Conservation of Magnetic Moment for Charged Particle Motion in a Time-Dependent Uniform Magnetic Field. SUNGHWAN YI (Cornell University Ithaca, NY 14853) R. C. DAVIDSON (Princeton Plasma Physics Laboratory, Princeton, NJ, 08543)

The adiabatic magnetic moment invariant for the motion of a charged particle in a spatially uniform, time-dependent magnetic field B(t) is studied numerically. The robustness of the magnetic moment invariant µ = mv²/2B is explored for slowly varying and rapidly varying magnetic field B(t), for a charged particle moving in a long solenoid with time-varying current. The numerical method used in this study is a fourth-order Runge-Kutta method, which is used to integrate the nonlinear differential equations for the particle dynamics. Where high accuracy over a long evolution period is desired, a fourth-order symplectic integration method may be used instead. In the case of a slowly varying magnetic field, where the time-scale of the change in the magnetic field is much larger than the particle gyroperiod, it is shown numerically that the adiabatic magnetic moment m is asymptotic to a recently discovered exact magnetic moment invariant M, which is conserved even for rapidly varying magnetic fields. By examining numerically the effects of various functional forms of B(t) on the conservation of the adiabatic magnetic moment invariant, the precise conditions under which m is conserved are identified. Thus, this work characterizes the validity of the adiabatic approximation of the magnetic moment invariant, a fundamental assumption in plasma physics that has never been rigorously quantified.

Development of an auto-convergent free-boundary axisymmetric equilibrium solver. JONATHAN HUANG (Dartmouth College Hanover, NH 03755) DR. JON MENARD (Princeton Plasma Physics Laboratory, Princeton, NJ, 08543)

The calculation of the magnetic flux given an assumed value for the current profile in axisymmetric toroidal plasmas is essential in studying the effects of various magnetohydrodynamic (MHD) instabilities upon controlled fusion. To this end, an iterative, modular algorithm coupled with a fast, direct elliptic solver for the Grad-Shafranov equation has been used to reconstruct the desired free boundary equilibrium solution. This free-boundary Grad-Shafranov (FBGS) equilibrium algorithm is modified with the application of the von Hagenow method for determining the flux on the computational boundary, greatly reducing the time cost from O(N ³) to O(N ²ln N) machine operations as compared to current Green's function methods. The inherent variance in implementing the von Hagenow method gives a mean error bound of 0.1 percent with respect to the normal Green's method. The improvements will allow the grid resolution to be increased efficiently and automatically to reduce the maximum Grad-Shafranov error to values needed for accurate stability calculations on a more effective time scale.

Gain Optimization for the NSTX Power Supply Control System. JOHN SMITH (Colorado School of Mines Golden, CO 80401) RONALD HATCHER (Princeton Plasma Physics Laboratory, Princeton, NJ, 08543)

A time-saving gain optimization procedure is described for the National Spherical Torus Experiment (NSTX) power supply control system. An algorithm has been designed for determination of the optimal gains for prescribed levels of convergence to the reference current over specified time intervals. Simulink is used to emulate feedback control behavior and plant response while imposing realistic constraints on the power supply and control system models. A MATLAB routine containing the algorithm rates convergence based on weighted considerations of rise-time, steady-state error and overshoot in user-specified regions, adjusting both proportional and integral gains accordingly. Coil reference currents from multiple NSTX shot data files provide set points for benchmarking the algorithm. Use of the MATLAB Optimization Toolbox function lsqnonlin (non-linear least squares) in conjunction with dynamic interval setting has been found to be an excellent candidate for gain adjustment. Eventual application may include adaptive, efficient gain optimization and setting for the NSTX power supply control system.

Gyrokinetic Stability Studies of the Microtearing Mode in the National Spherical Torus Experiment H-mode. JESSICA BAUMGAERTEL (University of Washington Seattle, WA 98105) MARTHA REDI (Princeton Plasma Physics Laboratory, Princeton, NJ, 08543)

Insight into plasma microturbulence and transport is being sought using linear simulations of drift waves on the National Spherical Torus Experiment (NSTX), following a study of drift wave modes on the Alcator C-Mod Tokamak. Microturbulence is likely generated by instabilities of drift waves, which cause transport of heat and particles. Understanding this transport is important because the containment of heat and particles is required for the achievement of practical nuclear fusion. Microtearing modes may cause high heat transport through high electron thermal conductivity. It is hoped that microtearing will be stable along with good electron transport in the proposed low collisionality International Thermonuclear Experimental Reactor (ITER). Stability of the microtearing mode is investigated for conditions at mid-radius in a high density NSTX high performance (H-mode) plasma, which is compared to the proposed ITER plasmas. The microtearing mode is driven by the electron temperature gradient, and is believed to be mediated by ion collisions and magnetic shear. Calculations are based on input files produced by TRXPL following TRANSP (a time-dependent transport analysis code) analysis. The variability of unstable mode growth rates is examined as a function of ion and electron collisionalities using the parallel gyrokinetic computational code GS2. Results show the microtearing mode stability dependence for a range of plasma collisionalities. Computation verifies analytic predictions that higher collisionalities than in the NSTX experiment increase microtearing instability growth rates, but that the modes are stabilized at the highest values. There is a transition of the dominant mode in the collisionality scan to ion temperature gradient character at both high and low collisionalities. The calculations suggest that plasma electron thermal confinement may be greatly improved in the low-collisionality ITER.

Particle Diffusion by Waves in Mirror Geometry. TIANHUI LI (Princeton University Princeton, NJ 08540) NATHANIEL FISCH (Princeton Plasma Physics Laboratory, Princeton, NJ, 08543)

Due to their relative simplicity, magnetic mirror geometries have been considered as candidate devices for achieving thermonuclear fusion. One byproduct of nuclear fusion is hot "ash," which can breed instabilities that disrupt plasma confinement. Here, we discuss a novel technique that takes advantage of the mirror physics to stochastically cool these particles with radiation. By employing a spatially-localized single-frequency wave, a resonance with particles of a fixed parallel energy is created which selectively perturbs their perpendicular energy in a chaotic manner. Adiabatic invariants guarantee that the particles will return with the same resonant energy profile as they bounce between mirror points. The net effect of the wave is to create a diffusion path along the mid-plane phase space and the larger position space. When the particles diffuse to a low enough energy, they are removed from the system. We demonstrate the physics behind these wave-particle interactions and solve the diffusion equation for this problem using various software tools. The results show how different spatially-varying diffusion coefficients affect the evolution of the particle distribution. The analysis provides a framework for discussing and optimizing specific wave-diffusion problems.

Period of Validity of Adiabatic Invariance for a Resonant Mathieu Equation. NATHANIEL WILLIAMS (Whitworth College Spokane, WA 99251) HONG QIN (Princeton Plasma Physics Laboratory, Princeton, NJ, 08543)

The Mathieu equation describes a periodically perturbed harmonic oscillator that is resonant when the ratio of the natural frequency of the oscillator to the frequency of the perturbation is near integer and half integer values. The principle of adiabatic invariance tells us that the action variable of a system will be nearly constant over a time interval of order 1/e where e is the order of the rate of change the perturbed system's frequency. Adiabatic invariance is a useful theoretical tool that can greatly simplify calculation. The time scale over which such a simplification is valid must be know before implementation. In plasma physics, adiabatic invariance is the reason why magnetic mirror machines are capable of confining charged particles in a plasma. It is desired to know whether the period of validity of the adiabatic invariant can be extended to higher orders of 1/e. The WKB method, developed by Wentzel, Kramers, and Brillouin, is used to obtain an approximate solution to the Mathieu equation so that its adiabatic invariance can be analyzed. The calculation indicates that the change in the action variable over any interval is of order e. The approximation turns out to be asymptotic only for periods with length of order 1/e². This result verifies the adiabatic invariance for t less than 1/e and extends the result to order 1/e². The adiabatic invariance of the Mathieu equation can be consider constant over time periods up to order 1/e². There is reason to believe this can be extended to higher order but this can not be done by the method employed here.

Pulsed Electrical Discharge in a Gas Bubble in Water. ERICA SCHAEFERE2 (Hartwick College Oneonta, NY 13820) SOPHIA GERSHMAN (Princeton Plasma Physics Laboratory, Princeton, NJ, 08543)

This experiment is an investigation of the electrical and optical characteristics of a pulsed electrical discharge ignited in a gas bubble in water in a needle-to-plane electrode geometry. Argon or oxygen gas is fed through a platinum hypodermic needle that serves as the high voltage electrode. The gas filled bubble forms at the high voltage electrode with the tip of the needle inside the bubble. The discharge in the gas bubble in water is produced by applying 5 - 15 kV, microsecond long rectangular pulses between the electrodes submerged in water. The voltage across the electrodes and the current are measured as functions of time. Electrical measurements suggest a discharge ignited in the bubble (composed of the bubbled gas and water vapor) without breakdown of the entire water filled electrode gap. Time-resolved optical emission measurements are taken in the areas of the spectrum corresponding to the main reactive species produced in the discharge, e.g. OH 309 nm, Ar 750 nm, and O 777 nm emissions using optical filters. The discharge properties are investigated as a function of the applied voltage, the distance between the electrodes, the gas in the bubble (Ar or O₂). Work supported by the US Army, Picatinny Arsenal, NJ and the US DOE (Contract number DE-AC02-76CH03073). ¹Hartwick College, Oneonta, NY, USA ²Rutgers University, Piscataway, NJ, USA ³Stevens Institute of Technology, Hoboken, NJ, USA

SILICON WAFER TRANSMISSION WINDOW FOR ELECTRON-PUMPED LASER SYSTEMS. CHRISTOPHER MCGUFFEY (University of Oklahoma Norman, OK 73072) CHARLES GENTILE (Princeton Plasma Physics Laboratory, Princeton, NJ, 08543)

An electron beam transmission window is being developed as a crucial component for the Electra Krypton Fluoride (KrF) laser at the Naval Research Laboratory (NRL). Such KrF lasers will be employed to provide direct drivers for Inertial Fusion Energy (IFE). The transmission window is composed of a 1/4" thick aluminum frame arrayed with 24 holes, each covered by a 2" round 150 µm thick silicon wafer. The goal is to efficiently allow transmission of a 750 KeV electron beam into the KrF lasing medium. The window must withstand 2.3 atm pressure, high temperature (400 C) from electron bombardment, endure =10⁸ shots and allow high electron transmission efficiency (=80%). Usually, this is achieved with a thin metal foil. However, we believe this method will provide the same transmission efficiency with a greater safety factor in strength because of silicon's mechanical strength, elastic deformation, thermal properties, and electron transmission. The wafers are coated with a 1.2 µm diamond layer to protect the silicon from the corrosive fluorine gas. Silicon wafers are bonded to the aluminum frame using Room Temperature Vulcanizing (RTV) sealant. The RTV becomes a seal that can withstand high temperature and pressure. We tested various RTV sealants for desired performance. We successfully tested individual wafers for strength by applying up to 3.5 atm pressure and baking in a 600 C oven. A prototype window was produced and tested at the laser site at NRL. The overall result was an improvement in durability by a factor of four compared to the previous frame which used square wafers. However, durability is still below operable levels- the wafers shattered after 180 shots. Convection correlations combined with finite element analysis simulations indicate that the silicon wafers were heated well beyond softening temperature. These thermal stresses could have caused the wafers to fail. Conductive RTV and metal contacts should be used in the next round of experiments to provide sufficient heat transfer away from the wafers. Because silicon is a crystal, a repeatable solution can be found that will last practically infinitely. If the proper parameters can be found to handle steady-state operation, silicon windows will provide the desired combination of strength and electron transmission.

Spectroscopic Studies of Merging Spheromak Plasmas in the Magnetic Reconnection experiment. ALEXANDER CARVER (University of Wisconsin Madison, WI 53706) STEFAN GERHARDT (Princeton Plasma Physics Laboratory, Princeton, NJ, 08543)

Magnetic reconnection, the topological breaking and reconnection of magnetic field lines, occurs in many magnetized plasmas e.g. in the solar corona, Earth's magnetosphere, and tokamaks. The ubiquity of plasmas in the universe and the potential use of current-carrying plasmas in fusion power plants warrant an improved understanding of magnetic reconnection. The Magnetic Reconnection eXperiment (MRX) is dedicated to improving our understanding of magnetic reconnection. We used nine fiber optic guides leading to a spectrometer and CCD camera to measure spectral line widths and shifts along many lines of sight within MRX, hence mapping the MRX ion temperature and toroidal plasma velocity. This diagnostic allows us to study flow patterns and ion heating during the merging of two spheromaks. 439 MRX shots and spectrometer images were taken over six days. Averaged ion temperatures ranging from 0 to 30 eV were observed. The average bulk plasma flow was away from the observer at the vacuum vessel edge and towards to observer at the vacuum vessel center with velocities up to 15 km/s. Further study of these results will allow comparison with Tokyo University's TS-3 experiment. These measurements and comparisons are another step toward the realization of fusion power plants and the improved understanding of magnetic reconnection. A.J. Carver was supported by the Department of Energy's Summer Undergraduate Laboratory Internship program. Contract number DE-AC02-76CH03073

Transport and Imaging of Fluorescent Dust in a DC Glow Discharge Plasma. WILL GANNETT (Harvey Mudd College Claremont, CA 91711) ANDREW POST-ZWICKER (Princeton Plasma Physics Laboratory, Princeton, NJ, 08543)

The study of dusty plasmas has wide applications, from astrophysics to chip fabrication. A fluorescent dust cloud illuminated by a longwave mercury ultraviolet (UV) lamp rather than the traditional laser has been produced in a DC glow discharge plasma. The luminescence of the dust particles in the wide UV beam allows imaging anywhere in the chamber, making it possible to observe the initial formation of a cloud as well as dust phenomena not in anticipated locations. The luminescence of the dust particles allows them to be recorded by a charge coupled device (CCD) camera at 30 frames per second, which can be analyzed to obtain a two-dimensional velocity profile for the cloud. This velocimetry is far simpler than contemporary laser methods yet provides temporal and spatial resolution sufficient to analyze a variety of dust phenomena, including dust acoustic waves. Using this ability of examining a large spatial range, we can analyze different modes of transport within and between the dust clouds that form in our chamber. A comparison of dust types and illumination sources will be presented, as well as observations of dust cloud formation and transport.

Velocity Measurements of Turbulent Structures on the National Spherical Torus Experiment (NSTX) with High Speed Cameras. BRETT MCGEEHAN (Dickinson College Carlisle, PA 17013) ROBERT KAITA (Princeton Plasma Physics Laboratory, Princeton, NJ, 08543)

Measuring the characteristics of edge turbulence in fusion plasma devices allows physicists to better understand the confinement properties of fusion plasmas. Edge turbulence is studied with diagnostics such as gas puff imaging (GPI) and the Shifted Wavelength/Interference Filter Technology (SWIFT) diagnostic. In the GPI diagnostic, a neutral gas puff is introduced at the plasma edge to enhance the visible hydrogen emission so that turbulent structures can be seen with a camera viewing along magnetic field lines. The GPI allows for 2D spatial imaging and temporal resolution of the turbulence. The SWIFT diagnostic can yield additional information on the velocity of the turbulent structures normal to the viewing plane. This technique has been demonstrated with single-point measurements, and its extension to 2D imaging is being investigated. Through the use of an Ultima SE CMOS digital camera, manufactured by Photron, Ltd., turbulent structures are captured at framing rates between 4500 and 40,500 frames per second with exposure times of 222 and 25 microseconds, respectively. Images from the edge of the plasma were obtained using a helium filter in a helium plasma, and from the region around the center stack in a deuterium plasma using a deuterium filter. Data analysis has shown that for viewing the edge of the plasma, the maximum frame rate that can be used is 13,500 frames per second to yield a useable signal; for center stack viewing, 40,500 fps is possible. *In collaboration with S. Paul and L. Roquemore (Princeton Plasma Physics Laboratory) and N. Nishino (Hiroshima University).

Water Quality and Pollution in Our Enviornment. LAURA LIZARZABURU (California State University Long Beach Long Beach, CA 90840) CARL SZATHMARY (Princeton Plasma Physics Laboratory, Princeton, NJ, 08543)

This unit will consist of a series of experiments about the properties of water and the effects of water pollution. Water is perhaps the most important life sustaining resource on Earth. The importance of unpolluted water in sustaining human, animal and plant life can't be overstated. Yet, each day, millions of gallons of water are lost to various contaminants. Water pollution is a serious global problem. Much of the damage is due to human activity. An important factor that plays a role in the degradation of our water sources is simple ignorance of the affect that our daily activities have on the global ecosystem. Awareness and prevention are important ways to control water pollution. It is essential that we inform our children of these issues regarding water pollution and quality. The knowledge that the students will gain will empower them to make positive changes in the future. This unit will familiarize students with the properties of water and pollutants. It will also allow students to familiarize themselves with common laboratory practices. Students will learn to collect samples in the field and perform water quality tests for nitrates, dissolved oxygen, and pH.