Session JP8: Poster Session IV: Education and Outreach; Undergraduate Research; Electron and Ion Beam/Space Charge; DIII-D I; Reversed Field Pinches; Energetic Ions and Electrons in Helicons

Plasma Physics/Fusion Energy Education at the Liberty Science Center

The Liberty Science Center (LSC) is the largest (300,000 sq. ft.) education resource in the New Jersey-New York City region. A major {\$}109 million expansion and renewal was recently completed. Accordingly, PPPL has expanded the science education collaboration with the Center into three innovative, hands-on programs. On the main floor, a new fusion exhibit is one of the focuses of ``Energy Quest.'' This includes a DC glow discharge tube with a permanent external magnet allowing visitors to manipulate the plasma while reading information on plasma creation and fusion energy. In the section of LSC dedicated to intensive science investigations (20,000 sq. ft) we have added ``Live from NSTX'' which will give students an opportunity to connect via video-conferencing to the NSTX control room during plasma operations. A prototype program was completed in May, 2007 with three high school physics classes and will be expanded when NSTX resumes operation. Finally, a plasma physics laboratory in this area will have a fully functioning, research-grade plasma source that will allow long-term visitors an opportunity to perform experiments in plasma processing, plasma spectroscopy, and dusty plasmas.   

Educational Outreach at CASPER

The CASPER Educational Outreach program with support from the Department of Education, the Department of Labor and the National Science Foundation advances physics education through a variety of avenues including CASPER's REU / RET program, High School Scholars Program, spiral curriculum development program and the CASPER Physics Circus. These programs impact K-12 teachers and students providing teachers with curriculum, supporting hands-on material and support for introducing plasma and basic physical science into the classroom. The most visible of the CASPER outreach programs is the Physics Circus, created during the 1999-2000 school year and funded since that time through two large grants from the Department of Education. The Physics Circus is part of GEAR UP Waco (Gaining Early Awareness and Readiness for Undergraduate Programs) and was originally one of 185 grants awarded nationwide by the U. S. Department of Education in 1999 to help 200,000 disadvantaged children prepare for and gain a pathway to undergraduate programs. The CASPER Physics Circus is composed of intense science explorations, physics demonstrations, hands-on interactive displays, theatrical performances, and excellent teaching experiences. Examples and efficacy data from the above will be discussed.   

Plasma Science and Applications at the Intel International Science and Engineering Fair

Three years ago, the Coalition for Plasma Science (CPS) established a plasma prize at the Intel International Science and Engineering Fair. The APS/DPP and the IEEE/PSAC have helped make this effort a success by helping to identify judges. Each year since then, the number of plasma-related projects has increased. This year's prize was awarded for an instrument that, based on the ratio of spectral emission in two bands, detects when a high-pressure street light is about to fail. This allows time for an, efficient, scheduled replacement rather that an emergency service call. The CPS is a broadly-based group of institutions and individuals whose goal is to increase the understanding of plasmas for non-technical audiences. CPS activities include maintaining a website, http://www.plasmacoalition.org, developing educational literature, organizing educational luncheon presentations for Members of Congress and their staffs, and responding to questions about plasmas that are received by the CPS e-mail or toll-free number. The science fair prize and other CPS activities depend on the voluntary labor of CPS members and associates. New participants are needed to expand CPS activities and reach a larger audience. Send an e-mail to the CPS at CPS@plasmacoalition.org for information.   

Effective Technology Integration Shows New Frontiers in Education

In this ever-changing world, technology is affecting how people view learning and the overall educational process. For an educator, the successful implementation of technology can be one of the most effective tools in the classroom. The introduction of virtual simulations of real life situations into what was once considered a teacher-centered classroom, allows the educator to meet the complex differentiated needs of a multi-faced student population. In this modified classroom, the focus naturally shifts on the students and their interaction with the rest of the class and beyond. Effective integration of technology literally opens a window onto the outside world providing students with increased motivation and with the necessary expertise to enter the workforce or successfully pursue higher education. This work analyzes the impact of technology, the methodologies currently in use, advantages and disadvantages, providing examples on how to successfully implement effective programs under budgetary constraints.   

Measurement and Analysis of ECH Power Injected Into DIII-D

The 6 ECH waveguides at DIII-D are on the order of 100 meters in length with up to 16 miter bends. Accurate measurement of the ratio of generated-to-transmitted power gives the transmission line efficiency directly and is essential for analysis of experiments. The power generated by the gyrotrons is measured calorimetrically for each pulse, but direct measurements of the injected power have relied on analysis of modulated plasma heating, which can overlook significant power where plasma volumes are large and ECH driven temperature fluctuations are small. High power tests of efficiencies of individual components have been difficult due to mutual interaction of components, sensitivity of power monitors to polarization, and the generally high efficiency of the components. We report a direct measurement of the efficiencies of complete transmission lines, using a high power dummy load placed at the end of each DIII-D waveguide. Experimental results will be compared to previous measurements and to theoretical calculations of the performance of the components and waveguide lines.   

Power Accounting in DIII-D

The plasma facing components in a fusion reactor will be exposed to high levels of heat and particle flux. A full accounting of where the plasma energy is deposited is important for designing future fusion reactors. To understand where the power is going, we do a total power accounting in DIII-D for different conditions such as H-mode, ohmic, and ELM-free H-mode plasmas. We use measurements from IR cameras, bolometers, Langmuir probes, and thermocouples to determine the distribution and magnitude of power deposition inside the tokamak as well as the consistency of the different measurements. We compare the thermal response measurements with both a simple thermal diffusion model and a finite element thermal model of the target plate tiles. A basic parameter that relates heat and particle flux at the plasma/materials interface is the power transmission factor. By comparing the particle flux and heat flux, we can measure the sheath factor profile for each of the above conditions.   

UV Induced Motion of a Fluorescent Dust Cloud in a DC Glow Discharge Plasma

Understanding dust dynamics is a key concern for both processing and astrophysical plasmas. To this end, an experiment was designed where a silica ($<$5 $\mu $m) and fluorescent dust mixture was added to an argon DC glow discharge plasma. The fluorescent dust allows one to observe the entire 3D structure of the cloud when it is illuminated by a 100 watt UV ($\lambda $ = 365 nm) lamp. This method offers an advantage over laser scattering techniques that only allow 2D slices of the cloud to be observed and is simpler than scanning mirror techniques or PIV (Particle Image Velocimetry). Under typical parameters (P=150 mTorr, V$_{anode}$= 100 V, V$_{cathode}$= 400 V, I$_{total}=<$2mA) when the cloud is exposed to the UV, the mixture fluoresces, moves $\sim $2mm towards the light source and begins rotating. Particle rotational velocities in excess of 3 $^{mm}$/$_{s}$ have been observed near the cloud's periphery while particle velocities decrease towards the center of the cloud. Both cloud translation and rotational velocity were found to be a function of UV intensity. Theoretical and experimental results will be presented.   

ECR Plasma Deposition of Copper

ECR plasma is used in processing due to its ability to produce stronger, denser, and more uniform plasma as opposed to other processing plasmas. Having a more controlled plasma makes it easier to prevent unintentional damage to the sample, by having fewer stray ions come in from undesired angles. Samples were sputtered on silicon wafers at various pressures, powers, and sample distances from the plasma, and then analyzed with a scanning electron microscope to determine the thickness, uniformity and contamination. A typical plasma's parameters would have a microwave power of 2500watts, a target bias of 125volts, and an argon pressure of 0.46mtorr. An optical spectrometer was utilized to measure impurity content within the chamber. In addition, two-line spectroscopy was performed to measure electron temperature in lieu of a Langmuir probe. These initial measurements allow one to undertake more advanced projects on this apparatus, as well as refine the measurements of electron temperature through additional resources or statistical calculations and acquire more precise values with less uncertainty by acquiring apparatus that is able to be more finely calibrated.   

Construction of a Plasma Dynamo Prototype

A new plasma experiment to investigate the self-generation of magnetic fields has been proposed. Here, a prototype experiment is described which plans to verify the concept of inducing the rotation of a nearly magnetic field free plasma (confined at the boundary by a highly localized multicusp magnetic field). The experiment consists of a cylindrical vacuum chamber with a series of insulated permanent magnet rings in a cusp geometry (poles facing inward with alternating polarity along the walls and end caps of the cylinder). The resulting field is axisymmetric and decays quickly away from the walls. Metal electrodes positioned between the magnet rings are biased such that the resulting electric field induces plasma rotation through the ExB drift. The principle is quite general and by controlling the poloidal profile of the toroidal rotation, high magnetic Reynolds number plasmas flows can be generated that result in magnetic field self-generation or plasma flows unstable to the magnetorotational instabilty.   

$H\alpha$ power loss in SSPX

An absolute calibration has been performed on each of the seven chords of the $H\alpha$ diagnostic [Z. Wang, G.A. Wurden, C.W Barnes, et al., Rev. Sci. Instrum. 72, 1059 (2001)] at SSPX. Simple models are used to estimate the total power lost to $H\alpha$ radiation throughout experimental shots. Using these models, high energy shots (Te $>$ 500 eV) are compared to low energy shots.   

Electrostatic dust detector with improved sensitivity

Measurement of dust inventories in next-step fusion devices will be necessary to ensure compliance with safety regulations. A device for detection of dust on remote surfaces, consisting of an ultrafine grid of interlocking copper traces biased to 30-50V, has been developed and tested[1]. Impinging dust particles produce temporary short circuits and the resulting current pulses are recorded using nuclear counting electronics. A digital oscilloscope was used to analyze the current pulse waveform under various experimental conditions in order to enhance the sensitivity of the device. Preliminary results indicate an order of magnitude increase in sensitivity to carbon dust particles is possible. This would enable the detector to measure the low levels of dust ($\sim$5 ng/cm$^2$/shot) produced in NSTX. Results will be presented from both small 12x12 mm and large 50x50 mm detectors, using both carbon and tungsten dust. [1] C.V. Parker et al., J. Nucl. Mater., 363-365 (2007) 1461.   

Multi-element Magnetic ``B-dot'' Probe

We describe a 24-element magnetic probe consisting of miniature commercial chip inductors that will be used to investigate the evolution of the magnetic field lines during a reconnection event. Eight clusters of three mutually orthogonal inductor coils mounted in a linear array provide \textit{dB/dt }data in the $x$, $y$, and $z$ directions with a spatial resolution of 0.5 cm. The probe will be part of the Reconnection Scaling Experiment (RSX) at Los~Alamos National Laboratory, which creates multiple magnetic flux ropes of H$^{+}$ plasma. Using numerical integration, we expect to measure magnetic field strengths of 1-10 gauss. The plasma columns of RSX that undergo magnetic reconnection, merging, and bouncing evolve on a characteristic timescale of 1-10 $\mu $s, which is well within the probe's expected time resolution.   

Structural Properties of Yukawa Tubes

Due to the highly charged dust particles, complex plasma systems become strongly correlated and often arrange in interesting structures [1]. Direct measurements of plasma parameters are difficult [2], but simulations have been proven to work as a diagnostic tool for the plasma crystals being studied. Here, we investigate a one component Yukawa plasma limited in radial movement by a confining potential but unrestricted in the lateral direction. We performed extensive Monte Carlo simulations for different densities in a system with periodic boundary conditions and compared the results with an analytic theory. The dust particles are found to arrange in particularly interesting structures, which can be compared to 2D plasma crystals [3] in the radial direction, but unique in the chains created laterally which were found to be dependent on the density, the screening parameter in the Yukawa interaction, and the temperature.\newline \newline [1] O. Arp et al., Phys. Rev.Lett. 93, 165004 (2004)\newline [2] M. Bonitz et al. Phys.Rev. Lett. 96, 075001 (2006)\newline [3] V.M. Bedanov et al., Phys. Rev. B 49, 2667 (1994)   

Rotation Generation in Helicon Plasmas

Angular momentum transport in accretion discs occurs significantly faster than predicted by classical viscosity. Magnetorotational instability (MRI) is proposed to generate the required turbulence necessary to enhance angular momentum transport. However, the physics of MRI is studied mostly by theory and simulation. Recently, study of MRI is beginning using liquid metal. In order to study MRI in plasmas, controlled rotation must first be generated. Radial DC current is a means for generating jxB torque when an axial magnetic field is applied. To accomplish this initial goal, two concentric cylindrical electrodes were designed, built, and will be inserted into helicon plasma. The radial profiles of both velocity and electron density will be obtained by Mach and Langmuir probes, and if available, initial results will be reported on the search for MRI.   

Validating the simulation of the effects of secondary neutrals on the MSE gas-filled-torus calibration

A common procedure of injecting a neutral beam into a gas-filled torus with known magnetic fields in vacuum is used to calibrate motional Stark effect (MSE) diagnostics on many toroidal magnetic devices. A cause of anomalies encountered in this calibration has been explained as a consequence of secondary neutrals from the ionized beam. Under certain conditions, these re-neutrals emit H-alpha spectra that have the proper Doppler shift to pass through the MSE filters yet have a different polarization than those from the primary beam neutrals, thus contaminating the measured Stark electric field angle. Existing IDL code has been adapted to simulate the gas-filled-torus calibration of MSE in Alcator C-Mod, NSTX, and TFTR vessel geometries. A sensitivity study involving the post-processing of outputs with different gas pressures, beam injection angles, magnetic field pitch angles, and system resolutions will benchmark the code against the respective experimental data.   

Soft X-ray Tomography at DIII-D

Two new 32 channel SXR pinhole cameras have been recently installed in the DIII-D tokamak. They are sensitive to photons in the 2-20 keV range, but an interchangeable set of diamond filters with five settings allows selection of the range of energies of interest. New tomographic inverters were developed and validated against analytic models and magnetically reconstructed EFIT equilibria. Tomographic inversion techniques suitable for use with the new diagnostic geometry and preliminary inversions of new SXR data will be presented, along with re-analysis of earlier measurements of disruption-generated fast electrons and equilibria. Thanks to a temporal resolution of a few microseconds, progress has also been made in the tomographic reconstruction of rapidly moving, relatively weak emitters such as rotating islands.   

Advanced Diagnostic Design for Paul Trap Simulator Experiment (PTSX)

The Paul Trap Simulator Experiment (PTSX) is a compact laboratory Paul trap that uses a pure-ion plasma to simulate a long, thin charged particle bunch coasting through a kilometers-long magnetic alternating-gradient transport system. Current PTSX experiments are exploring the limits of the smooth focusing model, and using the detection of collective mode oscillations to infer key bunch properties such as the line density and transverse temperature. These experiments require the use of advanced diagnostics to measure the transverse distribution of the plasma perticles at a given instant in time. One set of experimental diagnostics uses a CCD camera with a short exposure time to collect light from Laser Induced Fluorescence (LIF) of the cross section of a barium plasma beam. A second set of experimental diagnostics utilizes capacitive coupling of the ions with four electrodes, which are connected to high- input-impedance active filters. Details of the design and performance of the laser system, CCD camera system, and collective mode diagnostic electronics will be presented.   

Retarding Field Energy Analyzer Measurements of Ion Velocity Distributions in a Helicon Plasma Source

A four grid retarding field energy analyzer (RFEA), with a fifth grounded entrance grid, has been constructed based on published design criteria [Charles et al., Phys. Plasmas \textbf{7}, 5232 (2000).]. A fast amplifier is used to sum the current collected by the suppressor grid and the collector current. Measurements of the ion velocity distribution function (ivdf) as a function of neutral pressure and magnetic field mirror ratio in the HELIX plasma source will be presented. The ivdf measurements will also be compared to laser induced fluorescence measurements made at the same location in the expansion region of the plasma source.   

Development of a diagnostic array for the measurement of velocity profiles across open-channel liquid metal flows

An array of potential probes utilizing the Hall effect to measure liquid metal flow velocity is developed and implemented in the Liquid Metal Experiment (LMX) at PPPL, a study of magnetohydrodynamic (MHD) stability in open-channel flow. The channel experiment has applications in the study of the dynamics of ``plasma oceans'' on the surface of neutron stars. Furthermore, liquid metal is studied as a possible material for plasma-facing components in fusion reactors, an avenue of research requiring an understanding of turbulent liquid metal flow under the influence of magnetic fields. Liquid gallium alloy circulates with a flow height of 1 cm through the open channel of dimensions 15 cm wide by 70 cm long within a uniform perpendicular magnetic field of strength up to 0.7 T. A series of 16 electrode pairs, one per centimeter from wall to wall across the width of the channel, detect potential differences across 2 mm sections of flow normal to the mean velocity and the magnetic field. For flow speeds of 0.2 m/s and magnetic field strengths of 0.1 T, a raw signal of about 40 $\mu $V is expected, which will be amplified with a gain of 1000. Velocity profiles will be measured at various heights in the flow. Design considerations, calibration procedures and results will be presented.   

Correlative data studies in NSTX: Studies of magnetic topology with the motional Stark effect diagnostic

The motional Stark effect diagnostic has been implemented to measure the magnetic field pitch angle in the National Spherical Torus Experiment (NSTX). By measuring the polarization of H-alpha emission from the system's neutral beam injectors, it is possible to gather time-resolved data and observe the evolution of the pitch angle over the duration of a plasma discharge. This data facilitates inquiry into magnetic topology changes, including reconnection events that may be occurring. Understanding magnetic reconnection is vital to eventually achieving a stable burning plasma, as well as being of interest in space and astrophysical phenomena. Here, IDL is used to correlate data from the pitch angle and other diagnostics to gain insight into instabilities and reconnection events that occur within NSTX. Such insights are presented with illustrative examples of data.   

High Harmonic Fast Wave Propagation and Heating on NSTX

Recent experiments on the National Spherical Torus Experiment (NSTX) show that the high harmonic fast wave (HHFW) core heating efficiency depends on the antenna phasing and plasma conditions. [1]. Power losses in the edge due to rf sheath formation or other parasitic absorption processes could occur if the waves propagate nearly parallel to the wall in the edge regions and intersect nearby vessel structures. To investigate this possibility, the 3D HHFW propagation in NSTX has been studied both analytically and numerically with the ray tracing code GENRAY. Initial calculations show that for certain values of the launched parallel wave number and magnetic field, the waves in NSTX are launched at a shallow angle to the vessel wall. In contrast, for ICRF heating in C-Mod or ITER, the initial ray trajectories tend to be more radially oriented. Comparisons of the GENRAY results with 2D TORIC full wave simulations for the power deposition will also be discussed. \newline [1] See invited talk by J. C. Hosea this meeting.   

Modeling of Neutral Beam Ion Prompt Loss from NSTX Plasmas

Neutral beam injection is a frequently used and effective means of heating magnetically confined fusion plasmas. While most of the injected neutrals are ionized and captured within the plasma, a fraction can be lost immediately to the wall due to being born on unconfined orbits, termed prompt loss. To minimize the computation time of calculating these prompt loss ions, the neutral beam ion phase space is reduced to two dimensions by coupling a simple beam deposition model with a constants of motion (COM) approach. In particular, we work with the magnetic moment and the canonical toroidal angular momentum. This approach allows easy visualization of the fast ion population in phase space and rapid calculation and display of the boundary between confined and lost particles. Since NSTX is equipped with a scintillator type fast loss ion probe, we are also evaluating whether this method can be used to predict the pitch angle profile of the prompt loss signal in the probe. In principle, this representation of the particle phase space might also be useful for simulation of other fast ion diagnostic signals. Example calculations and status of this work will be presented.   

Calculation of Divertor Thermal Response as a Function of Material Composition for NSTX

Present tokamak designs use a magnetic divertor to deposit heat from the edge plasma onto Plasma Facing Components (PFCs) designed to remove the heat. Studying how this heat is distributed under various discharge conditions gives insight into how heat deposition can be optimized, and how different materials respond to plasma heating. In the National Spherical Torus eXperiment (NSTX), infrared cameras are used to measure divertor surface temperature, from which heat flux is computed using a 1D semi-infinite slab model with constant thermal conductivity. Here, a 1D simulation of the PFCs incorporating temperature-dependent thermal properties is used to compute heat flux profiles resolved across time and tile thickness. The PFC response to a given heat flux is also computed, and comparisons of resulting temperature profiles are made for a variety of materials including ATJ graphite (presently in the NSTX divertor), pyrolytic graphite, molybdenum, and tungsten.   

Plasma Sheath and RF Wave Interaction in Tokamaks

This project is part of recent efforts to theoretically and computationally model the radio frequency (RF) heating of tokamak plasmas. The antenna and containment vessel surface have important effects on the heating efficiency of the RF waves. Power loss in the sheath that forms at the edge of the plasma is a primary concern. The magnetic field topology at the vessel surface is important for nonlinear absorption mechanisms. We used archived data from the Alcator C-Mod tokamak at MIT, and prepared it through IDL and Fortran procedures to be used as a boundary condition at a simulated vessel wall in the TORIC code that simulates RF wave propagation in a tokamak. The code was run in an iterative fashion to address the nonlinearity of the situation and achieve a self-consistent solution for power deposition and sheath width, as described in [D. D'Ippolito and J. Myra, Phys. Plasmas 13, 102508 (2006)]. Conclusions could then be drawn regarding the locations of high power loss.   

Calculation of charge-changing cross sections of ions or atoms colliding with fast ions using classical trajectory method

Evaluation of ion-atom charge-changing cross sections is needed for many accelerator applications. A classical trajectory Monte Carlo simulation has been used to calculate ionization and charge exchange cross sections. For benchmarking purposes, an extensive study has been performed for the simple case of hydrogen and helium targets in collisions with various ions. To improve computational efficiency, several integration methods, including Runge-Kutta with adaptive stepsize and Bulirsch-Stoer with Stoermer's Rule, were compared. Despite the fact that the simulation only accounts for classical mechanics, the calculations are comparable to experimental results for projectile velocities in the region corresponding to the vicinity of the maximum cross section.   

Extensions to DG, a Graphical Tool for Editing 2D Edge Plasma Quasi-Orthogonal Computational Meshes

DG is a tool used, in combination with mesh generating codes such as Carre and Sonnet, to create and modify ``structured curvilinear quasi-orthogonal meshes''\footnote{R.\ Marchand and M.\ Dumberry, Comp. Phys. Comm. {\bf 96}, 232 (1996).} for use in modeling plasma and neutral transport in the boundary of tokamak magnetic confinement experiments. DG has already been used to define the geometry used by the B2-Eirene code in simulating the neutral transport behavior in the ITER divertor\footnote{A.\ S.\ Kukushkin et al., Nucl. Fusion {\bf 45}, 608 (2005).}. Another recent application is DEGAS 2 modeling of Gas Puff Imaging experiments on the National Spherical Torus eXperiment\footnote{D. P. Stotler et al., J. Nucl. Mater. {\bf 363--365}, 686 (2007)}. We describe how we brought DG into compatibility with the freely available Open Motif 2.x library, allowing it to be run reliably on the LINUX cluster at PPPL. In addition, several new features added to DG are presented. Together, these improvements allow precisely tailored and general meshes to be generated more quickly and easily, accelerating the progress of computational studies on tokamak plasmas.   

Exact canonical drift Hamiltonian formalism with pressure anisotropy and finite perturbed fields

A Hamiltonian formulation of the guiding center drift orbits is extended to pressure anisotropy and field perturbations in axisymmetric systems. The Boozer magnetic coordinates are shown to retain canonical properties in anisotropic pressure plasmas with finite electrostatic perturbations and electromagnetic perturbed fields that affect solely the parallel component of the magnetic vector potential. The equations of motion developed in the Boozer coordinate frame are satisfied exactly by direct verification of the drifts.   

Tokamak Plasma Equilibrium Controllability Limitations Due to Delays

When designing the control loops for tokamaks, it is important to acknowledge the effects of time delays. An assumption which is sometimes made is that if the system open loop response is intrinsically slow, due for example to substantial vessel shielding or to the imposition of limits on rate of change of control currents, then extra time delays which are individually shorter than these will not have significant undesirable effects on control. However, because delays and phase lags are in general cumulative in effect, this assumption is typically incorrect. This study examines and quantifies these effects in the axisymmetric control loop in superconducting tokamaks, for the case of plasma current control, radial and vertical position control, and plasma boundary control. Delays in the power supplies, data acquisition, and vessel structure are taken into account. Methods for remediating the negative effects due to time delays are also presented.   

Effects of Magnetic Measurement Uncertainty and Non-axisymmetry on Tokamak Equilibrium Reconstruction

Constraints must be imposed on the pressure and current profiles to solve the Grad-Shafranov equation during equilibrium reconstruction of tokamak plasmas. Rigorous consideration of magnetic measurement uncertainty is necessary to impose physically consistent constraints, yielding the best solution. Discharges from DIII-D are analyzed with two versions of EFIT. The first is the currently public version. The second utilizes a newly added magnetic uncertainty matrix based on detailed estimates of uncertainty in magnetic measurements of DIII-D expected to improve the accuracy of reconstruction and of estimates of error in reconstruction. Reconstructions using these methods are compared to determine the effects of the uncertainty matrix. Preliminary results indicate the new EFIT returns similar values for global plasma parameters such as $\beta_{p}$, $l_{i}$, and shape with a more realistic $\chi ^{2}$ than the public version. Furthermore, the effects of non-axisymmetry on reconstructions are explored.   

Magnetic Mapping Techniques for Poloidally Diverted Tokamaks

Resonant magnetic perturbations have recently been used to control type-I ELM instabilities by controlling the edge pressure gradient of the DIII-D tokamak. To characterize the 3D structure of the perturbed magnetic field, we have developed an efficient symplectic mapping technique based on the Hamilton Jacobi method. We first numerically determine the resonant Hamiltonian of the magnetic field lines inside DIII-D. Then the Hamilton Jacobi method is used to construct a symplectic map describing the spatial structure of the magnetic field near the separatrix. We use this map to numerically compute a number of quantitative features of the tokamak. We determine the Lyapunov exponents, describing the divergence of the field lines inside the tokamak. We also study the fractal nature of the magnetic field near the divertor plates. The results are compared with other methods of numerical approximation as well as analytic techniques.   

Computational Fluid Dynamics (CFD) simulation of the Madison Dynamo Experiment.

The Madison Dynamo Experiment is designed to study a self-generated magnetic field called a dynamo. The flow characteristics of a water experiment that is dimensionally similar to the liquid sodium experiment has been modeled using the Computational Fluid Dynamics (CFD) software \textit{Fluent.} Results from the CFD simulations are used to confirm flow characteristics measured experimentally by both Laser Doppler Velocimetry (LDV) and Particle Imaging Velocimetry (PIV). Simulations can also give insight into the flow characteristics in regions of the experiment which are not accessible via the LDV and PIV systems. The results from the simulations are also used as input for a MHD code to predict the threshold for Dynamo onset. The CFD simulations -- in conjunction with the MHD dynamo prediction code -- can be used to design modifications to the experiment to minimize costly changes. The CFD code has shown that the addition of an equatorial baffle along with several poloidal baffles can lower the threshold for Dynamo onset.   

MHD Mode Identification Using Magnetic Probes and Its Application to the Edge Harmonic Oscillation

Magnetohydrodynamic instabilities in tokamak plasmas are usually known for their role in limiting plasma performance. However, the edge harmonic oscillation (EHO) seen in quiescent H-mode plasmas has advantageous effects because it increases edge particle transport, allowing control of the edge pressure. By operating with edge pressures stable to peeling-ballooning modes, edge localized modes (and their intense bursts of heat to the wall) can be avoided. This study aims to improve the understanding of the EHO through the creation of a filament-based toroidal current model capable of simulating both plasma and induced vessel currents. This model predicts the magnetic fields measured by Mirnov probes, serving as a synthetic diagnostic for the presence of MHD instabilities. After tests validate the model against 2/1 and 3/2 tearing modes, it will be used to localize the EHO. This will be accomplished with a least squares fit of simulated m/n modes to experimental observations of the EHO.   

Linear and Nonlinear Studies of Trapped Electron Mode Turbulence

Linear stability diagrams are presented to clarify the onset of toroidal drift modes, including ITG, and resonant and non-resonant TEMs, as a function of density and temperature gradients. Several hundred linear gyrokinetic stability analysis were performed with the GS2 code\footnote{W. D. Dorland \textit{et al.}, Phys. Rev. Lett. 85 (2000) 5579.} to generate a stability diagram, varying density and temperature gradients around the ``Cyclone Base Case.'' Two separate studies have previously found that zonal flows play very different roles in TEM turbulence. The first,\footnote{D. R. Ernst \textit{et al.} Phys. Plasmas 11(5) (2004) 2637. Also IAEA-CN-149/TH/1-3 (2006).} found that zonal flows play a strong role near threshold, where they produce a nonlinear upshift. The second,\footnote{T. Dannert \textit{et al.} Phys. Plasmas 12 (2005) 072309.} for a case well above threshold, found that zonal flows have little effect on the turbulent saturation level. To better understand this behavior, we are performing a series of nonlinear gyrokinetic simulations to analyze the anisotropy of the turbulent eddies, and the role of zonal flows, as a function of drive.   

Comparative Study to Determine an Optimal Material for Tritium Production in a Direct Drive IFE Reactor

An important technical and economic consideration in designing the prospective direct drive inertial fusion energy (IFE) reactor is the determination of a suitable mechanism for tritium breeding. A comprehensive review is undertaken to determine the optimal breeding material, examining two candidate compounds: 83Pb-17Li and (LiF)$_{2}$BeF$_{2}$ (FLiBe). In this study, the compounds are evaluated based on chemical and physical properties, structural requirements, feasibility, hazards, and costs of application. Preliminary results seemed to indicate that FLiBe may be the more practical option, due to its mechanical utility and the relative projected efficacy of blanket design. However, much remains to be investigated, particularly the properties of breeder and structural materials in the specific conditions of a reactor. This evaluation process will require further theoretical modeling as well as practical trial, currently planned in other progenitor reactor designs. This paper will present the results of the analysis of these candidate breeder materials.   

Conceptual Design for a 2 GW Inertial Fusion Energy (IFE) Direct-Drive Power Reactor Employing Magnetic Intervention

Presented is a conceptual design for a 2 GW IFE direct drive fusion power reactor. This design employs a cusp field to deflect IFE-generated ions away from the dry first wall of the target chamber and into specifically designed ion dumps. The reactor operates at 5 Hz, consuming $\sim $450,000 tritium targets/day, injected at $>$100 m/s into the target chamber and uniformly illuminated by laser light, stimulating detonation. The resulting fusion energy is collected by equatorial ion dumps equipped with heat exchangers. The reactor will breed and recycle its own fuel through the use of breeder blankets and a fuel recovery system. To minimize target-particle interference, the chamber will be kept at $<$0.5 mTorr through the use of magnetically levitated turbomolecular pumps (TMPs) and corresponding backing pumps. Under investigation are the principles of magnetohydrodynamics (MHD) which may be applied to attenuate and harness the energy residing in the post detonation ion fields.   

Concept to Employ Magnetohydrodynamic (MHD) Conversion in a 2 GW Direct Drive Inertial Fusion Energy (IFE) Power Reactor

The conceptual design of a 2 GW direct drive IFE power reactor may provide an opportunity to directly harness~the power in the post detonation ion fields. Conceptually, this can be accomplished by utilizing a magnetic cusp field to guide the ions into equatorial and polar ion dumps. The ion fields resulting from this magnetic intervention configuration pose a distinct challenge, as their intensity may have the potential to damage the ion dumps. One method of addressing this challenge is by employing MHD conversion to transform the internal energy of the fields directly into electrical energy, a process which would also reduce the fields' strength. In order to analyze the potential of MHD conversion in IFE, results of previous work in other applications are examined in the context of this project. Preliminary assessment reveals that MHD conversion is a promising solution to this issue, although a number of engineering and practical concerns will need to be addressed. This paper concentrates on the primary issues associated with MHD conversion. \textit{Support for this research was provided by the U.S. Department of Energy's Science Undergraduate Laboratory Internship (SULI) Program.}   

Implementation of Au Transmission Photocathode for Laboratory Astrophysics Diagnostics Research

The development of laser driven experiments with a focus on Inertial Confinement Fusion has allowed scientists to carry on studies in Astrophysical phenomena that were previously impossible to duplicate. A type of tool used for the diagnostics of this experiments is known as an X-ray framing camera. This device makes use of the X-rays produced by plasma during such experiments and converts them into electrons that are detected by a phosphor material. We have implemented a detached Au transmission photocathode (160 Angstroms thick) on a MCP and are evaluating it using a 1.5 keV Al K-alpha X-ray source. We will report the results of measurements to determine whether this improves the effective quantum efficiency of the X-ray detection system.   

Elemental Analysis of Carbon Disks using Proton Induced X-ray Emission

An experimental method for determining the $\rho $R and ($\rho$R)$^{2}$ of high energy-density inertial confinement fusion targets has been developed, which involves measuring the yield of tertiary neutrons with energies higher than 20 MeV. Carbon activation is a suitable technique for this measurement due to its high energy neutron reaction threshold and the availability of ultra high-purity samples at a relatively low cost. The tertiary neutron yield is more than six orders of magnitude lower than the primary neutron yield, so ultra pure carbon samples that are free from any positron-emitting contaminants are essential to this diagnostic. The goal of this project was to use proton induced x-ray emission (PIXE) as a technique for determining trace amounts of contaminant elements in the carbon disks.   

Measuring Positron Annihilation in NaI(Tl) Detectors as the Final Stage in a Carbon Diagnostic.

This study was performed to increase the detection efficiency of 511 keV annihilation radiation from decaying C-11 by indentifying and eliminating different forms of background radiation originating from the source and the ambient background in the gamma ray coincidence spectrum. Cu-64 was substituted for C-11 in this investigation since it could be easily made from Cu-63 via neutron capture using a PuBe neutron source. Using Cu-64, the effect of ambient background and source induced radiation in the NaI detectors was examined in three coincidence spectra. The spectra were generated by pairing the output signals of the three NaI(Tl) detectors and displaying them as two dimensional spectra. Different gamma ray background contributions to the coincidence spectrum were studied, including annihilation radiation from pair production in the detectors and the lead shielding. Detector geometries and source materials which modified the Compton scattering background were also investigated.   

VELoCiRaPTORS.

The Venting and Exhausting of Low Level Air Contaminants in the Rapid Pneumatic Transport of Radioactive Samples (VELoCiRaPTORS) system is constructed to transport radioactive materials quickly and safely at the NIF. A radioactive sample will be placed inside a carrier that is transported via an airflow system produced by controlled differential pressure. Midway through the transportation process, the carrier will be stopped and vented by a powered exhaust blower which will remove radioactive gases within the transport carrier. A Geiger counter will monitor the activity of the exhaust gas to ensure that it is below acceptable levels. If the radiation level is sufficient, the carrier will pass through the remainder of the system, pneumatically braking at the counting station. The complete design will run manually or automatically with control software. Tests were performed using an inactive carrier to determine possible transportation problems. The system underwent many consecutive trials without failure. VELoCiRaPTORS is a prototype of a system that could be installed at both the Laboratory for Laser Energetics at the University of Rochester and the National Ignition Facility at LLNL.   

Noble Gas Analysis for the OMEGA Gas Sampling System

The OMEGA Gas Sampling System (OGSS) at the Laboratory for Laser Energetics can be used to study a wide variety of implosion parameters in inertial confinement fusion. By doping a target capsule with carefully chosen detector nuclei, nuclear reactions between fusion products and detector nuclei can produce noble gas isotopes.~Following a capsule implosion, these gases are pumped out of the target chamber and are collected into sample bottles.~We have developed a bench-top analysis station at Geneseo capable of determining the number of noble gas atoms present in the sample bottles.~A needle valve is used to admit gas from the sample bottles into a vacuum chamber at a controlled rate.~The conductance of the needle valve is a function of pressure and gas type. A residual gas analyzer (RGA) is used to measure the partial pressures of each type of noble gas in the vacuum chamber. The RGA is calibrated with a calibrated leak, which allows known amounts of different gases into the chamber at a constant rate.~ Analysis of the gasses collected following a D$^{3}$He implosion is currently underway.   

Modeling a Carbon Diagnostic System Using MCNPX

Monte-Carlo N-Particle Extended (MCNPX) is currently being used to model various carbon diagnostic configurations for use at OMEGA with plans to design a similar system for the NIF. The purpose of such models is to optimize the carbon diagnostic's detection of signature products (i.e. tertiary neutrons) from a self-sustaining inertial confinement fusion (ICF) implosion. Results will be presented.   

Impact of Cryogenic Temperatures on the Mechanical Properties of \textit{Steatoda Triangulosa} Spider Silk

The mechanical properties of dragline spider silk from the species \textit{Steatoda Triangulosa} are examined at 77K. Dragline silk is used as a structural material to support deuterium - tritium laser fusion targets at the Laboratory for Laser Energetics (LLE) in Rochester, NY. As the targets are filled, the dragline is exposed to cryogenic temperatures. To simulate this environment, silk is dipped into liquid nitrogen. The strength, toughness, and modulus of elasticity of silk in liquid nitrogen are compared to these properties in air. Cryogenic dragline is 200{\%} as strong, 125{\%} as tough, and has an elastic modulus of 300{\%} compared to silk in air at room temperature.   

Preparation of Deuterated Polymer Targets for the OMEGA Magnetic Recoil Spectrometer

Uniform deuterated polymer films on tantalum substrates are used as targets for the new Magnetic Recoil Spectrometer (MRS) at the OMEGA laser system at the University of Rochester's Laboratory for Laser Energetics. The MRS is designed to measure the neutron energy spectrum produced in inertial confinement fusion (ICF) experiments by detection of deuterons elastically scattered from the polymer target. The goal of our project is to produce circular films with areas ranging from 2 to 15 cm$^{2}$ and thicknesses ranging from 40 to 300 microns. Design parameters stipulate that the polymer thicknesses must be characterized to within 5{\%} with less than 5{\%} variation throughout the sample. Methods for preparing and characterizing these films will be discussed.   

Improvements in Target Fabrication for Laboratory Astrophysics Experiments at the University of Michigan

Laboratory astrophysics seeks to study astrophysical phenomenon by modeling them in a micro-scale experiment, called a ``target'', which mimics the conditions and behavior of stellar phenomenon. Once built, the targets are transported to the Omega Laser Facility and placed in the laser chamber, where 5kJ of energy is fired onto a pinhead-sized area in order to create the necessary pressure required to launch the experiment. Collected data is then used to better understand the physics behind these various space phenomenon. Due to their extremely small size, targets must be built with a high degree of accuracy; therefore, continuously improving the process of target fabrication is crucial to experimental success. Some advancements in the target build process include more fully utilizing our machining capabilities, which allows for consistently cleaner, more accurately built targets. Another improvement is consolidating multiple functions into a single piece. This reduces the number of additional components, which reduces opportunities for error, as well as the overall build time. These changes have already been shown to improve our ability to collect successful data. *This research was sponsored by the NNSA through DOE Research Grants DE-FG52-07NA28058, DE-FG52-04NA00064, and other grants and contracts.   

Experimental Study of Effects due to Perturbations on Boundary Conditions on Couette Flows

When fluid flows between two independently rotating cylinders at low aspect ratios (the ratio of the height to the difference in radii), the flow is seen to deviate substantially from ideal Couette flow due to Ekman circulation along the end caps. In the case where the end caps are attached to the outer cylinder, fluid with less angular momentum is advected into the bulk flow, which decreases the mean velocity as predicted by the ideal case. In order to study the stability of Ekman circulation, an experiment was devised to perturb the Ekman boundary layer by modifying the inner cylinder. Water flows between an aluminum inner cylinder and acrylic outer cylinder and its velocity is measured using a Laser Doppler Velocimeter (LDV) scanned radially from underneath to obtain 2-D velocity profiles. When the inner cylinder is perturbed, the flow is closer to the ideal Couette case if Ekman circulation is reduced. The robustness of the Ekman layer along with flow discontinuities at the edges where the inner and outer cylinder meet will be studied against perturbations of varying magnitudes.   

A Smart Filtering Method for Space-Charge Dominated Beam Simulations

We present a ``smart'' filtering method that removes the small-wavelength noise in beam simulation programs which can occur due to numerical errors. This method utilizes Fourier transforms and a low-pass filtering scheme to remove noise from space-charge generated electric fields. In particular, for a uniform-density (beer can) beam distribution, we find the necessary amount of Fourier k-space for removing field errors while maintaining the electric field's maximum peak value and its full width at half maximum. The term ``smart'' refers to the method's applicability for general beam distributions which have equivalent root-mean-square sizes as the uniform-density case. We demonstrate the ability of the algorithm to filter the longitudinal and radial components of the electric field in both one dimension and two dimensions. This method has the potential to reduce computational run-time while maintaining a high level of accuracy, i.e. less than two percent field error.   

Phase Space Tomography and Slice Emittance Measurement of Beams with intense Space Charge

We report a simple and portable tomographic method to map the beam phase space, which can be used in the majority of accelerators. The tomographic reconstruction process has first been compared with results from simulations using the particle-in-cell code WARP and the results show excellent agreement. Our diagnostic has also been successfully demonstrated experimentally on simple scaled set-up which uses high-current, low energy electron beams to study the transverse dynamics of beams in both emittance and space charge dominated regimes. Finally, using a fast ($<$5ns decay time) phosphor screen and a gated PIMAX2 ICCD camera we report slice tomographic measurements of transverse phase spaces over a beam pulse and conclude by deriving interesting physical insights on space charge dynamics.   

Halo creation and propagation in the University of Maryland Electron Ring

The University of Maryland Electron Ring (UMER) is a scaled low-energy electron machine, designed to access the intense regime of beam operation in particle accelerators. One of the phenomena that can arise during the transport of intense beams is the creation of halos around the beam core. This can significantly deteriorate the quality of the beam and complicate the maintenance of the facility. In this study, we use the WARP particle-in-cell code to numerically investigate a number of causes of halo in intense beams and the propagation of the halo downstream. In particular, we focus on the UMER beam, where halos have been observed and compare the simulation results to the experimental data.   

Measurement and Simulation of Source-Generated Halos in the University of Maryland Electron Ring (UMER)

An area of nonlinear beam physics that is important in a number of beam systems, and is inadequately understood, is the generation and evolution of beam halos. Study of beam halos therefore has served as one rationale for recent research on UMER. While it was expected that halo formation would primarily result from nonlinear dynamics during beam propagation, recent experiments and simulations have instead identified imperfections in the source geometry, particularly in the region near the emitter edge, as a potentially significant source of halo particles. The edge-generated halo particles, both in the experiments and the simulations are found to pass through the center of the beam a short distance downstream of the anode plane. Understanding the detailed evolution of these particle orbits is therefore important to designing any aperture to remove the beam halo. Both experimental data and simulations will be presented to illustrate the details of this process, as well as proposed means of mitigation.   

Detection of Collective Beam Modes in the Paul Trap Simulator Experiment

Experiments have been performed to excite and detect collective transverse symmetric and quadrupole modes $(m= 0,2)$ in the Paul Trap Simulator Experiment (PTSX). PTSX is a compact laboratory Paul trap that simulates a long, thin charged-particle bunch coasting through a kilometers-long magnetic alternating-gradient transport system by putting the physicist in the frame-of-reference of the beam. The transverse dynamics of particles in both systems are described by the same sets of equations -- including nonlinear space-charge effects. The frequency spectrum of collective mode oscillations depends on the details of the distribution function, the focusing field strength, the self-field intensity parameter, and geometric effects such as the proximity of the conducting wall. These oscillations typically involve various combinations of the frequencies $\hat \omega_q$, $\hat \omega_p$, and $(\hat \omega_q^2 - \hat \omega_p^2/2)^{1/2}$ (where $\hat\omega_q$ is the average transverse focusing frequency and $\hat\omega_p$ is the plasma frequency) modified by geometric effects $(r_p/r_w)$. Initial experiments focus on identifying collective modes whose signature will serve as a robust diagnostic for key properties of the beam, such as line density and transverse emittance. The experimental results are compared with the output of particle-in-cell simulations performed using the WARP code.   

Experimental verification of random error-induced beam degradation in high intensity accelerators using a compact Paul trap

The effects of random errors in quadrupole magnets on intense beam propagation have been investigated in the Paul Trap Simulator Experiment (PTSX). The PTSX device is a compact linear Paul trap that can simulate the nonlinear transverse dynamics of intense beam propagation over large equivalent distances through an alternating-gradient (AG) transport lattice. The amplitude of the voltage waveform applied to the electrodes in the PTSX device corresponds to the quadrupole focusing field strength in an AG lattice system. Hence, by slightly modifying the voltage amplitude of the PTSX electrodes in every half focusing period, the effect of randomly distributed quadruploe focusing gradient error in high intensity accelerators can be effectively studied. Initial results show that the transverse beam emittance increases linearly with error amplitude and holding time. The experimental results are also compared with results obtained from 2D WARP simulations.   

Beam plasma interaction in the solenoidal focusing of intense ion beams

Extreme longitudinal and transverse bunching of space charge dominated ion beams is required to heat targets into the warm dense matter regime. Longitudinal bunching factors in excess of 70 with a several millimeter spot have been demonstrated on the 300-keV, 27-mA K+ ion beam Neutralized Drift Compression Experiment in rough agreement with particle-in-cell end-to-end simulations. To achieve the necessary spot size for target heating ($<$ 1 mm), a strong final focus solenoid is currently being fielded. To neutralize the large perveance beam, a plasma with density greater than that of the beam must be injected into or produced within the solenoid. In this paper, we present theory and simulation of the neutralization of such an ion beam in a highly magnetized plasma. Beam neutralization and instability in the plasma are modeled in highly resolved simulations. The impact of instabilities and resulting turbulence on the focusing ion beam phase space is studied.   

Meter-Long Plasma Source for Heavy Ion Beam Charge Neutralization

Plasmas are a source of unbound electrons for charge neutralizing intense heavy ion beams to focus them to a small spot size and compress their axial length. The source should operate at low neutral pressures and without strong externally-applied electric or magnetic fields. To produce long plasma columns, sources based upon ferroelectric ceramics with large dielectric coefficients have been developed. The source utilizes the ferroelectric ceramic BaTiO$_{3}$ to form metal plasma. The drift tube inner surface of the Neutralized Drift Compression Experiment (NDCX) is covered with ceramic material. High voltage ($\sim $ 8 kV) is applied between the drift tube and the front surface of the ceramics. A BaTiO$_{3}$ source comprised of five 20-cm-long sources has been tested and characterized, producing relatively uniform plasma in the 5x10$^{10}$ cm$^{-3}$ density range. The source has been integrated into the NDCX device for charge neutralization and beam compression experiments. Initial beam compression experiments yielded current compression ratios $\sim $ 120. Future research will develop longer and higher density sources to support beam compression experiments for high energy density physics applications.   

Warm-fluid theory of a thermal equilibrium for a charged-particle beam in a periodic quadrupole magnetic focusing field

A new warm-fluid thermal equilibrium theory is developed for charged-particle beam propagation in a periodic quadrupole magnetic focusing field. Warm-fluid equilibrium equations are solved in the paraxial approximation. The equation of state for the thermal equilibrium is adiabatic. The beam density profile, the beam envelope equations and self-consistent Poisson equation are derived. The numerical algorithm for solving the self-consistent Poisson equation is discussed. Examples of thermal beam equilibrium will be presented for low intensity and high intensity beams propagating in periodic quadrupole magnetic focusing fields.   

Perturbative Particle Simulation Studies of Periodically Focused Intense Charged Particle Beams

High intensity charged particle beam propagation in a periodic focusing lattice has been studied numerically using a model in which the beam equilibrium and dynamical behavior are described self-consistently by the nonlinear Vlasov-Maxwell equations. To carry out this investigation, the Beam Equilibrium Stability and Transport (BEST) code, which uses a 3D low-noise perturbative particle simulation method, has been extended to periodic-focusing systems. The scheme begins with a smooth-focusing lattice, which is the smooth-focusing approximation for the periodic lattice, and adiabatically replaces the smooth-focusing lattice by the periodic-focusing lattice. Using this approach, periodic-focusing solenoidal configurations have been investigated using a slow turn-on time to minimize beam mismatch, and periodic-focusing quadrupole configurations have also been studied using this approach.   

Acceleration Gap Effects on the Longitudinal Compression of Intense Ion Beams in the Neutralized Drift Compression Experiment

Longitudinal compression of space-charge-dominated ion beams to high currents in nanosecond pulses for warm dense matter and heavy ion fusion applications is achieved by imposing a time-dependent velocity tilt to the charge bunch across the acceleration gap of a linear induction accelerator. The subsequent neutralization of the beam by a pre-formed plasma allows the intense charge bunch to compress above the traditional space-charge limit for quiescent propagation and longitudinal focusing. The detailed physics and implications of acceleration-gap effects and focusing aberration on optimum current compression are reviewed. Quantitative examples using particle-in-cell simulations explore the dependency of the axial compression on effects such as the finite-size acceleration gap, voltage waveform, and the beam's initial temperature, pulse length, intended fractional velocity tilt, kinetic energy uncertainty, and distribution function.   

Nonlinear Delta-f Particle Simulations of Energy-Anisotropy Instabilities in High-Intensity Bunched Beams

The self-consistent Vlasov-Maxwell equations and a generalized delta-f particle simulation algorithm are applied to high- intensity finite-length charge bunches. For bunched beams with anisotropic energy, there exists no exact kinetic equilibrium because the particle dynamics do not conserve transverse energy and longitudinal energy separately. A reference state in approximate dynamic equilibrium has been constructed theoretically. The electrostatic Harris instability driven by strong energy anisotropy relative to the reference state have been simulated using the generalized delta-f algorithm for bunched beams. The observed growth rates are larger than those obtained for infinitely-long coasting beams. The growth rate decreases for increasing bunch length to a value similar to the case of a long coasting beam. For long bunches, the instability is axially localized symmetrically relative to the beam center, and the characteristic wavelength in the longitudinal direction is comparable to the transverse dimension of the charge bunch. A smooth, automatic-switching scheme between the delta-f and total-f methods is being used to simulate the nonlinear phase of the instability.   

Filamentation of a Radially Converging Heavy Ion Beam in a Background Plasma with External Solenoidal Magnetic Field

Heavy ion inertial fusion and high energy density physics experiments with intense heavy ion beams require the transverse focusing of the ion beam pulse onto a small focal spot. Plasma is used to neutralize the beam's space charge to achieve maximum compression. Unfortunately, a heavy ion beam propagating in a background plasma may be subject to the filamentation instability. The beam can be severely disrupted by the instability before it reaches the target. An external solenoidal magnetic field can be used to stabilize the instability. This paper analyzes the influence of both the transverse convergence and an applied solenoidal magnetic field on the filamentation instability of a cold heavy ion beam propagating in neutralizing background plasma. We employ the WKB approach to analyze the space-time development of the instability and compare it with the results of simulations using the particle-in-cell code LSP. The results of the investigations identify the instability growth rates, levels of saturation, and the conditions for quiescent beam propagation.   

Controlling Charge and Current Neutralization of an Ion Beam Pulse in a Background Plasma by Application of a Small Solenoidal Magnetic Field

Propagation of an intense charged particle beam pulse through a background plasma is a common problem in astrophysics and plasma applications. The plasma can effectively neutralize the charge and current of the beam pulse, and thus provides a convenient medium for beam transport. The application of a small solenoidal magnetic field can drastically change the self-magnetic and self-electric fields of the beam pulse, thus allowing effective control of the beam transport through the background plasma. 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. The analytical studies show that the solenoidal magnetic field starts to influence the self-electric and self-magnetic fields when $% \omega_{ce}> \omega_{pe}\beta_{b}$, where $\omega_{ce}=eB/m_{e}c$ is the electron gyrofrequency, $\omega_{pe}$ is the electron plasma frequency, and $\beta_{b}=V_{b}/c$ is the ion beam velocity relative to the speed of light. Analytical formulas are derived for the effective radial force acting on the beam ions, which can be used to minimize beam pinching. The results of analytical theory have been verified by comparison with the PIC simulation results, which show good agreement.   

New Spectral Method for Halo Particle Definition for Intense Charged Particle Beams

Spectral analysis of a mismatched charged particle beam has been utilized in particle-in-cell simulations performed with the WARP code. It is shown that the betatron frequency distribution function of a mismatched space-charge-dominated beam has a bump-on-tail structure attributed to beam halo particles. A new spectral method for halo particle definition is proposed in this work that provides the opportunity to carry out a quantitative analysis of halo particle production by beam mismatch. Furthermore, the spectral analysis of the mismatch relaxation process provides important insights into the emittance growth attributed to the halo formation and the core relaxation processes. Numerical simulations are performed using the smooth focusing approximation, which describes the average effects of an alternating-gradient lattice, and by using a full quadrupole focusing field model, taking into account the effects of the alternating-gradient quadrupole field.   

Optimized Photonic Crystal Accelerating Cavities

Photonic crystal (PhC) cavities may provide a useful replacement for metallic accelerating cavities used in linacs today. The main advantage of PhC cavities lies in their ability to suppress higher-order modes (HOMs). Because of the frequency bandgaps found in PhCs, certain disruptive HOMs can be made to propagate out of a PhC structure. One disadvantage with PhC cavities, however, is their size. For a PhC cavity, many layers of scattering elements are needed to attain Q-values comparable to metallic cavities, because of the radiative losses from the trapped mode. In response, we show how optimizing the positions and size of the individual scatterers can increase the maximum Q due to radiation losses by $\sim$ 2 orders of magnitude for a specified number of scatterers, and thus decrease the physical extent required for cavities of this type. We present here examples of optimized PhC accelerating cavities and discuss their individual resonant mode spectra. We also show results from simulations of particle beams passing through these cavities without significant excitation of HOMs.   

Photonic Crystal Structures for Particle Acceleration

An electromagnetic resonant cavity with only a single mode can be created using a photonic crystal structure to trap the fields. Because photonic crystals can reflect only radiation within a small frequency range, they can trap only the fundamental mode of a cavity, while higher frequency modes propagate out through the crystal. The absence of higher modes can benefit accelerator cavities, in which higher order modes (wakefields) excited by the beam degrade the beam quality. We examine the fields of an electron beam in a photonic crystal cavity using computer simulations.   

Simulations of neutral loading process in ECR sources

High intensity, high charge-state beams for a broad variety of ions are a requirement for next-generation heavy-ion beam accelerators. As the intensities produced by current Electron Cyclotron Resonance (ECR) sources insufficient for many ions, the ion beam production has to be optimized. Efficient loading of the neutrals into the ECR plasma is one of the key elements for optimizing the ion beam production. Kinetic simulations provide a means to understanding where along the interior walls the uncaptured metal atoms are deposited and, hence, how to optimize loading of the metal into the ECR plasma. We are currently extending the plasma simulation framework VORPAL with models to investigate effective loading of heavy metals into ECR ion sources via alternate mechanisms, including vapor loading, ion sputtering and laser ablation. Here we will present the models, simulation results of vapor loading and initial comparisons with experiments at the VENUS source at LBNL.   

Development of a 25 keV Ion Beam Source for Fast-Ion Studies on the Large Plasma Device

A helium ion beam source (25 kV, 3 A) has been constructed for studying the fast-ion physics on the large plasma device (LAPD). The source has been designed to match the ion beam speed with the Alfv\'{e}n speed in the LAPD plasma. The ion beam will be injected at a variety of pitch angles into the LAPD. The ion-beam source has an inductive RF source to produce $\approx 10^{19}$ m$^{-3}$ helium plasma in a ceramic dome (volume: $\approx 0.04$ m$^3$). The beam is accelerated using a rectangular (8 cm x 8 cm), multi-aperture, three-grid system. A pulsed DC power supply (25 kV, 4 A) has been developed to deliver the acceleration voltage to the grids during the time interval (0.1 -- 2.0 ms, rep rate: 1 Hz) of the beam injection. A EUV grazing incidence monochromator (for the Doppler-shift measurements) and Langmuir probes are main diagnostic tools. The source is presently being conditioned in a test facility. We plan to present the initial results on the characterization of the ion-beam and its interaction with the LAPD plasma.   

Transport of Fast Ions Modulated by Shear Alfv\'{e}n Waves

The interaction of fast particles with Alfv\'{e}n instabilities is important in magnetic fusion devices and natural plasmas. In this experiment, shear Alfv\'{e}n waves (SAW) modulate fast ion transport through Doppler shifted cyclotron resonance, in addition to the classical collisional diffusion. A Li$^{+}$ ion source is inserted in the LArge Plasma Device (LAPD) with ion energy up to $\sim $2000 eV, detected by a collimated fast ion energy analyzer. RF antennas launch waves with amplitude of $\backslash $delta B/B $\sim $ 0.1{\%} that propagate along the machine axis. When launched in (out of) phase with the perpendicular wave electric field, fast ions gain (lose) energy from (to) the wave. A $\sim $10{\%} increase in the beam radial width and beam signal modulation at SAW frequency are observed. These fast ion transport phenomena peak near the predicted resonance condition. ($\omega _{Alfv\mbox{\'{e}}n}$ -- k$_{z}$v$_{z}=\omega _{fast-ion})$   

Numerical Optimization Studies of the NDCX Induction Accelerator

The Heavy Ion Fusion Science Virtual National Laboratory is designing the Neutralized Drift Compression Experiment (NDCX) at the Lawrence Berkeley National Laboratory. NDCX will help develop novel, still unexplored beam manipulation techniques in order to establish the physics limits on compression of heavy ion beams for creating high energy density matter and fusion ignition conditions. The NDCX components include an injector that delivers a lithium ion beam, and an accelerator that boosts the energy to 2.8 MeV. Further beam manipulations will compress the beam to a final spot radius of less than 1 mm and a pulse length of 1 ns. In order to reach those final parameters, it is required to extract a high brightness beam and minimize the transverse and longitudinal emittance growth along the accelerator. We will present numerical optimization studies of the injector which is based on the Accel-Decel concept, and the accelerator which is based on acceleration by induction gaps.   

Initial Operation of Pulsed Ion Beam system for NBI of All Japan ST Program

The UTST experiment at Univ. Tokyo is expected to produce ultra high-beta Spherical Tokamak (ST) using mega-watt heating power of ST merging/reconnection. A key issue after the formation is to maintain the produced ultra-high-beta ST over 100 Alfven times for its stability research. The following three heating methods has been arranged for the sustainment experiment: (1) advanced RF heating method developed in TST-2, (2) low-cost pulsed neutral beam injection (NBI) system under development and (3) intermittent merging/ reconnection by TS-3 and 4. The NBI system for UTST was designed to realize (1) low voltage (15kV for low-field side of a ST) and high current (20A), (2) maintenance-free, (3) low-costA SUS washer gun has been employed for the first time to realize the maintenance-free plasma (ion) source, in sharp contrast with the conventional filament type plasma source. In the initial operation of plasma source, the electron and ion density profile suitable for the ion beam extraction had been observed. Now evaluation of characteristics of the extracted plasma has been performed. Further results of the developed NBI will be presented   

Further studies of a simple gyrotron model equation

Work with other authors, \textit{J. Phys. A: Math. Theor.}\textbf{ 40}, 2203 (2007), is extended. Analytic and computational methods are applied to examine desirable start-up conditions in a gyrotron and to minimize deleterious bunching effects. Analysis permits extensive, but incomplete exploration of the dynamics, while computation with the simple model provides essential, more complete results. Several of the conclusions of the cited paper are significantly modified.   

Recent DIII-D Research in Support of ITER

The DIII-D research team has made several recent contributions that are impacting the design of key components for ITER. Using criteria determined from recent DIII-D experiments showing the importance of island overlap in the edge, researchers have evaluated various non-axisymmetric coil configurations for ITER. DIII-D experiments have established criteria for stabilization of the most serious instabilities in ITER: resistive wall modes (RWMs) and neoclassical tearing modes (NTMs). Analysis suggests that a small level of toroidal rotation is sufficient to stabilize RWMs even at $\beta _{N}$=4. DIII-D experiments were instrumental in the choice of an improved ECCD mirror design for ITER, enabling the ability to simultaneously stabilize the m=3/n=2 and m=2/n=1 NTMs with $\sim $10~MW in ITER. Recent studies on DIII-D simulating the current ramp phase in ITER indicate a risk of peaked current density profiles and an associated susceptibility to vertical instability. Results of other research on disruption mitigation using massive gas injection and on the choice of plasma facing materials in ITER will also be presented.   

Understanding Magnetic Field Error Correction in DIII-D

A comparison was made between the measured DIII-D magnetic field error and an ideal MHD plasma response model. New measurements of TF coil errors reduced the bounds of unknown errors. Empirical error corrections for DIII--D standard left-handed-pitch plasmas were refined, and a new empirical correction was developed for right-handed-pitch plasmas. Empirical corrections were analyzed by the new Ideal Perturbed Equilibrium Code, which computes the linear free-boundary plasma response to prescribed external error and/or correction fields in real geometry. This analysis explained the paradox of why the DIII-D C-coil empirical correction is $\sim $3 times the error field on a vacuum field basis: the plasma strongly modifies the error and correction fields differently, and the total fields actually come to partial cancellation. The theory provides guidance for error correction with imperfectly matched fields. Separately, a short proof of principle experiment showed that further improvement (locked mode avoidance) is possible if the remaining TF coil current feed error were reduced.   

Low Frequency Response of Plasma to MHD Perturbations

MHD stability of the plasma depends critically on the frequency and wave length of the perturbation. Future tokamaks are expected to operate in regimes where the external macro-scale perturbations have much lower frequencies than the intrinsic dynamical time scales of the particles [1]. This situation calls for a detailed re-examination of the assumptions on previous models of the response of the plasma to MHD perturbations [2]. The kinetic formulation of MHD response [3] is examined numerically in this work. The energy and momentum flux across the plasma surface is expressed in terms of the MHD perturbations. Implication on the stability and plasma response [4] relevant for the resistive wall mode, with its time scale dramatically reduced by the external resistive wall, is discussed. \newline [1] B. Hu, \textit{et al.,} Phys. Plasmas \textbf{12}, 057301 (2005). \newline [2] A. Bondeson and M.S. Chu, Phys. Plasmas \textbf{3}, 3013 (1996). \newline [3] T.M. Antonsen, Jr. and Y.C. Lee, Phys. Fluids \textbf{25}, 132 (1982). \newline [4] Y.Q. Liu, \textit{et al.,} Phys. Plasmas \textbf{7}, 3681 (2000).   

Development of State-Space Model-Based Kalman Filter for n$\ge $1 Resistive Wall Mode (RWM)

While significant progress has been made for $n=$1 RWM identification and control, it is now predicted that $n$~\textbf{$>$} 1 RWMs could appear even after the $n=$1 RWM is suppressed. Algorithm development, as well as diagnostic capability enhancement, is being done in order to identify the $n=$ 2 or 3 RWMs in the presence of a stabilized $n=$1 RWM for DIII-D. Specifically, taking advantage of the successful development of the Kalman filter to discriminate ELM noise from an $n=$1 RWM [1], a more advanced Kalman filter is being developed to detect both $n$=1 and $n$ \textbf{$>$} 1 RWMs. Noise characterization and modeling is deemed critical to determine the optimized Kalman gain. This multi-mode state-space model will also serve as a basis to design a model-based RWM feedback controller. [1]~Y. In \textit{et al.}, Phys. Plasmas \textbf{13}, 062512 (2006).   

Numerical Analysis of the 2D Newcomb Equations for the Resistive Wall Modes (RWMs)

Stabilization of the RWM is one of the most important design issues for future reactors operated in the advanced tokamak regime. The MARG2D [1] stability code, which solves the 2D Newcomb equations [2], is extended to study the stability of the RWM. The linear dynamics of the perturbations in RWM obeys the functional [3] $\delta $W$_{r}=\delta $W$_{p}+\delta $W$_{IV}+\delta $W$_{OV}$+D$_{w}$=0, where $\delta $W$_{p}$ is the plasma potential energy, $\delta $W$_{IV(OV)}$ the vacuum magnetic energy inside (outside) the resistive wall, and D$_{w}$ the energy dissipated in the resistive wall. In MARG2D, $\delta $W$_{p}$ and $\delta $W$_{OV}$ are given by bilinear functionals of the displacements and the perturbed magnetic field. $\delta $W$_{IV}$ is described by a scalar potential and solved by the finite element method. Results from the MARG2D code are compared with those given in [3]. The solutions of the eddy current on the resistive wall will also be compared with new WKB solutions. [1] N. Aiba, \textit{et al.,} Plasma Phys. Control. Fusion \textbf{46}, 1699 (2004). [2] S. Tokuda and T. Watanabe, Phys. Plasmas \textbf{6}, 3012 (1999). [3] M.S. Chu, \textit{et al.,} Nucl. Fusion \textbf{43}, 441 (2003).   

Observation of n$>$1 Mode During ELM-Driven RWM Experiments in DIII-D

In recent resistive wall mode (RWM) experiments in DIII-D, edge localized modes (ELMs) were found to trigger RWMs in high rotation plasmas, which are well above the rotation threshold [1]. Interestingly, the ELM-induced $n$=1 perturbations are almost always accompanied by significant amounts of $n$=3 modes. While an $n$=1 ELM-driven RWM grows but can be suppressed by active feedback, the influence of $n$=3 mode needs to be investigated. A clear example that an ELM-driven $n$=3 mode grew without being hindered by $n$=1 feedback will be presented. It is noteworthy that the $n$=3 mode appeared to cause $\beta $ and rotation collapses, similar to $n$=1 RWM. Detailed MHD analysis is in progress to investigate whether the $n$=3 mode is attributable to $n$=3 RWM in the vicinity of $n$=1 wall-stabilized plasmas [2]. We will discuss the stability calculation results and the details of the $n$=3 mode observation. [1] E.J. Strait, \textit{et al., }Bull. Am. Phys. Soc. \textbf{50}, 79 (2005). [2] Y. In, \textit{et al., }to be submitted for publication.   

Robust Control of Resistive Wall Mode in DIII-D Based on Eigenmode Approach

Control of the resistive wall mode (RWM) is a major focus of the DIII-D experimental program. The FAR-TECH DIII-D/RWM model represents the plasma surface as a toroidal current sheet and represents the wall using an eigenmode approach [1]. The magnitude and phase of the RWM plasma deformation is determined from a set of 22 poloidal field probes and saddle loops, and 12 in-vessel coils are used to oppose the deformation. The resulting model is reformulated into a robust control framework, with a parameter that maps to the growth rate of the system modeled as an uncertain parameter. A robust controller that stabilizes the system for a range of practical growth rates is proposed, tested through simulations, and compared to other control techniques. Implications for experimental implementation and use are discussed. [1]~Y.~In, \textit{et al., }Phys. Plasma \textbf{13}, 062512 (2006).   

Study of RWM Stabilization by Plasma Rotation Using Active MHD Spectroscopy

Active MHD spectroscopic measurements have been used to probe the stability of the n=1 and n=2 kink modes in various DIII-D scenarios. The response of the plasma to externally applied slowly rotating non-axisymmetric fields, measured with magnetic field sensors, yields damping rates and mode rotation frequencies. The measurements show the transition from an ideal MHD stable plasma to a weakly damped resistive wall mode (RWM) at the ideal MHD, no-wall stability limit. Active MHD spectroscopy also tests kinetic theory, which is thought to be responsible for the observed RWM stabilization by plasma rotation. In contrast to measurements of the rotation threshold, which is likely caused by a nonlinear interaction of residual error fields with the weakly damped RWM, the spectroscopic technique at sufficiently low amplitude can be directly compared to linear predictions.   

Challenges for Robust Feedback Stabilization of ELM-Driven Resistive Wall Mode (RWM)

The RWM can be stabilized by modest plasma rotation. However, even when plasma rotation is well above the critical value, MHD activities such as ELMs and Fishbones excite RWMs. Feedback plays several crucial roles against RWM onset. Minimizing the amplification of residual error fields due to MHD events is the first necessary step for providing robust feedback RWM stabilization. Below the no-wall $\beta _{N}$ limit, feedback can reduce the residual n=1 RWM amplitude and consequently the amplification is reduced as indicated by the edge T$_{i}$. Near the high $\beta _{N}$ operational limit, ELM events suddenly increase the amplitude of stable RWM resonating with residual error field, presumably triggered by the n=1 component of ELM or by the rapid change of the RWM mode pattern during ELMs. The existence of finite amplitude leads to fast unstable RWM growth. When the feedback can completely reduce the resonant process, high $\beta $ plasmas remain stable.   

Excitation of Resistive Wall Mode Instabilities by Transient MHD Events in DIII-D

The resistive wall mode (RWM) often limits the performance of high-beta plasmas that rely on wall stabilization of low-n kink instabilities. The RWM can be stabilized by plasma rotation, but DIII{\-}D experiments show that even discharges with significant rotation are sometimes observed to develop a large-amplitude RWM immediately following an edge-localized mode (ELM) or other transient MHD event. This is thought to be the result of a nonlinear process in which the ELM resonantly drives the stable RWM to a finite amplitude, followed by magnetic braking of the plasma rotation. Open issues include the importance of magnetic shielding by the rotating plasma, the question of whether or not the RWM develops a positive growth rate during this process, and the possible role of scrape-off layer currents. Experimental results will be compared with a simple 0-D model.   

Sawtooth Suppression by Tearing Modes in Hybrid Plasmas on DIII-D

Hybrid discharges have the remarkable property that the m/n=3/2 neoclassical tearing mode (NTM) raises the central safety factor (q$_{0})$ above unity and suppresses sawteeth. Experiments on DIII-D are trying to distinguish between several sawtooth suppression mechanisms. One mechanism that can be tested for is the redistribution of the beam ions by the 3/2 NTM, which would increase the off-axis neutral beam current drive (NBCD). The NBCD profile can be determined from the evolution of the poloidal flux measured by motional Stark effect (MSE) polarimetry. Also, the fast ion D$_{\alpha }$ (FIDA) diagnostic can measure the fast ion density profile for hybrid discharges with and without the 3/2 NTM. Another analysis tool is TRANSP simulations of the current profile evolution, which shows that diffusion of the beam ions is unlikely to raise q$_{0}$ above 1. Other possible sawtooth suppression mechanisms are hyper-resistivity, counter current drive in the plasma core via a coupling between the 3/2 NTM and a 2/2 sideband, and magnetic flux pumping.   

Flow Shear and Tearing Stability in DIII-D

The reorientation of one neutral beam in DIII-D from co to counter injection has allowed tests of the effects of rotation on tearing stability. It is found that reduced plasma rotation and flow shear has a destabilizing effect. Existing modes get bigger. Otherwise stable modes are destabilized, i.e. the stable beta limit is lowered. Experimental examples in the saw-teething H-mode, the hybrid scenario, and the advanced tokamak will be presented. A significant level of stabilizing flow shear is of the order of the inverse of the product of the local magnetic shear length $L_{s}$ and the Alfv\'{e}n time $\tau _{A}$; removing this flow shear by going from all co to near balanced injection decreases the tearing stability. Preliminary experimental analysis suggests that the relative sign of the flow shear and the magnetic shear also plays a role. The literature on the theory of tearing and flow will be reviewed. New studies of the effects of flow shear on tearing both analytically and with codes are in development.   

Behavior of Escaping Fast Ions From DIII-D Tokamak

The behavior of escaping fast ions from DIII-D Tokamak is investigated. Two pairs of thin foil Faraday collectors provide the energetic ion loss signals from the co/counter plasma current directions. The data are compared with neutron flux and fast ion deuterium alpha (FIDA) measurements. Comparative studies show that the signals are correlated with toroidal field and certain plasma parameters, such as plasma current, loop voltage, temperature and rotation. Further studies on the modulation of prompt ion loss induced by neutral beam injection, and enhanced fast ion loss from ion cyclotron radio frequency and MHD are reported. The secondary electron emission effect, which is believed to be responsible for the negative signal from blind background foil [1], is observed and qualitatively proven by active foil biasing experiments. \newline [1]~M.~Isobe,\textit{ et al.,} Rev. Sci. Instrum. \textbf{77}, 10F508 (2006).   

Reversed Shear Alfv\'{e}n Eigenmode Stabilization by Localized Electron Cyclotron Heating

Reversed shear Alfv\'{e}n eigenmode (RSAE) activity in DIII-D is observed to be stabilized by electron cyclotron heating (ECH) near the minimum of the safety factor (q$_{min})$ in neutral beam heated discharges with reversed magnetic shear. The degree of RSAE stabilization and the volume averaged neutron production (S$_{n})$ are highly dependent on ECH deposition location relative to q$_{min}$. Ideal MHD simulations predict RSAE existence during ECH, indicating that the mode disappearance is due to kinetic effects not taken into account by the ideal MHD model. While discharges with ECH stabilization of RSAEs have higher S$_{n}$ than discharges with significant RSAE activity, neutron production remains strongly reduced (up to 60{\%}), indicating the bulk of the deficit is not due to RSAEs alone.   

Central Flattening of the Fast-Ion Profile in Reversed-Shear Discharges With Alfv\'{e}n Eigenmode Activity

Neutral beam injection into a plasma with reversed shear produces a rich spectrum of Alfv\'{e}n eigenmodes (AE) in DIII-D. Application of fast-ion D$_{\alpha }$ (FIDA) spectroscopy shows that the central fast-ion profile is anomalously flat in the inner half of the discharge. Neutron and equilibrium measurements corroborate the FIDA data. The temporal evolution of the current profile is strongly modified. Calculations by the ORBIT code do not explain the observed fast-ion transport for the measured mode amplitudes. A simulation of this discharge with the HMGC code suggests that transient energetic particle modes may be primarily responsible for the fast-ion transport, while the experimentally obvious toroidal AE (TAE) and reversed shear AE (RSAE) may be relatively unimportant. A search for the predicted energetic particle modes is planned. An empirical study of the correlation of profile flattening with varying amounts of Alfv\'{e}n activity in different discharges will also be presented.   

First Current and Radial Electric Field Profile Measurements using the Full Co- Plus Counter-Beam Motional Stark Effect Diagnostic on DIII-D

The motional Stark effect (MSE) diagnostic on DIII-D has been expanded to include 24 additional channels viewing a neutral beam injected counter to the direction of the beam viewed by the existing MSE system. Using data collected from a variety of discharge types, we compare current and E$_{r}$ profiles determined using only the co-beam MSE channels with the same using co- plus counter-beam MSE channels. This comparison is meant to evaluate how well the improved spatial resolution and reduced B$_{z}$ and E$_{r}$ uncertainty in the new channels improve the accuracy of the reconstructed equilibrium. Special attention is paid to discharges designed to have high beta and bootstrap fraction. The expanded system is also capable of providing a direct measurement of E$_{r }$without relying on EFIT reconstruction. These measurements are presented and compared with those derived using the charge exchange recombination diagnostic.   

Measurement and Modeling of the Response of the Current Profile Evolution to Feedback Control Actuators in DIII-D

For closed loop control of the $q$ evolution during the plasma current ramp up, available actuators are electron heating power, I$_{p}$ ramp rate, electron density and co-counter beam balance to modify the net neutral beam current drive. Measurements of the effects of these actuators on the current profile evolution are compared to transport code predictions from ONETWO, TRANSP, CRONOS, and CORSICA to test the model of the plasma response in the control process. Measurements of the dynamic response of the $q$ evolution, particularly to electron heating, provide input to the controller development process. A proportional/integral controller with empirically determined gains and provision to avoid $\beta _{N}$ excursions has been demonstrated to regulate $q_{min}$ at the start of the high-performance phase of the discharge for a variety of initial and target conditions.   

Development of Model-Based Feedback Control for the Current Profile in DIII-D

A key goal in control of an advanced tokamak (AT) discharge is to maintain safety factor (q) and pressure profiles that are compatible with MHD stability at high beta and at high fraction of bootstrap current. This will enable high fusion gain and non-inductive sustainment of the plasma current for steady-state operation. Active feedback control of the q profile evolution at DIII-D has been already demonstrated [1], and an open-loop control scheme has been proposed [2]. We report up-to-date progress towards enabling model-based active control of the current profile during the plasma current ramp-up phase. New results on closed-loop control design, simulation assessment with Corsica, and initial open-loop-control experiments are presented. [1] J.R. Ferron, et al., Proc. 32nd EPS Conf. on Plasma Physics, vol. 29C (2005) 1069. [2] Y. Ou, et al., Proc. Am. Control Conf., New York (2007).   

Model-Based Design for Operational Plasma Shape Control in DIII-D

Formerly, tokamak plasma control emphasized empirical tuning of simple controllers during experimental operations. Now, physics-based tokamak plasma response models are maturing and increasingly used as the basis for control design. This is essential for controller development for devices under design or construction, and key to maximizing the physics productivity of limited experimental time in operating devices. We report on experience at DIII-D and other tokamaks with shape control algorithms developed using physics-based models. We also describe a large and growing collection of Matlab functions, collectively known as the Tokamak System (TokSys) Toolbox, which standardizes much of the process of development and validation of tokamak plasma response models. Such standardization enables rapid model development, validation, and control design for operating and planned devices. Application to control development for several devices is described.   

ROM-Based Current Profile Control in DIII-D

The evolution in time of the current profile in a tokamak is related to the evolution of the poloidal flux, which can be modeled in cylindrical coordinates using a partial differential equation (PDE) usually referred to as the magnetic diffusion equation. Based on the proper orthogonal decomposition (POD) method, we propose a reduced-order model (ROM) for the magnetic diffusion equation (represented by an ordinary differential equation (ODE) with constrained diffusivity-interior-boundary actuators). We use a receding-horizon control scheme based on the reduced-order magnetic diffusion model to design a suboptimal control law that matches as close as possible a desired current profile within a pre-specified interval of time. Simulation results demonstrate the efficiency of the proposed control strategy.   

EFIT 3D Reconstruction and Recent Developments

Recent 3D extension of the EFIT equilibrium reconstruction code to model toroidally asymmetric effects due to error and externally applied perturbation magnetic fields and other developments are presented. The 3D extension is based on an expansion of the MHD equations. Other developments include a new computational structure based on Fortran 90/95 with a unified interface that can conveniently accommodate different tokamak devices and grid sizes, as well as a Python-based GUI. New computational links that allow easy integration with transport and stability physics modules to facilitate kinetic reconstruction and stability analysis are also being developed. A new more complete uncertainty matrix for magnetic diagnostics based on knowledge about their fabrication, installation, calibration, and operation has also been implemented into EFIT and tested. Reconstructions with the new magnetic uncertainty matrix yield results similar to those using the existing one but with more realistic fitting merit figures.   

Integration of MHD Stability and Transport to Model DIII-D Pedestal Physics and ELMs

Improving the predictive capability to model the H-mode edge pedestal is one of the critical tasks for tokamaks and ITER. Typically transport equations are solved with boundary conditions imposed well inside the pedestal. To accurately model the pedestal region, it is necessary to couple an edge stability code like ELITE to a transport model that is valid in the pedestal region. Our recent efforts in this area to model DIII-D pedestal height and edge localized modes (ELMs) is presented including the development of a simplified ELM-crash model to relax the edge J and temperature profiles. The edge electron and ion transport coefficient are set to large values based on the shape of the unstable eigenfunction from ELITE, if the edge P' exceeds the stable limit. Without an edge relaxation model, the predicted edge J tends to significantly exceed the experimental values. The effects due to ELMs will be discussed.   

Modeling of Momentum Transport in DIII-D Discharges Due to Magnetic Drags Induced by MHD Activities

Toroidal rotation and rotational shear provide many beneficial effects to stabilize MHD instabilities and suppress turbulence that are crucial for attainment of high beta and high confinement envisioned for tokamak and ITER high performance regimes. MHD activities such as RWMs can interact with the plasma and slow down the rotation by breaking the toroidal symmetry to induce a toroidal viscosity. Preliminary results using ONETWO transport code with a simple inductive motor model indicate that the resonant magnetic drag effect alone cannot fully describe the evolution of the rotation profile in DIII-D RWM discharges. In these simulations, only the effects due to the perturbed radial magnetic fields estimated from experimental measurements at the q=2 surface were considered. Non-resonant magnetic damping effects due to ripple and neoclassical viscosity are being implemented in ONETWO and likely play a role. The results will be presented.   

Simulations of DIII-D Sawtooth Oscillations Using Theory-Based Transport and Sawtooth Models

Development and validation of a predictive sawtooth model is an important research topic for present-day tokamaks and ITER. Analysis using ONETWO to model the DIII-D sawtooth behavior due to the interactions between FW and NBI fast ions, predicts the observed reduction in the axis safety factor $q_{0}$ due to current profile evolution. Preliminary analysis indicates that the predicted drops in $q_{0}$ within a sawtooth cycle follow closely the experimental values from the EFIT code using MSE data. In ONETWO simulations, the evolution of $q_{0}$ within a sawtooth period is modeled with neoclassical resistivity and the experimental density and temperature profiles in two neighboring giant sawtooth cycles. Initial analysis using the Kadomtsev sawtooth model indicates that the sawtooth crash can be qualitatively reproduced with an appropriately chosen triggering parameter. The Porcelli sawtooth model is being implemented into ONETWO to more comprehensively predict the sawtooth crash.   

Transport, MHD, and Stability Investigations of a Proposed Fusion Development Facility (FDF)

Recent simulations of a compact next generation testing facility tokamak, FDF, indicates that favorable H-mode, AT-type operation with high boostrap current fractions, is possible. Our simulations assumed an \textit{apriori} fixed, stable edge pressure stable and peeling-ballooning modes and favorably shaped but fixed density profiles. Heating and current drive was supplied by on and off axis ECH and low energy, 120 keV, beams directed near the plasma edge. The resulting rotation speed profile is highly sheared at the plasma edge. Under these conditions we were able to simulate a suite of internal transport barrier confined discharges using the GLF23 transport model with the \textsc{Onetwo} transport code. Ongoing work includes extending these simulations to include fixed boundary MHD calculations, density evolution and dynamic ELM control using the \textsc{Elite} edge stability code. We present the results and methodology required to perform these simulations. \newline [1] R.E. Waltz, \textit{et al., }Phys. Plasma \textbf{4}, 2482 (1997).   

Modeling ITER and DIII-D Current Ramps for Startup Similarity Experiments

We have begun similarity experiments on DIII-D to validate ITER startup scenarios and to explore possible alternatives. The reference startup scenario for ITER specifies breakdown near the outer limiter with shape variations correlated with the current ramp to give constant q until X-point formation. This evolution differs from startup prescriptions for existing tokamaks. Corsica simulations of the ITER current ramp indicate that the prescribed l$_{i}$ may be difficult to achieve. Corsica is used to simulate ITER similarity experiments on DIII-D to validate startup design models. Possible alternatives that maintain vertical stability and the possibility for higher safety factor, q$_{min}>$1, more conducive to advanced tokamak and hybrid modes will be explored. The simulations use free-boundary evolution coupled with radial transport to assess the shape evolution and vertical stability.   

Feasibility Studies of Off-Axis Neutral Beam Current Drive in DIII-D

The objective of off-axis neutral beam (NB) current drive (CD) is to supplement the off-axis electron cyclotron current drive for development of steady state, advanced tokamak scenarios. A modification being considered is to tilt the present neutral beam lines (BL) by raising the source end of the BL by $\approx $~1.5~m. The driven current is calculated using the TRANSP and ONETWO/Nubeam Monte-Carlo codes taking into account finite orbit effects. When the beam is injected in the same direction as the toroidal field, a wide but localized off-axis CD ($\approx $~40~kA/MW at $\rho $~= 0.5 with FWHM of 0.45) is calculated. The normalized CD efficiency ($\zeta $~= 0.22) is comparable or somewhat better than electron cyclotron current drive. Sensitivities to fast ion diffusion and the use of the off-axis CD for scenarios with high steady-state performance in DIII-D will be discussed.   

Modulated Electron Cyclotron Current Drive for Control of the m/n=2/1 Neoclassical Tearing Mode in DIII-D

The m/n=2/1 neoclassical tearing mode (NTM) is a helical island structure at q=2 in the magnetic field of a high beta tokamak plasma that can degrade confinement and lead to disruption. The DIII-D control system has previously suppressed this NTM by driving continuous-wave (cw) current at q=2 using localized electron cyclotron current drive (ECCD). The control system has now been upgraded to modulate the ECCD so that current is driven only when the island passes by the deposition point. This modulation is expected to increase the effectiveness of the ECCD, in particular when the deposition region is broad relative to the island width, as will be the case in ITER. Experiments using modulated ECCD with a broad profile relative to the island width have been performed in DIII-D to control the 2/1 NTM. Results of these experiments will be presented.   

Status and Plans for the 110 GHz ECH/ECCD System on DIII-D

There are now 5 gyrotrons in operation on DIII-D, producing 4~MW at 110~GHz for pulse lengths which are limited administratively to 5~s. The efficiency of transmission from the gyrotrons to the tokamak is about 80{\%}, resulting in over 3~MW injected power. A sixth gyrotron is being repaired and will begin operation when a high voltage power supply now under construction is available. Stress fractures of the collectors due to cyclic fatigue resulted in vacuum failures on three of the first group of gyrotrons in the installation. New algorithms and equipment for sweeping the electron beams in the collectors have reduced the peak power loading in the collectors to levels $<$~600~W/cm$^{2}$, which results in predicted lifetimes of 50,000 gyrotron pulses where the fatigue limit is now determined not by single pulse stress but by fatigue due to the 5~Hz sweeping of the electron beam. A new fast fault processing system based on FPGA technology is being commissioned.   

Power Calibration for the Electron Cyclotron Heating System on DIII-D

The generated rf power for each of the five gyrotrons in the DIII-D system is calculated based on calorimetry, using temperature and flow measurements from the gyrotron and waveguide system cooling circuits for the cavity, window, collector, matching optics unit (MOU) and dummy loads. Analysis of the data involves fitting the dissipated energy versus time curves and integration of the energy for each of the circuits. The cavity signal is used to calculate the total generated energy, using a previously determined relationship between cavity loading and rf production, with other cooling circuits as a check. The time dependence of the rf power is determined using a diode pickoff at the first miter bend in the transmission line normalized to the integrated calorimetry measurement. The MOU calorimetry response provides a direct measurement of the percentage of rf in the Gaussian mode and the efficiency of coupling the rf into the waveguide. The losses in each transmission line are taken into account to calculate the power transmitted to DIII-D.   

Improved Measurements of Injected Electron Cyclotron Power in DIII-D

Direct measurements of the rf power injected into the DIII-D tokamak from the ECH gyrotrons are being made using a high power dummy load at the tokamak. The measurements will permitt power monitors, which measure the rf leakage from well-aligned gaps in the vacuum waveguides near the tokamak, to be calibrated for various elliptical polarizations of the rf propagating in the HE$_{11}$ waveguide mode. Using these measurements, correlations with calorimetric measurements of the gyrotron cooling circuits, the usual basis for rf power measurements in the system, will be made. Low power rf measurements and theoretical and experimental estimates of the transmission efficiencies of the individual components in the transmission lines will be compared with the direct measurements.   

Threshold Wave Amplitude Required for Non-adiabatic Wave-Particle Interaction

Non-adiabatic interactions between wave and ion in radiofrequency heating have typically been modeled as a quasi-linear diffusive process in velocity space. It assumes strong decorrelation in the relative phase difference between wave and ion through successive kicks. Since decorrelation depends strongly on the combination of applied wave amplitude, wave frequency, the magnetic field inhomogeneity and the energy of resonant ion, this assumption may not always be valid. We extend the previous work on threshold wave amplitude [Whang, \textit{et al.}, Nucl. Fusion \textbf{23}, 481 (1983)], which is only valid for the fundamental harmonic, using standard linear mapping theory, and obtain more generalized expressions for arbitrary harmonic number with finite k$_{\vert \vert }$ and ion finite Larmor radius effects. Analytical results for the stochasticity onset will be compared with numerical results evaluated from the code ORBIT-RF. We apply this formula to elucidate the validity of quasilinear diffusion for C-Mod minority ion fundamental harmonic as well as DIII-D energetic beam ion high harmonic heating regimes.   

Experimental Comparison of Fast Wave Absorption on Fast Ions at Fourth and Sixth Harmonics

In recent DIII-D experiments, we have compared the absorption of fast waves (FWs) on injected deuterium beams at the fourth and sixth deuterium cyclotron harmonics. Direct electron absorption also plays an important part in the core absorption. Up to 2~MW of FW power at 90~MHz is compared with a similar level of 60~MHz power in low-density L-mode discharges at 2~T with 1--2~MW of deuterium beam injection at 80~keV. Changes in the neutron rate and in the central sawtooth behavior are correlated with the observed acceleration of the beam ions by the rf as measured by the D$_{\alpha}$ charge exchange recombination diagnostic. Results obtained with hydrogen beams in which second and third harmonic absorption at 60~MHz and 90~MHz are compared will be presented. Lower global absorption efficiency observed for higher cyclotron harmonics in this multiple-pass absorption regime is attributed to the effect of an edge loss that competes with the core absorption mechanisms.   

Results of Pilot Run of Next-Generation Thomson Scattering Diagnostic on DIII-D

A new prototype polychromator assembly and data acquisition system has been deployed during plasma operations at DIII-D for electron temperature and density measurement. The new polychromator features detectors that incorporate 500~MHz bandwidth amplifiers (OPA656) with low input bias current and an overall gain of 360 and an integration and a sample-and-hold circuit to provide analog output into a data acquisition digitizer. It also incorporates a TEC cooling circuit to maintain the avalanche photo-diodes (APDs) at 17\r{ }C with a stability of $\pm $0.1\r{ }C in order to reduce the environmental noise and reduce temperature fluctuations. The data acquisition system is a D-TACQ DT100 system with a 96 channel 250~kSPS ACQ196CPCI board. The new system provides the flexibility to increase both spatial and time resolution by removing limitations imposed by the old CAMAC system. Calibration and discharge data, along with measured electron temperature and density, will be compared to the ones obtained with the existing system.   

New Optics for the Soft X-ray Diagnostic on DIII-D

The optics for the soft x-ray poloidal array on the DIII-D tokamak have been upgraded to include a new set of 64 photodiodes and an adjustable filter wheel. The wheel includes three titanium-coated diamond filters for measuring soft x-ray emission and two unfiltered settings for fast bolometry. We present the specifics of the design, including filter transmission functions, and techniques used to reduce pickup noise from nearby coils. Recent results from the revamped system will be analyzed with a focus toward categorizing MHD instabilities observed in DIII-D plasmas.   

Theoretical Progress on Runaway Electron Suppression by Massive Gas Injection

Development of techniques to mitigate the severity of emergency plasma termination/plasma disruptions is deemed one of the highest priorities for ITER. The current method of mitigation by massive gas injection (MGI) is not fully understood; whether MGI can achieve sufficient density to avoid avalanche runaway electron formation in the high toroidal electric field E$_{\phi }$ is presently uncertain. It will be shown why direct penetration of broad gas jets cannot happen: ablation pressure drag (or magnetic pressure imbalance) exerted over the frontal surface of the jet is too strong for usual jets. Evidence on DIII-D is that MHD processes, occurring predominately during the short thermal quench TQ phase, cause inward diffusion of gas jet ions ``stuck'' at the plasma edge. To explore this process we have developed a 1-D large-aspect-ratio circular flux surface code for the evolution of E$_{\phi }$ with radiation and transport cooling. We use resistive wall boundary conditions, and a 2D axisymmetric CFD code describes the heavily-fueled vacuum region and plasma boundary conditions.   

Experiments With a 6-Valve Array for Massive Gas Injection for Disruption Mitigation in DIII-D

A 6-valve array was installed on the DIII-D to test massive gas injection for suppression of runaway electrons during disruptions. Previous experiments were limited by the peak flow rate from a single valve. Initial experiments show somewhat improved electron assimilation before the core thermal quench (TQ). Peak core mixing efficiencies of impurities injected into the vacuum vessel through the TQ are $\sim $10{\%}-40{\%}. Tests using up to 5 valves were done in H$_{2}$, He, and 98{\%} H$_{2}$-2{\%} Ar. These experiments injected as much gas before the TQ as previously obtained during the entire TQ/I$_{p}$ decay. They also showed the importance of maintaining the gas flow during the I$_{p}$ decay to maintain the density. Densities of up to 2x10$^{21}$ m$^{-3}$ were obtained ($\sim $10{\%} of the Rosenbluth density for runaway suppression), but it was still increasing with added valves.   

Runaway Electron Modeling Using Radiation Emitted From Impurity Pellets Injected in DIII-D

Energy and spatial distribution of runaway electrons generated during disruptions and fast shutdowns are important for understanding the formation, loss, and mitigation of runaway electrons to prevent catastrophic damage in future tokamaks like ITER and DEMO. Monte Carlo simulations were performed to investigate injection of impurity pellets during disruptions to diagnose runaways in DIII-D. Interaction of runaways with solid pellets, and of emitted $\gamma $-rays with the vessel walls and scintillators placed outside the walls, including photo-neutron, are simulated. Energy straggling of $\gamma $s passing through the vessel walls significantly skews the measured $\gamma $ energy distribution; the spatial distribution of radiation associated with relativistic bremsstrahlung is found to provide good energy information in the expected runaway energy of 1-20~MeV. Temporal radiation intensity variations after pellet injection can reveal information on the spatial distribution of runaways. A proposed diagnostic using an array of 10-20 scintillators, and preliminary tests, will be presented.   

Experiments Toward Understanding Impurity Assimilation During Massive Gas Injection for Disruption Mitigation in DIII-D

Impurity assimilation following massive gas injection (MGI) is desirable for collisional suppression of runaway electrons (RE). Experiments on the DIII-D tokamak have shown that impurity ions created at the plasma edge by MGI initially mix inward quite slowly toward the plasma core. When the associated cold front reaches the $q$=2 rational surface, impurity mixing is accelerated due to destabilization of low-order tearing modes, leading to the thermal quench (TQ). Average core mixing efficiencies of impurities injected into the vacuum vessel up through the TQ are of order 10{\%}. Typically, RE suppression ratios $\gamma _{crit}$~= $E_{crit}$/$E_{\vert \vert }$~$\approx $ 0.01 are obtained using argon. Better suppression ratios $\gamma _{crit}$~$\approx $ 0.06 are obtained with low-$Z$ (H$_{2}$ or He) injection and firing five MGI valves simultaneously.   

Overview of MST Results and Plans

MST progress in producing well-confined high beta plasmas continues. In high current plasmas with improved confinement through current density profile control (transient), the electron temperature is increased to 2 keV and the ion temperature is increased (through reconnection heating) to 1 keV. With pellet injection plasma beta (volume averaged pressure/surface magnetic pressure) increases to 26\%, beyond linear stability limits for pressure-driven tearing and Mercier instability. Physics results on ion heating (correlated with reconnection), particle transport from stochastic fields, high frequency turbulence, momentum transport from tearing modes, and two-fluid reconnection are also obtained. In preparation for finer current profile control, lower hybrid (LH) and electron Bernstein waves are injected at about 175 kW, with LH- produced hard x-rays observed. New major projects under development include 1 MW neutral beam injection for auxiliary power deposition, programmable control of the toroidal field and poloidal loop voltage, oscillating field current drive at increased power, and fast Thomson scattering for electron temperature fluctuation measurements.   

High-$\beta $, improved confinement RFP plasmas at high density

In MST discharges with improved confinement, pellet injection has quadrupled the density, with n$_{e}$ reaching 4x10$^{19}$m$^{-3}$. The energy confinement time of these high density plasmas is comparable to that at low density, and $\beta _{tot}$ now reaches 26{\%}. This beta exceeds the Mercier limit for interchange stability, but as yet no indication of interchange is detected experimentally. Beta is also now high enough for global $m$ = 1 tearing modes to be linearly unstable, with the instabilities being driven by the pressure gradient rather than the current gradient. Although a $\beta $ limit has not yet been reached, both the $m$ = 1 fluctuation levels and energy transport do increase modestly at high $\beta $, suggesting the possibility that beta may eventually be limited by pressure-driven tearing. Work supported by USDOE.   

Generation and confinement of hot ions and electrons in MST

During impulsive magnetic tearing and reconnection in MST, many MW of ion heating power are derived from the energy stored in the magnetic field, causing T$_{i}$ to jump well above 1 keV. By subsequently and quickly suppressing the reconnection, ion energy confinement is improved at least ten-fold, and T$_{i}$ above 1 keV is retained in the plasma. During the period of reconnection suppression, electron energy confinement is also improved, and the ohmically-heated electrons reach a temperature approaching 2 keV. Impulsive reconnection is a common feature of MST plasmas, driven by peaking of the current profile, but in this work, the reconnection and conversion of magnetic energy is intensified. Reconnection suppression is achieved with the now-standard PPCD technique, wherein parallel current is inductively driven to flatten the current profile.   

Fast Ion Generation in the MST

Reversed-field pinch plasmas in the MST are punctuated by bursts of tearing mode activity, which release energy stored in the magnetic field and strongly heat the ions. There are two indications that some of these reconnection events generate a population of suprathermal ions. The first is that the neutron flux from the plasma tends to be higher than that expected from thermal fusion based on the measured impurity temperature. Because the D-D fusion cross section is much larger for higher energy ions, a small, fast population can resolve this discrepancy. The second is that fast, charge exchange neutrals are sometimes observed in a neutral particle energy analyzer. An attempt to experimentally reconstruct the energy spectrum of these particles will be described. One hypothesis for these observations is that a mean electric field associated with current profile relaxation is creating runaway ions. To investigate, computational work has been done to determine the implied ion distribution function and the conditions necessary to produce it.   

Fokker-Planck modeling of 2 keV Thomson Scattering electron temperature measurements on the MST.

On the MST RFP some 2 keV high confinement plasmas display an off-axis peak in the electron temperature profile measured by the Thomson scattering diagnostic. The distribution function computed by the Fokker-Planck modeling code CQL3D is used to predict the spectral distribution of the scattered radiation from a Nd:YAG laser pulse. The off- axis peak in the temperature profile may be explained by a distortion of the electron distribution in the parallel direction, caused by the high parallel electric field in the plasma. This distortion of the parallel distribution function influences primarily the off-axis scattered spectral distribution; on axis, the Thomson scattering diagnostic is sensitive only to the perpendicular electron distribution. The signal-to-noise ratio of the data is insufficient to allow direct inversion to an electron distribution function, so comparison to Fokker-Planck modeling predictions is key to understanding unusual features in the temperature profile and spectral distribution.   

High Time Resolution Analysis of Thermal Transport and Magnetic Stochasticity During a Sawtooth Event in MST

New measurements with the multi-point, multi-pulse, Thomson scattering system on MST have enabled the analysis of the radial thermal diffusion ($\chi_e$) profile within tens of microseconds of magnetic reconnection events known as sawteeth. Diffusion of thermal energy out of the plasma along stochastic magnetic field lines is believed to be the major mechanism of heat loss during these magnetic relaxation events. At the sawtooth crash the magnetic fluctuations are large and the magnetic field becomes fully stochastic throughout much of the plasma volume. By ensembling data from many similar shots, we have determined the evolution of the $\chi_e$ profile through the sawtooth crash with much higher time resolution than was previously possible. These new measurements cover the critical half millisecond around the sawtooth crash with 50$\mu$s wide bins. The evolution of the $\chi_e$ profile obtained from experiment is compared to Rechester-Rosenbluth predictions and results of MHD simulations done with the DEBS code.   

Electron temperature fluctuation measurements using a two-pulse Thomson scattering diagnostic on MST

Advanced Thomson scattering diagnostic capabilities enable exploration of fast electron dynamics that may be associated with several physical processes such as tearing modes, dynamo mechanisms and electrostatic fluctuations. The photon sources for the Thomson scattering diagnostic on MST are two independently triggerable Nd:YAG lasers. The two lasers can be fired arbitrarily close together in time. Data acquisition becomes the limiting factor in time resolution. Overall the system is capable of measuring changes in the radial electron temperature profile with a temporal resolution of 200 ns and with a spatial resolution of 2 cm or less. A fluctuation power spectrum can be built up over an ensemble of shots. The power spectrum of electron temperature fluctuations near tearing mode frequencies (5-30 kHz) is presented as well as a correlation analysis of temperature and magnetic modes. How this method can be applied to higher frequency fluctuations is discussed. The research was performed under appointment to the Fusion Energy Sciences Fellowship Program and supported by US DOE.   

Construction of a Pulse-Burst Laser System for Fast Thomson Scattering on the MST RFP

A ``pulse-burst'' laser system is being constructed for addition to the Thomson scattering diagnostic on the MST RFP. This laser will produce a burst of up to 200 approximately 1 J Q-switched pulses at repetition frequencies 5-250 kHz. This laser system will operate at 1064 nm and is a master oscillator, power amplifier (MOPA). The master oscillator is a compact diode-pumped vanadate laser, intermediate amplifier stages are flashlamp-pumped Nd:YAG, and final stage(s) will be flashlamp-pumped Nd:glass (silicate). The burst train of laser pulses will enable the study of Te and ne dynamics in a single MST shot, and with ensembling, will enable correlation of Te and ne fluctuations with other fluctuating quantities.   

Dynamic Heavy Ion Beam Probe Measurements in the Madison Symmetric Torus

The Heavy Ion Beam Probe in operation on the Madison Symmetric Torus is now utilizing two new diagnostic features. The first is a programmable computerized control system which is enabling measurements in plasmas with gradual, deliberate equilibrium variations such as those which occur during improved confinement discharges. The system tracks dynamic equilibria using tailored temporal adjustments of the sweep and analyzer voltages; the primary goal of the system is to enable continuous measurements and the secondary goal is to maintain fixed sample volume locations. The second new diagnostic feature is an aperture which facilitates inference of the secondary beam position and velocity. This information, combined with the velocity and location of the primary ion beam as it enters the plasma, is useful as a constraint for magnetic equilibrium reconstruction. The accuracy of magnetic equilibria impacts HIBP sample volume localization, size, and orientation calculations, which in turn effect electric field and wavenumber measurements. Data acquired with, and overviews of the computerized control system and beam velocity aperture will be presented.   

Time-resolved measurements of equilibrium profiles in MST

Based on the high-speed, three-wave, far-infrared polarimeter-interferometer measurement of $B_{pol}$ profiles and external coil measurements of $B_{tave}$ and $B_{tw}$, a new method is developed to derive $B_{tor}$ and other equilibrium profiles (J$_{//}$ and q) with high time resolution. Using Faraday's law, the inductive electric field (E$_{//})$ profile is also deduced from the temporal derivatives of the time-resolved magnetic field profiles. The derived $B(0)$ values have excellent agreement with direct measurements using a Motional Stark Effect (MSE) diagnostic. Evolution of equilibrium profiles during single sawtooth events in MST, both the slow linear ramp and crash phases, are presented. Profile scaling with plasma current I$_{p}$ and reversal parameter F is also explored. MHD stability is tested from the spatial gradients of the $J_{//}$ and q profiles, and correlation with fluctuation mode amplitude is investigated. Future improvements to equilibrium reconstruction are expected by measuring $B_{tor}$(r,t) directly via Cotton-Mouton interferometry.   

Locally Improved Particle Confinement in QSH Plasmas

A multichord array of CdZnTe detectors is used on MST to infer electron particle diffusion in improved confinement plasmas by measuring hard-x-ray (HXR) flux emitted by runaway electrons. In quasi-single-helicity (QSH) plasmas, where one mode dominates the core tearing mode spectrum and forms an island on its resonant surface, we expect closed flux surfaces to appear inside the island and improve confinement. HXRs are observed when an island emerges, as detected by a SXR diagnostic and the HXR flux oscillates in phase with the rotation of this island. While HXR energies measured during QSH reach those of improved confinement, pulsed parallel current drive (PPCD) plasmas, other diagnostics show a smaller improvement in global confinement, indicating that regions of improved confinement are localized. Modeling with the ORBIT code shows that runaway electrons are better confined inside the island than in the exterior stochastic region. Work supported by the USDOE.   

X-ray emission maps in the MST reversed field pinch

We present two-dimensional images of the soft x-ray (SXR) emissivity distributions in the core of the MST reversed field pinch plasma. The measurements have been obtained with the SXR tomographic diagnostic comprised of four cameras (each with a multichannel photodiode array) viewing the plasma at different poloidal angles, with a total of 74 channels. An overview of results obtained in enhanced confinement plasmas (PPCD experiments) will be shown. Individual islands and helical structures can be resolved by the high spatial resolution of the diagnostic, and their time evolution can be followed thanks to the high time resolution of the electronics. The measurements have been performed exploring various SXR energy ranges by alternatively changing the beryllium foils thicknesses in the photocameras. Examples of SXR distributions with the same filter thickness in all the four probes will be presented and will be analyzed together with those measured with different foils for each camera. When the SXR emissivity is measured with only two filters in the same shot a 2-D estimate of the electron temperature in the plasma core can be obtained by using the standard two-foil technique. Some initial results on $T_e$ calculations will be shown.   

Tearing Mode Flow Measurements in MST

Fluctuating flows driven by resistive tearing modes are observed in a number of laboratory and astrophysical plasmas, including the MST reversed field pinch. Carbon emission from neutral beam-induced charge exchange recombination is collected by a custom-built, high throughput spectrometer yielding measurements of carbon impurity ion velocity localized to +/- 1 cm with high bandwidth (100 kHz). We have measured the correlation between poloidal velocity fluctuations and magnetic fluctuations associated with tearing modes resonant across the plasma radius providing correlated flow fluctuations resolved to better than 500 m/s. Strong correlations are observed for a range of $m$ = 1 magnetic modes, and the measurements are consistent with tearing mode flows parallel to the mean magnetic field. Correlations are largest near the tearing mode resonant surfaces, and are narrow in space, in contrast to the broad structure of magnetic fluctuations. However, flow fluctuations associated with the dominant mode broaden during quasi-single-helicity plasmas. Theoretical calculations and computational modeling of linear and nonlinear tearing mode flows have been performed, and comparisons with the experimental results will be presented. Work supported by USDoE and NSF.   

Hall dynamo, charge transport, and plasma rotation due to magnetic fluctuations in the MST RFP

Standard discharges in the Madison Symmetric Torus (MST) Reversed-Field Pinch (RFP) are characterized by cyclical rapid relaxation events (sawteeth), when substantial toroidal magnetic flux is generated in the plasma edge. In the framework of the two-fluid Ohm's law, it can be shown that Hall and MHD dynamo mechanisms play an important role. We will present detailed measurements of the radial profile of the Hall dynamo $\left< {\bf \tilde j} \times {\bf \tilde B} \right>_{||}$ in the edge. These measurements were performed with a newly developed magnetic probe, which combines six magnetic coil triplets. Hall dynamo is peaked at the reversal surface, but is reduced near the edge, where, according to the past measurements, it is replaced by the MHD dynamo. We will also report edge measurements of the fluctuation induced non-linear $\left <\tilde j_{||} \tilde B_{r}\right>_{F.S.}$ term, which is expected to play an important role in governing charge and particle transport, as well as to be significant in providing torques, which cause intrinsic (without external momentum input) plasma rotation. In addition, we will discuss experiments on inducing plasma rotation with bias electrodes inserted into the plasma edge. This work is jointly supported by the U.S. DOE and NSF.   

Edge Measurements of Plasma Momentum Dynamics in MST

In the MST reversed field pinch, the dynamics of plasma momentum during reconnection are governed by two fluctuation induced nonlinear terms: the Reynolds stress, $\rho (\mathbf{ \widetilde{v}\cdot\nabla)\widetilde{v} } $, and the Maxwell stress, $\mathbf{ \widetilde{j} \times \widetilde{B} }$. Previous measurements in both the edge and core plasma show the Maxwell stress to be about 10 times larger than either the inertial or the viscous term in the momentum balance equation. Recently, measurements of the Reynolds stress have been performed in the edge plasma of MST using probes. A spectroscopic probe looking at He II line emission is used to measure radial velocity fluctuations, and a Mach probe is used to measure the toroidal and poloidal velocities. The Reynolds stress, as reconstructed from these measurements, is shown to balance the Maxwell stress in the edge and both are an order of magnitude larger than the inertia, thus indicating that these two stresses dominate edge plasma dynamics during reconnection.   

Measurements of Linear and Nonlinear Hall Reconnection

Previous measurements in MST have established that two-fluid Hall effects produce a dynamo during sawtooth relaxation events, and therefore two-fluid dynamics are important when evaluating the macroscopic effects of reconnection. This was established by measuring the nonlinear Hall term $(J_1 \times B_1)$ in the axisymmetric (flux-surface averaged) Ohm's Law. Here, we report measurements of terms in the non-axisymmetric Ohm's Law, including the \em linear \em Hall term, $(J_1 \times B_0 + J_0 \times B_1)$, and other spatially varying quantities. These measurements are a more direct indicator of the role of two-fluid effects on reconnection. Measurements are performed by probes in the vicinity of the reversal surface to measure reconnection associated with modes of poloidal mode number m=0. Results show that the linear Hall term is large compared to $\eta \widetilde{J}_{||}$, indicating the possibility of fast collisionless reconnection. Results are compared to a theoretical interpretation based on two-fluid MHD.   

Measurements of core density and magnetic field fluctuations on the MST

Fluctuations play an important role in anomalous particle, momentum and energy transport. Core magnetic and density fluctuations are measured using a high-speed, laser-based, Faraday rotation-interferometry system with a bandwidth of 500 kHz and 8 cm chord spacing. Line-averaged measurements of magnetic and density fluctuations can be inverted using a newly developed inversion method to obtain the local spatial profiles. Spatial structure for modes with m=1, n=6 up to n=16, as well as the m=0, n=1 mode are identified. Fluctuation profiles for modes of given helicity show noticeable changes during the sawtooth cycle. These measurements can also be exploited to determine the local plasma displacement ($\xi _r ={\delta n} \mathord{\left/ {\vphantom {{\delta n} {\nabla n_0 }}} \right. \kern-\nulldelimiterspace} {\nabla n_0 })$ and radial velocity fluctuations ($\tilde {v}_r ={\partial \xi _r } \mathord{\left/ {\vphantom {{\partial \xi _r } {\partial t}}} \right. \kern-\nulldelimiterspace} {\partial t})$ associated with stochastic magnetic fields. Using these parameters, issues related to anomalous particle and momentum transport are addressed. Detailed modeling of local particle density and magnetic fluctuations will be presented.   

Measurements of High Frequency Magnetic Fluctuations in MST

Reversed field pinch plasmas are rich in magnetic fluctuations, dominated by low frequency tearing modes ($\sim$10-30 KHz) which play important roles in magnetic self-organization and transport. However, the origin of high frequency fluctuations ($>$100 KHz) remains unclear. The increase of high frequency fluctuation power during fast reconnection events (sawteeth) suggests that magnetic energy may cascade from the tearing modes to the high frequency fluctuations. Here we present detailed measurements of edge magnetic fluctuations in MST using an insertable magnetic probe, where the toroidal and poloidal mode numbers, n and m, were obtained using the two- point correlation method. The radial dependence of the fluctuation characteristics (power spectra, dispersion relations, etc.) was quantified. The time evolution of the fluctuations during the sawtooth cycle is also resolved. Interestingly, at the sawtooth crash the high frequency fluctuations ($\sim$200-400 KHz) become almost parallel- propagating relative to the equilibrium field, and the phase velocity is close to the ion thermal velocity. This suggests that these high frequency fluctuations may be magnetosonic waves, expected to be strongly damped to produce strong ion heating.   

Lower Hybrid Current Drive Experiments on MST

Lower hybrid current drive has been offered as a means to reduce tearing f\/luctuations and improve confinement in the reversed field pinch. The third generation interdigital-line antenna has been installed in MST and preliminary testing has been completed. Source power to the antenna has been increased to $>$220kW in both feed directions. At high power, the $n_{\|}$ spectrum has been measured and is peaked at $\sim\!\!7.5$ as expected with excellent directionality. Hard x-ray bremsstrahlung emission from rf-generated fast electrons with energies up to and beyond 60 keV has been observed using CdZnTe detectors. Emission in the co-current drive direction is toroidally localized in the plane of the antenna while the counter-current drive direction produces an order of magnitude less flux and peaks off-plane of the antenna. It is surmised that this localization results from diffusion of fast electrons away from a local current structure created by launch into low-confinement plasmas. Collimated x-ray emission profiles near the antenna will also be presented.   

Diagnosis and Modeling of the Lower Hybrid Wave Injection on MST

RF current drive is predicted to reduce tearing fluctuations in reversed field pinches. Lower hybrid experiments with coupled power up to 125 kW have been undertaken on the Madison Symmetric Torus. The lower hybrid antenna exhibits good coupling under a variety of plasma conditions. Experimental studies have been undertaken to determine the optimal conditions for antenna operation. Additionally, an effort is underway to model plasma loading and launch spectrum using AORSA and RANT. Thirteen CdZnTe detectors are used in conjunction with a 16-channel CdZnTe camera in order to diagnose lower hybrid discharges. X-rays with energies over 60 keV are detected during such discharges. This x-ray emission is observed to be toroidally localized to the area within $60^\circ$ of the lower hybrid antenna. The spectrum also shows a dependence on launch direction. In order to expand our understanding of these results, several different plasmas have been modeled with GENRAY and CQL3D. Experimental results with source power up to 200 kW and current modeling results will be presented.   

EBW Injection Experiment in the MST

A 0.25 MW system designed to heat electrons and drive current via the electron Bernstein wave is in its early stages of operation on the MST reversed field pinch. The antenna is a grill of four half-height S-band waveguides with each arm powered by a separate, phase controlled traveling wave tube amplifier. Coupling to the plasma (as measured by ratio of reflected power) is very dependent on the relative phasing between adjacent waveguides. The total reflected power can be maintained at or below 25\%, similar to that measured for a two-waveguide full height grill [1]. The antenna face is outfitted with a pair of triple Langmuir probes to measure local electron density; the density gradient at the upper hybrid resonance (typically within 1-2 cm of the antenna) is expected to strongly influence coupling efficiency. Conditioning of the antenna is currently underway (near the 0.2MW level) and total system power is expected to reach 0.25MW, or roughly a fourth of the Ohmic input power in target plasmas. The x-ray spectrum (5-200 keV) is monitored as a way to detect modification to the electron distribution as full transmitter power is approached. \noindent This work is supported by USDOE. \newline \newline [1] M. Cengher, J.~K. Anderson, C.~B. Forest, V. Svidzinski, {\em Nuc Fusion} {\bf 40}, 521 (2006).   

Fokker-Planck Modeling of X-ray Emission Due to Electron Bernstein Wave Heating in MST

Experiments on MST are underway to test the viability of using electron Bernstein waves (EBW) to heat and drive current in the reversed field pinch. This proof-of-principle experiment uses 250 kW of rf power at 3.6 GHz, a power level that is typically much lower than the Ohmic input power in MST. Power coupling experiments show that power launched into the plasma chamber exceeds 120 kW; the response of various diagnostics to this EBW power is modeled for comparison with experiment using GENRAY ray-tracing and CQL3D Fokker-Planck codes. This procedure inhibits variation of the current profile from equilibrium and allows the inductive electric field to respond on short time scales to maintain a constant current density. CQL3D then predicts the x-ray fluxes and Thomson scattering signals corresponding to the modified electron distribution, which are compared to experimental data. Initial modeling results indicate that the main response can be interpreted as electron heating and that non-thermal features in the distribution function are difficult to detect using x-ray diagnostics. This work is supported by the United States Department of Energy.   

High Power Neutral Beam Injection System for the MST

Good fast ion confinement in the RFP plasma has been established for some time. Currently, a high power neutral beam injection system for the MST reversed field pinch is being designed and built. The hydrogen neutral beam will have power of 1MW, energy of 25 keV, and duration of 20 ms. Among the goals of the beam injection experiment are: (a) to investigate the beam energy and momentum deposition into the plasma, (b) to study the effect of the fast particles pressure (beta) on plasma confinement, and (c) to study the effect of the fast particles on the tearing and kinetic instabilities in the MST. The injection system details and modeling of the beam-plasma interaction will be presented   

Energy and Helicity Balance in Oscillating Field Current Drive Experiments

Oscillating field current drive (OFCD) is a proposed method of efficient, steady-state toroidal plasma current sustainment using AC poloidal and toroidal loop voltages. OFCD is added to a standard RFP in the MST device, increasing the net plasma current by $\sim $10{\%}. Magnetic fluctuations are modulated by the OFCD cycle, affecting energy and helicity balance. While the central electron pressure oscillation is large ($\sim $50{\%} amplitude), the total beta (=2$\mu _{0}<$p$_{e}$+p$_{i}>$/B$^{2}$(a)) oscillation is smaller, and the cycle-average beta ($\sim $7{\%}) is about the same as the standard RFP case without OFCD. The energy confinement time also oscillates with a cycle-average ($\sim $1 ms) about the same as the standard case. The measured helicity content is nearly equal to the measured injection minus the measured equilibrium dissipation. The residual may be coherent with the modulated MHD activity, implying some fluctuation-induced helicity dissipation, which will be measured in future tests. The experimental results are generally consistent with 3D resistive-MHD simulations.   

Upgraded Oscillating Field Current Drive on MST

The oscillating field current drive (OFCD) system for MST has been upgraded for higher power capability to investigate larger current drive. In OFCD, two frequency-matched ac magnetic fields are inductively applied to the plasma, one in the poloidal direction and the other in the toroidal direction. The fields interact to inject net magnetic helicity into the plasma depending on their phase difference, thereby driving a toroidal current. The basic design of the OFCD system remains the same: two pre-charged LC tank circuits inductively couple to MST's main magnet circuits. The upgraded tank circuits operate at double the previous voltage and are more strongly coupled to the main circuits, both of which allow more input power into the plasma. So far, the input power at the phase which produces the maximum plasma current has been increased to about 400 kW compared to 200 kW with the previous system. Larger current drive by OFCD is observed ($>$10{\%} increase over the baseline current at low current). However, magnetic fluctuations due to the unavoidably larger equilibrium modulation and/or plasma-wall interaction appear to be more important as limiting factors at these higher power levels. Tests at larger baseline current are underway. This work was supported by the US DOE.   

A new hybrid inductive scenario for a nearly steady-state Reversed Field Pinch

Steady-state current sustainment is challenging for the Reversed Field Pinch (RFP). The current magnitude is large, while the pressure-driven (bootstrap) current is small, even at the RFP's high beta $>$20\%. In the TITAN (RFP) system study [1], the current was designed steady-state using Oscillating Field Current Drive (OFCD), i.e., steady magnetic helicity injection using phased AC induction. Experiments and theory for OFCD are so far promising, but OFCD's reliance on magnetic relaxation could turn out incompatible with energy confinement requirements. Meanwhile inductive current profile control has demonstrated tokamak-like confinement in the RFP. Such control is inherently not steady-state. A hybrid scheme is proposed using OFCD to ramp the current, followed by a pulsed-burn during which inductive profile control maintains high confinement. The current is not constant but never goes to zero (sawtooth-like waveform). The current drive (and profile control) is efficient induction, simply applied at the plasma surface. The pulsed-burn phases could be separated by only a few seconds. Optimization of the hybrid cycle and other issues will be discussed. \newline [1] http://aries.ucsd.edu/LIB/REPORT/TITAN/final.shtml   

Numerical Simulation of Pulsed Parallel Current Drive in RFPs

The effects of applying inductive electric field pulses to saturated reversed-field pinch states are investigated numerically with the NIMROD code [1]. Simulation diagnostics are used to measure power transfer among groups of harmonics, and the instantaneous free energy in the mean fields is assessed with linear analysis techniques. The most effective technique in the Madison Symmetric Torus applies pulses of poloidal electric field while simultaneously reducing the loop voltage. Nonlinear simulations show that the initial response is an increase in edge parallel current that promptly decreases power transfer from the mean fields to core- and edge-resonant helical fluctuations. Linear analysis finds a consistent trend toward stabilization for these harmonics. The normal nonlinear balance is altered, reducing the power to nonlinearly sustained m=0 modes and decreasing the overall fluctuation level. Reducing loop voltage is shown to have little effect initially, but it keeps the mean profile from evolving to a more pinched and unstable configuration. \newline [1] Sovinec et al., JCP 195, 355 (2004). \newline [2] Chapman et al., PoP 9, 2061 (2002).   

Features of ITG Modes in the RFP

Global tearing modes, which normally dominate core transport in the RFP, are largely stabilized when the current profile is externally controlled. This allows small-scale modes to become a significant factor in RFP confinement, both global confinement and edge particle confinement. The driving source of the small-scale modes observed in the RFP has never been determined. Drift modes, resistive g-modes, and rippling modes are too weak in the strong magnetic shear to explain observations. We examine here the linear stability of the ion temperature gradient mode, Using GYRO [1] in a low beta, collisionless limit, linear gyrokinetic simulations in real toroidal RFP geometry have been performed. To benchmark and assess the results we make comparisons with fluid theory and prior calculations. To determine the nature of the instability we study parametric scalings and mode structure. We evaluate growth rates for MST parameters, and using mixing length arguments, determine if the instability is relevant to the small-scale turbulence observed in MST. \newline \newline [1] J. Candy and R.E. Waltz, J. Comp. Phys. 186, 545 (2003).   

Magnetic Fluctuation Spectrum in the RFP

Cascading magnetic turbulence is observed in MST. However, the spectrum is better fit by exponential decay than a power law, suggesting dissipation is important. To probe the processes at play we extend the dissipation range energy transfer arguments of Corrsin\footnote{S. Corrsin, Phys. Fluids 7, 1156 (1964).} to MHD turbulence, and consider multiple dissipation mechanisms, including energy absorption by impurity ions from cyclotron resonance damping. The latter is believed to be important from anomalous ion heating observations. When cyclotron damping dominates at lower wavenumber than viscous or resistive dissipation, and the densities of multiple charge state impurities produce a cyclotron damping rate that is roughly constant in wavenumber, exponential decay in the dissipation range gives way to an inertial range power law at higher wavenumber. We fit the theoretical spectrum to MST data, obtaining values for the cyclotron damping rate and the turbulent dissipation rate. These are compared to independent theoretical calculations. Implications for solar wind and interstellar turbulence are discussed.   

Preliminary Results from ULQ Experiments in RFX-mod

Plasma configurations with Ultra-Low safety factor, ULq , have been set up in RFX-mod, a RFP study oriented machine (R=2m, a=0.46m). The first tests have been carried out with the following parameters: $I_p=250 \div 500 $kA, $q=0.2 \div 0.6$, pulse length up to 100 ms, $I/N = 1 \div 5 \cdot 10^{-14} $A m. Plasma current evolution exhibits a staircase-like behaviour, likewise in other previous experiments, with a natural tendency to sustain the configurations with discrete \textit{q} values at the edge, which are near to the major rational numbers. The plasma current flat phases are preceded by the raise of very large single modes, having n,m numbers depending on the q-value at the edge: a large kink deformation of the plasma column, with strong interaction with the wall, is present during that time. The flat current phase is characterized by both low and high frequency MHD activity (modes $m=1$, $n=1 \div 20$) with very low amplitude, more than one order of magnitude lower than the corresponding RFP pulses in RFX-mod. Very low I/N pulses have been established, with density near or slightly over the Greenwald limit and a peaked profile, differently from the RFP configurations of RFX in which the high density produced always hollow profiles. We report the details of the ULq experimental results and comparison with RFP plasmas, together with the plan for future experiments with improved \textit{q}-value and plasma control.   

3D nonlinear MHD simulations for Ultra-Low q plasmas

Nonlinear 3D MHD simulations for Ultra-Low safety factor, ULq , plasmas have been performed with the SpeCyl code [1] in the simple frame of visco-resistive zero pressure model. This configuration is the intermediate state between the Tokamak and the Reversed Field Pinch. The experimental observation of the staircase-like behaviour in the evolution of the edge $q$-value, show that ULq plasmas have the natural tendency to select discrete $q_{edge}$ which are about the major rational numbers, suggesting plasma self-organization. Similar behaviour is obtained in numerical modelling when driving the system from the RFP regime to the Tokamak one: the transition of the q-value somewhat inside the plasma edge from a plateau level (near the mode rational number) to the next one occurs in concomitance with the development of a kink deformation of the plasma column, whose stabilization yields a nearly axisymmetric state. This numerical study, and the preliminary experimental results obtained exploiting the flexibility of the experiment RFX-mod [2], indicate the possibility to explore the impact on transport of such different MHD behaviour within the same experiment [1]. S. Cappello {\&} D. Biskamp Nuclear Fusion \textbf{36}, 571 (1996) [2] see on the web: R. Piovan, et al. \textit{First results of Ultra-Low q experiments in RFX-mod }12th IEA-RFP Workshop, Kyoto, Japan, 26-28 March 2007.   

Recent results of the RFX-mod Reversed Field Pinch

The experiments recently performed in the Reversed Field Pinch device RFX-mod are presented. The plasma operation regimes have been extended both in the current (0.3 MA$\le $ Ip $\le $ 1.5MA) and density space (0.1$\le $n$_{e}$/n$_{Greenwald}\le $0.8). Temperatures above 1 keV have been obtained, with discharge durations as long as $\approx $ 0.5 s. RFX-mod is a state of the art facility for active control of MHD modes, with a set of 48 (toroidal) x 4 (poloidal) saddle coils, independently driven, which cover the whole plasma surface. The aliasing of the sidebands generated by the discrete saddle coils has been corrected in real time, and new results on RWM stabilization and tearing modes control will be presented. Various enhanced confinement regimes, such as Oscillating Poloidal Current Drive, Quasi Single Helicity states are discussed.   

Stability Threshold of Ion Temperature Gradient Driven Mode in RFP plasmas

The Ion Temperature Gradient driven (ITG) mode and the related transport are of current interest in the RFP community. To understand the behavior of this mode in RFP plasmas; as the first step, the linear threshold of ITG mode in the RFP configuration is investigated in the small Larmor radius limit. Compared to tokamak, RFP configuration has a shorter connection length and stronger magnetic curvature drift. These effects result in a stronger instability driving mechanism in the fluid limit. However, the kinetic damping effects (Landau and magnetic drift resonance) also become stronger than those in tokamak; which ultimately determine the stability threshold. The numerical analysis shows that the ITG (adiabatic electrons) instability in RFPs requires a rather steep temperature profile, which usually may not exist in the plasma core of the current RFP experiments. The required temperature slope may be found in the very edge of the plasma where the temperature cools down rapidly near vacuum vessel or near the board of the dominant magnetic island during the quasi-single helicity state of the discharge. The case of positive density gradient of the plasma and/or trapped electron effects will also be discussed.   

Transport reduction and heating in the helical core of the reversed-field pinch

We describe the use of the M1TeV transport code to interpret the strong heating which is observed inside magnetic islands in the core of a reversed-field pinch during the quasi-single helicity (QSH) state. M1TeV describes the evolution of an internal kink mode in a Tokamak, using helical flux coordinates\footnote{F.Porcelli \textit{et al.}, Phys. Rev. Lett. \textbf{82}, 1458 (1999).}. We adapted the code to the $q$ profile typical of the reversed-field pinch, and we stopped the reconnection process at an intermediate stage to study 2D electron heat diffusion. Results show that inside the magnetic island the heat transport coefficient is two orders of magnitude lower than in the chaotic background, and its values fall in the Tokamak range. The M1TeV code is also capable of reproducing quite well the observed temperature profiles measured by the Thomson Scattering diagnostic at the RFX-mod experiment in Padova, Italy.   

Density limit, radiation and magnetic topology in the reversed-field pinch

In this paper we analyze the density limit in the reversed-field pinch machine RFX-mod, whose upgrades (in particular, the new feedback control system\footnote{S.Martini and the RFX team, Nucl. Fusion \textbf{47}, 783 (2007).}) have greatly ameliorated plasma-wall interaction issues. In fact, when $n/n_G < 0.35$ (with $n_G$ the Greenwald density), there is no signature of enhanced radiation outside the regions of the residual localized plasma-wall interaction. On the contrary, when $n/n_G > 0.35$ a localized enhancement of the radiation is observed, not necessarily associated to the region of maximum plasma-wall interaction. This localized radiation has the shape of a poloidal ring, and appears in correspondence to edge magnetic islands, originated from the MHD $m=0$ modes ($m$ is the poloidal mode number). Besides the local decrease of particle diffusivity $D$ associated to the magnetic islands, the presence of highly radiating rings can be related to a reduction of the turbulent edge transport\footnote{see P.Scarin, this conference.}, which takes place approximately at the same values of $n/n_G$. In this respect, the microscopic cause of the density limit could be similar to the MARFE phenomenon in Tokamaks.   

Hydrodynamic mode associated with the pinch flow in RFP simulations

We present a systematic study of single helicity (SH) states and quasi-single helicity (QSH) states in RFPs. We begin with cylindrical paramagnetic pinch equilibria with uniform resistivity, characterized by a single dimensionless parameter proportional to the toroidal electric field, or the RFP toroidal current parameter $\Theta$. For sufficiently high $\Theta$, there are several unstable $m=1$ ideal MHD instabilities, typically one of which is nonresonant, with $1/n$ just above $q(r=0)$. We evolve these modes nonlinearly to saturation for low Hartmann number H. We show the existence of a new class of unstable modes [1], besides the electromagnetic kink modes typically responsible for the reversal of the axial magnetic field at the edge in RFPs. This new instability is hydrodynamic in nature and is due to the inward equilibrium pinch flow and suitable boundary conditions. In these circumstances, the total angular momentum of the system must grow in response to the flux of particles coming from the boundary. The hydrodynamic mode dominates the nonlinear phase of the velocity field but has little effect on the dynamics of the magnetic field. \newline [1] G.L. Delzanno, L. Chac\'on, J.M. Finn, Hydrodynamic mode associated with the pinch flow in Reversed Field Pinch simulations, submitted (2007).   

Kinetic effects in RFP plasma

Strong tearing mode activity is present at sawtooth crashes in the Madison Symmetric Torus reversed field pinch (RFP). It is believed that tearing modes are responsible for strong ion heating and change in plasma flow profile at the crash. Our results based on both linear and nonlinear resistive MHD models showed that the spatial scale of velocity, electric field and current profiles in the tearing mode near resonance surface is comparable to ion gyroradius. The ion gyroradius is relatively large in RFPs because of smaller equilibrium magnetic field. In these conditions both two fluid and kinetic effects can be significant. We study ion kinetic effects on tearing modes in RFP plasmas. We consider RFP-like equilibrium in plane geometry and solve for linear eigenmodes in resistive MHD, two fluid and fully kinetic models. In the first two models we solve an eigenvalue problem, in the last we use particle in cell code VPIC and follow linear time evolution of the fastest growing mode. Also we examine nonlinear effects in tearing modes by running 2-D nonlinear time evolution in plane geometry in resistive MHD and PIC models. We analyze how the scale of plasma flow and flow amplitude in the mode are effected by the finite ion gyroradius effect, to what plasma component (ions or electrons) the magnetic energy of initially unstable equilibrium is transfered. Results of this analysis will be presented.   

Initial results from a low-aspect ratio RFP machine ``RELAX''

The low-aspectratio (A) RFP may have the potential to open a new regime of RFP configurations in that its equilibrium has such an advantage for confinement improvement as less densely spaced mode rational surfaces in the core region. It might also be desirable for staedy state operation relying on the neoclassical bootstrap current. We have constructed a low-A RFP machine ``RELAX'' ($\bf{RE} $versed field pinch of $\bf{L}$ow-$\bf{A}$spect ratio e$\bf{X} $periment) with aspect ratio of 2 ($R$=0.51m/$a$=0.25m) to explore the new RFP regime. The RFP discharge parameters in initial RELAX experiments are as follows. The plasma current $I_{p}$ is in the range from 40-80kA with discharge duration of > 2ms. The discharge resistance $R_{p}$ decreases with increasing $I_ {p}$, from 4m$\Omega$ (at $I_{p}$=40kA) to 1m$\Omega$ (at $I_{p} $=80kA). The pinch parameter $\Theta$ tends to be somewhat higher ($\Theta$ = 1.8-3.0) and the field reversal parameter $F$, deeper ($F$ = -0.5 - -1.0), when compared with those in medium- aspect ratio RFP. We will discuss on the MHD stability properties in RELAX by comparing the poloidal and toroidal mode spectra with experimental MHD equilibrium configurations.   

Characteristics of magnetized plasma flow for helicity injection into reversed-field pinch

The magnetized plasma flow injection experiment has been performed on the large sized reversed-field pinch (RFP) device of TPE-RX. The magnetized plasma flow injection has been demonstrated to support RFP formation fueling and helicity injection. In the start-up experiment with the plasma flow injection, reduced density pump-out, loop voltage and Da emission have been observed clearly. Also the effect of plasma flow on the RFP with improved confinement by PPCD technique has been evaluated. To determine the efficiency of fueling and helicity injection, density, temperature and magnetic structure have been measured by using Langmuir and magnetic probe arrays.The series of experiments will show the magnetic structure and actual helicity and energy contents of injected magnetized plasma flow.   

Measurements of Ion Flow and Neutral Depletion in an Argon Helicon Plasma with Magnetic Nozzle

Argon helicon plasmas are generated using 13.56 MHz RF power of up to 3 kW in a 10-cm-diameter Pyrex vacuum chamber attached to a 45-cm-diameter stainless steel chamber. Magnetic field strengths range up to 1 kG in the helicon source region and 1.5 kG at the peak of a downstream magnetic nozzle. 105 GHz microwave interferometry and a Langmuir probe are used to measure plasma densities in the range of 10$^{12}$ - 4x10$^{13}$ cm$^{-3}$ with electron temperatures in the range of 4 - 8 eV. A maximum density is observed for any given neutral gas pressure in the range of 0.1 - 5 mTorr (at RF powers typically between 1 and 1.5 kW), decreasing for greater powers, suggesting neutral depletion. Tunable diode laser-induced fluorescence is used to examine ion dynamics in the presence and absence of a magnetic nozzle. Near-sonic (M = 0.7) ion flows of up to 2.7 km/s have been observed in initial experiments. The axial plasma potential variation is measured using probe diagnostics.   

Spectroscopic Measurements of Electron Temperature on the University of Texas at Austin Argon Helicon Experiment

Absolutely calibrated spectroscopic measurements of the argon plasma in the helicon experiment at UT were used to estimate the electron temperature in the plasma core under the antenna. The helicon antenna was operated at 13.56 MHz with 1 kW absorbed power. Langmuir probe measurements of the electron density were used in a collisional-radiative model simulation$^{[1]}$ to estimate the electron temperature from argon ion (Ar II) line intensities. An electron temperature of 3.3 eV was obtained, agreeing with the Langmuir probe measurements. Argon neutral (Ar I) lines were then used with a second collisional-radiative model$^{[2]}$ to estimate the neutral density. \newline [1] http://adas.phys.strath.ac.uk \newline [2] Amy. M. Keesee and Earl E. Scime. Rev. Sci. Instrum. 77, 10F304 (2006)   

Comparison between modeled and experimental emission rates in ASTRAL argon plasmas.

Argon emission rate coefficients are measured in the ASTRAL helicon plasma source using a 0.33 m scanning monochromator and a CCD camera. ASTRAL produces bright intense Ar plasmas with the following parameters: n$_{e}$ = 10$^{12}$ - 10$^{13}$ cm$^{-3}$ and T$_{e}$ = 2 - 10 eV, B-field $\le $ 1.3 kGauss, rf power $\le $ 2 kWatt. A rf compensated Langmuir probe is used to measure T$_{e}$ and n$_{e}$. In this experiment Ar I, Ar II and Ar III transitions are monitored as a function of T$_{e}$ while n$_{e}$ is kept constant. Thus, experimental emission rates are obtained as a function of T$_{e}$ and compared to theoretical predictions. Using the ADAS suite of codes, we present spectral modeling of Ar plasmas produced in the ASTRAL helicon plasma source. Recent R-matrix electron-impact excitation data are combined with a new R-matrix calculation that includes pseudo-states contributions. Our collisional-radiative formalism assumes that the excited levels are in quasi-static equilibrium with the ground and metastable populations.~ Good to excellent agreement has been obtained by including T$_{e}$ and n$_{e}$ profiles in the modeling. The experiment-theory comparison confirms that T$_{e}$ is the dominant parameters in determining the emission rate coefficients in these plasmas.