmas on magnetic surfaces. MiniCNT is a glass vacuum chamber capable of holding pressures six orders of magnitude below atmospheric pressure. Unlike CNT, in which plasmas are invisible, MiniCNT allows some collisions with neutrals, causing it to glow. Using two twelve-volt car batteries to power four magnetic coils, MiniCNT generates a 0.02 Tesla magnetic field. While CNT, being larger, is obviously more accurate, there are multiple benefits in MiniCNT. First, it is more flexible and can be adjusted to fit many scenarios easily. The car batteries can be switched for other power sources, the coils can be realigned, and the chamber can be pumped to various pressures of various gases. Also, it is visually accessible; while CNT has glass viewing ports and its plasma is dark, MiniCNT is made of glass and its plasma glows, allowing visualization of the magnetic surfaces.   

Using LabVIEW for Complete Systems Control of an ECR Thin Film Deposition System.

ECR produces a high-density plasma maintainable at low pressure, typically 10$^{-2}$ Torr, which increases ion directionality and mean free path, improving deposition rate and precision. The ECR deposition system requires that its gas flow control, magnets, 2.45 GHz source, and other components all work in concert. Operating the system requires a user to constantly compensate for the dynamics of the system, such as Argon gas pressure and magnetic field. This is an inconsistent method and requires the constant presence of an experienced operator. Using LabVIEW, all of the individual components of the ECR deposition system can be linked and ultimately automated. A single LabVIEW VI is being used to control microwave power, magnet current, target bias voltage, vacuum and compressed gas valve position, chamber pressure, and robotics commands. The VI takes many factors into account simultaneously such as chamber pressure, ion current and spectroscopic data in order to make decisions about the system state. The use of complete software control also reduces complex routines such as robotics and startup procedures to a mouse click. Details of the feedback based logic will be discussed further. Data on copper deposition rates, uniformity and spectroscopic data will also be presented.   

Modeling a Graphite Diagnostic System using MCNPX

Inertial Confinement Fusion (ICF) implosions can be characterized by the target areal density ($\rho $R). The $\rho $R of ICF targets in the National Ignition Facility (NIF) target chamber can be determined by tertiary-induced neutron activation of elements with appropriately high thresholds. In such materials as $^{12}$C, neutron activation results in beta decay and the emission of 511-keV coincidences which are detected by a pair of NaI(Tl) detectors. Optimal diagnostic thickness, contamination effects, and detector response have been modeled using MCNPX. Results will be presented.   

Instrumentation development and theoretical analysis for the Driven Relaxation Experiment (DRX)

Magnetic relaxation in plasmas could potentially provide efficient fusion energy configurations, and help explain cosmological magnetic structures. Magnetic relaxation is thought to be constrained by energy barriers, limiting plasmas to fall below the first eigenstate of the linear force-free equation. The Driven Relaxation Experiment (DRX) will attempt to create a driven steady-state above the first energy barrier using a coaxial plasma gun at higher gun current/flux ratio than conventional experiments. This project has involved instrumentation development and theoretical analysis for DRX. Instrumentation development includes: (1) design/construction/calibration of gun current, voltage, and magnetic field diagnostics, and (2) assembly and testing of a hydrogen injection system including gas puff valves, and capacitor bank power supply. Theoretical analysis has focused on analytic and numerical solutions of the nonlinear (partially relaxed) force-free equation relevant for the DRX setup. The analytic solutions are compared to the linear (fully relaxed) solution and to numerical solutions of the partially relaxed problem.   

Focusing of a 100 Gw Laser With an Open Waveguide

High laser power makes closed waveguides problematic due to ohmic power loss on the metallic walls and plasma formation at the boundaries, while the series of apertures of an open iris waveguide, which are much larger than the laser wavelength, provide at least 70{\%} laser power transmission over 10 cm. We present initial designs and measurements of the open waveguide used to guide a plane polarized TEM mode, 10.6 micrometer, 100 Gw laser pulsed at 200 ps pulse length over a 10 cm path length at a beam waste optimized for low power loss at 0.5mm. This waveguide will be used in an Inverse Free Electron Laser (IFEL) acceleration scheme in the Neptune laboratory at UCLA.~ Initial measurements are performed with a low power CO2 laser and once design limitations are optimized in this regime measurements will be taken at higher powers where design problems such as plasma formation at the aperture boundaries may need to be considered.~ Other problems such as initial coupling of the beam into the apertures and phase lag of the beam are also addressed.   

Measurement and Analysis of Plasma Radiation from a 20-channel Bolometer Array to Investigate Energy Loss from Impurity Radiation

Fusion is one possible alternative for a long-term energy supply. A field reversed configuration (FRC) plasma has several desirable properties in fusion research, because it is robust, it can be compressed without changing the structure of the plasma, and it has simple geometric and magnetic properties. The use of rotating magnetic fields (RMF) to build and sustain the magnetic flux of FRC plasmas with the translation, confinement, and sustainment (TCS) FRC experiment is being investigated at the University of Washington. A bolometer array diagnostic has been designed and built to measure the total power radiated per unit length in this experiment. This project included building, testing, and calibrating the bolometer array diagnostic. The 20-channels on the bolometer array will improve the resolution of the radial profile of the radiation. This will provide information on energy loss due to impurity radiation and enable a power balance estimate for the TCS experiment.   

Imaging polar currents of a dipole-confined plasma using a high-speed, variable gain amplifier system.

One of the main objectives of the Collisionless Terrella Experiment (CTX) is to measure equilibrium and perturbed plasma structures. For plasmas confined by strong dipole magnets, like planetary magnetospheres, these structures can be diagnosed by imaging the loss current to the magnetic poles. In CTX, the polar current is recorded at high speed (once every $\mu$sec) with an array of more than 70 gridded particle detectors uniformly distributed in polar longitude and latitude. We have designed, built, and tested a high-frequency, variable-gain transimpendance amplifier that both increases the bandwidth and permits a wider range of plasma loss currents to be observed. The new amplifiers use of a second gain stage and an analog switch that is used to quickly adjust the overall gain of the amplifier array. The new amplifier system will allow the first dynamical measurements of (i) high-density plasma structures and (ii) the full dynamics of the low-to-high density ``phase-transitions'' that follow programmed gas puffing.   

Electrostatic Dust Detection and Removal in Tokamaks

The inventory of in-vessel dust particles in next-step tokamaks will increase with the rise in stored energy and pulse duration. Dust levels will need to be measured and controlled for safety reasons and to avoid plasma contamination. A novel electrostatic dust detector has been developed with a sensitivity appropriate for the carbon dust levels expected in next-step devices.$^{23}$ Higher sensitivity is desired for real-time measurements in contemporary tokamaks that have less dust. We report on results from a larger area, more sensitive detector. A 2\textquotedblright~x 2\textquotedblright~circuit board has two interlocking combs of copper traces spaced by 25 microns and biased at 30-50 V. The carbon test dust is delivered to the circuit board by a mesh tray vibrated at 60 Hz. The impinging dust creates a short circuit and the resulting current pulse is recorded. We will present results on the dust detection sensitivity and dust removal efficiency of these new detectors in three environments: air, vacuum, and inert gas. \newline $^{2}$ C. Voinier \textit{et al.}, J. Nucl. Mater. 346 (2005) 266-271. \newline $^{3}$ C. Parker \textit{et al.}, PPPL Report, PPPL-4169.   

Spectral Diagnostics of Plasma Confined within a Field Reversed Configuration

A field reversed configuration (FRC) consists of a toroidal plasma current confined by closed magnetic field lines within a cylindrical chamber. The FRC at the University of California Irvine is estimated to operate in a temperature range of 1eV-5eV at a density of approximately 5x10$^{13}$ cm$^{-3}$. An impurity ion survey and temperature measurement are to be performed by analyzing the visible light emitted by the plasma. In order to determine the different species of ions confined within the field, a spectrometer with a resolution of one nanometer will be used. Light from the chamber will be collected using a collimating probe and transmitted to the spectrometer via fiber optic cable. Software will be used to analyze the data, which will then be compared to the NIST Atomic Spectra Database. Expected impurities include oxygen and carbon ions from the plasma injectors. Measurements of the ion temperature will be performed by an observation of the Doppler broadening of the H-alpha emission line. Assuming an ion temperature of 5eV, a resoultion of approximately one angstrom is needed to observe this effect. Due to limitations of the spectrometer, the light from the fiber optic cable will instead be sent through a high resolution spectrometer and imaged using a gated intensifier. By observing the H-alpha line shape the ion temperature can be determined.   

Time-Dependent Modeling of Feedback Control of Resistive Wall Modes in Low-Rotation DIII-D Plasmas

Resistive wall modes (RWMs) are plasma instabilities that occur at high beta in magnetically confined plasmas. In DIII-D, suppressing these instabilities via plasma rotation has allowed up to a factor of 2 increase in beta [1], which is a significant step forward toward realizing an economical fusion reactor. In the absence of plasma rotation, active feedback using magnetic coils is a promising approach to RWM stabilization. The finite bandwidth of realistic electronics poses two limitations on a linear feedback system: 1) limitation on the largest stabilizable growth rate, and 2) limitation on the largest stable feedback gain. Here, time-dependent simulations with a simple, ideal magnetohydrodynamics model show that the largest, linearly stable feedback gain can be exceeded with hardware limitations providing pseudo-stability. The largest stabilizable growth rate depends on the type of feedback sensor and algorithm. Modeling of the DIII-D feedback system is compared to experimental results.\par \vskip6pt \noindent [1] A.M. Garofalo, et al., Phys. Plasmas 9, 1997 (2002).   

Perpendicular Resistivity and Effects of Toroidal Magnetic Field Changes

The occurrence of current-driven plasma instabilities in tokamaks is highly influenced by the toroidal current profile. Recent DIII-D experiments used a time-varying toroidal magnetic field to broaden the current profile. When changing magnetic field is applied, poloidal electric field is induced. The parallel component of the induced electric field drives the desired current along the confining magnetic field, but the effect of the perpendicular component is not well understood. The presented analysis examines possible effects of poloidal electric field on both poloidal currents and radial plasma flow. A simplified model of tokamak plasma having a circular cross section and large aspect ratio uses single-fluid equations, keeping all terms in Ohm’s law. The model results will be compared with data from toroidal magnetic field ramp experiments. The relaxation of possible perpendicular current should depend on the plasma resistivity. If model predictions differ significantly from experiment, other mechanisms influencing perpendicular resistivity in the plasma may be identified.   

Adding Collisional Energy Diffusion to the GS2 Gyrokinetic Code

The GS2 gyrokinetic code\footnote{M. Kotschenreuther, G. Rewoldt, and W.M. Tang, Comp. Phys. Comm. 88, 128 (1995).}$^,$\footnote{W. Dorland, F. Jenko, M. Kotschenreuther, and B.N. Rogers, Phys. Rev. Lett. 85, 5579 (2000).} solves the nonlinear gyrokinetic-Maxwell equations to model the time evolution of the distribution function. Present gyrokinetic continuum codes utilize a Lorentz collision model. We are upgrading the collision operator in GS2 to include energy diffusion and appropriate conserving terms. The distribution function in GS2 is calculated from initial values using a fully implicit scheme. Our implementation of collisional energy diffusion is also fully implicit, and utilizes a parallel processing architecture. The new operator will be tested using simple initial conditions with known solutions. The impact of the new terms on thresholds for TEM and ITG instability modes will then be examined.   

Effects of Magnetic Measurement Uncertainty on Tokamak Equilibrium Reconstruction

Reconstruction of the magnetic topology and current density profile from external magnetic diagnostics is vital to the study of tokamak plasmas. It has long been suspected that external magnetic measurements may contain information about the current density near the edge of a shaped plasma. To better reconstruct this feature, the sensitivity of the reconstruction to uncertainty in magnetic measurements must be determined. This is done by analyzing existing DIII-D data for the effect of measurement uncertainty on the edge current density and the location of the separatrix. The new magnetic uncertainty matrix recently added to EFIT provides a basis for this numerical analysis, and these calculations are compared with simple analytical models. This study begins with examination of measurement error in the tokamak with no plasma, and continues to the more complicated plasma scenario. The relative importance of the various measurements can be determined, with the divertor X-point likely to be the most sensitive to the edge current density.   

Motional Stark effect with laser-induced fluorescence diagnostic development

The motional Stark effect with laser-induced fluorescence (MSE-LIF) diagnostic is being developed to measure the magnetic field pitch angle and magnitude in a variety of plasma conditions; in particular, at low magnetic fields ($<0.5$T). When passing through a magnetic field, the H-alpha emission from a neutral hydrogen beam is split and polarized by the linear Stark effect due to the \textbf{v}$\times $\textbf{B }electric field. The pitch angle can be determined from the polarization and the magnitude from the line splitting. The energy spread of the neutral beam causes line broadening. The neutral beam source has been modified since its original construction in attempts to minimize the energy spread. The neutral beam source has been characterized. A plasma of $\sim 10^{12}$ cm$^{-3}$ density with a diameter over 10 cm is required to collect an observable MSE-LIF signal above $\sim .01$T. To that end, a spiral antenna helicon plasma source has been constructed and characterized. Results will be presented.   

Particle Flux Profiles During ELM Control Experiments

Periodic magnetohydrodynamic instabilities known as edge-localized modes (ELMs) present a significant obstacle in plasma fusion operation in magnetic confinement reactors due to impulsive heating of the divertor target plates and inner chamber walls. At DIII-D, resonant magnetic perturbations at the plasma edge have been used to reduce or eliminate ELMs in high-confinement mode (H-mode) plasmas. A new array of high spatial resolution Langmuir probes capable of handling large heat fluxes have been installed along the divertor target plates at DIII-D to investigate the effect of resonant magnetic perturbations on the divertor plasma. Profiles of the target plate particle fluxes at the outer strikepoint will be examined to characterize the edge plasma response under ELM-suppressed conditions. Experimental data can then be used to validate theoretical predictions of the non-axisymmetric particle flux distribution.   

Evaluation of New Magnetic Perturbation Coils for DIII-D

Experiments show that non-axisymmetric magnetic fields deleteriously affect tokamak plasma confinement, e.g., reducing turbulence-stabilizing velocity shears by braking plasma rotation and causing plasma locked modes that may lead to disruption. Externally applied perturbations can also be useful, e.g., to control edge-localized modes, stabilize resistive wall modes, and make stochastic magnetic layers, among others. DIII-D has two sets of non-axisymmetric coils (C-coils and I-coils) that have been used extensively for these purposes, but their fields penetrate deeply into the plasma, which is not always desirable. Present work investigates possible new conceptual perturbation coils for DIII-D to make stochastic fields in a narrower layer close to the plasma edge with less core penetration, and to broaden the plasma strikepoint width at the divertor target to reduce peak thermal load. The new coils may be on the vacuum-vessel center-post, floor, and ceiling. Magnetic-field Fourier analysis and line-tracing codes are used to evaluate the perturbing fields. Results will be presented.   

Rocket Propulsion Through Multiply Charged Ions From a Mirror Plasma

Plasma propulsion is of interest for space exploration because the high exit velocity of the propellant, compared to that of chemical means, generates a high final spacecraft velocity with reduced propellant mass. This project evaluates the viability of using plasma in a magnetic mirror to produce multiply charged ions as propellant. Electron cyclotron heating of a mirror plasma produces deeply trapped hot electrons which strip heavy ions of electrons. The ambipolar potential accelerates the greatly charged ions to high velocity as they exit the end of the magnetic mirror open to space, generating thrust. We model the distribution of ion charge states to include all relevant atomic processes using the conservation of particle and energy equations in tandem with cross-sections from the ADAS database. The system of equations is then optimized to determine the feasibility of plasma propulsion. The results of this model in a high- density rocket regime are benchmarked against experimental data in low-density mirror plasmas.   

Construction and Operation of a Retarding Field Energy Analyzer for a Helicon Plasma Source

A retarding field energy analyzer (RFEA) suitable for measurements in high density rf plasmas has been constructed and tested in two helicon plasma sources at West Virginia University. Similar RFEA's have been used to measure the acceleration of ions and the plasma potential in the double layers that spontaneously form in low pressure, expanding helicon plasmas [Charles et al., Phys. Plasmas 7, 5232 (2000)]. The stainless steel probe head contains four layers; each consisting of a Mylar insulator, nickel mesh, and a copper support ring. The layers are biased to provide non-target species repulsion, energy selection, secondary suppression, and current collection. In this work, we will describe details of the probe head design, preliminary measurements in argon, helium, and nitrogen plasmas, and comparison of RFEA and laser induced fluorescence measurements of ion energy distributions in argon plasmas.   

Time-Dependent Uniform Magnetic Fields and Non-Adiabatic Heating

It is well known that the magnetic moment of a charged particle moving in a magnetic field is an adiabatic invariant. As such, periodic changes in the magnetic field intensity, which are slow compared to the particle's gyrofrequency, produce no net change in the particle's kinetic energy. If the magnetic field varies rapidly, however, the magnetic moment is no longer conserved, and it becomes possible to affect the particle's kinetic energy. This possibility is investigated numerically and analytically for several configurations of periodically varying, solenoidal magnetic field. General effects on the particle's trajectory are explored, with particular attention paid to the response of a particle's kinetic energy to various initial conditions and magnetic field waveforms. The resulting analysis and further optimization could provide useful insights into a method of non-adiabatically heating the plasma in a nuclear fusion reactor.   

Numerical modeling of the m = 1 diocotron mode in toroidal electron plasmas

A new toroidal electron plasma apparatus is coming online at Lawrence University: the Lawrence Nonneutral Torus II (LNT II). The primary means of diagnosing the plasma will be by way of measurements of image charge induced on sections of a gold-plated electrode. Numerical modeling methods are employed to solve Poisson's equation in toroidal geometry and determine image charge on the wall sections. The calculated electric field at the center of the plasma is used to determine the E x B drift velocity and consequently the trajectory of the plasma. We present numerical calculations of the signals arising from the m = 1 diocotron mode in toroidal geometry. The numerical model will be used to extract properties of the plasma from experimental data obtained in the LNT II device. In particular, the frequency of the m = 1 diocotron mode determines the total charge in the plasma while the mode amplitude and character yield information about the m = 1 motion of the plasma.   

Analysis of one-dimensional flows in a dc glow discharge dusty plasma

Dusty plasmas are four component plasmas consisting of ions, electrons, neutrals, and charged microparticles. The charged microparticles (i.e., the dust) are suspended and confined by potential wells in the plasma. This experiment utilizes a new “segmented” electrode that is used to control the plasma. The electrode is separated into two section: a “well” section that is used to form a stable cloud and a “channel” section which is used to create a linear path for dust flows. To actively control the dust motion, the two sides can be biased independently. The electrode has been used inside the Auburn Dusty Plasma Experiment (DPX) to investigate one-dimensional flows in a dusty plasma. Two-dimensional particle image velocimetry (PIV) techniques are used to illuminate the particles and measure their transport. By analyzing these flows along the direction of their motion, the motion of the dust is characterized. Results of this analysis will be presented.   

LIF-MSE Diagnostics

The motional Stark effect (MSE) is a standard technique for measuring magnetic field pitch angle in plasma experiments. The pitch angle is found with a beam of neutral hydrogen atoms which when traveling through a magnetic field perceive a Lorentz electric field in their own frame. However, while MSE is extremely effective for fields $>$ 1 T, it can be difficult to resolve weaker fields as a consequence of line broadening from collection optics. To counter line broadening, a method using Laser Induced Fluorescence (LIF) to excite specific atomic transitions in the hydrogen beam has been proposed. The purpose of this project has been to implement a data acquisition and control system for the diagnostic neutral beam and Spiral Antenna Helicon High Intensity Background (SAHHIB) experiment, which is currently being developed as a plasma test bed for LIF-MSE. The resulting program logs a variety of measurements including those necessary for calculating the expected LIF-MSE signal. Should the MSE-LIF device on SAHIB prove successful, it will be employed at the National Spherical Torus experiment (NSTX).   

Internal Pressure Measurements in Princeton Magnetorotational Instability Experiment

The high rate of accretion which is observed in accretion disks must be accompanied by some efficient means of transferring angular momentum radially outward. One candidate mechanism for the momentum transfer is Magnetorotational Instability (MRI). The MRI experiment at the Princeton Plasma Physics Lab is attempting to study the mechanism experimentally. In the experiment, liquid gallium or water is used in Couette flows between two cylinders to simulate the conditions in the disks. Understanding the dynamics of the flow requires internal measurement of important physical quantities. One such diagnostic is to measure the pressure at various points. A thin probe, designed to have as little effect on the gallium flow as possible, was mounted with three small pressure sensors. By comparing the voltage across two wires, one with a variable resistance determined by the pressure, the sensors can detect pressures up to several atmospheres, and are precise to a tenth of an atmosphere. The probe was calibrated using simple air- pressure tests. Initial measurements will be obtained in gallium or water flows. Results will be reported if available.   

Calibrating Radiographic Images from Omega Experiments

Astrophysical phenomena can be studied by creating well-scaled experiments simulating Rayleigh-Taylor instabilities using the Omega Laser. X-ray radiography is used to obtain images of the shock and interface that can be calibrated and analyzed. Targets include a gold grid with fiducial cutouts for spatial and magnification calibration. Prior to the experiment the grid location is measured, which allows absolute calibration of radiographic images. Then using a reference point, e.g. a grid corner or fiducial, the image is rotated and a coordinate system is added. Measurements are taken of the interface position, and shock thickness and position, from which speeds and growth rates are calculated. Calibration can be made more accurate by adding multiple reference point inputs and measurement scale alteration. The accuracy of data analysis depends highly on the reliability of calibration of the x-ray radiograph. Results of these improvements will be shown. This research was sponsored by the National Nuclear Security Administration under the Stewardship Science Academic Alliances program through DOE Research Grants DE-FG52-03NA00064, DE-FG53-2005-NA26014, and other grants and contracts.   

Plans and Progress of Electrode Biased Plasmas in the Magnetic Reconnection Experiment

Compact Toroid (CT) plasmas such as Spheromaks are known to exhibit a global instability known as the tilt mode, where the magnetic moment of the CT tilts to align itself with the external magnetic field, as well as other non-rigid body instabilities. Possible tilt stabilizing mechanisms for these instabilities include external field shaping, nearby passive stabilizers, and plasma rotation. The proposed research focuses on reducing the growth of the tilt instability by introducing toroidal rotation in spheromaks formed in MRX. Rotation is introduced by the use of interior and exterior electrodes; the result is a J$_{bias}$ x B$_{internal}$ torque on the CT plasma which in turn leads to toroidal rotation of the CT plasma. In order to power the bias electrode a 450 V 8800 $\mu $F capacitor bank capable of delivering up to 450 amperes was constructed along with the required control and triggering circuitry. Solid state switches allow for fast turn on and turn off times of J$_{bias}$. The bias current and the voltage drop across the electrodes are measured using a current shunt and voltage divider respectively, and the resulting flow is measured with a Mach probe. Internal arrays of magnetic probes and optical diagnostics will be used to parameterize the performance of the CT plasma during bias. Construction and testing of all necessary components and diagnostics is complete; preliminary results will be presented.   

Removal of Deposits from Diagnostic Mirrors employing an Nd:YAG Laser

A noninvasive laser ablation process for the removal of deposited carbon and beryllium particles on diagnostic mirrors is investigated in support of ITER and other similar fusion devices. The need to maintain in-vessel mirrors in a clean and reflective condition is critical when such surfaces are required to reflect plasma light to appropriate diagnostic systems. A configuration including a q-switched 1064nm Nd:YAG laser coupled to a quartz fiber optic, laser scanning system, and lens will be employed to determine optimal conditions for the ablation of deposited particles, while mitigating physical effects on the mirror surface. The effectiveness of this in situ cleaning method will be evaluated while varying such parameters as the laser focus, scanning speed, pulse frequency, and surface temperature.   

Formation, transport and effects of UV light on a fluorescent dust cloud.

Typically, the behavior of laboratory dusty plasmas is studied by laser scattering techniques, which give a 2D slice of the dust cloud, or by the use of scanning techniques through the cloud's volume. A new diagnostic technique has been devised to study 3D behavior and cloud formation with a single charge-coupled device (CCD) camera. A fluorescent organic dust is used to create a dust cloud in an argon DC glow discharge plasma. By using a 100W ultra-violet (UV) light, the fluorescent particles can be clearly seen during and after cloud formation. Rapid upward motion of particles (Vmax=100mm/s) is observed during formation, followed by an expansion of the cloud (Vmax=30mm/s) and transport along the boundary of the plasma. After the dust cloud has formed, the UV light causes rotation of the edge of the cloud ($\approx $ 3mm/s), while particles in the center of the cloud remain stable. Displacements of several millimeters up and towards the UV light have also been recorded by modulating the UV light. Results from observations and probe measurements will be presented.   

Analytical model for charge and current neutralization of an ion beam pulse propagating in a plasma in a solenoidal magnetic field

An analytical model is developed to describe the self-magnetic field of a finite-length ion beam pulse propagating in a cold background plasma in a solenoidal magnetic field. Previously, we developed an analytical model to describe the current neutralization of a beam pulse propagating in a background plasma. In the presence of an applied magnetic field, however, the system of equations describing the self-magnetic field becomes much more complicated. Importantly, the slice approximation fails, i.e., the current profile in different transversal cross sections of the beam pulse cannot be treated independently. Nevertheless, the two-dimensional problem can be solved analytically in Fourier space. These results shed light on the effects of the applied magnetic field on the degree of charge and current neutralization and on the complex structure of electron density perturbations generated by the beam pulse. For a strong enough applied magnetic field, two poles emerge in Fourier-space. These poles are an indication that whistler and low-hybrid waves have been excited by the beam pulse.   

Preliminary analysis of coherent modes in NSTX using the motional Stark effect (MSE) diagnostic

Magnetic and density perturbations in NSTX are analyzed using fast digitized data from the motional Stark effect diagnostic. Power spectra created from the fast digitized data are investigated over multiple sightlines for the presence of coherent modes. Frequency, amplitude, and phase of these modes are tracked as a function of time to characterize the oscillating component of the pitch angle and/or the intensity of the signal. Example cases of pitch angle oscillations and density fluctuations will be shown along with preliminary results where both may be present.   

An Ultraviolet Survey of the Compact Toroid Injection Experiment

Light is emitted during the formation and acceleration of a compact toroid (CT) plasma in the Compact Toroid Injection Experiment (CTIX). A low-resolution (35nm) survey in the 150 to 500 nm range of the ultraviolet spectrum of this light will be taken using a 1-meter Acton spectrometer using a 300 line/mm grating, on loan from the Electron-Beam Ion-Trap group at LLNL, with a 16-channel linear photodiode array. This survey will allow bright regions of the emitted spectrum to be identified for various diagnostic purposes. At moderate spectrometer resolution, line intensities may be used to infer plasma impurity content, while line ratios may be used to infer plasma temperatures. At high resolution, axial plasma velocity can be determined using Doppler shifts, while plasma temperature can be determined using Doppler broadening. Higher resolution experiments will be completed if time allows or continued by a future student.   

University of Michigan Target Fabrication Facility for High Energy Density Physics Experiments

An overview of University of Michigan's target fabrication facility will be presented. Our group constructs targets that are well scaled to astrophysical phenomena to be used at the Omega Laser Facility. These targets are used in experiments studying the Rayleigh-Taylor instability, radiatively collapsing shocks and Thomson scattering. This facility is constantly working to improve our designs and methodologies so that a wider variety of precision targets can be built for increasingly complex High Energy Physics experiments. This research was sponsored by the National Nuclear Security Administration under the Stewardship Science Academic Alliance through DOE Grant DE-FG52-03NA00064, and DE FG53 2005 NA26014.   

Flow Measurements on Single and Merging Spheromaks at SSX

We present new experimental results concerning flow dynamics in single spheromaks and counter-helicity spheromak merging at the Swarthmore Spheromak Experiment (SSX). Local flow is measured with a Mach probe, consisting of six directional ion collectors in a boron nitride sheath. Calibration made with the assistance of an edge array of magnetic probes provides a calibration constant k of approximately 1.6 for the Mach probe. This value is consistent with other values determined both theoretically and experimentally for Mach probes in the unmagnetized realm. In the single spheromak we observe initial axial flows of twice the sound speed followed by a rapid reversal of flow at the center and edge of the chamber. Later azimuthal flows could indicate a flipping of the plasma due to formation instabilities. During counter-helicity merging, we observe the expected azimuthal flow on average at a radius outside the reconnection region, but fail to obtain a clear direction of flow at the inner radius. Results from a larger Mach probe (magnetized realm) will be presented if available. A two-dimensional magnetic probe array with high spatial resolution (2.3 mm) is being constructed and will be used to analyze magnetic fields near the reconnection plane during counter-helicity merging.   

High Time Resolution Measurements of Electron Temperature in a Laboratory Plasma

We present 1 $\mu $s time resolution calculations of the electron temperature and density of the Swarthmore Spheromak Experiment (SSX) plasma during magnetic reconnection. The non-LTE excitation kinematics code PrismSPECT is used to simulate emission spectra for a variety of plasma conditions. These model spectra are compared to experimental data from two main diagnostics: a vacuum ultraviolet (VUV) monochromator and a low-resolution soft x-ray detector (SXR). Analysis of simulation results reveals that the plasma quickly ($<$ 10 $\mu $s) approaches coronal equilibrium conditions in the density regime of interest; as a result we can safely use steady-state simulations for comparisons with the data. Measured UV line strength ratios depend primarily on the electron temperature in the plasma, so we are able to use observations of carbon impurity emission lines in conjunction with SXR measurements as a temperature diagnostic. In particular, the CIII 97.7 nm / CIV 155 nm line intensity ratio proves to be extremely useful, while the CIII 229.7 nm line appears anomalously strong in experimental measurements.   

Initial Hydrodynamic Results for a Free-Surface Liquid Gallium Channel Flow

Free-surface MHD shear flows have application to both astrophysics and fusion plasmas, but very little relevant experimental research has been done on them. To measure and observe physics relevant to these topics, a channel has been fabricated for the free surface flow of magnetized liquid gallium. This channel is 16cm wide, 2cm deep, and 70cm long. As a benchmark, initial water data was taken using Laser Doppler Velocimetry (LDV). Average flow profiles and fluctuations were measured as a function of Reynolds number.   

Calculation of Particle Bounce and Transit Times on General Geometry Flux Surfaces

Stabilizing the resistive wall mode (RWM) is important to maximize the plasma pressure in tokamaks and spherical tori. Rotational stabilization of the RWM is predicted from kinetic damping theory to depend strongly on particle bounce and transit times. [1] Previous calculations of bounce and transit times have assumed high aspect ratio and circular flux surfaces, approximations unsuitable for the National Spherical Torus Experiment (NSTX). Analytic solutions for the bounce and transit times were derived as functions of particle energy and magnetic moment for low aspect ratio and elliptical flux surfaces. The solutions were found to scale as the elongation at low aspect ratio, and as the square root of the elongation at high aspect ratio. For typical values of the parameters the bounce and transit times were found to differ from the high aspect ratio, circular results by as much as 250-300{\%}. Numeric solutions were also computed using Mathematica and IDL and are being compared with the analytic forms. Preliminary results show good agreement between the analytic and numeric solutions. Full analytic and numeric solutions will ultimately be compared against experimental data from DIII-D and NSTX. Work supported by the U.S. Department of Energy. [1] A. Bondeson and M.S. Chu, Phys. Plasmas \textbf{3}, 8 (1996)   

Evaluating parallel algorithms in Extender, a stellerator field evaluator code

The parallel code ``Extender'', originally developed by Michael Drevlak at IPP-Garching, is used to evaluate the magnetic field inside a stellerator at positions between the surface of the plasma and the first wall. This calculation has a number of applications in the design of NCSX. These include positioning the diagnostics and generating a database of information for different possible plasma equilibria. Two parallel algorithms were examined: a master-slave algorithm and an equal-distribution algorithm. The master-slave algorithm adds inter-process communication overhead, but under certain conditions, it uses the available processors more efficiently. The equal-distribution algorithm minimizes communication, but its efficiency relies on calculations taking a consistent amount of time to complete. In ``Extender'', some calculations take longer than others to finish. When these calculations take significant time compared to the time expended in one MPI communication call, as they generally do in ``Extender'', the master-slave algorithm performs reasonably well. Even in these cases, the equal-distribution approach does run somewhat faster.   

Energy Deposition before Voltage Collapse in Cylindrical Wire Arrays on COBRA

The COBRA pulsed power generator at Cornell produces 1MA pulses with 100 nsec rise times and has been used to implode cylindrical wire arrays with 8-16 wires.. Because of the design of this machine it has been possible to install an inductive voltage monitor to measure the voltage applied to the load. Upon close examination of this signal, early in the pulse, it is possible to see a precipitous drop in the voltage characteristic of the classic collapse that has been observed in single wire initiation experiments. The resistive component of this voltage signal can be extracted and coupled with load current to estimate the energy deposited in the array wires before the current is diverted from the wire cores to the coronal plasma. Results will be presented for cylindrical arrays with 8 to 16 Tungsten or Aluminum wires of several different diameters. This research was supported by DOE grant DE-FG03-98ER54496, by Sandia National Laboratories contract AO258, and by the NNSA Stockpile Stewardship Academic Alliances program under DOE Cooperative Agreement DE-FC03-02NA00057.   

Expansion of Single Wires with Enlarged Diameters at the Electrical Contacts.

The energies deposited before voltage collapse in single wires have been measured comparing straight, uniform diameter wires with wires that have enlarged diameters at the electrode contacts. The single wires were driven by our XP-Pulser that produced 5 kA pulses with risetimes of 10$^{4}$ A/s and can drive single wires through the voltage collapse. Tungsten wires with an initial diameter of 50 $\mu $m were etched down to 25 $\mu $m over a 1.9 cm length. Diffraction techniques were used to measure the diameter of the etched wires along their length and to center the 25 $\mu $m section between the electrodes that were placed 2 cm apart. The energy deposition in these etched wires were compared to that deposited in 50 $\mu $m wires that were etched to 25 $\mu $m over their entire length and wires that started out with a 25 mm diameter. In all cases these wires passed through 0.013 inch holes in the electrodes, large compared to the diameters of the wires. In general the results showed that more energy was deposited in the wires with large diameters at the electrode ends than in the uniform diameter wires. This research was supported by DOE grant DE-FG03-98ER54496, by Sandia National Laboratories contract AO258, and by the NNSA Stockpile Stewardship Academic Alliances program under DOE Cooperative Agreement DE-FC03-02NA00057.   

Characterization of the plasma jet from a cylindrical Hall thruster

The principle of operation of the cylindrical Hall thruster is in many ways similar to that of a conventional coaxial Hall thruster, i.e., it is based on a closed ExB electron drift in a quasineutral plasma with magnetized electrons. The cylindrical configuration offers a novel approach for scaling Hall thrusters to low power regimes, desirable for future microsatellite applications. Owing to the complex magnetic configuration of the cylindrical thruster with a strong axial component of the magnetic field, one might expect a large beam divergence and high energy ions escaping the thruster at large angles with respect to the thruster axis. In this study we use a two grid retarding potential analyzer to measure the angular ion energy distribution of the plasma plume for a miniaturized cylindrical Hall thruster. Preliminary results indicate the presence of a large population of energetic ions at large angles. It is also shown that the fraction of these ions can be substantially reduced for an optimized thruster configuration [A. Smirnov, invited speaker at this conference].   

Numerical Stability Analysis of Linear Wave Propagation in Extended MHD Modeling

Extended MHD (2-fluid) modeling of fusion plasmas using a split semi-implicit time-advance based on a particular high-order finite element with C$^{1}$ continuity has been shown to offer significant advantages in efficiency and accuracy[1,2]. However, the method requires the introduction of several viscosity and hyper-viscosity coefficients to provide robust numerical stability. As a code-validation exercise, we report on a systematic study of the simulation of wave propagation in the linear regime. We initialize the simulation in a stable linear eigenmode of the extended MHD equations and follow the evolution to measure the numerical dispersion relation for the 3 sets of MHD waves. We present results showing how the stability, dispersion and dissipation depend on grid size, time step, and the magnitude of the viscosity and hyper-viscosity coefficients. These linear perturbation tests act as useful benchmarks and guides for numerical stability for nonlinear simulations. [1] S. Jardin, J. Comput. Phys. 200 (2004) 133 [2] S. Jardin and J. Breslau, Phys. Plasmas 12, 056101 (2005)   

Investigation of Coaxial Multipactor in the Presence of a Magnetic Field

In Alcator C-Mod, ion cyclotron range of frequency heating is the primary auxiliary heating system. One of the keys to successful ICRF heating is the antenna performance, and a number of issues can limit the antenna performance including poor voltage and power handling. On C-Mod, high density discharges can yield neutral pressures at which antenna voltage handling is severely decreased (T. Graves et al., J. Vac. Science Tech. A 24 512, 2006). This neutral pressure limit may be related to phenomena associated with antenna ELM (edge localized mode) interactions. We investigate the influence of the magnetic field on the electron distributions and trajectories for the two primary geometries found in the RF transmission system, coaxial and stripline, via Monte Carlo simulation. We have also expanded the capability of the coaxial multipactor experiment with magnetic field coils for experimental confirmation of the simulation data. Results from the simulations and initial experimental results will be presented.   

Simulations of Standard and X-divertor Edge Plasmas for Reactors

UEDGE simulations confirm the expected reduction of heat flux by the X-divertor magnetic geometry for partially detached cases. ITER configurations with both the standard divertor and an X-divertor with reactor power levels are compared and despite the complications introduced by the atomic physics, the naive expectation that the thermal flux capability increases with the flux expansion parameter was confirmed. Possible enhancement of heat flux limits of standard divertor geometries using impurities levels above typical ITER values is also considered. The power handling capability is found to saturate at impurity levels above ITER so that the power handling capacity of partially detached cases is not substantially improved. One dimensional models to capture the basic physics of this saturation are also presented.   

Magnetic equilibria for X-Diverted plasmas

The X-divertor has been proposed to solve heat exhaust problems for reactors beyond ITER. By generating an extra X-point downstream from the main X-point, the X-divertor greatly expands magnetic flux at the divertor plates. As a result, the heat is distributed over a larger area and the line length is greatly increased. We have developed coil sets for X-diverted magnetic equilibria for many devices (NSTX, PEGASUS, EAST, HL-2A, CREST, and a CTF). These demonstrate that the XD configuration can be created for highly shaped plasmas using moderate coil currents. For reactors, all coils can be placed behind 1 m of shielding. We have also shown that XD configurations are robust to modest plasma perturbations and VDEs; this is in contrast to the sensitivity of highly tilted divertor plates.   

Examination of radiating mantles for ITER and fusion reactors

Simple calculations show that pure coronal radiation inside the separatrix is not an adequate solution for the critical heat exhaust problem of burning plasmas. However the idea of using a radiating mantle to solve the problem gets a boost from current experiments which show that the radiating capacity of a mantle is vastly increased by mechanisms which may be collectively called non-coronal. We have investigated if these enhancing mechanisms scale to two cases of future interest: ITER (steady state ITB scenarios where the ITER divertor appears inadequate) and the higher power fusion reactor. Semi-analytic arguments and preliminary calculations show that even the inclusion of non-coronal effects due to neutral D,T atoms as well as impurity diffusion does not allow a working radiating mantle that will solve the reactor heat exhaust problem. Scaling from the current experiments to future experiments fails, primarily because of the much longer confinement times and higher temperatures in ITER and reactor.   

Modeling of Dust Dynamics in Tokamaks

The experimentally proved presence of dust in fusion devices is a recognized issue that may have large impact on tokamak operation and can present safety threat for fusion energy. In this work, transport and distribution of dust particles in tokamaks are studied using computer simulations with the dust transport DUSTT code. Recent developments of the DUSTT code are reported. The improved model accounts for thermionic and secondary electron emission; heat fluxes on the dust are refined using the Orbital Motion Limited theory; corrections for small body thermal radiation and dust-impurity interaction are also introduced. The effect of these processes on dust dynamics is evaluated. Reproducing of experimentally obtained dust tracks in NSTX tokamak allows tuning and verification of the code. Statistical averaging over ensemble of dust trajectories is used to obtain volume distributions of dust characteristics. It is predicted that transport of dust accompanied with ablation can cause significantly enhanced penetration of impurities toward the core in comparison with impurity ion transport. As shown, collisions of the dust particles with walls are critical for dust transport due to loss of kinetic energy and mass. It is shown that dust can experience net mass deposition in relatively cold contaminated plasma regions.   

1D study of thermal instability caused by plasma-wall interactions

Based on simple 0-D model in Ref. [1] it was shown both analytically and numerically that the interactions of plasma with first wall saturated with hydrogen can cause thermal instability resulting in massive desorption of gas from the wall. In a tokamak it can lead to the formation of MARFE, transition to detachment, or even disruption. The physics of this instability is related to the positive loop associated with an increase in neutral desorbing rate with increasing wall temperature and the further increase of wall temperature caused by an increase of heat flux to the wall caused by charge exchange and radiation loss of plasma energy. In the paper, we refine and extend the model from Ref. [1] by using 1D approximation for plasma particle and energy transport, neutral hydrogen transport in plasma, wall energy balance, and hydrogen desorption processes. We analyze both stability condition and growth rate of thermal instability and compare our results with both 0D model from Ref. [1] and available experimental data. We also discuss possible implications of such thermal instability for steady-state operation conditions in ITER. [1] S. I. Krasheninnikov and T. K. Soboleva, ``Thermal instability caused by plasma-wall coupling'', to appear in Phys. Plasmas 2006.   

In-Situ Cavity Ringdown Spectroscopy of Methane Produced by Chemical Erosion of Carbon Surfaces by Deuterium Ions

Carbon plasma-facing surfaces in tokamaks are subject to chemical erosion due to hydrocarbon (e.g.CD$_{4}$,$_{ }$C$_{2}$D$_{6})$ formation when deuterium ions and atoms are present. Understanding the formation, transport, breakup, and redeposition of these hydrocarbons is important for predicting the amount of tritium, which will become stored in the walls of ITER during operation. Traditionally, CD$_{4}$ release from carbon surfaces is estimated by using passive spectroscopy of CD-band emission. Calibration of these measurements requires either complex modeling of the CD$_{4}$ to CD breakup chain in the plasma or injection of a calibrated flow of CD$_{4}$ from the material surface. Ideally, one would like a direct, non-perturbing measurement of the methane production at the plasma-facing surface under a variety of plasma conditions. We are developing a technique that accomplishes this by using near-IR cavity ringdown spectroscopy: a high-Q cavity whose optical path includes the near-surface region of the carbon tile allows for in-situ monitoring of CD$_{4}$ production in the PISCES-A plasma device. By simultaneously measuring the absorption of IR radiation by CD$_{4}$ molecules and emission of CD-band photons, we can determine the range of plasma conditions where CD emission provides an accurate measure of CD$_{4}$ release. This work supported by grant DE-FG03-95ER-54301 from the US DoE.   

Carbon Atom and Cluster Angular Sputtering Distribution under Low Energy Noble Gas Bombardment

Energetic particle bombardment of a surface can cause sputtering of both atoms and clusters of atoms. Carbon atom and cluster (C$_{2}$ and C$_{3})$ angular sputtering distributions are measured during different noble gases (Xe, Kr, Ar, Ne and He) bombardment from a plasma, with incident ion energy $E_{i}$ ranging between 75 - 225 eV and having normal incidence. A quadrupole mass spectrometer (QMS) is used to detect the fraction of sputtered neutrals that is ionized in the plasma, and to obtain the angular distribution by changing the angle between the target and the QMS aperture. We observe a clear decrease of the cluster (C$_{2}$ and C$_{3})$ to atom sputtering ratio as the incident ion mass decreases. For the higher mass bombarding gases, Xe and Kr, the carbon atom signal is under the detection limit while the C$_{2}$ and C$_{3}$ cluster signals are detectable, exhibiting an ``under-cosine'' angular sputtering distribution with a maximum at around 60\r{ }. For the lower mass bombarding gases, Ar, Ne and He, we observe an ``under-cosine'' angular distribution of the carbon atoms, with the maximum at around 60-75\r{ }, 60\r{ } and 45\r{ } respectively, and no detectable carbon cluster signal. The Monte Carlo TRIDYN code is used to compare these results with simulations and to investigate possible cluster emission mechanisms.   

Parametric study of shear flow in a linear magnetically confined plasma device

Previous experimental studies carried out in the Controlled Shear Decorrelation Experiment (CSDX) plasma device demonstrated the existence of an azimuthally symmetric radially sheared plasma fluid flow (i.e., a zonal flow). This flow was shown to be sustained by the Reynolds stress against viscous damping in an Argon plasma with 3mTorr gas pressure and 1000 Gauss magnetic field. Previous studies have also shown that the magnetic field is an effective parameter in controlling the transition to plasma turbulence. A study of the evolution of zonal flow shearing rate for different plasma parameters, such as gas pressure and magnetic field, is carried out, with the specific aim of assessing whether the shear flow remains in self-consistent force balance with the Reynolds stress and collisional damping. In this work, a fast-framing imaging camera is used to infer time-average velocity field of plasma fluctuations, and a multi-tip Langmuir probe for measuring the Reynolds stress.   

Direct Simulation Monte Carlo Study of Neutral and Ion Transport in an Inductively Coupled Plasma

A hybrid type direct simulation Monte Carlo (DSMC) method was applied to a one- dimensional electrostatic plasma in Argon/Nitrogen mixtures to simulate neutral and ion transport in a radial symmetric inductively coupled plasma. The ambi-polar electrostatic field obtained from the measured plasma density profile was imposed in the simulation, and electrons were treated as background particles with measured electron density and temperature profiles. Neutral gas depletion observed in both the experiment and simulation is in excellent agreement and indicates that gas heating and the required pressure balance is responsible. The gas heating is mainly due to ion-neutral collisions with the ions accelerated by the ambi-polar electric field and neutral collisions with Frank-Condon dissociated atoms.   

Transient heating experiments on C in a Be seeded plasma in PISCES B

A transient heating system has been installed on the PISCES-B experimental system. This heating system uses a pulsed positive bias to draw electrons from the plasma and transiently heat the surface of the plasma-exposed sample ohmically. This heating can be used to investigate the effects of transient heating in plasma facing components expected during ELMs in ITER-like devices. An experimental investigation of the effects of transient heating on Be films on C substrates in deuterium plasmas has been conducted in PISCES-B. It has been shown previously that Be film growth on C can form carbide layers that reduce the chemical erosion of C during deuterium ion bombardment. Results from transient heating on the chemical erosion and on deuterium retention in C targets will be presented. A scaling expression for chemical erosion suppression due to Be$_{2}$C formation developed previously will be extended to include transients with varying peak surface temperature and duty cycle of the thermal transients.   

Experiments to test for MAR in detaching plasmas in the PISCES-A divertor simulator

Normally, Electron-Ion Recombination (EIR) is considered the dominant volume recombination process in detaching divertors. More recently, Molecular-Activated Recombination (MAR) was suggested as a possible volume recombination channel [Pigarov, Phys. Scripta]. Indirect experimental evidence for MAR has been seen in previous experiments [NAGDIS PRL]. We describe experiments which attempt to more conclusively establish the presence of MAR in detaching divertors. The EIR rate is obtained in PISCES-A He plasmas by absolutely calibrating high n He-I line emission associated with EIR in the cool ($<$1 eV) halo region of the plasma column. A small amount of H$_{2}$ gas is injected into this plasma, resulting in a collapse of EIR emission in the halo region. Concurrent with this collapse, an increase in the H$\alpha $/H$\gamma $ ratio is observed in the halo region and suggests the presence of MAR, which produces H neutrals in low excited states in contrast to EIR. Additionally, preliminary particle conservation measurements used to estimate the magnitude of the recombination sink in the plasma edge will be presented.   

Measured effect of radiation trapping on He I line intensity ratio technique used for estimating electron density and temperature

He I line intensity ratios are commonly used to estimate electron density, $n_{e}$, and temperature, $T_{e}$, in helium plasmas. Previously, UV radiation trapping has been invoked to obtain better agreement on $n_{e}$ and $T_{e}$ with other diagnostics. In the linear divertor simulator PISCES-A we have experimentally confirmed radiation trapping of the He I UV resonance transition (1$^{1}$S - 3$^{1}$P: 53.7 nm) from the radial profile of He I visible line emission (2$^{1}$S - 3$^{1}$P: 501.6 nm), which has the same upper state as 53.7 nm; and also from the radial profile of plasma radiated power measured with an AXUV photodiode array. The radiation trapping effect has been implemented into a collisional-radiative code by using the optical escape factor method. $n_{e}$ and $T_{e}$ derived from He I line intensity ratios (667.8nm/728.1nm and 728.1nm/706.5nm) calculated with the modified code agree well with those from probe measurement at neutral pressure of above a few mTorr. The discrepancy at low pressure may be due to the presence of nonthermal electrons.   

Kinetic simulation of Macroscopic Physics in the Pedestal/Scrape-off region

Understanding and predicting the pedestal/scrape-off plasma behavior from first principles kinetic physics is one of the top priority issues for ITER. Previous studies modeled the edge plasma with fluid plasma models using phenomenological diffusion coefficients. The edge plasma distribution functions are likely to be non-Maxwellian with many important physics to be determined by the kinetic ion orbit dynamics. A self- consistent inclusion of the neutral particle dynamics is another essential element. We have obtained from the edge PIC code XGC-1, for the first time, comprehensive kinetic macroscopic solutions in the pedestal/scrape-off region, after averaging over the turbulent fluctuations. As indicated by many experiments, the simulation shows negative electrostatic potential in the H-mode layer where a strong plasma pedestal exists, and a positive potential in the scrape-off plasma. The simulation also shows formation of the co-current flow in the scrape-off layer. The flow in a steep pedestal shoulder region is always in the co-current direction, indicating a co-rotation source for the core plasma. The parallel flow in the vicinity of the separatrix appears sensitive to the neutral density. Another new physics found from XGC-1 is the existence of the global ExB convective flow pattern in the scrape-off region, which may have an important implication to the divertor design. \newline *SciDAC Fusion Simulation Prototype Center for Plasma Edge Simulation   

Simulations of 4D edge transport and dynamics using the TEMPEST gyro-kinetic code

Simulation results are presented for tokamak edge plasmas with a focus on the 4D (2r,2v) option of the TEMPEST continuum gyro-kinetic code. A detailed description of a variety of kinetic simulations is reported, including neoclassical radial transport from Coulomb collisions, electric field generation, dynamic response to perturbations by geodesic acoustic modes, and parallel transport on open magnetic-field lines. Comparison is made between the characteristics of the plasma solutions on closed and open magnetic-field line regions separated by a magnetic separatrix, and simple physical models are used to qualitatively explain the differences observed in mean flow and electric-field generation. The status of extending the simulations to 5D turbulence will be summarized. The code structure used in this ongoing project is also briefly described, together with future plans.   

Numerical Methods for Nonlinear Fokker-Planck Collision Operator in TEMPEST

Early implementations of Fokker-Planck collision operator and moment computations in TEMPEST used low order polynomial interpolation schemes to reuse conservative operators developed for speed/pitch-angle ($v$, $\theta$) coordinates. When this approach proved to be too inaccurate we developed an alternative higher order interpolation scheme for the Rosenbluth potentials and a high order finite volume method in TEMPEST ($\epsilon, \mu$) coordinates. The collision operator is thus generated by using the expansion technique in ($v$, $\theta$) coordinates for the diffusion coefficients only, and then the fluxes for the conservative differencing are computed directly in the TEMPEST ($\epsilon, \mu$) coordinates. Combined with a cut-cell treatment at the turning-point boundary, this new approach is shown to have much better accuracy and conservation properties.   

Numerical Solution of the Gyrokinetic Poisson Equation in TEMPEST

The gyrokinetic Poisson (GKP) model in the TEMPEST continuum gyrokinetic edge plasma code yields the electrostatic potential due to the charge density of electrons and an arbitrary number of ion species including the effects of gyroaveraging in the limit $k_{\perp} \rho \ll 1$. The TEMPEST equations are integrated as a differential algebraic system involving a nonlinear system solve via Newton-Krylov iteration. The GKP preconditioner block is inverted using a multigrid preconditioned conjugate gradient (CG) algorithm. Electrons are treated as kinetic or adiabatic. The Boltzmann relation in the adiabatic option employs flux surface averaging to maintain neutrality within field lines and is solved self-consistently with the GKP equation. A decomposition procedure circumvents the near singularity of the GKP Jacobian block that otherwise degrades CG convergence.   

Transport Simulations for the Scrape-off Layer and Divertor Plasmas in KSTAR Tokamak

Two-dimensional simulation results are presented for the transport of plasma and impurities in the edge scrape-off layer region of KSTAR discharges using B2.5 code. The effect of the injected impurities on divertor power dispersal and global confinement is predicted for the radiative divertor experiments which are planed for effective removal of heating power in KSTAR. The characteristic two dimensional patterns of heat and particle flows driven by cross-field drifts are also discussed in conjunction with in-out asymmetry of divertor plasmas and power loading to the first wall.   

Two-dimensional Simulation on Self-consistent Transports of Plasma, Neutrals, and Carbon Impurities in a Divertor Region of the KSTAR Tokamak

A two-dimensional numerical modeling has been carried out to analyze the transport phenomena of plasma, neutrals and intrinsic carbon impurities in a divertor domain of the Korea Superconducting Advanced Research (KSTAR) tokamak. In this numerical simulation, spatial distributions of these divertor species are calculated in a self-consistent way by coupling the respective transport code modules iteratively. Transports of the plasma and carbon impurities are computed based on the two- dimensional Braginskii’s multi-fluid formulation, while the neutral distributions are obtained from the transmission and escape probability (TEP) method by adapting the GTNEUT$^{1}$ code. The TEP method has accuracy comparable to a Monte Carlo method with fast computing time and flexibility of coupling with plasma fluid codes. As results of the simulation, time evolutions of edge plasma characteristics such as density and temperature are presented for the baseline operation scenario of the KSTAR tokamak. The calculated results show that the excessive heat flux on the divertor plate is likely to result in the severe target erosion even though the neutrals and impurities play a positive role in reducing the heat flux in this divertor region, as reported previously in many other tokamak devices. \newline [1] J. Mandrekas, Comput. Phys. Comm., 161, 36 (2004)   

Simulations of Edge Transport Barrier in a Tokamak using B2 and ELITE

The Edge Transport Barrier(ETB) is one of the critical issues in Tokamak due to its strong impact on the global confinement. The dependence of the width and height of ETB is simulated using the combined model of B2 transport code and ELITE stability code. In this model, several radial transport models are considered including the multi-mode, drift Alfven turbulence, and intermittent models. The neutral transport is also important for ETB modeling and well-benchmarked fluid diffusion model is used. The calculated profiles will be compared with DIII-D pedestal profiles and it will be discussed the relative roles of radial transport and stability on the structure of ETB based on the DIII-D pedestal profiles and modeling.   

Plasma-Neutrals Physics in Centrifugal Confined Plasma

A simple model is developed for the penetration of neutrals into plasma for a rotating mirror configuration, for example, the Maryland Centrifugal Experiment (MCX). In such configurations, the inward confining force originating from the centrifugal force competes with the tendency of the plasma to expand in the parallel direction. By including ionization, charge exchange, and recycling in this model, the distribution of neutrals in the centrifuge is calculated. An exponential relation between the centrifugal confining force and the neutral density at the axial wall is demonstrated. The distribution of neutrals at the wall crossfield to the plasma has been considered earlier. The crossfield physics is different from the axial physics and disparate neutral wall densities are found. The combined neutral distribution in 2D is not well understood yet. We have developed a 2D code for this purpose. In the crossfield direction, classical diffusion losses are allowed. All the parameters are set to close to MCX parameters in order to investigate the effects of confinement on the neutral-plasma profiles/interactions. It is of great interest to understand the effect of neutrals on dragging the supersonic rotation (mainly in the mid-plane) and the role they play in the Hartmann layers expected at the axial end-plates.   

Hybrid Diverter Sheath Model

The plasma sheath near the diverter plate of a fusion device is modeled using a particle-fluid hybrid model. Electrons are modeled as an inertia-less (Boltzmann) fluid with conservation of charge enforced by a time-dependent flux balance at the walls for a Maxwellian distribution at a specified temperature. Flux flows in from the edge plasma, and out at the diverter and also in the upstream direction. Ions are modeled using the PIC methodology. Parameters for the run are taken from the UEDGE gyrokinetic code. The modeling methodology for the iterative nonlinear solver is presented. The hybrid model is compared to full PIC runs and runs with a fixed ion background using a similar parameter regime as well as results from the UEDGE code.   

Nonlinear Modeling of ELMs with the NIMROD Code

Understanding how to obtain the high performance of the ELMy H-mode regime while minimizing the deleterious effects of ELMs is an important problem facing the fusion community. Theoretical progress in understanding of ELMs has been made by investigating the stability boundaries of the peeling-ballooning mode using an ideal MHD model [1,2]. Nonlinear extended MHD codes offer the possibility of improving these studies by allowing; e.g., studies of the nonlinear spectral energy transfer, and propagation of plasma energy into the region of open field lines. In addition, because these codes do not rely on an ideal MHD ballooning-type formulation, implementation of additional effects such as resistivity, other diffusivities, and two-fluid effects are more straightforward to implement; however the challenges are that a strict vacuum formulation is not possible and the ability simulate the both the hot plasma, closed field-line region and the cold plasma, open-field line region presents many numerical difficulties. In this work, we present analysis of recent NIMROD nonlinear runs, in particular with the evolution of the magnetic topology and heat deposition on the walls. [1] P. B. Snyder et.al., Phys. Plasm. 9, 2037 (2002) [2] H. R. Wilson et.al., Phys. Plasm. 9, 1277 (2002)   

Mechanisms for Carbon Migration and Deuterium Retention in Tore Supra CIEL Long Discharges

The co-deposition mechanism in long discharges with high extracted power has been modeled in greater detail. A 1D core, 3D scrape-off layer and detailed 3D wall impurity generation model are coupled to follow the C balance in steady state and describe the complex 3D erosion/deposition zones of the realistic Tore Supra CIEL surface, including impurity generation from intra-tile gaps and from the poorly adhered layers of re-deposited material in shadowed areas. Results have been compared with CII/Da spectroscopy for a power scan in a database of 50 discharges. The model reproduces the observed increase in CII emission with power. Sources due to D+ physical sputtering saturate at higher net power levels, while self-sputtering contributions continue to increase. Significantly different scaling trends are predicted for sources due to physical/self-sputtering, and for chemical erosion using flux-independent and empirical flux suppression models. By incorporating IR measurements of local temperature to evaluate chemical erosion rates, contributions due to intra-tile-gap emission are found to be important in enhancing predicted chemical erosion rates. A new mechanism, radiant heating with CX bombardment, causes layer decomposition and transport. This mechanism can produce large scale deposits (flakes) at locations very remote from plasma fluxes. *ORNL. Supported by U.S.DOE Contract DE-AC05-00OR22725.   

Surface Fitting for Three-Dimensional DEGAS 2 Modeling

The \urllink{DEGAS 2}{http://w3.pppl.gov/degas2} neutral transport code is proving to be a valuable tool in modeling the edge regions of plasma devices. To date, the code has been applied to two dimensional or nearly axisymmetric three-dimensional systems. The logical next step is to perform fully three-dimensional simulations. A new geometry definition code consisting of a hermite interpolation and singular value decomposition algorithm has been developed for this purpose. The algorithm is used to fit the Fourier moments representation commonly used for stellarator plasma flux surfaces and vacuum vessel components to the quadratic surfaces required by DEGAS 2. This fitting technique will be applied to model neutral transport in the National Compact Stellarator Experiment (NCSX) being built at the Princeton Plasma Physics Laboratory (PPPL).   

Emission Rates in ASTRAL Argon Plasmas.

Relative Emission rates measured in the ASTRAL (\textbf{A}uburn \textbf{S}teady s\textbf{T}ate \textbf{R}esearch f\textbf{A}ci\textbf{L}ity) helicon plasma source are compared to theoretical predictions. A spectrometer which features a 0.33 m Criss-Cross Scanning monochromator and a CCD camera is used for this study. ASTRAL produces bright intense Ar plasmas with the following parameters: n$_{e}$ = 10$^{12}$ to 10$^{13}$ cm$^{-3}$ and T$_{e}$ = 2 to 10 eV. A rf compensated Langmuir probe is used to measure T$_{e}$ and n$_{e}$. In a first series of experiment Ar I, Ar II and Ar III transitions are monitored as a function of plasma density and this for constant electron temperature. In the second series of experiments, the same transitions are observed as a function of T$_{e}$ while n$_{e}$ is this time kept constant. Observations revealed that T$_{e}$ is by far the most significant parameter affecting the emission rate coefficients in the ASTRAL plasma. The spectroscopy measurements are compared with spectral modeling from the ADAS suite of codes.~ Our collisional-radiative formalism assumes that the excited levels are in quasi-static equilibrium with the ground and metastable populations.~ We use existing standard R-matrix electron-impact excitation data in our modeling, and assess this dataset against the results from a new R-matrix with pseudo-states calculation.   

Robust methods for calculation of the charge-changing cross sections of ions or atoms by fast ions

Ion-atom charge-changing cross sections are needed in many applications employing the propagation of fast ions through matter. The validity of two most frequently used approximations, the Born approximation and classical trajectory approximation, has been studied by comparing the results of simulations with available experimental data [1]. A hybrid method has been developed by combining the two approaches in the regions of impact parameters in which they are valid, and summing the results to obtain the total cross section [2]. As a result, typical computations take only few minutes. The hybrid approach has been tested by comparison with available experimental data and full quantum mechanical calculations. A new scaling formula for the ionization and stripping cross sections of atoms and ions by fully stripped projectiles has also been developed [1]. [1] I. D. Kaganovich, E. A. Startsev and R. C. Davidson, ``Formulary and scaling cross sections for ion-atom impact ionization,'' http://arxive.org/abs/physics/0407140 ; to be published in New Journal of Physics (2006). [2] Igor D. Kaganovich, et. al., Nucl. Instr. and Methods A \textbf{544}, 91 (2005).   

Existence and Stability of Relativistic Solitary Waves in Warm Plasmas

A variational mehod for one dimensional relativistic solitons is established, within the two fluid model framework, including finite temperature effects. Our starting point is a Lagrangian for a two species fluid plasma, which allows the deduction of the conserved quantities of the system by means of Noether's theorem, as well as the model equations. At a first stage, travelling wave solutions are studied with the usual shape of envelope solitary waves. It is found that bounded travelling waves (bright solitons) exist for most velocities, if both ions and electrons are assumed to be relativistic, except for a window at small values of $v/c$. In order to study their stability, we obtain the evolution equations of the solitary wave parameters.   

Physical properties of Plasma Jets Emitted in Pulsed Capillary Discharges.

Open ends pulsed capillary discharges (PCD) establish natural conditions for the generation of plasma jets. We have investigated the physical properties of the plasma jet emitted in a PCD, operating in a continuous pulsing mode at 10 kV ($\sim $2 kA, 10 ns), with frequencies up to 50 Hz. The discharge is operated in argon and nitrogen, at pressures in the 0.4---1.0 Torr range. A dual, optoisolated, fast Langmuir probe, placed at the anode side, close to the capillary exit, is used to measure the characteristic electron temperature (T$_{e})$ and electron density (N$_{e})$ of the plasma jets, with temporal and spatial resolution. Time integrated visible spectroscopy is used to identify the plasma jets components. Characteristic values of T$_{e}$ and N$_{e}$ are found to be in the tens of eV and 10$^{13}$ cm$^{-3}$, respectively. Based on these measurements, a comprehensive characterization of the PCD plasma jets will be presented.   

Kinetic Study of the Collisionless Expansion of Spherical Nanoplasmas

The collisionless expansion of spherical plasmas composed of cold ions and hot electrons is analyzed using a novel Lagrangian model [1], which allows a highly accurate, kinetic description of the radial motion of the ions and of the three-dimensional motion of nonrelativistic electrons (the validity of the model is checked both with 3D particle-in-cell simulations, performed with the OSIRIS framework [2], and using a new, ad-hoc developed particle method). The paradigmatic case of initially-Maxwellian electrons is investigated in detail for a wide range of initial conditions: simple relationships are deduced for the key expansion features [1], and a threshold in the electron energy is identified, beyond which the energy spectrum becomes monotonic and the Coulomb explosion regime is approached. Non-Maxwellian initial distributions of the electrons are also considered. [1] F. Peano\textit{ et al.}, Phys. Rev. Lett. \textbf{96}, 175002 (2006). [2] R.A. Fonseca \textit{et al}., Lect. Notes Comp. Sci. \textbf{2331}, 342 (Springer-Verlag, Heidelberg, 2002).   

Numerical studies of nonlocal effects of the low mode numbers tearing modes and their mitigation in the DIII-D

In this work, the method of maps [1-4] is used to study the trajectories of magnetic field lines in the DIII-D tokamak. Data from the DIII-D shot 115467 is used to determine the parameters in the maps. Effects of the m=1, n=$\pm $1 tearing modes and the dipole perturbation from the C-coils on the motion of field lines are calculated. Internal tearing modes produce non-local effects on the magnetic footprints, and destroy their symmetry. Dipole perturbations mitigate the effects of the tearing modes, spread the heat-flux on the plates over a wider area, reduce the peak heat-flux, and reorganize the phase space structure in a new pattern that has the same symmetry as that of the external perturbation. The low dimensionality of the system and its symplecticity impose severe restrictions on the motion of the system in phase space forcing it to take on the symmetry properties of the perturbations. This work is done under the DOE grant number DE-FG02-01ER54624. 1. A. Punjabi, A. Boozer, and A. Verma, \textit{Phys}. \textit{Rev. lett.}, \textbf{69}, 3322 (1992). 2. H. Ali, A. Punjabi, and A. Boozer, \textit{Phys. Plasmas }\textbf{11}, 4527 (2004). 3. A. Punjabi, H. Ali, and A. Boozer, \textit{Phys. Plasmas} \textbf{10}, 3992 (2003). 4. A. Punjabi, H. Ali, and A. Boozer, \textit{Phys. Plasmas} \textbf{4}, 337 (1997).   

Effects of shear on the magnetic footprint and stochastic layer in double-null divertor tokamak

We have developed a new area-preserving map, called the Adjustable Shear Map, to calculate effects of shear on the magnetic footprint and stochastic layer in double-null divertor tokamak. The map is given by equations$x_{n+1} =x_n -ky_n [(1-y_n^2 )(1+sy_n )+sx_{n+1}^2 ),y_{n+1} =y_n +kx_{n+1} [1+s(x_{n+1}^2 +y_n^2 )]$. k is the map parameter and s is the shear parameter. O-point of the map is (0, 0), and the X-points are (0, 1), and (0, -1). For s=0, k=0.6, the last good surface is y=0.9918 with q $\sim $3. Here we will report on the effects of shear on the stochastic layer and magnetic footprint as the shear parameter is varied from 0 to -1. Here we will report the preliminary results on the effect of shear on the magnetic foot print and the stochastic layer where the shear parameter $s$ has values between -1 and 0. using method of maps [1-4]. This work is done under the DOE grant number DE-FG02-01ER54624. 1. A. Punjabi, A. Boozer, and A. Verma, \textit{Phys}. \textit{Rev. lett.}, \textbf{69}, 3322 (1992). 2. H. Ali, A. Punjabi, and A. Boozer, \textit{Phys. Plasmas }\textbf{11}, 4527 (2004). 3. A. Punjabi, H. Ali, and A. Boozer, \textit{Phys. Plasmas} \textbf{10}, 3992 (2003). 4. A. Punjabi, H. Ali, and A. Boozer, \textit{Phys. Plasmas} \textbf{4}, 337 (1997).   

Diffusion of chaotic field lines in tokamaks

An important instability for the destruction of magnetic surfaces in tokamaks due to island overlapping is the tearing modes. Magnetic fields perturbed by tearing modes are given by the sinusoidal form $B_r =-\frac{1}{rR}\sum\limits_{m,n} {b_m^n \sin \left( {m\theta -n\varphi } \right)} $. The sinusoidal nature of perturbation creates islands structure near resonant surfaces. In this work, we consider two modes, $\left( {m_1 ,n_1 } \right)$and $\left( {m_2 ,n_2 } \right)$that interact with each other, leading to two chains of islands, called primary islands. We use a previously derived Hamiltonian map, the \textit{$\psi -\theta $ map,} with and without higher order control terms to study the diffusion of chaotic field lines. We will present and discuss the results of this work, and discuss its implications with regard to magnetic transport barriers for a fixed $q$-profile and increasing strength of magnetic perturbations. This work is done under the DOE grant number DE-FG02-01ER54624. 1.A. Punjabi \textit{et al}, \textit{Phys}. \textit{Rev. lett.}, \textbf{69}, 3322 (1992). 2. H. Ali, A. Punjabi, and A. Boozer, \textit{Int. J. Comp. Num. Ana. Applications} \textbf{6}, 17 (2005).   

Chaotic magnetic fields and their effect on particle motion

A simple configuration consisting of a circular current loop and a current carrying straight wire can generate three-dimensional chaotic magnetic fields. The parameters controlling the onset of chaotic fields are the ratio of the current in the loop to that in the wire, and the relative positions of the two current systems. This configuration can be described by a Hamiltonian which can then be used to study the onset of chaotic fields. We will present analytical and numerical studies on the generation of chaotic magnetic fields and the nature of these fields. A description of the motion of charged particles in such chaotic magnetic fields will also be presented. Possible application to energetic charged particle transport in space plasmas will be discussed.   

Recent results of invariant torus breakup in nontwist maps

As simple models for degenerate Hamiltonian systems, nontwist maps have been used to describe, e.g., magnetic field lines in toroidal plasma devices with reversed magnetic shear profiles. Of particular interest in these maps are the so-called shearless invariant tori which correspond to transport barries in the physical system. We investigate the breakup of shearless tori in several maps and with several different winding numbers, in order to understand the dependence of the details of the breakup on the winding number and on the symmetries of the map model. Here we report on recent results of this investigation.[1]\\ \noindent $[1]$ K.~Fuchss, A.~Wurm, A.~Apte, and P.J.~Morrison, to appear in Chaos (2006); K.~Fuchss, A.~Wurm, and P.J.~Morrison, preprint/submitted to PRL (2006).   

Characterization of Atmopheric RF Plasma by an Optical Emission Spectroscopic Method

Although the atmospheric pressure plasmas are used for modification, sterilization, and cleaning of surfaces, it is hard to make the uniform and glow plasma in atmospheric pressure since the collisional mean-free path is very short. Hence, their applications are limited by these non-uniform characteristics. Recently, the atmospheric pressure RF jet has been issued since they have many characteristics similar to low-pressure glow discharges, such as non-thermal and uniform glow characteristics, etc. Atmospheric RF plasma jet is developed with the frequencies of 13.56 MHz and the powers of up to 1 kW with He and ambient air mixtures. With optical emission spectroscopic (OES) measurement, the exhausted plasmas are characterized with rf power, gas flows, and inlet gas ratio. Data is analyzed via LTE (Local Thermodynamic Equilibrium)/Collisional-Radiative/Corona model for atomic spectra, and via Fulcher alpha-band spectra for the molecular spectra. Controlling the discharge by flow rate and RF power, OES measured plasma parameters of each conditions. Details of atmospheric plasma generators and diagnostic models are going to be addressed.   

Addition of an rf plasma source to ALEXIS

The ALEXIS (Auburn Linear EXperiment for Instability Studies) device is a 170 cm long, 10 cm diameter magnetized plasma column. To date, most studies in ALEXIS have focused on the generation of current and flow shear driven electrostatic ion cyclotron type instabilities through the active modification of the radial potential profile. However, there also exists a branch of electromagnetic ion cyclotron instabilities that can be investigated in finite beta plasmas. To access this regime, it is necessary to increase the plasma density in ALEXIS by a factor of 50 to 100. This presentation discusses a recent upgrade to the ALEXIS device to generate higher density plasmas. A new helicon-type, rf plasma source has been added to ALEXIS. This presentation will give preliminary measurements of the plasma parameters during rf plasma operations.   

Electric and magnetic field cutoffs of low frequency instabilities in a magnetized, linear plasma column

Flows generated in plasmas due to the presence of crossed electric and magnetic fields are of relevance to both the fusion and space plasma communities. Studies in the ALEXIS device, a 170 cm long, 10 cm diameter magnetized plasma column, seek to determine the stability regimes for driven flows. This presentation focuses on the electric and magnetic field cutoffs of low frequency (in the ion cyclotron regime) instabilities observed in the ALEXIS device. These oscillations are generated by the presence of axial and transverse flows, which are modified by radial potential structures externally imposed on the plasma. This poster will present initial measurements of the effects of modifying the magnetic and radial electric fields on the frequency and amplitude of these ion cyclotron waves.   

Drift Wave Turbulence in Helicon High-Density Linear Plasma I: Experimental Device and Plasma Performance

We have been investigating the drift wave turbulence in the helicon high-density (up to 10$^{19 }$cm$^{-3})$ linear plasma [1]. Upgrading this machine has been carried out recently to increase the axial size from 170 to 370 cm and the magnetic field from 1.2 to 1.5 kG with the vacuum vessel diameter of 45 cm in order to excite drift waves more easily in a wide range of operation parameters. New device can accept flexible access of various diagnostic ports, and developing electrostatic probe systems was also conducted such as 48 and 64 probe tips in the azimuthal direction and the two-dimensional moving probe. Changing the magnetic field and field configurations, argon gas pressure and the magnetic field, we could obtain the relative density fluctuation level up to 20 {\%}, which is comparable to our previous experiment in the old short device. [1] S. Shinohara, Y. Miyauchi and Y. Kawai, Plasma Phys. Control. Fusion \textbf{37}, 1015 (1995).   

Drift Wave Turbulence in Helicon High-Density Linear Plasma II: Fluctuation Dynamics

In order to investigate drift wave turbulence and its structural formation mechanism, we have been developing strong turbulence in linear magnetized plasmas. In experiments of the last fiscal year, we have observed a transition process in the drift wave frequency range from weak turbulence (fundamental mode and their higher harmonics coexisting) to semi-strong turbulence (broadband spectra) in the Large Mirror device. In the semi-strong turbulence, fluctuations at spectral peaks propagate in the electron diamagnetic drift direction, and have a poloidal mode number of 3 and an axial mode number of 1-2. Radial wavenumbers of the fluctuations have different signs between center and edge region of the fluctuation profile, indicating wave fronts and/or phases of the fluctuations are modulated. The modulation contributes to Reynolds stress gradient, and we also observed a consistent profile of Reynolds stress gradient. In the poster, we will present details of linear/nonlinear analyses of the turbulent fluctuations, and will discuss about energy transfers between spectral peak and higher frequency fluctuations.   

Drift Wave Turbulence in Helicon High-Density Linear Plasma III: Multi-Probe Measurements

Plasma turbulence excited by drift waves and the associated formation and the transport processes have been investigated in many torus and linear devices. In these objectives, high-density (up to 10$^{19}$ m$^{-3})$ helicon plasma was generated in new Large Mirror Device (LMD) with 370cm axial length and 45 cm inner diameter, where the wave with a peak frequency of 3-5 kHz was obtained in the strong area in density gradient. In order to examine the structure of this drift wave in more detail, we introduced a developed probe system, using an azimuthal multi probe array (48ch-probe) to measure the poloidal $k $--$\omega $ spectrum. The 48ch-probe consists of 16 units with 3 tungsten electrodes ($\phi $ 0.8 mm, L 4 mm), and when located at $r$ = 4 cm, it aligned at an azimuthal interval at 5.2 mm, at the axial position of $z$ = 162.5 cm. Since each unit is movable in the radial direction, it can also measure the space structure. Here, the ion saturation current or the floating potential can be stored by the fast data sampling logger system (1 $\mu $sec sampling). Other types of probes such as 2-dimensional moving probe and another set of 64ch-probe will be also tested.   

Resonant power absorption in helicon plasma sources: Experiment

Helicon discharges produce plasmas with a strong density gradient across the confining magnetic field. Theoretically, such a non-uniform plasma can create a radial potential well for non-axisymmetric whistlers, allowing radially localized helicon (RLH) modes. This work presents new experimental evidence that RLH modes play a significant role in the power absorption mechanism of helicon plasma sources. Experimentally, the mode has been identified by its resonant response to a low power rf-generator with variable frequency. The 2D plasma density profile was measured with Langmuir probes and then used to calculate the corresponding eigenfrequency and RLH mode structure for the experimental parameters. The resulting mode frequency matches the driving frequency of the rf-antenna. The calculated power deposition into the plasma is comparable to the experimental value for a relevant electron collision frequency. Wave fields in the plasma are measured and compared with the calculations.   

Resonant power absorption in helicon plasma sources: Theory

It is very common for helicon discharges to produce plasmas with a strong density gradient across the confining magnetic field. Such a nonuniform plasma can create a radial potential well for non-axisymmetric whistlers, allowing radially localized helicon (RLH) modes. This work presents new evidence that RLH modes play a significant role in helicon plasma sources. Experimentally, the mode has been identified by its resonant response to a low power rf-generator with variable frequency. The 2D plasma density profile was measured and then used to calculate the corresponding eigenfrequency and RLH mode structure for the experimental parameters. The calculations were performed using a 2D field solver for a single resonant azimuthal harmonic (m=1) under the assumption that the density profile is axisymmetric. The resulting mode frequency matches the driving frequency of the rf-antenna. The calculated power deposition into the plasma is comparable to the experimental value for a relevant electron collision frequency. It is noteworthy that the RLH mode, rather than the electrostatic modes, is responsible for the rf-power absorption in most of the plasma volume for the measured density profile.   

Infrared Radiometery and Heat Flux Calculation for a Helicon Plasma

Using an infrared camera, we measured the external temperature of a quartz tube containing a 1 kW helicon Argon plasma. An Inframetrics model 600 IR camera connected to a computer DAQ system records the temperature evolution of the quartz tube surface in the vicinity of the antenna during and after the pulse. Using these measurements, we estimated the heat flux profile from the plasma into the quartz tube walls. A MATLAB code uses pre- and post- pulse snapshot images from the video to estimate the heat flux into the quartz from the plasma. Initial results have shown a broad heating profile with localized power input into the quartz under the helical antenna. We find approximately 30\% of the total RF power deposited into the tube as heat, and heating directly under the antenna accounts for about 30\% of this heat input.   

Characterization and Overview of the HELCAT (HELicon-CAThode) Dual-Source Linear Plasma Device

The HELCAT (HELicon-CAThode) device is a dual-source linear plasma device that has recently begun full operation at the University of New Mexico. HELCAT is 4 m long, 50 cm diameter, with axial magnetic field $<$ 2.2 kG. An RF helicon source of tunable frequency 10 -- 30 MHz and P $<$ 5 kW, resides at one end of the device, while a thermionic BaO-Ni cathode capable of discharge currents up to 2.5 kA is located at the other end. Nominal parameters are: Te $\sim$ 5 -- 10 eV, ne $\sim$ 10$^{12}$ /cc (cathode), 10$^{13}$ -- 10$^{14}$ /cc (helicon), plasma diameter 15 -- 20 cm. Diagnostics now online include electrostatic and magnetic probes, mm wave interferometry, visible spectroscopy, and LIF. Several basic plasma physics experiments are underway, including active feedback control of turbulent transport, physics of edge convective transport, Alfven wave-neutral particle interactions, and physics of expanding high density magnetized plasma ``bubbles'' in the background discharge. An overview of the device characteristics and initial experimental results will be presented.   

Lithium Ion Sources for Investigations of Fast Ion Transport in Magnetized Plasmas

In order to study the interaction of ions of intermediate energies with plasma fluctuations, two plasma immersible Lithium ion sources of different size, based on solid–state thermionic emitters (Li-6 Aluminosilicate), were developed. Compared to discharge based ion sources \footnote{H. Boehmer et al., Rev. Sci. Instrum., 75, 1013 (2004)}, they are compact, have zero gas load, small energy dispersion, and can be operated at any angle with respect to an ambient magnetic field of magnitude generally found in plasma experiments. Beam energies range from 400 eV to 2.0 keV with typical beam current densities in the 1 mA/cm2 range. Because of the low ion mass of 6 amu, beam velocities of 100--300 km/s are in the range of Alfv\'{e}n speeds in Helium or Hydrogen plasmas. Design considerations and operation in a high vacuum test chamber as well as in the high density, magnetized plasma of the LArge Plasma Device (LAPD) at UCLA will be detailed.   

Characterization of an Inverted Geometry Helicon Plasma Source

Helicon plasmas are useful as hot, dense sources requiring low magnetic fields. Since Boswell's$^{1}$ use of helicon waves in low pressure gas, no single theory fully explains the wave-plasma coupling mechanism. However, Trivelpiece-Gould modes$^{2}$ remain a strong candidate. An inverted geometry helicon plasma source is further explored, using a dielectric-covered helicon antenna, placed within a vacuum chamber, in contrast to conventional antennas that surround a dielectric cylinder. A Nagoya Type III antenna is used, other antennas are equally feasible. Many industrial advantages of such a system exist; namely, more efficient electromagnets, as well as producing a plasma with a larger radius than the antenna. With this arrangement, diagnostic measurements can be made arbitrarily close to the antenna. To characterize the plasma, an RF-compensated Langmuir probe measures electron temperature and density, while a B-dot probe measures the field shape inside and outside of the antenna region. In addition, optical emission spectroscopy observes changes in plasma intensity for mode jumps, and measures line ratios. 1. R.W. Boswell, Phys. Lett. 33A, 457 (1970) 2. A.W. Trivelpiece and R.W. Gould, Jour. App. Phys. 30 (11) (1959)   

Characteristics of helicon-plasma produced using a segmented multi-loop antenna

The usefulness of using a flat spiral antenna, which is installed just outside a insulator window at the end of a vacuum chamber, to generate helicon-plasma has been proven in a large device [1--2]. We have applied a similar technique to a smaller device (20 cm in diameter and 100 cm in axial length), but using a newly designed flat antenna for plasma production. The antenna consists of four concentric loops. Each of three outer loops is equally divided into four segments. The central loop is divided into two equal length segments. By varying the electrical connection among the antenna segments, it is possible to excite not only waves with m=0 but also waves with m=±1 or higher, where m is the azimuthal mode number. With the m=0 excitation, helicon-plasma (n$_{e} \quad \ge $ 10$^{12}$ cm$^{-3})$ can be obtained at P$_{rf}\ge $2 kW (Ar, 2 mTorr range). With the m=±1 excitation, it is more difficult to attain helicon-plasma. The input rf power of 4 kW or higher is necessary. [1] S. Shinohara and T. Tanikawa, Rev. Sci. Instrum. \textbf{75}, 1941 (2004); Phys. Plasmas \textbf{12}, 044502 (2005). [2] T. Tanikawa and S. Shinohara, Thin Solid Films \textbf{506-507}, 559 (2006).   

Measurements of Electron Energy Distribution and Metastable Atom Density in the Afterglow of an RF ICP Discharge in Helium

In previous work [1], it was shown that even a small number of nonlocal fast electron, which do not significantly affect the overall mean electron energy, can dramatically change the plasma and near-wall sheath properties. In this work, Langmuir probe measurements of electron density, temperature, energy distribution functions (EEDF), metastable atom density and their temporal evolution in the afterglow of low-pressure (50 mTorr) helium rf ICP discharges have been carried out. The experimental setup is described in [2]. The primary focus of this work is the investigation of the high energy portion of the EEDF which shows peaks corresponding to electrons with energies 14.4 and 19.8 eV. These peaks arise from electrons produced in Penning ionization with metastable helium atoms and metastable-electron collisions of second kind. ~This fast component of the EEDF can be controlled independently on the slow electrons, which is a direct consequence of the EEDF nonlocality. \newline [1] V. Demidov et al. \textit{PRL} \textbf{95}, 215002 (2005). \newline [2] W. Guo et al., \textit{PSST} \textbf{10}, 43 (2002).   

Using particle-in-cell simulations to study non-local effects in inductively coupled plasmas

In the low pressure, low frequency regime, electron dynamics in finite temperature inductively coupled plasmas is dominated by thermal motion: the mean free paths are large relative to device size and trajectories are strongly curved by the induced rf magnetic field. This causes problems for the classical, local theory of the anomalous skin effect, which is unable to describe the nonlinear behaviour. We use a particle-in-cell simulation to study the ponderomotive force and surface impedance, while retaining the full complexity of the problem. If the nonlinearities are ignored, the simulated PMF is proportional to the amplitude of the driving electromagnetic wave squared, in agreement with analytic theories. When the magnetic field and longitudinal electric field are included, the exponent becomes dependant on temperature.   

New Apparatus to Study Fast Atomic Recombination in Ultracold Plasma

We have constructed an apparatus to study the early evolution (0-1000 ns) of ultracold plasma, produced by photo-ionization of rubidium atoms in a magneto-optical trap. We report on progress toward measuring recombined atomic populations in ultracold plasma using ramped field ionization. The new setup features fast deflector plates to avoid saturation of the multi-channel plate detector, as well as close atmospheric access to the ultra-high vacuum interaction region.   

Neutral Helium Profile Measurements in the WVU Helicon Source

We report spatially resolved measurements of excited state neutral helium density, temperature, and flow velocities in the WVU helicon plasma source (HELIX). While ion dynamics are studied extensively, neutral particle characteristics such as density and temperature are frequently neglected in low temperature plasmas and assumed to be spatially uniform. Measurement of the neutral flow is also important, specifically for researchers who use line integrated spectroscopy, since flows along the line of sight can artificially broaden the line width of emission lines. Recent work by Holland \textit{et al.} on spontaneous flow shear illustrates the need for spatially resolved measurement profiles of the neutral particle parameters. Inclusion of a spatially varying ion-neutral momentum dampening parameter in theoretical models would not only give a more comprehensive understanding of the physics, but could lead to increased shear. Profile measurements were made using the 2D stage described in Hardin \textit{et al.} C. Holland, J. H. Yu, A. James \textit{et al.}, Phys. Rev. Lett. 96, 195002 (2006). R. Hardin, X. Sun, E. Scime, Rev. Sci. Instrum. 75, 4091 (2004).   

Production of negative ion plasmas using perfluoromethylcyclohexane (C$_{7}$F$_{14})$ .

Negative ion plasmas are produced by electron attachment to neutral molecules when an electronegative gas is introduced into a plasma. One of the most widely used gases is sulfur hexafluoride, SF$_{6}$ which has a relatively high electron attachment cross section for low energy ($<$0.05 eV) electrons, making it particularly attractive for use in Q machines, where T$_{e} \quad \sim $ 0.2 eV. However, in discharge plasmas having T$_{e}$ $\sim $ several eV, multiple negative ion species are also formed, including F$^{-}$, which can be corrosive to vacuum system components. As an alternative, we have investigated the use of C$_{7}$F$_{14}$ to produce negative ion plasmas, both in a Q machine and in a hot-filament, multidipole device. The maximum attachment cross-section is $\sim $ 6 times higher than that of SF$_{6}$, and occurs at a higher energy, 0.15 eV, so that the attachment efficiency should be enhanced both in the Q machine and in the discharge plasma. Details of the experimental setup and Langmuir probe characteristics obtained in the plasma with C$_{7}$F$_{14}$ will be presented.   

How fast are ions lost from plasma with two ion species?

The Bohm sheath criterion in single and two-species plasma is studied with Laser-Induced Fluorescence (LIF) of Ar ions using a diode laser in low pressure unmagnetized dc hot filament Ar and Ar/Xe discharges confined by surface multi-dipole magnetic fields. The Ar ion velocity distribution function is measured as a function of position relative to a negatively biased boundary plate. Ion acoustic wave phase velocity data are combined with the argon LIF data to determine the Xe ion velocity. Emissive probes provide the plasma potential profile in the plasma sheath and presheath. The ion concentrations of the two-species in the bulk plasma are calculated from measured ion acoustic wave phase velocity. Results are compared with previous experiments with Ar-He plasmas in which the Ar ions were the heavier ion species. Preliminary results are consistent with both ion species reaching close to the system sound velocity at the presheath/sheath boundary.   

Radio Frequency Plasma-Based Non-ambipolar Electron Source

A Radio Frequency (RF) plasma-based electron source that does not rely on electron emission at a cathode has been constructed and is able to produce 15 A of electron current when using 15 sccm Ar, 1200 W RF power at 13.56 MHz. All of the random electron flux in the device is extracted through an electron sheath resulting in total non-ambipolar flow when the ratio of the ion loss area to the electron loss area is approximately equal to the square root of the ratio of the ion mass to the electron mass, and the ion sheath potential drop at the chamber walls is much larger than Te/e. The Non-ambipolar Electron Source (NES) has an axial expanding magnetic field of 100 Gauss that creates a uniform plasma potential across a 1cm diameter aperture allowing for uniform electron extraction without the need for grids. The electron current extracted from NES is 300 times greater than the Bohm current that could be extracted through the same aperture. NES has comparable current densities to and the promise of longer operational lifetimes than conventional electron sources such as hollow cathodes, where the operational lifetime is ultimately limited by cathode deterioration.   

Revisiting the capacitive sheath.

Traditional theory of the capacitive sheath assumes that the large negative charge at the electrode is screened by the ion space charge and the transition to the small rf electric field in the plasma occurs abruptly within the narrow transition region of the Debye length. However, careful self-consistent kinetic treatment of the problem reveals existence of additional transition layer of length $V_T /\omega $, where $V_T $ is the electron thermal velocity and $\omega $ is the discharge frequency [1,2,3]. Electrons interacting with the capacitive sheath acquire velocity modulations. As a result, the electron density bunches appear in the region adjacent to the sheath. These electron density perturbations decay due to phase mixing over a length of order $V_T /\omega $. The electron density perturbations polarize the plasma and produce an electric field in the plasma bulk. This electric field, in turn, changes the velocity modulations and total power deposition. Recent particle-in-cell simulations [4,5] confirm the prediction of analytic theory. [1] L. D. Landau, J. Phys. (USSR) \textbf{10}, 25 (1946). [2] Igor D. Kaganovich, Phys. Rev. Lett. \textbf{89}, 265006 (2002). [3] I. D. Kaganovich, O. V. Polomarov, and C. E. Theodosiou, IEEE Trans. Plasma Sci. \textbf{34}, 696 (2006). [4] H. C. Kim, G. Y. Park, and J. K. Lee, Phys. of Plasmas \textbf{13}, 023501 (2006). [5] E. Kawamura, M. A. Lieberman, and A. J. Lichtenberg, Phys. of Plasmas \textbf{13}, 053506 (2006).   

Multiple-Ion Species Effects in IEC Modeling

A simple model for the effect of various molecular and atomic processes (charge exchange, ion impact ionization, and dissociation) between deuterium ions (D$^{+}$, D$_{2}^{+}$, and D$_{3}^{+})$ and the background gas on the performance of spherical, gridded IEC devices has been developed. Ions enter the intergrid region primarily as D$_{3}^{+}$ ions and, while being accelerated by the falling electrostatic potential, interact with the background gas to produce a source of cold ions (D$^{+}$ and D$_{2}^{+})$ through interactions with the background gas. These cold ions are accelerated by the potential and produce additional cold ions through interactions with the background gas. A formalism has been developed which includes the bouncing motion of ions in the electrostatic potential well and sums over all generations of cold ions. This leads to a set of coupled Volterra integral equations for each ion species. The integral equations are solved numerically, and the energy spectrum of the ion and fast neutral flux is calculated. Macroscopic quantities, such as the current collected by the cathode, and the fusion rate between ions and fast neutral atoms and molecules with the background gas, are calculated. Comparison of the results from the multiple ion species model with an atomic ion model and with experimental data for the Wisconsin IEC device will be presented. Research supported by the US Dept. of Energy under grant DE-FG02-04ER54745.   

Plasma Characteristics of the Ion Source Region In the University of Wisconsin IEC Device

The ion source region of the UW-Inertial Electrostatic Confinement device consists of a filament assisted DC discharge plasma that exists between the wall of the IEC vacuum chamber and the grounded spherical steel grid that makes up the anode of the IEC device. The plasma characteristics of the source region have been investigated using a planar Langmuir probe and an antenna used for the propagation of ion acoustic waves. Using these diagnostics the average ion mass of the deuterium source plasma has been measured and is consistent with a mostly D$_{3}^{+}$ plasma. These results are consistent with a 0-D theoretical model of the source plasma. Variations in the floating potential, the plasma potential, and the plasma density have been investigated by varying the radial location of the planar probe. Variations in voltage on the IEC cathode have been shown to affect the floating potential in the source region as well as the spatial extent and density of the plasma in the source region.   

Measurement of $^{3}$He($^{3}$He,2p)$^{4}$He Reactions in an IEC Device

An inertial electrostatic confinement (IEC) device has been used to measure $^{3}$He($^{3}$He,2p)$^{4}$He reactions. The experimental setup consists of a spherical vacuum vessel approximately 61 cm in diameter held at ground potential and a spherical cathode centered within the vessel that can be biased from 0 to -200kV. The ion source is an externally mounted high-density helicon source which provides a beam of up to $\sim $ 6*10$^{16}$ ions/s. This source allows for IEC operation to occur at $^{3}$He background pressures of $<$ 0.02 Pa, reducing atomic effects and allowing for more straightforward code validation. An integral equation approach models atomic physics processes and nuclear reactions in order to predict the energy spectrum of the $^{3}$He ions(details in poster by Emmert and Santarius, this conference). The integral equation is solved numerically by finite differences. The $^{3}$He($^{3}$He,2p)$^{4}$He fusion reaction rates measured experimentally will be compared to those generated by the computer code.   

Kinetic Equations for the description of Neoclassical Tearing Modes

Our ordering of the magnetic island width is determined by requiring that the time-scales for `island-flattening' by parallel and perpendicular transport are of the same order, $\chi_\|/l_\|^2 \sim \chi_\perp/w^2$(narrow islands are washed away by perpendicular transport, while as island width increases the time for parallel transport to flatten pressure also increases). Assuming gyroBohm like perpendicular transport and classical parallel transport this requirement leads to a width scaling $w \sim \epsilon^{1/2} L$. Using $\epsilon^{1/2}$ as the small parameter, we expand the Fokker-Planck equation in the region of the island, $(\psi - \psi_0)/\psi$, applying the well known Chapman-Enskog method. This procedure yields 2-D equations for the evolution of the electron and ion distribution functions. These equations are solved subject to boundary conditions provided by matching to an external MHD solution. This model forms an appropriate basis for the consistent inclusion of micro-turbulence in the neoclassical tearing mode problem.   

Two-fluid modeling with the NIMROD code

Many applications of macroscopic simulation are incomplete without two-fluid effects, the most important of which are magnetization flows and fast reconnection. Nonetheless, they have rarely been included in global simulations, primarily due to temporal stiffness. Here, we briefly review an implicit leapfrog algorithm that has been developed for the NIMROD code and describe benchmarks and initial applications. The model includes the magnetization flows found in the Braginskii equations, and it has a two-fluid Ohm's law that reproduces dispersive waves and fast reconnection. Nonlinear computation is applied to modeling dynamo in sheared-slab and cylindrical configurations, where the former focuses on single-helicity dynamics, and the latter shows multi-helicity coupling. Open-field configurations relevant for spheromaks are also considered. Finally, we describe two-fluid modeling of edge-localized modes in the DIII-D tokamak at General Atomics.   

A Preconditioning Strategy for Fully Implicit Newton-Krylov Simulations of Resistive Magnetohydrodynamics

Computational MHD of tokamak plasmas poses severe challenges due to its wide range of spatio-temporal scales, strong anisotropy and nonlinearity. Additionally, resistive MHD experiences increased ill-conditioning as the spatial meshes are refined to resolve diffusive layers. We present a fully implicit Jacobian-Free Newton-Krylov method for resistive MHD. Within this strategy, we present a preconditioning approach efficiently solve the linear system during the Krylov stage. The preconditioning stragegy is based on operator splitting in which the hyperbolic and diffusive sub-systems of the equations are separately preconditioned. The hyperbolic or ideal MHD part is preconditioned by an eigenmode decomposition, similar to those employed in upwind methods, and considering the fast and/or Alfv\'en waves. The diffusive sub-system of the equations is preconditioned using a multigrid technique. We demonstrate that such an approach grows increasingly necessary for efficient solution strategies as the spatial mesh is refined. We demonstrate our method with examples from MHD wave propagation, and magnetic reconnection.   

Resistive MHD in HYDRA Using Vector Finite Elements on 3D ALE Structured Hexagonal Meshes

The electromagnetic diffusion equations in the small Hall parameter limit are discretized using a mixed vector finite element method on 3D semistructured grids. The discretizations are based on H(grad), H(curl) and H(div) conforming finite element spaces combined with an implicit, unconditionally stable time differencing method. The electric field solve follows a formulation developed by Bochev et.al. augmented by the addition of the electron pressure gradient term from the generalized Ohm's law. The conforming finite element spaces provide an approximation to an exact De Rham complex preserving the divergence free magnetic field over all space and time. The electromagnetic field time advancement works in conjunction with HYDRA, an ALE radiation-hydrodynamics code, providing force coupling and an arbitrary divergence preserving remap of the magnetic field. A constrained transport method with good energy conservation properties utilizes the conforming finite element spaces for the remap. This development represents the first stage of an effort to develop a more complete electron Hall MHD model for electron thermal transport in HYDRA. Bochev, et al, ETNA, Vol 15 (2003).   

Spectral-element adaptive refinement magnetohydrodynamic simulations of the island coalescence instability

A recently developed spectral-element adaptive refinement incompressible magnetohydrodynamic (MHD) code is applied to simulate the problem of island coalescence instability (ICI) in 2D. The MHD solver is explicit, and uses the Elsasser formulation on high-order elements. It automatically takes advantage of the adaptive grid mechanics that have been described in [Rosenberg, Fournier, Fischer, Pouquet, J. Comp. Phys., {\bf 215}, 59-80 (2006)], allowing both statically refined and dynamically refined grids. ICI is a MHD process that can produce strong current sheets and subsequent reconnection and heating in a high-Lundquist number plasma such as the solar corona [cf., Ng and Bhattacharjee, Phys. Plasmas, {\bf 5}, 4028 (1998)]. Thus, it is desirable to use adaptive refinement grids to increase resolution, and to maintain accuracy at the same time. Results are compared with simulations using finite difference method with the same refinement grid, as well as pesudo-spectral simulations using uniform grid.   

PIXIE3D: A Parallel, Implicit, eXtended MHD 3D Code

We report on the development of PIXIE3D, a 3D parallel, fully implicit Newton-Krylov extended MHD code in general curvilinear geometry. PIXIE3D employs a second-order, finite-volume-based spatial discretization that satisfies remarkable properties such as being conservative, solenoidal in the magnetic field to machine precision, non-dissipative, and linearly and nonlinearly stable in the absence of physical dissipation.\footnote{L. Chac\'on, \emph{Comput. Phys. Comm.}, {\bf 163} (3), 143-171 (2004)} PIXIE3D employs fully-implicit Newton-Krylov methods for the time advance. Currently, second-order implicit schemes such as Crank-Nicolson and BDF2 ($2^{nd}$ order backward differentiation formula) are available. PIXIE3D is fully parallel (employs PETSc for parallelism), and exhibits excellent parallel scalability. A parallel, scalable, MG preconditioning strategy, based on physics-based preconditioning ideas,\footnote{L. Chac\'on et al., {\em J. Comput. Phys}. {\bf 178} (1), 15- 36 (2002); {\em J. Comput. Phys.}, {\bf 188} (2), 573-592 (2003)} has been developed for resistive MHD,\footnote{L. Chac\'on, {\em 32nd EPS Conf. Plasma Physics}, Tarragona, Spain, 2005} and is currently being extended to Hall MHD.\footnote{L. Chac\'on et al., {\em 33rd EPS Conf. Plasma Physics}, Rome, Italy, 2006} In this poster, we will report on progress in the algorithmic formulation for extended MHD, as well as the the serial and parallel performance of PIXIE3D in a variety of problems and geometries.   

Fully implicit adaptive mesh refinement algorithm for reduced MHD

In the macroscopic simulation of plasmas, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. Traditional approaches based on explicit time integration techniques and fixed meshes are not suitable for this challenge, as such approaches prevent the modeler from using realistic plasma parameters to keep the computation feasible. We propose here a novel approach, based on implicit methods and structured adaptive mesh refinement (SAMR). Our emphasis is on both accuracy and scalability with the number of degrees of freedom. As a proof-of-principle, we focus on the reduced resistive MHD model as a basic MHD model paradigm, which is truly multiscale. The approach taken here is to adapt mature physics-based technology\footnote{L. Chac\'on et al., \emph{J. Comput. Phys}. \textbf{178} (1), 15- 36 (2002)} to AMR grids, and employ AMR-aware multilevel techniques (such as fast adaptive composite grid --FAC-- algorithms) for scalability. We demonstrate that the concept is indeed feasible, featuring near-optimal scalability under grid refinement.\footnote{B. Philip, M. Pernice, and L. Chac\'on, {\em Lecture Notes in Computational Science and Engineering}, accepted (2006)} Results of fully-implicit, dynamically-adaptive AMR simulations in challenging dissipation regimes will be presented on a variety of problems that benefit from this capability, including tearing modes, the island coalescence instability, and the tilt mode instability.   

A Plasma Algorithm for Plasmoid Accelerator Modeling

In this paper we present a discontinuous Galerkin approach to resistive/ideal MHD and Hall MHD plasma models. Divergence cleaning is used to ensure that divergence errors are contained. Results of typical plasma physics benchmarks and axisymmetric simulations of FRC accelerators for high powered spacecraft propulsion will be presented.   

Fully implicit moving mesh adaptive algorithm

In many problems of interest, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. The former is best dealt with with fully implicit methods, which are able to step over fast frequencies to resolve the dynamical time scale of interest. The latter requires grid adaptivity for efficiency. Moving-mesh grid adaptive methods are attractive because they can be designed to minimize the numerical error for a given resolution. However, the required grid governing equations are typically very nonlinear and stiff, and of considerably difficult numerical treatment. Not surprisingly, fully coupled, implicit approaches where the grid and the physics equations are solved simultaneously are rare in the literature, and circumscribed to 1D geometries. In this study, we present a fully implicit algorithm for moving mesh methods that is feasible for multidimensional geometries. Crucial elements are the development of an effective multilevel treatment of the grid equation,\footnote{L. Chac\'on, G. Lapenta, {\em J. Comput. Phys.}, {\bf 212} (2), 703 (2006)} and a robust, rigorous error estimator. For the latter, we explore the effectiveness of a coarse grid correction error estimator, which faithfully reproduces spatial truncation errors for conservative equations. We will show that the moving mesh approach is competitive vs. uniform grids both in accuracy (due to adaptivity) and efficiency.\footnote{G. Lapenta, L. Chac\'on, {\em J. Comput. Phys.}, accepted (2006)} Results for a variety of models 1D and 2D geometries will be presented.   

Stability Properties of the Bell Finite Element as applied to Convection Problems

The $C^{1}$ continuous Bell finite elements (also called the ``reduced quintic,'' or $Q_{18})$ in two- dimensions offer a number of advantages over other representations [1]. These include error scaling as order $h^{5}$ in space, the ability to directly represent $\partial ^{4}$ operators using the Galerkin method, and a compact representation with asymptotically only 3 degrees of freedom (DOF) per triangular element. Here we examine the properties of a $\theta $-implicit time integration method using this element to solve the convection equation: $\frac{\partial \phi }{\partial t}=\alpha \cdot \nabla \phi $. We find that even for $\theta $=1 (backward Euler) there are a number of undamped sub-element modes in the corresponding eigensystem. In order to selectively damp the numerical, short wavelength eigenmodes of the system while leaving the physical modes intact, we evaluated the effects of adding small amounts of diffusion (2$^{nd}$ order) and hyper-diffusion (4$^{th}$ order) to the equation. These results are presented in terms of the shift of the corresponding eigenvalues in the complex plane, and on the effect of a plane wave propagating at an arbitrary angle with respect to the element orientation. \newline \newline [1] S. C. Jardin, J. Comput. Phys. 200 (2004) 133   

A collision scheme for hybrid fluid-particle simulation of plasmas

Desorption phenomena at the wall of a tokamak can lead to the introduction of impurities at the edge of a thermonuclear plasma. In particular, the use of carbon as a constituent of the tokamak wall, as planned for ITER, requires the study of carbon and hydrocarbon transport in the plasma, including understanding of collisional interaction with the plasma. These collisions can result in new hydrocarbons, hydrogen, secondary electrons and so on. Computational modeling is a primary tool for studying these phenomena. XOOPIC [1] and OOPD1 are widely used computer modeling tools for the simulation of plasmas. Both are particle type codes. Particle simulation gives more kinetic information than fluid simulation, but more computation time is required. In order to reduce this disadvantage, hybrid simulation has been developed, and applied to the modeling of collisions. Present particle simulation tools such as XOOPIC and OODP1 employ a Monte Carlo model for the collisions between particle species and a neutral background gas defined by its temperature and pressure. In fluid-particle hybrid plasma models, collisions include combinations of particle and fluid interactions categorized by projectile-target pairing: particle-particle, particle-fluid, and fluid-fluid. For verification of this hybrid collision scheme, we compare simulation results to analytic solutions for classical plasma models. [1] Verboncoeur et al. Comput. Phys. Comm. 87, 199 (1995).   

Free-boundary simulation of ITER hybrid scenario

A free-boundary plasma evolution code, DINA-CH, and an advanced core transport code, CRONOS, are combined for the simulations of ITER plasma which require both self-consistent magnetic and kinetic computations. DINA-CH calculates the evolution of a free-boundary plasma equilibrium while taking into account the variation of externally induced currents in the full tokamak system. CRONOS directly makes use of it for the computation of heat and particle sources and their transport. Advanced source and physics based transport models in CRONOS have been used for simulations. Diagnostic models are integrated into DINA-CH for increasing the capability of realistic equilibrium and plasma profile control. For the investigation of fast free-boundary features without degrading the computational performance of either code, additional control of the computation time-steps of the source models has been developed. The free-boundary evolution of the ITER hybrid scenario during the flat-top phase is presented as an illustration of this work.   

TRANSP and PTRANSP at PPPL: Status and Plans.

The PPPL TRANSP code suite is a set of tools for time dependent simulation of tokamak plasmas. The entire system consists of over a million lines of fortran-77, fortran-90, C, and C++ code. Although pieces of the code are over 25 years old, the code has been continually upgraded and modernized, now representing over 60 manyears of labor invested. TRANSP now runs as a service on the Fusion Grid, supporting plasma physics research groups around the world. In this poster, status and plans for TRANSP and associated predictive modeling upgrades (PTRANSP) are summarized. Recent TRANSP code development highlights include: (a) deployment of TRANSP heating modules (NUBEAM and TORIC) as MPI-parallel services, and (b) deployment of the entire TRANSP code as a service supporting separate free boundary predictive simulation of ITER and other future experiments. A summary of recent TRANSP utilization is presented, along with plans for future development of all aspects of the code. Posters covering TRANSP-related topics in greater detail are cross referenced.   

Web Interfaces to Fusion Codes

From our experience in programming methods we can deploy efficient web-based, graphical interfaces that run in a browser and provide secure Internet access to site-specific data and computational physics applications. We present 2 case studies: (1) reflectometry diagnostic simulation, and (2) plotting results of transport analysis runs for tokamak experiments. In case study (1), the user defines the input plasma and reflectometer. The plasma can be parametrically modeled or based on data acquired from experiments. Visualization of the full wave solution is displayed along with the correlation of frequencies between receivers to identify turbulence and fluctuation in the plasma. Case study (2) is a new interface for interactive display of TRANSP results. Both graphical user interfaces, running in web browsers for portability and convenient access, communicate with fusion codes running on compute servers maintained at PPPL. The web service approach facilitates collaboration, enforces security, eliminates software installation, and eases access to scientific applications.   

Progress and plans for the Free-Boundary PTRANSP project

We describe progress on a two-year multi-institutional project to develop a Free-Boundary PTRANSP capability. A prototype PTRANSP client-server configuration has now been developed and successfully tested using ITER simulation data.~ In this configuration, TRANSP acts as a server, computing RF, neutral beam and fusion product heating and current drive at the request of the free boundary predictive code client.~ The TRANSP server simultaneously carries out an analysis of the predictive code results, using the same methods as currently employed for tokamak experimental data analysis.~ A standard TRANSP archive output is produced.~ Equilibrium and profiles are communicated using the NTCC XPLASMA module; synchronization is done by ascii signaling files. The longer range vision is for an integrated predictive transport code that is fully coupled to the UEDGE edge transport code and to a number of existing MHD equilibrium and stability codes and transport models.   

XTranspin, a Visual Data Input Utility for TRANSP

XTranspin is a Motif-based graphical user interface written in C, that facilitates preparing TRANSP and TRDAT namelist files for TRANSP runs. The utility is menu driven and grouped by physics categories. It is easy to install and to use, provides extensive help features and performs data-model consistency checks. XTranspin includes an extensive capability for customization to specific sites or for specific tokamak experiments. In a significant technical change that was made based on physicist user feedback, the code was recently upgraded with a ``minimal change'' algorithm for namelist text. This means that Xtranspin namelist edits only affect the TRANSP namelist file formatting and comments to the minimal extent possible; thus, it is now feasible for users to invoke a text editor for some changes, and use XTranspin for others, without disturbing the TRANSP namelist file layout. XTranspin also supports submitting runs to the TRANSP Fusion Grid Server. The source can be downloaded from the NTCC web site (w3.pppl.gov/NTCC) as part of the tr{\_}client module.   

Status of TRANSP Parallel Services

The PPPL TRANSP code suite has been used successfully over many years to carry out time dependent simulations of tokamak plasmas. However, accurately modeling certain phenomena such as RF heating and fast ion behavior using TRANSP requires extensive computational power and will benefit from parallelization. Parallelizing all of TRANSP is not required and parts will run sequentially while other parts run parallelized. To efficiently use a site's parallel services, the parallelized TRANSP modules are deployed to a shared ``parallel service'' on a separate cluster. The PPPL Monte Carlo fast ion module NUBEAM and the MIT RF module TORIC are the first TRANSP modules to be so deployed. This poster will show the performance scaling of these modules within the parallel server. Communications between the serial client and the parallel server will be described in detail, and measurements of startup and communications overhead will be shown. Physics modeling benefits for TRANSP users will be assessed.   

Progress in Verification and Validation of the PTRANSP Code

The PTRANSP code is the result of modifying the TRANSP code in order to enable the predictive computation of plasma profiles. The NTCC PEDESTAL Module has been added to the PTRANSP code to compute height of the H-mode pedestal. A preliminary verification and validation of the PTRANSP code is carried out using either the MMM95 or GLF23 transport model. Simulation results are compared with experimental data for a variety of H- mode discharges and also compared with corresponding BALDUR simulation results. The BALDUR code inputs are adjusted so that the profiles for power deposition, impurity concentration, magnetic q-value, and elongation are matched, to extent possible, with the corresponding PTRANSP profiles. In the comparisons, the height of the H-mode pedestal is kept nearly constant in time. The effect of changes in the q-profile caused by varying the magnetic reconnection fraction during sawtooth crashes is explored. Numerical artifacts associated with the way the transport equations are solved are investigated. Solutions obtained using new transport equation solvers are compared with previous solutions obtained by smoothing transport over time or space. The objectives of this verification and validation of PTRANSP simulations using the MMM95 and GLF23 models are to develop standardized protocols for integrated modeling simulations of H-mode discharges in tokamaks.   

ITER Simulations Using the PEDESTAL Module in the PTRANSP Code

PTRANSP simulations with a computed pedestal height are carried out for ITER scenarios including a standard ELMy H-mode (15 MA discharge) and a hybrid scenario (12MA discharge). It has been found that fusion power production predicted in simulations of ITER discharges depends sensitively on the height of the H-mode temperature pedestal [1]. In order to study this effect, the NTCC PEDESTAL module [2] has been implemented in PTRANSP code to provide boundary conditions used for the computation of the projected performance of ITER. The PEDESTAL module computes both the temperature and width of the pedestal at the edge of type I ELMy H-mode discharges once the threshold conditions for the H-mode are satisfied. The anomalous transport in the plasma core is predicted using the GLF23 or MMM95 transport models. To facilitate the steering of lengthy PTRANSP computations, the PTRANSP code has been modified to allow changes in the transport model when simulations are restarted. The PTRANSP simulation results are compared with corresponding results obtained using other integrated modeling codes.\newline [1] G. Bateman, T. Onjun and A.H. Kritz, Plasma Physics and {\hbox{Controlled Fusion,}} {\bf 45}, 1939 (2003).\newline [2] T. Onjun, G. Bateman, A.H. Kritz, and G. Hammett, Phys.~Plasmas {\bf 9}, 5018 (2002).   

Comparison of Anomalous Transport Models

It has been found that simulation results obtained using different transport models agree with experimental data about equally well, but they do not agree when predicting the performance of ITER [1]. To aid in understanding these differences, a comparison is made between transport models such as the widely used MMM95 and GLF23 models. A driver program was written to accept standardized inputs for transport models (e.g., ion and electron densities and temperatures, normalized temperature and density gradients, magnetic $q{\rm-value}$, magnetic shear $s$, and effective charge $Z$) and to compute transport coefficients. The driver program is used to carry out comparative scans over the ion and electron temperature gradient as well as scans over dimensionless parameters including $q$, $s$, $r/R$, $\beta$, collision frequency, and $T_i/T_e$. Different channels of transport, such as ion thermal, electron thermal, and particle transport, are considered in the comparison between the models, and qualitative features of these comparative scans will be discussed. To facilitate using the GLF23 model, a new GLF23 interface routine was written to ensure that the evaluation of the model is strictly local to each flux surface and does not make use of information from adjacent flux surfaces.\newline [1] J. Kinsey et al., Nucl.~Fusion {\bf 43}, 1845 (2003).   

New MHD Equilibrium Solver Options in TRANSP

TRANSP users have access to several prescribed boundary MHD equilibrium solvers. The most frequently used solvers in the past have been VMEC, ESC and RZSOLVER. All solvers take the plasma boundary, and some representation of the current profile, external field, and pressure profile as given from the TRANSP input data and/or simulation. Recently, the highly regarded TEQ equilibrium solver was extracted from the LLNL Corsica transport code and installed in TRANSP. TEQ has performed well on data from numerous experiments, and has shown particular promise in addressing difficulties encountered by other solvers modeling low aspect ratio equilibria from such tokamaks as NSTX and MAST. In addition, the low aspect ratio optimized solver ISOLVER is being ported from IDL to fortran for use within TRANSP. ISOLVER is capable of including a plasma rotation-modified pressure term which is important for many low aspect ratio tokamak experiments. This poster will focus on the status of TEQ and ISOLVER in TRANSP, comparing their results with results from the older solvers for selected input data.   

Development of Tokamak Transport Solvers for Stiff Confinement Systems

Leading transport models such as GLF23 [1] and MM95 [2] describe turbulent plasma energy, momentum and particle flows. In order to accommodate existing transport codes and associated solution methods effective diffusivities have to be derived from these turbulent flow models. This can cause significant problems in predicting unique solutions. We have developed a parallel transport code solver, GCNMP, that can accommodate both flow based and diffusivity based confinement models by solving the discretized nonlinear equations using modern Newton, trust region, steepest descent and homotopy methods. We present our latest development efforts, including multiple dynamic grids, application of two-level parallel schemes, and operator splitting techniques that allow us to combine flow based and diffusivity based models in tokamk simulations.\par \vskip6pt \noindent [1]~R.E.\ Waltz, et al., Phys.\ Plasmas {\bf 4}, 7 (1997).\par \noindent [2]~G.\ Bateman, et al., Phys.\ Plasmas {\bf 5}, 1793 (1998).   

Incorporating time-dependent parallel kinetics in NIMROD

Incorporating the physics of rapid parallel particle motion in plasma fluid codes requires a kinetic treatment that admits arbitrary mode, collision and parallel transit frequencies. In this work, we present numerical solutions of the time-dependent, Chapman-Enskog-like drift kinetic equation (CEL-DKE) that emphasize the dominant parallel motion, and subsequent closure of the plasma fluid equations evolved by the NIMROD code. This solution proceeds first via an expansion of the kinetic distortion in a pitch-angle basis. The diagonalization of the parallel free-streaming/time-derivative operator proceeds via an expansion in the eigenbasis of the free-streaming matrix. A massively parallel computational approach then solves each equation in this decoupled system of PDE's on separate groups of processors. This approach ensures scalability to thousands of processors. The remaining speed dependence is handled by solving the separated PDEs on a grid of Guass-Laguerre nodes which renders integration over the speed weighting of the desired $\vec q$ and $\Pi_\|$ closure moments exact. Application of these time-dependent closures in simulations of NTMs and ELMs is discussed.   

Neoclassical parallel closures in axisymmetric toroidal plasmas

Neoclassical closures for the parallel conductive heat fluxes and stresses are derived. A Chapman-Enskog-like approach is adopted with time-dependent effects small compared to parallel free streaming and collisional effects. Distribution function is written as the sum of a dynamic Maxwellian and a kinetic distortion, $F$, expanded in Legendre polynomials $P_l (v_\| /v)$. To lowest order, the magnetic moment and total energy of the particles are conserved. For an accurate treatment of collisional effects, a moment approach is applied to the full, albeit linearized Coulomb collision operator. In contrast to previous derivations,\footnote{E.D. Held, {\it et al}., Phys. Plasmas {\bf 10}, 3933 (2003).} this work does not use a bounce-average to aid in the solution of the drift kinetic equation. Instead, the parallel gradient operator, which acts on $F$ as well as $v_\| /v$, is inverted via the Legendre-polynomial expansion and subsequent diagonalization of the differential equation system for the expansion coefficients. This approach allows for parallel acceleration as well as examination of the closures in higher regimes of collisionality i.e., the plateau and Pfirsch-Schlueter regimes. The application of these closures to NTM simulations using the NIMROD code is also discussed.   

Framework for Modernization and Componentization of Fusion Modules

There are several ongoing efforts to develop a software framework for integrated fusion simulations in the US (SWIM and CPES) the EU (ITM-TF) and Japan (BPSI). The European and Japanese efforts emphasize a standardization of the interfaces to codes within each subgroup (transport, equilibrium, linear stability, MHD, RF, turbulence, et cetera). The US efforts emphasize pairwise coupling of specific codes. The project ``Framework for Modernization and Componentization of Fusion Modules'' (FMCFM) primarily aims to complement the ongoing and future US integrated-modeling efforts by developing standard interfaces to US fusion codes and implement these interfaces by writing wrapper code for existing fusion libraries (transport, equilibrium and linear stability). Standardized interfaces will make it easier to validate codes and will simplify the maintenance for integrated fusion simulations by allowing drop-in replacement of components. FMCFM will also continue to liaise with related European projects and as far as possible try to ensure compatible standard interfaces. Some effort will also be spent on implementation of more robust and scalable solvers for both the Grad-Shafranov and transport equations. A comprehensive test suite for transport solvers will be developed. We will present results from the successfully concluded Phase I project and our plans for the Phase II project in more detail. *This work is funded by DOE through an SBIR grant.   

Overview of the Plasma Science and Innovation Center (PSI-Center)

A principal goal of the Plasma Science and Innovation Center (PSI-Center) is the refinement of overlapping computational tools with sufficient physics, boundary conditions, and geometry to be calibrated with experiments to achieve significantly improved predictive capabilities. The Center is for ICC experiments, especially EC experiments. The PSI-Center will initially concentrate on five focus areas: 1) two fluid / Hall physics, 2) kinetic and FLR effects, 3) reconnection and relaxation physics, 4) transport, atomic physics and radiation, and 5) boundary conditions and geometry. An overview of the progress in these areas will be given. The entire ICC community is invited to participate in this center while eleven experimental programs are now providing the database. These eleven experiments are: 1) Caltech reconnection experiments, 2) FRX-L, 3) HIT-SI, 4) MBX, 5) MST, 6) PHD, 7) Pegasus, 8) SSPX, 9) SSX, 10) TCS, and 11) ZAP.   

MHD Simulation with Insulated Conducting Boundaries and Circuit Interactions

The advantages of insulating plasma from its surrounding conductors have been known since the early days of theta pinch research. In a theta pinch, this insulation allows flux to enter and spread out uniformly over the surface of the plasma, producing a symmetrical pinch. Modern ICC experiments, such as those using inductive helicity injection and rotating field current drive, use insulation to allow flux from multiple circuits to enter and form complex patterns of rotating E{\&}M fields over the surface. The insulating layer between the plasma and the conducting wall allows magnetic flux to move along the surface at the speed of light, which is considered to be infinite. It will move until it finds an equilibrium configuration consistent with the plasma and circuit conditions it encounters on each time step. The solution to this 2D surface equilibrium problem determines how the field will distribute itself throughout the insulator and provides local boundary conditions for the 3D MHD solution in the plasma. The surface equilibrium equations and progress towards solving them will be presented.   

The Semi-implicit Time-stepping Algorithm in MH4D

The Plasma Science and Innovation Center (PSI Center) at the University of Washington is developing MHD codes to accurately model Emerging Concept (EC) devices. Examination of the semi-implicit time stepping algorithm implemented in the tetrahedral mesh MHD simulation code, MH4D, is presented. The time steps for standard explicit methods, which are constrained by the Courant-Friedrichs-Lewy (CFL) condition, are typically small for simulations of EC experiments due to the large Alfven speed. The CFL constraint is more severe with a tetrahedral mesh because of the irregular cell geometry. The semi-implicit algorithm [1] removes the fast waves constraint, thus allowing for larger time steps. We will present the implementation method of this algorithm, and numerical results for test problems in simple geometry. Also, we will present the effectiveness in simulations of complex geometry, similar to the ZaP [2] experiment at the University of Washington. References: [1]Douglas S. Harned and D. D. Schnack, Semi-implicit method for long time scale magnetohy drodynamic computations in three dimensions, JCP, Volume 65, Issue 1, July 1986, Pages 57-70. [2]U. Shumlak, B. A. Nelson, R. P. Golingo, S. L. Jackson, E. A. Crawford, and D. J. Den Hartog, Sheared flow stabilization experiments in the ZaP flow Zpinch, Phys. Plasmas 10, 1683 (2003).   

Boundary conditions in MH4D, a tetrahedral mesh MHD code

Boundary condition enhancements have been made to MH4D, a parallelized, tetrahedral mesh finite volume MHD code. Multi-directional periodic boundary conditions have been implemented and tested by simulating obliquely propagating linear sound waves and shear Alfven waves in a triply periodic box. Dispersion relations were found to be in good agreement with expected values. An insulating boundary condition has been added such that plasma interaction with electrically isolated electrodes can be modeled. A plasma-armature railgun has been simulated in rectangular geometry. Initial simulations of the ZaP z-pinch experiment have been conducted. This poster describes these boundary condition implementations and associated simulations.   

Integral parallel heat flux closure applied in SSPX transport simulations and closing the kinetic equation

Recent SSPX simulation with the NIMROD code\footnote{C. R. Sovinec {\it et al}., Phys. Rev. Lett. {\bf 94}, 035003 (2005).} reveals a discrepancy in temperatures between the simulation and the experiment. The discrepancy may be due to adopting the collisional Braginskii closure despite the existence of low-collisionality regime over a large region of the plasma. In this work the integral heat flux closure based on the pitch-angle scattering operator\footnote{E. D. Held {\it et al}., Phys. Plasmas {\bf 8}, 1171 (2001). } is applied in place of the Braginskii closure. Initial application of this integral closure with limited integration along field lines increases core temperatures by tens of eV's, yielding more consistency with experimental observations. Improvements to the derivation of general closures will also be discussed. The general moment equations with the full linearized collision operator will be introduced for a more rigorous treatment of the collision operator and from which a general scheme for closing the kinetic equation will be presented.   

FRC Simulations using the NIMROD Code

The recently formed Plasma Science and Innovation Center (PSI-Center) is benchmarking and refining the NIMROD code for simulations of field-reversed configurations (FRCs). The NIMROD code can resolve highly anisotropic heat conduction and viscosity [C.R. Sovinec, et al., JCP 195, 355 (2004)]. This combined with its ability to include two-fluid effects, allows us to capture more detailed physics than previous calculations. Recent modifications to the radial boundary conditions capture most of the effects of multiple discrete coils found in many FRC experiments. With this enhancement combined with the ability to include Hall physics, we have begun testing the ability of the code to predict FRC formation and translation, as well as toroidal field generation due to non-symmetric formation. We will also test the prediction of the details of FRC spin-up due to end-shorting, and investigate recent observations [H.Y. Guo, et al., Phys. Rev. Lett. 95, 175001 (2005)] that imply that a small toroidal field could help stabilize the n=2 rotational instability.   

The Plasma Science and Innovation Center Interfacing Group

The Interfacing Group of the Plasma Science and Innovation Center (\urllink{PSI--Center}{http://www.psicenter.org}) facilitates simulations of collaborating Innovative Confinement Concept (ICC) experiments. This includes helping set up meshes for simulations of experiments, assisting in comparison of simulations with experimental data, acquiring and disseminating information about simulations to PSI--Center computational groups, and acting as a conduit of information between experiments. Present collaborating experiments include the Bellan Plasma Group (Cal-Tech), FRX--L (Los Alamos National Laboratory), HIT--SI (Univ of Wash --- UW), MBX (Univ of Texas--Austin), MST, Pegasus (Univ of Wisc--Madison), PHD (UW), SSPX (Lawrence Livermore National Laboratory), SSX (Swarthmore College), TCS (UW), and ZaP (UW). The Interfacing Group also administers a local development computational cluster and network. PSI--Center 3-D resistive MHD codes include \urllink{NIMROD}{http://www.nimrodteam.org} and MH4D. Results from NIMROD runs, and improved numerical diagnostics and data visualization for collaborating experiments will be presented.   

Simulation of ITER Control Scenarios with Corsica Plasma Models

We are developing capabilities for using the Corsica equilibrium and transport code as the nonlinear plasma model, and synthetic diagnostic set, to explore ITER state-space controller techniques. The state-space controllers are implemented in the Mathworks Matlab/Simulink environment. Corsica is coupled to Simulink via remote procedure call (rpc) allowing Simulink to access the Corsica internal database. The Simulink state-space controllers use the rpc interface to communicate active control coil currents to Corsica which calculates and updates the equilibria and transport for free-boundary plasma evolution. When a time step is complete, Simulink retrieves the feedback gap, current, and flux data through the same rpc access. The rpc interface allows the Corsica plasma simulations to be run on a remote high performance Linux cluster while the Simulink graphical interface is run on the local desktop. We will report on the progress in simulating vertical stabilization , and current and shape control experiments.   

ECCD Power Required for NTM Stabilization

High values of plasma $\beta$ can cause ideally nested magnetic flux surfaces to tear and reconnect, leading to the formation of magnetic “islands”. The Neoclassical Tearing Mode (NTM) instability drives the islands to grow to their saturated widths, at which they can persist stably in the plasma. The bootstrap current density is nearly absent within each island because of the local flattening of the pressure profile. One common method of stabilizing NTMs and therefore shrinking the island widths involves replacing this lost current via Electron Cyclotron Current Drive (ECCD). The level of ECCD power required for the stabilization of the NTM is studied using the ISLAND module [1], implemented in the BALDUR code, for noncircular axisymmetric plasmas with multiple islands. In the absence of feedback stabilization, NTM driven islands are predicted to cover more than 25\% of the plasma minor radius, which severely degrades plasma confinement and fusion power production in ITER simulations [2]. The current density within each island is governed by the current peaking factor, which is varied in simulated ITER tokamak discharges. The dependence of the stabilizing power level on the misalignment between the ECCD and the island, as well as on other uncertainties of the system, is part of the numerical study.\newline [1] C.N. Nguyen, {\sl et al.}, Phys.~Plasmas, {\bf 11}, 3460 (2004).\newline [2] F.D. Halpern, {\sl et al.}, Phys.~Plasmas, {\bf 13}, 062511 (2006).   

Adaptive Extremum Seeking Control of ECCD for NTM Stabilization

Neoclassical Tearing Modes (NTMs) drive magnetic islands to grow to their saturated widths, at which they can persist stably in the plasma. The presence of magnetic islands leads to a local flattening of the current density and pressure profiles, which degrade plasma confinement. Since the bootstrap current density is proportional to the pressure gradient, this current is nearly absent within each island. One common method of stabilizing NTMs and therefore shrinking the island widths involves replacing the lost current via Electron Cyclotron Current Drive (ECCD). In order for ECCD to be successful at shrinking the island widths, the current must be driven at the flux surfaces that contain the islands. Moreover, in order to shrink each island with minimal ECCD power, the current must be deposited as close to the center of the island as possible. The difficulty lies in determining the locations of both the island flux surface and the ECCD deposition in real time. The Extremum Seeking feedback method is considered in this work for non- model based optimization of ECCD suppression of NTMs in tokamaks. Both ECCD steering and plasma position change will be considered as mechanisms to maximize in real-time the alignment between the island flux surface and the current deposition location, and thus to minimize the ECCD power required for NTM stabilization.   

Numerical Calculation of the Spectrum of the Flash Light from the Shock Heated Noble Gas

We numerically simulate a flash light generating system in which the light is produced from the noble gas heated by an explosive shock. The generation of the flash light and the shock heating of the noble gas is determined by a hydrodynamic simulation in which the detonation phenomena of the high- explosives can be described in detail. The absorption coefficients of the photons in plasmas are obtained by an ab initio calculation of the atomic properties of the noble gas. While the spectrum of the produced light can be roughly described by a black body radiation, they still shows the remnants of the spectral lines of the gas. The width of the bumps, which are formed by the broadening of the individual lines, is shown to be a characteristic of the system, some of which are compared with the relevant experimental measurements.   

Numerical Study of Active Shielding of a Spacecraft against Cosmic Rays

High-energy Cosmic Rays composed of predominantly 1-2GeV protons and alpha-particles pose a major hazard for subjects, biological materials and sensitive equipment in the Earth's orbit and on the inter-planetary missions. This factor has to be addressed continuously. We study numerically magnetic, electrostatic and hybrid shielding schemes by using computational framework, which embraces relativistic transport of particles, self-consistent electromagnetic fields and ambient plasma response. Numerical approach uses unstructured adaptive grid capturing important details of shield geometry in 3D. Results of the preliminary simulations of a spacecraft shielding against high-energy particles will be reported.