Session VP1: Poster Session VIII: Spher. Torus and Exploratory Conf. Concepts; RF Heating and Diag; Magnetic Reconnection; Plasma Sim: Kinetic Codes; Plasma Tech.

Noninductive startup and sustainment of ST plasmas by localized plasma sources

The development of a non-solenoidal startup and sustainment technique is crucial to the future development of the ST. Studies of plasma formation by discrete point helicity sources have been conducted on the Pegasus Toroidal Experiment. An array of these sources, which are composed of low-impurity, high-current ($>$ 2 kA) washer guns, has been installed in the lower divertor region of the vacuum vessel. Plasma is injected onto helical field lines produced by crossed toroidal and vertical fields. As the injected power and helicity are increased, individual current streams are observed to merge into a sheet plasma. If the toroidal current is large enough, the plasma poloidal field overwhelms the vacuum field and the plasma relaxes into a tokamak-like configuration. Data suggest that flux surfaces are closed in toroidal average. This technique has been used to produce plasmas with I$_{p}>$50 kA, I$_{p}$/I$_{tf}>$2, and I$_{N}>$12 at modest values of B$_{t}$ ($<$ 0.02 T). Rotating toroidal modes are observed to coincide with flux closure, with cascades of n=1,2, and 3 being observed. Plans to expand to an array capable of producing I$_{p} \quad >$ 0.1 MA are presented in anticipation of routine handoff of these plasmas to ohmic sustainment.   

Experiments at High I$_{p}$/I$_{tf}$ in the P\textsc{egasus} Toroidal Experiment

The operating space defined by the external kink mode boundary in a near-unity aspect ratio ST allows access to very high toroidal beta and I$_{N}$ through operations at high toroidal field utilization factors, I$_{p}$/I$_{tf} \quad >$ 1. In Pegasus, however, purely inductive-driven plasmas exhibit an operational limit of I$_{p}$/I$_{tf} \quad \sim $ 1 due to the onset of large-scale tearing modes in a wide volume of low shear near the plasma core region. A new operating regime has been accessed in recent experiments with the addition of electrostatic helicity and edge-current sources. Employing these sources in the lower divertor region as a pre-ionization source, inductive startup at very low field is facilitated and allows I$_{p}$/I$_{tf} \quad \approx $ 1.5 at low I$_{p}$ ($\sim $ 50kA). Using these sources for non-inductive startup via helicity injection provides access to I$_{p}$/I$_{tf} \quad \approx $ 2.3, again at low I$_{p}$. In both cases, no large-scale tearing modes are evident. These observations, coupled with magnetic reconstructions, indicating hollow j(R) with possible reverse shear, suggest the sources provide significant modifications to the j(R) profile to allow stable discharge evolution at minimal toroidal field. Experimental studies are focusing on extending these recent discharges to higher I$_{p}$.   

Magnetic equilibrium reconstruction of Pegasus plasmas

MHD equilibrium reconstruction on the Pegasus Toroidal Experiment is the major tool used to characterize the plasma across varied operational regimes. Reconstructions are complicated by the presence of wall currents. Since the vacuum vessel can carry currents comparable to the plasma current for much of the shot duration, vessel current estimates are constrained by an array of external flux loops. The characteristics of plasmas produced by helicity injection by plasma guns are of particular interest. Reconstructions of these plasmas indicate that the current profile J(r) is relatively hollow, as expected in cases where current is driven at the edge. This gives rise to reverse magnetic shear in the core region. In contrast, purely ohmically driven plasmas typically exhibit peaked J(r) profiles and minimal magnetic shear in the plasma interior. In the near future, data from a new 2D soft X-ray camera will be incorporated as a measurement of flux surface shape which provides a constraint on the current profile.   

Nonlinear MHD simulation of DC helicity injection in the Pegasus spherical tokamak

DC helicity injection has been successfully employed in spherical tokamaks (ST's) to produce a tokamak-like plasma with either a poloidal-gap voltage known as coaxial helicity injection [HIT-II, NSTX] or a biased cathode gun configuration [CDX, PEGASUS]. In PEGASUS, the tokamak-like plasma which is subsequently ohmically driven is the product of a reversal of vacuum poloidal flux and a merger of gun-injected current filaments. A 3D nonlinear MHD computation using the NIMROD code [Sovinec et al. JCP \textbf{195}, 355 (2004)] simulates the formation, merger, and relaxation of the gun-injected current filaments to the tokamak-like plasma. The reversal of poloidal flux due to the field induced by the helicity drive is reproduced and the MHD processes leading to the merger and relaxation of the current filaments are described. Over the lifetime of a helically-driven experimental shot (approximately 10ms), the extent to which the merged plasma exhibits amplication of poloidal flux and the injected current in the relaxed state, reported in PEGASUS, is explored. The results are compared with simulations of current drive in NSTX via coaxial helicity injection which exhibit an n=1 open field-line kink [Tang and Boozer, Phys. Plasmas \textbf{11}, 2679 (2004)].   

Impurity and radiated power measurements on the Pegasus Toroidal Experiment

Emissive plasma gun current sources are employed as helicity injection devices for non-inductive startup of ST plasmas in Pegasus. The characterization of plasma impurity content and radiated power loses is of special interest in these non-ohmic discharges. To that end, radiated power losses are measured by two 16-channel AXUV silicon diode arrays that view the plasma tangentially across the mid-plane from the center column to the outside limiter. These measured intensities are post-processed using an Abel Inversion technique and fitted plasma equilibria to produce radial emissivity profiles. Bolometry of gun-produced plasmas indicates a rapid increase in radiated power after flux closure. Impurity species content is provided by VUV spectra obtained using a SPRED spectrometer. This instrument is capable of delivering a full spectrum from 10 to 110 nm at a 5 kHz rate. Oxygen is typically the dominant impurity, although at highest injection powers, metallic impurities from the gun and/or diverter impact region become evident. Qualitative observations of the O-V/O-IV line ratio suggest Te $>$ 50 eV for these large start-up plasmas.   

Implementation of the Pegasus Digital Plasma Control System

A primary goal of the Phase II Pegasus ST experiment is to achieve high normalized current $I_{N}$ at low toroidal field. Active feedback control is required to adequately guide the plasma evolution and attain stable high $I_{N}$ operation at near-unity aspect ratio. To that end, the control of our programmable power supplies is transitioning to a digital Plasma Control System (PCS) based on the software framework currently in use on DIII-D. This architecture allows for implementation of arbitrary control algorithms. A near-term goal is to provide feedback control of $R\left(t\right)$, $Z\left(t\right)$, and $I_{p}\left(t\right)$ via in-shot analysis of magnetics measurements and adjustment to appropriate power supply demands. New hardware and software has been developed to support the PCS, including improved signal processing electronics and the creation of a cross-platform MDSplus compatibility layer for the LabVIEW 8.0 and Igor Pro programming environments. Control algorithm development is assisted by coupling improved power supply, vacuum vessel, and rigid plasma displacement response models into a comprehensive Pegasus simserver simulator.   

Programmable power supplies for the Pegasus Toroidal Experiment

The Pegasus power systems are composed of switching power supplies with active current feedback control using pulse-width modulation (PWM) controllers. The 72 MVA poloidal and toroidal field power systems use conventional IGBT switches (900V, 2.5 kHz) and analog PWMs. These systems have a flexible configuration to allow for a variety of operational scenarios. The 113 MVA OH power system uses IGCT switches (2.4 kV, 3 kHz) and a new digital PWM that was developed to avoid damaging switching events by defining minimum switching state intervals. OH switching transient suppression is achieved with RLCD snubbers and by minimizing the internal inductance of the switch structure. A passive LC filter in series with the OH solenoid provides a smooth V$_{loop}$(t) while maintaining a sub-ms response time. IGCT switch limitations due to finite driver energy have been measured, and are used to map the operating space for present experiments.   

Overview of MAST results

The MAST experimental programme is focused both on physics studies for ITER and on addressing key issues for the long term potential of the spherical tokamak. The ITER physics studies include areas such as: improvement of energy confinement scalings, physics of pellet fuelling and its effects on transport, physics of generation and sustainment of transport barriers, ELM and pedestal physics, scrape-off layer transport, error fields correction and fast particle driven instabilities. Critical research areas for long term application of the spherical tokamak are non-solenoidal start-up, current drive and plasma exhaust. Experiments are carried out in close collaboration with international partners including joint experiments with other devices. Studies are supported by many diagnostic enhancements and an upgrade to the neutral beam heating system. An overview of the latest MAST results in above research topics and future plans will be presented.   

Overview of Final CDX-U Experiments with Lithium Plasma-Facing Components

The final phase of Current Drive eXperiment – Upgrade (CDX-U) research involved plasma-facing surfaces nearly completely coated with lithium. The CDX-U device is a spherical tokamak with the following typical parameters: R=34 cm, a=22 cm, B$_{t}$=2 kG, I$_{p}$=100 kA, T$_{e}$(0)=100 eV, and n$_{e}$(0)=5x10$^{19}$ m$^{-3}$. Electron beam-induced evaporation from a lithium target and vapor deposition from a lithium-filled oven created lithium coatings. Convective flows for highly-efficient power dissipation were observed in the lithium with electron beam heating. Lithium layers up to 100 nm thick between were deposited between discharges. These coatings reduced global recycling coefficients to as low as 0.3, a record for magnetically-confined hydrogen plasmas. New magnetic diagnostics constrained equilibrium reconstructions that were used to determine energy confinement times. With lithium coatings, plasmas had the largest global confinement enhancement ever achieved in an Ohmically-heated tokamak, exceeding ITER98P(y,1) scaling by up to a factor of three.   

Particle Confinement Times for Discharges with Lithium Plasma-facing Surfaces in CDX-U

Recent experiments on the CDX-U spherical torus have successfully achieved a significant reduction in recycling with large-area liquid lithium plasma-facing surfaces. Modeling of low recycling discharges with DEGAS2, a neutral particle transport code, has been performed. Utilizing available spectroscopic data, this modeling allows a calculation of a global particle confinement time ($\tau_p$) for the low recycling discharges. The $\tau_p$ values deduced with the modeling were used with $\tau_p^*$ to obtain the recycling coefficient $R$. Measurements of $\tau_p^*$ were performed by using transient gas puffing and observing the time dependence of the plasma density with microwave interferometry. The effects of a liquid lithium toroidal limiter and evaporative lithium coatings on the recycling coefficient $R$ will be presented.   

Status of the Lithium Tokamak eXperiment (LTX)

Nonrecycling boundary conditions have been predicted to produce fundamental changes in magnetic confinement. Recent experimental results from CDX-U indicate that liquid lithium and lithium coatings can provide greatly reduced recycling and enhanced confinement in a spherical tokamak. The Lithium Tokamak eXperiment (LTX) is designed to nearly eliminate recycling with a full thin-film molten lithium wall. Electron temperature and current profiles, transport and stability properties which are qualitatively different from a conventional high recycling tokamak are expected to result. We will summarize the design and construction of LTX (scheduled for first plasma in late spring 2007). We will also briefly examine how the final results from CDX-U impact our expectations for the performance and plasma parameters achievable in LTX.   

Diagnostics for Experiments with Liquid Lithium Plasma-Facing Components in LTX

The goal of the Lithium Tokamak eXperiment (LTX) spherical tokamak is to investigate plasmas that are almost completely surrounded by a liquid lithium wall. Such a configuration is expected to be fully non-recycling, resulting in a novel, highly-stable tokamak plasma regime. Profound changes in the temperature and density profiles are predicted, making diagnostics to measure them particularly important. Thomson scattering is an established technique for obtaining such data, and a system is being implemented with multiple spatial views across the LTX midplane. Low recycling walls will also have a dramatic effect on the plasma fueling and particle confinement. This is reflected in the time evolution of the plasma density, which will be measured using a microwave interferometer initially configured with two channels. The absence of recycling will be manifest in the virtual elimination of edge emission, and this is to be confirmed with an array of filtered detectors, or filterscopes. The stability of LTX discharges will be studied with instruments that include multichord X-ray arrays for the core plasma, and external magnetic “pickup” coils for instabilities that couple to the edge. This presentation will discuss the present and planned diagnostic capabilities of LTX.   

Design and Fabrication of the Lithium Tokamak Experiment

The design objective of the lithium tokamak experiment (LTX) is to investigate the equilibrium and stability of tokamak discharges with near-zero recycling. The construction of LTX incorporates the conversion of the existing current drive experiment (CDX) vessel into one with a nearly complete plasma facing surface of liquid lithium This paper will describe the design, fabrication, and installation activities required to convert CDX into LTX. The most significant new feature is the addition of a plasma facing liner on a shell that will be operated at 300\r{ }C to 400\r{ }C and covered with an evaporated layer of liquid lithium. The shell has been fabricated in-house from explosively bonded stainless steel on copper to a rather unique geometry to match the outer flux surface. Other significant device modifications include the construction of a new ohmic heating power system, rebuilding of the vacuum vessel, new lithium evaporators, additional diagnostics, modifications to the poloidal field coil geometry and their associated power supplies. Details on the progress of this conversion will be reported.   

RF Experiments on TST-2 and Plans for TST-2 and UTST

TST-2 has resumed operation after relocating to Kashiwa Campus and performing upgrades to magnetic field coil power supplies and RF heating systems. The main heating scenario used so far is high harmonic fast wave (HHFW) electron heating. Up to 400 kW of RF power 21 MHz can be injected using a pair of poloidal loop antennas separated toroidally and excited out of phase. Electron heating is indicated by a doubling of soft X-ray emission while the density and the radiated power remained unchanged. Injection of RF power at a 10 kW level to a low current ($<$ 1 kA), low density ($<$ 1$\times $10$^{17}$m$^{-3})$ plasma produced by 4 kW of ECH at 2.45 GHz caused a doubling of the plasma current. The 200 MHz transmitters transferred from the JFT-2M tokamak are being prepared for plasma current start-up experiments using waves in the lower-hybrid frequency range. Plans of RF experiments on the newly constructed UTST device will also be presented.   

Initial Operation of UTST High-Beta Spherical Tokamak Merging Device

The spherical tokamak (ST) merging has been studied for high-power reconnection heating/ startup without central-solenoid (CS) coil. In TS-3 merging device, two STs with major radius$\sim $0.2m were merged together in the axial direction using magnetic compression by two acceleration coils. The magnetic reconnection transformed the magnetic energy of reconnecting magnetic field through the outflow energy finally to the ion thermal energy, increasing the plasma beta of ST up to 50{\%}. We up-scaled this merging/ reconnection heating experiments: TS-3 and 4 and also the RF heating/ current drive experiment: TST-2 to a new joint ultra-high-beta ST experiment, UTST (R$\sim $0.4m). In this device, all PF coils are located outside of the vacuum vessel, unlike the TS-3 and 4 devices to demonstrate the reactor-relevant merging startup. Its main research subjects are (1) double-null startup of STs without CS coil, (2) their reactor-relevant reconnection heating for high-beta ST formation and (3) their sustainment by advanced RF and NBI techniques. We completed the UTST device and started its initial test for the double-null startup and merging. The mega-watt heating power of reconnection is expected to transform the initial low-beta merging STs ($\sim $5{\%}) to the high-beta ST ($\sim $30-50{\%}) within short reconnection time.   

Development of Low-Cost Pulsed NBI system for UTST high-beta ST Experiment

The UTST experiment at Univ. Tokyo is expected to produce ultra-high-beta ($\sim $50{\%}) 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 over100 Alfven time for its stability research. The following three heating methods are arranged for the sustainment experiment: (1) advanced RF heating method developed by 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 STs), (2) high current (20A), (3) maintenance-free, (4) low-cost, and (5) pulsed operation. Its pulsed operation enables us to remove all cooling system from the electrode system with curvature radius 1500[mm] and effective diameter 218[mm], decreasing significantly the cost for the electrode system. A SUS washer gun was used for the first time to realize the maintenance-free plasma (ion) source, in sharp contrast with the conventional filament type plasma source. Our initial operation of plasma source already measured the electron density profile suitable for the NBI ion source. More detailed results for the NBI development will be presented.   

Interaction of rotating helical magnetic field with the HIST spherical torus plasmas

The physical mechanism of current drive by co-axial helicity injection (CHI) has been experimentally investigated on both spheromak and spherical torus (ST) configurations on the HIST device [1]. It has been observed that the n = 1 kink mode rotates toroidally with a frequency of 10-20 kHz in the \textbf{ExB} direction. It seems that the induced toroidal current by CHI strongly relates with the observed rotating kink mode. On the other hand, it is well known that MHD instabilities can be controlled or even suppressed by an externally applied helical magnetic field in tokamak devices. Therefore, we have started to install two sets of external helical coils in order to produce a rotating helical magnetic field on HIST. Mode structures of the generated rotating helical magnetic field and preliminary experimental results of the interaction of the rotating helical magnetic field with the HIST plasmas will be shown in the conference. \newline [1] M. Nagata, et al., Physics of Plasmas \textbf{10}, 2932 (2003)   

Injection of Compact Torus into the HIST spherical torus plasmas

The three-dimensional interaction of a spheromak-like compact torus (CT) plasma with spherical torus (ST) plasmas has been experimentally studied to understand magnetic reconnection, helicity current drive, particle fuelling and Alfv\'en wave excitation [1]. We have examined how the sign of helicity (Co-HI and Counter-HI) of the injected CT influences on the ST plasmas on HIST [2]. The dynamics of the CT have been identified to be significantly different between the both injection cases. Time-frequency analysis shows that the fluctuation induced in the co-HI case has the maximum spectral amplitude at around 300 -- 400 kHz that may indicate the magnetic reconnection. In this case, the CT particle is released quickly at a periphery region, but on the other hand, for the counter-HI case, the CT could penetrate deeply into the core region as accompanied by Alfv\'en wave due to no magnetic reconnection. \newline \newline [1] M. Nagata, et al., Nucl. Fusion \textbf{45}, 1056 (2005) \newline [2] M. Nagata, et al., Physics of Plasmas \textbf{10}, 2932 (2003)   

Overview of LDX Results

The levitated dipole experiment (LDX) is a new research facility that is investigating plasma confinement and stability in a dipole magnetic field configuration as a possible catalyzed DD fusion power source that would avoid the burning of tritium. We report the production of high beta plasma confined by a laboratory superconducting dipole using neutral gas fueling and electron cyclotron resonance heating (ECRH). The pressure results from a population of anisotropic energetic trapped electrons that is sustained by microwave heating provided sufficient neutral gas is supplied to the plasma. The trapped electron beta was observed to be limited by the hot electron interchange (HEI) instability, but when the neutral gas was programmed so as to maintain the deuterium gas pressure near 0.2 mPa, the fast electron pressure increased by more than a factor of ten and the resulting stable high beta plasma was maintained quasi-continuously for up to 14 seconds. Low frequency ($<$10 kHz) fluctuations are sometimes observed at low neutral base pressure.   

Campaign for Levitation in LDX

In the past year, preparations have been made for the first flight of the Levitated Dipole Experiment (LDX). LDX, which consists of a 560~kg superconducting coil floating within a 5~m diameter vacuum chamber, is designed to study fusion relevant plasmas confined in a dipole magnetic field. During the spring, a high temperature superconducting levitation coil was integrated into the LDX facility. Testing was undertaken to verify the thermal performance of the coil under expected levitation conditions. In addition, a real-time operating system digital control system was developed that will be used for the levitation control. In July, plasma experiments were conducted with all superconducting magnets in operation. While still supported, roughly 75\% of the weight of the floating coil was magnetically lifted by the levitation coil above. A series of plasma experiments were conducted with the same magnetic geometry as will be the case during levitation. During August, the second generation launcher system will be installed. The launcher, which retracts beyond the plasma's last closed field lines during operation, is designed to safely catch the floating coil following an unexpected loss of control. After this installation, levitation experiments will commence.   

Visible and x-ray imaging of a laboratory dipole plasma

Supported plasma experiments in the Levitated Dipole Experiment focus on producing hot electron, high beta plasmas in a dipole magnetic field. Plasmas were created using multifrequency electron cyclotron resonance heating, and we find that most of the plasma energy is stored in the fast electrons, $T_e \sim$ 50 keV. Imaging of the plasma bremsstrahlung reveals that the fast electron population is anisotropic. This likely results from a combination of the electron cyclotron heating and the losses along the field lines to the supports on the internal coil. We expect the anisotropy to be substantially reduced during levitated operation. The presence of low frequency modes in the plasma may indicate that the plasma is toroidally asymmetric. A sixteen channel photodiode array sensitive to visible light is used to investigate the structure of these modes. A second array is under construction so that both toroidal and radial structure can be observed simultaneously. Results from x-ray and visible imaging diagnostics will be presented.   

Microwave Interferometer for the Levitated Dipole Experiment

Measuring and understanding the evolution of the plasma density is an important goal for the Levitated Dipole Experiment (LDX). Theoretical considerations suggest that the density profile may naturally evolve to a highly peaked profile with $\delta (n V) \sim 0$, or $n \sim 1/r^4$. Knowledge of the density profile is also necessary for the reconstruction of the overall equilibrium parameters of the confined plasma. In LDX we have built and tested a 4-cord interferometer diagnostic using heterodyne receivers at 60 GHz. Using the multi-cord interferometer, we have measured the radial density profile and its evolution over time in a plasma confined by a supported dipole field. Initial measurments show a range of profiles---from peaked to flat---have been created in the supported-mode of LDX and that the maximum density is usually around $4$x$10^{10}$ cm$^{-3}$.   

High Beta Observations of the Hot Electron Interchange Instability

High frequency ($f > 1$ MHz) electrostatic fluctuations have been observed in high-beta plasma created in the Levitated Dipole Experiment (LDX). We have previously identified these fluctuations as the Hot Electron Interchange (HEI) instability.\footnote{E. Ortiz, \textit{et al.}, to appear in \textit{J. Fus. Energy}, (2006).} New observations have been made in the presence of the magnetic levitation fields. We find the HEI mode is characterized by frequency sweeping at the drift-resonance of trapped energetic electrons. The fluctuations often appear with coherent structures that have been detected on fast high-impedance electrostatic probes and edge Mirnov sensors. We observe phase shifts using multiple probes that will enable us to determine the toroidal mode number (m) and a higher sampling rate reveals frequency sweeping as high as 40 MHz. Measurements that characterize these modes now incorporate fast magnetic measurements in an attempt to put together a coherent picture of plasma behavior during these modes, including the consequences of these instabilities on plasma formation and pressure limits.   

Strong, nonaxisymmetric flows driven in a dipole-confined plasma

Previous studies using the Collisionless Terella Experiment (CTX) have shown plasma dynamics to be dominated by interchange mixing. Since the geometry of the dipole magnetic field has no shear, interchange turbulence and interchange transport becomes two-dimensional. The usually complicated study of plasma turbulence and transport becomes less so in dipole geometry, provided plasma dynamics is appropriately described with field-line averaged quantities. In this presentation, strong, nonaxisymmetric plasma flows are induced by application of electrostatic bias in two ways. The first approach employs a negatively biased ($\sim -1000$~V) large diameter probe inserted at various radii in order to charge a central flux-tube and drive nonaxisymmteric cross-field currents. The second approach employs a non-axisymmetric bias applied to a series of meshes located at the inner, equatorial edge of the plasma. Static biasing as well as triggered biasing have been investigated. Very strong plasma flows can be induced, and these allow systematic study of nonlinear effects such as electrostatic structure coupling. Additionally, we observe a dramatic decrease in low-frequency turbulent fluctuations when the strength of the nonaxisymmetric bias exceeds a threshold.   

Characterizing Interchange Turbulence In A Dipole Confined Plasma

The dipole magnetic field has closed field-lines without magnetic shear, and this confinement configuration allows large-sized fluting instabilities. When dipole-confined plasma is produced with ECRH, fast Hot Electron Instabilities (HEI) appear at low densities, and slower turbulent fluctuations occur at higher densities. The global mode structures of the fast HEI instability and centrifugal interchange are understood. However, the characteristics of the turbulent interchange fluctuations (that occur between HEI bursts and when the HEI is suppressed by fueling) are less well understood. These low frequency, non-stationary fluctuations exhibit a power-law like turbulence spectrum and intermodal coupling. Correlation analysis, modal decomposition Hilbert methods, time-frequency spectrograms, and bicoherence are used to characterize interchange turbulence in a dipole and to form a basis for understanding nonlinear plasma mixing.   

What we've learned so far about the stability of plasma confined by a laboratory dipole magnet

During the past decade, new experiments with collisionless plasma confined by magnetic dipoles have been built at Columbia University, MIT, and the University of Tokyo. These have resulted in detailed observations of interchange instability, convective mixing, and high-beta toroidal confinement without magnetic shear. This poster discusses these new results with the aim of understanding linear, nonlinear, and turbulent plasma physics due to interchange dynamics. To date, observations show interchange modes to be fixed-boundary modes with broad structures that are easily measured and understood theoretically. Additionally, for a strong dipole magnet, interchange modes create wave-particle kinetics that are essentially one-dimensional. Hence, observations of linear and nonlinear MHD, fast-particle drift-resonances, transport in magnetospheric and fusion systems, and the effects of strong plasma flows are dominated by low-dimensional dynamics and show good agreement between observation, theory, and numerical simulation.   

Drift Waves in the GAMMA-10 and Kinetically Stabilized Tandem Mirror

The tandem mirror remains an attractive magnetic confinement geometry. The absence of toroidal curvature and internal plasma parallel current gives the system strongly favorable stability and transport properties. Additionally, GAMMA-10 experimental results demonstrate that sheared rotation can suppress turbulent radial losses. We analyze electrostatic drift wave eigenmodes for two machines: the GAMMA-10 (Cho, \it et al.\rm, Nuclear Fusion 45 (12), 2005) and the Kinetically Stabilized Tandem Mirror reactor (Post \it et al.\rm, Fusion Science and Technology, 47 (49) 2005). We compare results with experimental data from the GAMMA-10. Recent achievements of this machine include 3 keV ion confinement potentials and $T_e > 500 $ eV. The implications of drift waves results on radial confinement times developed using Bohm, gyro-Bohm, and electron temperature gradient (ETG) scalings in Pratt and Horton (Phys. Plasmas (13), 2006) are discussed. The plug mirrors create an ambipolar potential that controls end losses; radial losses are driven by drift wave turbulence that controls the electron temperature profile through radial transport. Total energy confinement times for the GAMMA-10 experiment are significantly larger than corresponding empirical confinement times in toroidal devices. We conclude that the tandem mirror has a qualitatively different form of drift wave radial transport from that in toroidal devices. *Work supported by the Department of Energy Grant DE-FG02-04ER5474.   

Overview and Recent Results from the ZaP Flow Z-Pinch

The ZaP Flow Z-Pinch Experiment at the University of Washington investigates a magnetic confinement configuration that relies on sheared flow for stability in an otherwise unstable configuration. An axially flowing Z-pinch is generated with a coaxial accelerator coupled to a pinch assembly chamber. Magnetic probes measure fluctuation levels. The plasma is magnetically confined for an extended quiescent period where the mode activity is reduced. Multichord Doppler shift measurements of impurity lines show a sub-Alfvenic, sheared flow during the quiescent period and low shear profiles during periods of high mode activity. The plasma has a sheared axial flow that exceeds the theoretical threshold for stability during the quiescent period and is lower than the threshold during periods of high mode activity. A holographic interferometer measures a radially peaked density profile during the quiescent period. Density profiles are analyzed to determine magnetic field and temperature profiles. Internal magnetic fields have been recently determined by measuring the Zeeman splitting of impurity carbon emission. The measurements are consistent with a magnetically confined pinch plasma. Recent experimental measurements will be presented. This work is supported by a grant from DOE.   

Thomson Scattering Measurements on the ZaP Experiment

The ZaP Flow Z-Pinch Experiment is presently studying a magnetically confined plasma configuration that uses sheared flow to provide stability. During a quiescent period in the magnetic mode activity, a dense Z-pinch with a sheared flow is observed on the axis of the machine. The velocity shear agrees with the threshold predicted by linear theory. To better understand the potential of the concept more accurate equilibrium profiles are measured. A better comparison to theory can also be made knowing the pressure profile. A single point Thomson scattering system is presently being installed to directly measure the local electron temperature in the Z-pinch. The system has a 3 mm radial resolution and can collect scattered light up to 4 cm off of the axis of the machine. (The Z-pinch has a 1 cm characteristic radius.) The expected Thomson signal has been calculated to be 10 times the measured background radiation level. Initially the system will measure the electron temperature at a single point in the plasma. The design and hardware allow for the system to be upgraded to a multipoint Thomson scattering system which would measure the pressure profile of the Z-pinch. The design of the system and initial results will be presented.   

Modified Cathode Design for the ZaP Flow Z-Pinch Experiment

The purpose of the ZaP Flow Z-Pinch Experiment at the University of Washington is to investigate the stabilizing effects of sheared flows on gross plasma stability. The inner electrode (cathode) of the ZaP experiment has been redesigned and replaced by a larger diameter version. The previous cathode had an outer diameter of 10 cm and a single neutral-gas puff valve in its interior along with eight azimuthally-spaced valves from the outer electrode, while the modified cathode has an outer diameter of slightly greater than 15 cm, which allows for the installation of nine neutral-gas puff valves in its interior. This greater number of valves, along with the addition of a vacuum bypass system, will allow the ZaP experiment a greater quantity and better control of gas injection. It is expected that this will increase the length of the stable (quiescent) period, while the larger diameter will result in a greater degree of adiabatic compression that will significantly increase the temperature and density of the pinch. Temperature and density measurements will be measured with a Thomson scattering system. Results for hydrogen and xenon pinches, along with some theoretical treatment, are included here.   

Overview of the Maryland Centrifugal Experiment (MCX)

The mission of MCX is to study centrifugal confinement and velocity shear stabilization of interchange instabilities in a linear magnetic geometry. New results include measurements of the radial profiles of rotational velocity employing multi-chord high resolution spectroscopy of impurity ion spectral lines; these show velocity shear sufficient for stabilization. Measurements of the axial dependence of rotation velocity will also be presented. A higher voltage (20 kV) discharge capacitor bank has been implemented and a study of velocity limitations for a variety of discharge parameters and insulator configurations, including transitions between discharge modes, will be reported. A new multi-chord H$_{\alpha }$ emission array of detectors is being developed to measure radial profiles of neutral hydrogen and correlate with momentum confinement times. A collaboration with HyperV Technologies is underway to study the injection of plasmoids into MCX employing a new innovative plasma gun, which is nearing completion.   

Momentum transfer to rotating magnetized plasma from gun plasma injection

Numerical simulations are carried out to investigate the penetration and momentum coupling of a gun-injected plasma slug into a rotating magnetized plasma. An experiment along these lines is envisioned for the Maryland Centrifugal Experiment (MCX) using a coaxial plasma accelerator gun developed by HyperV Technologies Corp. The plasma gun would be located in the axial mid-plane and fired off-axis into the rotating MCX plasma annulus. The numerical simulation is set up so that the initial momentum in the injected plasma slug is of order the initial momentum of the target plasma. Several numerical firings are done into cylindrical rotating plasma. Axial symmetry is assumed. The slug is seen to penetrate readily and deform into a mushroom, characteristic of interchange deformations. It is found that upto 25\% of the momentum in the slug can be transferred to the background plasma in one pass across a cylindrical chord. For the same initial momentum, a high-speed low density slug gives more momentum transfer than a low-speed high density slug. Details of the numerical simulations and a scaling study are presented.   

Neutral Profile \& Momentum Confinement on MCX

H$_{\alpha}$ detectors employing photodiodes and interference filters have been employed by the Maryland Centrifugal eXperiment (MCX) to study ionization rates, characterize transitions between discharge modes, and estimate neutral hydrogen density with 2~$\mu$s time resolution. We are currently implementing a multi-chord array of these detectors to determine H$_{\alpha}$ emission at the midplane as a function of radius. These measurements will be compared to recent H$_{\alpha}$ emission profile measurements employing high resolution spectroscopy. Using approximate electron temperatures and average electron densities as well as Abel like inversion techniques, neutral density profiles will be determined and compared to existing theoretical models. The neutral profiles will be used to calculate volume averaged momentum confinement times due to ion neutral collisions and these will be compared with those directly measured from circuit analysis.   

Velocity Limits and Discharge Performance in MCX

A primary goal of the Maryland Centrifugal eXperiment (MCX) is the attainment and maintenance of high rotation velocities. As earlier experiments reported a limitation on achievable speed we have performed extensive studies involving variations to the applied voltage, magnetic field, and radial discharge extent to ascertain the conditions under which such a limit might exist. MCX has discovered two modes of operation, where the higher rotation (HR) mode seems to have surpassed earlier limits. The MCX rotational plasma then undergoes a spontaneous transition by which the plasma is shifted into a subsequent lower voltage mode characterized both by a depressed rotational velocity as well as a reduced stored energy. We have observed an optical bursting coincident with this transition localized at the surface of the insulators bounding the discharge region suggesting that these events are due to the formation of an undesired secondary breakdown. Possible methods of eliminating these aforementioned transitions have been implemented and will be discussed.   

Measurements of plasma isorotation on MCX

The Maryland Centrifugal Experiment (MCX) studies magnetically confined rotating plasma for fusion. Plasma is generated in a shaped mirror geometry magnetic field (B$_{end}$/B$_{mid} \quad \sim $ 8) by applying a static electric field perpendicular to the magnetic field. The dominant motion is the \textbf{E}$\times $\textbf{B} drift in a hydrogen plasma. Other drifts are smaller, typically because of the smallness of the gyroradius -- there are 50 --100 proton gyroradii across the field. MHD theory predicts that plasma angular velocity should be constant on a field line. Measurements on the isorotation of the plasma as obtained from spectroscopic measurements of the Doppler shift of impurity (C$^{+}_{, }$C$^{2+}$, O$^{+})$ and neutral lines are presented. The species angular velocity is measured simultaneously at the midplane and at 80 cm off-midplane. The dependency of the species angular velocity on the magnetic field -- for fixed mirror ratio -- as well as on the mirror ratio, applied voltage and static fill pressure is documented experimentally   

Electron cyclotron waves and current drive in a relativistic plasma

The importance of relativistic effects on wave damping for electron cyclotron waves has been established for the electromagnetic X and O modes [1], and for the electrostatic Bernstein mode [2]. We have developed a numerical code R2D2 to solve the dispersion relation for EC waves in a fully relativistic plasma [2]. The wave polarization, energy flow density, and density of power absorbed are also calculated. We investigate, in detail, the effects of relativity on EC wave damping and propagation. R2D2 is coupled to a kinetic code DKE [3] which solves the fully relativistic Fokker-Planck equation. Two different current drive mechanisms using EC waves -- the Fisch-Boozer and the Ohkawa schemes -- are studied. The importance of relativistic effects on these current drive mechanisms is determined. \newline \newline [1] I.P. Shkarofsky, Phys. Fluids \textbf{9}, 561 (1966). \newline [2] A.K. Ram, J. Decker, and Y. Peysson, J. Plasma Phys. \textbf{71}, 675 (2005). \newline [3] J. Decker and Y. Peysson, Euratom-CEA Rep. EUR-CEA-FC-1736 (2004).   

Disruption Mitigation with ECRH on FTU tokamak

Experiments have been carried out in FTU to study the direct influence of ECRH on disruption evolution. Controlled disruptions have done by injection of impurities (Mo) or by increasing the electron density above the Greenwald limit with gas puffing. At the energy quench ECRH (140GHz, 1.1MW) is switched on, using loop voltage as trigger. ECRH is found to be effective in disruption avoidance when power deposition is outside the q=2 in the impurity injection case. The softening of the current decay is also obtained in off-axis deposition, while no effects are observed in case of central heating. Application of central ECRH leads to the suppression of an internal (3,2) mode (which naturally leads to disruption), while the still present external (2,1) is smaller and stable. A dependency is found between the location of the main MHD activity and the power deposition radius, depending on the type of disruption.   

Fullwave coupling to a 3D antenna code using Green's function formulation of wave-particle response

Using the fullwave code, TORIC, and the 3D antenna code, TOPICA, we construct a complete linear system for the RF driven plasma. The 3D finite element antenna code, TOPICA, requires an admittance, \textbf{Y}, for the plasma, where $B=\mathbf{Y}\bullet E$. In this work, TORIC was modified to allow excitation of the ($E_\eta $, $E_\zeta)$ electric field components at the plasma surface, corresponding to a single poloidal and toroidal mode number combination (m,n). This leads to the tensor response: $\mathbf{Y_n}= \left( \begin{array}{ll} Y_{\eta \eta } & Y_{\eta \zeta} \\ Y_{\zeta \eta } & Y_{\zeta \zeta } \end{array}\right)$, where each of the $\mathbf{Y}_n$ submatrices is $N_m$ in size. It is shown that the admittance matrix is equivalent to a Green's function calculation for the fullwave system and the net work done is less than twice a single fullwave calculation. The admittance calculation is used with loading calculation from TOPICA to construct self consistent plasma and antenna currents.   

Evaluation of the RF Quasilinear Operator Using the TORIC Spectral Solver

Recently the full-wave solver TORIC has been modified to employ the plasma response for an arbitrary particle distribution [1]. In order to couple this code to a Fokker Planck solver for self-consistent evolution of nonthermal particle distributions it is first necessary to evaluate the RF quasilinear operator (D$_{ql}$) using the electric fields expressed in the spectral basis representation of TORIC [2]. The present work employs a technique [3] where D$_{ql}$ is written in terms of the local power dissipation, which has been reconstructed from the electric fields in the full-wave solver. This technique will also be compared with more simplified treatments of D$_{ql}$ that have been carried out in the past using TORIC [4]. \newline [1] E. Valeo et al., APS-DPP Meeting (2006). \newline [2] J. C. Wright, PhD Thesis, Princeton University, June, 1998. \newline [3] E. F. Jaeger et al., Physics of Plasmas \textbf{13}, 056101 (2005). \newline [4] M. Brambilla, Nucl. Fusion \textbf{34}, 1121 (1994).   

TOPICA/TORIC integration for self-consistent antenna and plasma analysis

TOPICA [1] is a numerical suite conceived for prediction and analysis of plasma-facing antennas. It can handle real-life 3D antenna geometries (with housing, Faraday screen, etc.) as well as a realistic plasma model, including measured density and temperature profiles. TORIC [2] solves the finite Larmor radius wave equations in the ICRF regime in arbitrary axisymmetric toroidal plasmas. Due to the approach followed in developing TOPICA (i.e. the formal splitting of the problem in the vacuum region around the antenna and the plasma region inside the toroidal chamber), the code lends itself to handle toroidal plasmas, provided TORIC is run independently to yield the plasma surface admittance tensors$\underline{\underline {\tilde {Y}}} (m,m',n_\varphi )$. The latter enter directly into the integral equations solved by TOPICA, thus allowing a far more accurate plasma description that accounts for curvature effects. TOPICA outputs comprise, among others, the EM fields in front of the plasma: these can in turn be input to TORIC, in order to self-consistently determine the EM field propagation in the plasma. In this work, we report on the theory underlying the TOPICA/TORIC integration and the ongoing evolution of the two codes. \newline [1] V. Lancellotti et al., Nucl. Fusion, \textbf{46} (2006) S476 \newline [2] M. Brambilla, Plasma Phys. Contr. Fusion (1999) \textbf{41} 1   

Analysis of large complex ICRF and LH antenna systems by TOPICA

Auxiliary ICRF heating systems in \textit{tokamaks} often involve large complex antennas, made up of several conducting straps hosted in distinct cavities that open towards the plasma. The same holds especially true in the LH regime, wherein the antennas are comprised of arrays of many phased waveguides. Upon observing that the various cavities or waveguides couple to each other only through the EM fields existing over the plasma-facing apertures, we self-consistently formulated the EM problem by a convenient set of multiple coupled integral equations. Subsequent application of the Method of Moments yields a highly sparse algebraic system; therefore formal inversion of the system matrix happens to be not so memory demanding, despite the number of unknowns may be quite large (typically 15000 or so). The overall strategy has been implemented in an enhanced version of TOPICA (Torino Polytechnic Ion Cyclotron Antenna) [1], a simulation and prediction tool for plasma facing antennas that incorporates commercial-grade 3D graphic interfaces along with an accurate description of the plasma. In this work we present the new proposed formulation along with examples of application to real life large ICRH and LH antenna systems. \newline [1] V. Lancellotti et al., Nucl. Fusion, \textbf{46} (2006) S476-S499   

ITER Reference ICRF Antenna Analysis with TOPICA Code

TOPICA (Torino Polytechnic Ion Cyclotron Antenna) code is an innovative tool for the 3D/1D simulation of Ion Cyclotron Radio Frequency (ICRF), i.e. accounting for antennas in a realistic 3D geometry and with an accurate 1D plasma model [1]. The TOPICA suite, validated against measurements and data of mock-ups and existing antennas, has been proved to be a reliable tool for antennas performance prediction during operating conditions. The first part of this work reports on an extensive set of comparisons between TOPICA code and RANT3D code [2] results adopting different geometrical model of an ITER Reference ICRF antenna. Furthermore, in the second part, a detailed analysis of the performances of an ITER-like ICRF antenna geometry has been carried out, underlining the strong dependence and asymmetries of antenna input parameters due to plasma conditions. Electric current distribution on conductors in the vacuum region and electric field distribution in the vacuum region and at the interface with plasma edge are shown as well. \newline \newline [1] V. Lancellotti et al., Nucl. Fusion, \textbf{46} (2006) S476-S499 newline [2] M. D. Carter et al., Nucl. Fusion, \textbf{36} (1996) S209   

RF Sheath BC for ICRF Modeling

An important problem in ICRF heating and current drive is the quantitative evaluation of the nonlinear sheath formation at rf wave contact points with material boundaries. Ion acceleration in the sheaths leads to unwanted impurity generation, parasitic power loss, and reduced heating efficiency. Recently, a boundary condition (BC) was proposed\footnote{D. A. D'Ippolito and J. R. Myra, Lodestar Report \#LRC-06-108 (2006).} for rf antenna and full-wave codes to allow self-consistent calculation of the rf fields and sheath voltage. A related BC was tested in plasma processing.\footnote{E. F. Jaeger, L. A. Berry, J. S. Tolliver, and D. B. Batchelor, Phys. Plasmas {\bf 2} 2597 (1995).} Here, we discuss applications of the sheath BC to analytic test problems relevant to fusion plasmas and a first attempt at its integration with a 1D full wave code as part of the rf SciDAC project. Prospects for numerical implementation in 2D and 3D antenna and full-wave codes will also be discussed.   

Ray tracing for ICRF, including mode conversion and caustics

We report on our program to apply ray methods to ICRF heating in tokamak geometry. With particular attention to mode-conversion regions and to caustics, we have implemented our algorithms [1] for ray splitting, to obtain the evolution, along a ray, of wave amplitude, polarization, phase, and focusing [2]. Since these methods require a hermitian dispersion matrix to yield a real-valued ray hamiltonian, they must be supplemented by an algorithm to deal with wave damping from resonant particles, to be discussed in this poster. The goal of this effort is to greatly speed up the calculation of the power deposition profile, and of current drive and flow drive, in realistic tokamak equilibria, achieving in seconds, using ray-tracing, what now takes hours using full-wave simulations. \newline 1. E R Tracy, A N Kaufman, A Jaun, Phys Lett A290 (2001) 309; ``Local fields for asymptotic matching in multidimensional mode conversion'' (submitted for publication, 2006). \newline 2. A Jaun, E R Tracy, A N Kaufman, ``Eikonal waves, caustics, and mode conversion in tokamak plasmas'' (submitted for publication, 2006)   

Full-wave Simulations of ICRF heating in toroidal plasma with non-Maxwellian distribution functions

At the power levels required for significant heating and current drive in magnetically-confined toroidal plasma, modification of the particle distribution function from a Maxwellian shape is likely, with consequent changes in wave propagation and the location and amount of absorption. As part of the RF SciDAC effort to achieve the capability to self-consistently compute wave-plasma interactions, the FLR, full-wave, hot-plasma, toroidal simulation code, TORIC\footnote{M. Brambilla, Plasma Phys. Control. Fusion {\bf 41} (1999) 1-34}, has been extended to allow prescription of arbitrary distributions of the form $f(v_\parallel, v_\perp, \psi, \theta)$. Initial simulation results for several choices, including slowing-down distributions ($\sim v^{-3}$ for $|v/v_{th}| >> 1 $), bi-Maxwellians, and distributions with a plateau at high energy will be presented.   

Stochastic Threshold in Wave Electric Field Amplitude from Fundamental to High Harmonic ICRF Heating Experiments on C-Mod and DIII-D Tokamak

Resonant interaction between ions and ion cyclotron range of frequency (ICRF) wave at arbitrary cyclotron harmonics has been usually treated as a diffusive process in velocity space. This assumes decorrelation in the relative phase difference of wave and ion between successive resonances. In a collisionless high-temperature plasma, the change in trajectory of ions due to the change of energy through the interaction may produce a decorrelated phase. Since the decorrelation of phase difference depends strongly on the combination of applied amplitude of ICRF wave, the wave frequency and the energy of ions, stochastic threshold amplitudes of wave above which non-adiabatic interaction takes place may be very different in fundamental thermal minority ion heating (C-Mod) and high harmonic energetic beam ion heating (DIII-D) cases. We apply the Hamiltonian guiding center drift orbit code ORBIT-RF to study these two different experiments and estimate the dependences of the threshold amplitude for on-set of stochastic interaction of ions.   

High frequency gyrokinetic (HFGK) particle simulation of ion heating in the cyclotron frequency range.

The linear gyrokinetic formulation for $\rho/L_B \ll 1$ can be generalized to describe the arbitrary frequency and wavelength dynamics, where $\rho$ is the ion gyroradius and $L_B$ is the scale length of the ambient magnetic field [H. Qin, W.~M. Tang, W.~W. Lee and G. Rewoldt, Phys.\ Plasmas \textbf{6}, 1575 (1999)]. We developed a high frequency gyrokinetic (HFGK) algorithm, which utilizes the separation of the ion gyromotion from its gyrocenter motion, and it is equivalent to the original Lorentz-force description for $\rho/L_B \ll 1$. We performed a nonlinear $\delta f$ gyrokinetic particle-in-cell simulation of the HFGK model to demonstrate its ability to study arbitrary frequency dynamics [R. A. Kolesnikov, W. W. Lee, Sherwood meeting (2006)]. The algorithm allows self- consistency and first principle based simulation of nonlinear heating dynamics. Separation of motions allows us to take advantage of the difference between finer timescales associated with the propagation of rf waves and larger timescales due to slower gyrocenter motion, which produces finite particle orbits as well as turbulence and radial heat transport. We present some simulation results of simple 2D electrostatic system to study the absorption of cyclotron waves and their effect on gyrocenter motion as well as development of non-Maxwellian tail in ion distribution function. The effects of this non- Maxwellian distribution function on the turbulence resulting from the drift wave instability will be presented.   

Advances in ITER Ion Cyclotron System Design

The ITER Ion Cyclotron (IC) Heating and Current Drive System is designed to couple 20 MW of power into an ELMy H-mode plasma for a period $>$ 1000 s at frequencies of 40-55 MHz. Two alternate launcher concepts are under development, both of which couple power through a 24-element array of four toroidal by six toroidal current straps. The ``internal'' approach features tuning elements connected in series with each current strap at a location inside the port but outside the torus vacuum. Straps are connected in poloidal pairs in a load-resilient arrangement with low VSWR in the twelve feed lines for all values of plasma resistive loading. The ``external'' approach utilizes triplets of poloidal straps connected together in parallel. This reduces the total number of tuning elements, but all matching elements are external to the port, so that the portion of the feed network with high VSWR is increased. Eight feed lines are connected in a configuration that is also load resilient. An overview of the mechanical and electrical design of each concept will be presented. The IC system also incorporates rf generators, power supplies, and transmission lines whose specifications differ depending on antenna concept. The present status of the design of these components will also be discussed.   

The Wavelet Approach to Solving the Mode Conversion Wave Equation

Existing ``state of the art'' full wave radio frequency (RF) field codes utilize a Fourier expansion for the wave fields on a fixed grid. In plasmas in which both short and long wavelength modes co-exist due to mode conversion, this solution method entails the filling and subsequent inversion of very large matrices, which limits the attainable resolution and requires significant computational time, even on the largest supercomputers. An alternate approach based on wavelet expansions for solving wave equations arising in the context of mode conversion between a fast and slow wave is presented. The merits of using either Gabor or modified Morlet wavelet expansions, as well as the effects of irregularly spacing the wavelets to increase the spatial resolution, are discussed. Initial results indicate that it is possible to reduce the computational load while maintaining numerical accuracy by utilizing the wavelet expansion to avoid computing matrix elements for short wavelength modes in regions where such waves should not exist, based on a dispersion relation analysis.   

Mode conversion in ITER

Fast magnetosonic waves in the ion cyclotron range of frequencies (ICRF) can convert to much shorter wavelength modes such as ion Bernstein waves (IBW) and ion cyclotron waves (ICW) [1]. These modes are potentially useful for plasma control through the generation of localized currents and sheared flows. As part of the SciDAC Center for Simulation of Wave-Plasma Interactions project, the AORSA global-wave solver [2] has been ported to the new, dual-core Cray XT-3 (Jaguar) at ORNL where it demonstrates excellent scaling with the number of processors. Preliminary calculations using 4096 processors have allowed the first full-wave simulations of mode conversion in ITER. Mode conversion from the fast wave to the ICW is observed in mixtures of deuterium, tritium and helium3 at 53 MHz. The resulting flow velocity and electric field shear will be calculated. \newline [1] F.W. Perkins, Nucl. Fusion 17, 1197 (1977). \newline [2] E.F. Jaeger, L.A. Berry, J.R. Myra, et al., Phys. Rev. Lett. 90, 195001-1 (2003).   

Chemical and Gas Modification of Surfaces for Vacuum Breakdown Reduction and Prevention

The Plasma Material Interaction Group at the University of Illinois and the Fusion Energy Division of ORNL have been conducting breakdown studies to improve voltage hold-off to ultimately improve the performance of ICRF antennas used in fusion applications. The current understanding of the breakdown initiation on RF systems points to the formation of a local microplasma initiated by field emission.\footnote{Advanced Themometry Studies of Superconducting Radio-Frequency Cavities. J. Knobloch. PhD Thesis Cornell University. 1997} The microdischarge formed enhances the local electric field to the point of producing an explosive emission of electrons. We are studying the chemical and gas modification of surfaces that will reduce field emission and prevent the formation of microdischarges that initiate the breakdown process. The effect of SF$_{6}$ and XeF$_{2}$, and other gases on well-characterized emitters is revealed.   

The Role of Gas Pressure and Magnetic Fields on RF Breakdown

RF breakdown/arcing is a major power-limiting factor in antenna systems used for RF heating and current drive in fusion experiments. The factors that contribute to breakdown include gas pressure, gas type, magnetic field, material coatings, and local plasma density. The effects of these factors on RF breakdown are being studied in a resonant 1/4-wavelength section of vacuum transmission line terminated with an open circuit electrode structure. The electrode structure is designed to determine the role of the RF electric field strength and magnetic field orientation on the breakdown process. The formation of arcs at the electrode or plasma in the transmission line limits the voltage that can be sustained in the system. Initial results show that the maximum RF electric field that can be sustained without breakdown starts to degrade as the gas pressure approaches 1 mTorr and can change with gas type. The addition of an external magnetic field causes the formation of a plasma at pressures below 1 mTorr. Details of the experimental results and future plans will be presented.   

Dense Hypervelocity Plasma Jets

High velocity dense plasma jets are under continued experimental development for a variety of fusion applications including refueling, disruption mitigation, rotation drive, and magnetized target fusion. The technical goal is to accelerate plasma slugs of density $>10^{17} cm^{-3}$ and total mass $>100$ micrograms to velocities $>200$ km/s. The approach utilizes symmetrical injection of very high density plasma into a coaxial EM accelerator having a tailored cross-section geometry to prevent formation of the blow-by instability. Injected plasma is generated by electrothermal capillary discharges using either cylindrical capillaries or a newer toroidal spark gap arrangement that has worked at pressures as low as $3.5 \times 10^{-6}$ Torr in bench tests. Experimental plasma data will be presented for a complete 32 injector accelerator system recently built for driving rotation in the Maryland MCX experiment which utilizes the cylindrical capillaries, and also for a 50 spark gap test unit currently under construction.   

Optimization Techniques for Alpha-Channeling in Mirror Machines

The alpha-channeling effect can be obtained by alpha particles resonant interaction with radiofrequency waves in mirror machines. The appropriate compositions of diffusion paths in the coupled velocity-configuration space are found and divided into topologically distinct categories. Based on this classification and further 'fine-tuning' of the best topologies, optimization techniques for alpha channeling are proposed. Computational models of different degrees of accuracy and complexity are used. In light of these computations, the feasibility of implementing this concept in practical systems is discussed.   

Progress towards a fast ion collective Thomson scattering diagnostic for ITER

Diagnosing the dynamics of confined fast ions is an important challenge for burning plasmas such as ITER, where the physics of fusion alpha particles will be a key research topic. Fast ion collective Thomson scattering (CTS) can meet this need, and is maturing in CTS experiments at TEXTOR and at ASDEX Upgrade. We present results of the TEXTOR CTS diagnostic, currently in operation using an 180kW, 110GHz gyrotron and an upgraded receiver. Scattered spectrums for localized ($\sim $10cm), time resolved (4ms) measurements of ion velocity distributions in plasmas with NBI have been obtained and tests with ICRH plasmas have started. The CTS diagnostic at ASDEX Upgrade will be operational in the next campaign using a new 1MW gyrotron at 105GHz with spatiotemporal resolutions similar to TEXTOR. Design of the proposed fast ion CTS diagnostic for ITER will also be presented. It contains two 60GHz, 1MW gyrotron beams viewed by two fixed receiver arrays located on the low and high field sides of the plasma. Measurements of the parallel and perpendicular components of the ion velocity distribution over the full plasma cross section with resolutions better than a/10 and 100ms will be possible. Supported by U. S. DoE and EURATOM.   

Gyrotron Frequency Measurements for Fast Ion CTS Diagnostics at TEXTOR and ASDEX Upgrade

The frequency spectrum of the 110 GHz gyrotron at TEXTOR and the 105 GHz mode of the two-frequency gyrotron at ASDEX-Upgrade (AUG) have been studied in support of fast ion collective Thomson scattering (CTS) diagnostics. High resolution (0.1 MHz) measurements over a 500 MHz bandwidth and a 50dB dynamic range were obtained by harmonic heterodyne frequency downshift followed by digital fast Fourier transform and fast scanning spectrum analyzer. The 180 kW, 0.2 s gyrotron at TEXTOR had a clean spectrum except for weak satellites (-40 dB) at 17.5 MHz and chirped down 27 MHz depending on duty factor. Under some conditions when viewing the plasma with both ICRH and NBI additional satellites at the ICRH 29 MHz frequency (-18 dB) and 58 GHz harmonic (-30 dB) were observed, apparently by feedback from the plasma along the gyrotron beam transmission line. The 500 kW, 5 s gyrotron at AUG had no satellites while not viewing the plasma and chirped down 104 MHz, mostly in the first 100 ms. Implications for CTS diagnostics will be discussed.   

Wideband ECE Imaging Upgrade for TEXTOR

A 128 channel 2-D Electron Cyclotron Emission (ECE) Imaging instrument has been routinely used to study MHD physics such as m=1 and m=2 modes on the TEXTOR tokamak. As presently configured, each array element of the 16 element mixer array measures plasma emission at 8 simultaneous frequencies over a 4 GHz span to form a 16$\times $8 image of electron temperature profiles and fluctuations over an area of 16 cm (vertical) by 6 cm (horizontal). This instrument will be upgraded in October 2006 with new wideband ECE electronics which increase the instantaneous frequency coverage by $>$50{\%} to 6.4 GHz with a corresponding increase in horizontal plasma coverage. Arranged in a new modular fashion, the system is easily extended to form a 16$\times $16 system spanning 12.8 GHz by employing two modules per array channel, or as high as 16$\times $24 spanning 19.2 GHz by employing three modules per array channel.   

ECEI/MIR on KSTAR: Conceptual Design

A plasma imaging diagnostic is being developed for the KSTAR tokamak to image electron temperature $T_{e}$ profiles and fluctuations via Electron Cyclotron Emission Imaging (ECEI) and electron density $n_{e}$ fluctuations via Microwave Imaging Reflectometry (MIR). The envisioned ECEI system consists of a pair of 32 element mixer arrays which span a frequency range of 172-216 GHz, yielding a 32$\times $48 or 1536 channel $T_{e}$ image. The MIR system consists of a pair of 20 element mixer arrays with a frequency range of 104-152 GHz, yielding a 20$\times $16 or 320 channel $n_{e}$ fluctuation image. Use of in-vessel reflective optics permits both systems to view the KSTAR plasma through a relatively small vacuum window. System details, including preliminary optical and electronics designs, will be presented.   

Advances in PAA Technology for MIR

Advanced millimeter-wave imaging technology is under development at UC Davis in support of Microwave Imaging Reflectometry (MIR). Foremost of these new technologies are microelectromechanical systems (MEMS) delay lines configured as a beam shaping phased antenna array (PAA). For plasma use, these are configured as an artificial lens with a voltage-controllable focal length for launching the MIR probe or illumination beam. Control of the ``lens'' permits the curvature of the illumination beam to be matched to that of the target plasma over a wide range of frequencies. An NSTX design will be presented along with preliminary testing results at a reduced frequency of 28 GHz for proof-of-principle testing.   

MIR on NSTX: Conceptual Design

A 3-D Microwave Imaging Reflectometry (MIR) instrument is being designed for the National Spherical Tokamak Experiment (NSTX). Reflections from multiple, extended plasma cutoff surfaces are imaged onto a 2-D mixer array (8$\times $2 or 8$\times $4 elements, depending upon the size of the viewing window). Through the simultaneous launch and collection of 8 probe frequencies spanning a frequency range of 38-52 GHz (extendable to 70 GHz), the result is a 3-D visualization (up to 8$\times $4$\times $8 or 256 channels) of plasma density fluctuations associated with MHD and microturbulence. Each probe frequency may be independently controlled for radial correlation studies, or scanned to collect localized fluctuation data over a large plasma volume. The 2-D nature of the mixer array allows the magnetic pitch angle to be determined through correlation studies of toroidally and poloidally separated channels. Technical details regarding the MIR system design will be presented together with that of an innovative adaptive optics approach under development at UC Davis which can match the curvature of the illumination beam to that of the target plasma in real-time.   

Evaluation Method of Local Density Fluctuation Using Heavy Ion Beam Probe in CHS

Density fluctuation measurement in a Heavy Ion Beam Probe (HIBP) contains not only local density fluctuation, but also density fluctuation along beam orbit (known as the path integral effect). We have developed a method to remove the path integral effect and to deduce the local density fluctuation from the detected beam fluctuation. In this method, it is necessary to know correlation property of fluctuations, supposed that the electron temperature and density are known from some other diagnostics to estimate the ionization cross-section. In CHS, the temperature and density are given, and the HIBP has three neighboring observation points that allow us to evaluate the correlation property. We have applied the developed method, and have obtained the reconstructed local density fluctuation profile successfully. Furthermore, the local density fluctuation spectrum is successfully deduced by treating Fourier components of fluctuations individually. The paper presents the method and the obtained results in CHS.   

Laser Induced Fluorescence Spectroscopy for Measuring Flow Vector in Scrape-Off Layer Plasma

The experimental study of flow of scrape-off layer (SOL) plasma upstream from the divertor target is crucial for clarifying the mechanisms of divertor plasma detachment. The novel diagnostic technique to measure a two-dimensional (2-D) vector field of flow on poloidal cross section is proposed and the new system using the technique is developed. This scheme employs Laser Induced Fluorescence (LIF) spectroscopy with RApid Frequency Scan (RAFS) Dye laser system [1]. A snap shot of the ion poloidal velocity space can be obtained from the time trace of fluorescence intensity. Toroidal component of flow velocity can be simultaneously obtained from the Doppler shift measurement. In this poster presentation, we will report the progress of construction of RAFS Dye laser system. [1] C. Honda, et al., Rev. Sci. Instrum. , Vol. 58, 758 (1987).   

A fast optical spectrometer for the spectroscopic diagnostic of RFX-mod.

The detection of charge exchange radiation requires the use of spectrograph with very high performances, good imaging quality and high spectral resolution, especially in RFP devices where relatively low temperature and ion flow velocities have to be measured. To face the need of highly space and time resolved measurements of the relevant plasma parameters a new spectrograph has been installed on RFX-mod. This spectrograph, characterized by a Littrow mounting, has been designed ensuring a large effective aperture (f/3). As the emission region of interest in RFX-mod is in the visible range, the spectrometer is based on a large, high resolution plane reflecting grating, a long focal length photographic objective lens and a bi-dimensional back-illuminated CCD camera. The system can simultaneously record spectra along five poloidal or toroidal viewing chords using fiber optics with 1 mm diameter core. The main purpose of this spectrograph is to study the radial distribution of the plasma flow, of the ion temperature and of the impurity densities, with a time resolution lower than 5 ms. Preliminary results from the measurements of ion temperature and both poloidal and toroidal velocity will be presented.   

Progress on the motional Stark effect with laser-induced fluoresence diagnostic

The motional Stark effect with laser-induced fluorescence (MSE-LIF) diagnostic is under development to extend the MSE magnetic pitch angle diagnostic to lower fields ( $<$ 0.5 T) and enable measurement of magnetic field magnitude as well as direction. The technique involves injecting a low energy-spread neutral hydrogen beam (30 kV, 30 mA) into plasma, and using a collinear laser to excite transitions from the n=2 to n=3 atomic states in the beam atoms. The subsequent fluorescence from the same transition (Balmer-alpha, near 650 nm for the Doppler-shifted beam) is observed, and its splitting and polarization due to the E = v $\times$ B electric field in the beam frame is used to determine the background magnetic field magnitude and direction. This poster will present recent results from MSE-LIF development. A new plasma testbed for MSE-LIF, a spiral antenna helicon source, has been built.   

ARRIBA: A novel in-situ plasma surface interaction diagnostic for magnetic fusion devices

The development and design of a novel plasma surface interactions diagnostic for fusion experiments is described. The Alpha Radioisotope Remote Ion Beam Analysis (ARRIBA) diagnostic is designed to provide in-situ, time and depth-resolved measurement of element concentrations and H/D/T fuel retention at any surface inside a magnetic fusion device, including those surfaces exposed to significant heat loads such as found in the divertor. simple JxB activated mechanical system retracts and flips a cylindrical material sample (f$\sim $10mm) during a plasma discharge, such that one end of the cylinder becomes exposed to the plasma. The opposite end is protected from plasma exposure by the tile and is mechanically positioned for surface analysis. Surface analysis is accomplished using non-destructive ion beam analysis (IBA) techniques: Rutherford backscattering (RBS), Nuclear Reaction Analysis and Elastic Recoil Detection (ERD). We will describe initial laboratory tests of an ARRIBA prototype and issues of radiological safety, engineering design, and diagnostic performance. The use of ARRIBA to measure H/D/T retention in ITER is also explored.   

Local three-dimensional tokamak plasma tomography using nonlinear weight matrix

Compared to the two-dimensional tomography which covers only one poloidal cross-section of the toroidal plasma, three-dimensional tomography in toroidal geometry is quite complicated because of the curved feature and the geometrical limitation. We introduce the Jacobian matrix in evaluating weight matrix for better performance of the three-dimensional tomography in the curved geometry. The Jacobian matrix executes coordinate transformation from the rectangular to the curved vector space. In this work, we performed tomographic tests with the coordinate transformation and the nonlinear weight matrix. The poloidal cross-section is divided into 35x25 pixels and 18 toroidal layers are considered in the reconstruction region. We chose the emissivity phantoms which were combined with the simulated equilibrium flux surfaces and the MHD modes. How to extract the MHD modes from the reconstructed result will be described. The reconstruction algorithm is based on the modified Phillips-Tikhonov regularization method.   

Comparison of conditional averaging and super-resolution method

Conditional averaging and cross-correlation analysis allow in-depth study of plasma turbulence with just two probe tips. Two-dimensional probe arrays are now employed to provide spatial-temporal resolution at plasma turbulence. Increasing the spatial resolution of probe arrays to those of two probe techniques is difficult to achieve. Typically, there is at least a factor of four less resolution in space for probe arrays. Recently, we introduced a super-resolution method to numerically enhance the spatial resolution of probe arrays by transfering information from time to space domain [1]. This allows us to compare two point techniques with spatial-temporal measurements directly. Here, we will use experimental data to discuss the prospects and limitations of two probe methods [2] in detail. \newline [1] I. Teliban, D. Block, A. Piel, and V. Naulin, PPCF 48 (2006). \newline [2] D. Block, I. Teliban, F. Greiner, and A. Piel, Phys. Scripta T122 (2006).   

Effects of Heating Sounding Rocket Langmuir Probes

Langmuir probes have long been used to determine plasma characteristics in various plasma environments. However, the current-collecting surface of a Langmuir probe can quickly become contaminated with adsorbed neutral gases when exposed to elevated neutral pressures. Measurements will be inaccurate when data is taken with probes whose surfaces have been contaminated. It has been shown that heating the probe will remove these contaminants and provide more accurate results [1]. This approach has recently been tested on sounding rockets, which have typically been heated in atmosphere up to the moment of launch. The effectiveness of this technique is being tested in the Naval Research Laboratory (NRL) Space Simulation Chamber, which has the capability of simulating the conditions that a sounding rocket would experience throughout its flight. Experiments will be performed to determine the benefit of probe heating up to the point of launch as well as the effect lack of heating may have. Results for a NRL Langmuir probe as well as a standard sounding rocket Langmuir probe will be presented. [1] Amatucci et al., Rev. Sci. Instrum., 72, 2052 (2001).   

A contracting island model of electron acceleration during magnetic reconnection

A Fermi-like model for energetic electron production during magnetic reconnection is described that explains key observations in the magnetosphere and solar corona [1]. Magnetic reconnection with a guide field leads to the growth and dynamics of multiple magnetic islands rather than a single large x-line [2]. Above a critical energy electron acceleration is dominated by the Fermi-like reflection of electrons within the resulting magnetic islands rather than by the parallel electric fields associated with the x-line. Particles trapped within islands gain energy as they reflect from ends of contracting magnetic islands. The pressure from energetic electrons rises rapidly until the rate of electron energy gain balances the rate of magnetic energy release. A Fokker-Planck equation for the distribution of energetic particles, including their feedback on island contraction, is obtained by averaging over the particle interaction with many islands. The steady state solutions in reconnection geometry result from convective losses balancing the Fermi drive. At high energy the electron distribution functions take the form of powerlaws whose spectral index depends on the initial electron $\beta$, lower (higher) $\beta$ producing harder (softer) spectra.\\ 1. Drake {\it et al.}, Nature, in press.\\ 2. Drake {\it et al.}, Geophys.\ Res.\ Lett.\ {\bf 33}, L13105, 2006.   

Anisotropic Anomalous Thermalization in Turbulence and Its Importance in Magnetic Reconnection

In magnetic reconnection, there has been a long-standing debate about how the anomalous resistivity affects magnetic reconnection, and if anomoluos resistivity can dissipate magnetic energy fast enough to explain the behavior of solar flare and substorm in magnetosphere. We present new results on this issue and its application in magnetic reconnection. Of particular, importance is the relationship between anomalous resistivity and particle heating. Based on quasilinear approximation and statistical concepts, we study how the macroscopic physical process are related to the microscopic instabilities. We define the turbulence-induced anomalous currents and anomalous joule heating tensor, and relate them to the turbulence drag force . We find that the anisotropic turbulence leads to anisotropic dissipation. We calculate the anomalous resistivity that can produce the dissipation required for fast magnetic reconnection. thermalization is on a special direction which leads to a component increase of temperature. The results indicate that the anomalous resistivity is possible to lead a fast magnetic reconnection. We also present a 3D PIC simulation of magnetic reconnection in which the Buneman instability increases the parallel component of electron temperature dramatically.   

The Dissipation Region of Magnetic Reconnection: Kinetic PIC Code Results for Large Systems

Magnetic reconnection is a fundamental magnetic energy release process in plasmas. Including Hall physics in reconnection models has been shown to play a critical role in allowing fast Alfv\'enic reconnection even for very large system sizes, which is consistent with observed energy release times. The scaling of the reconnection to large systems has not been performed for fully kinetic simulations, however, and recent simulations with open boundary conditions have found that the electron dissipation region becomes very long, throttling the reconnection rate and leading to secondary tearing and island formation. We present results of large scale kinetic PIC scaling studies of anti-parallel reconnection. The physics controlling the length of the electron dissipation is examined.   

Compressible Resistive and Hall MHD Dynamics of the m=1 Sawtooth Instability

In order to understand the mechanism underlying the sawtooth crash in a tokamak, we have undertaken simulations of the m=1 kink-tearing instability using the Magnetic Reconnection Code, which is a fully implicit code that integrates the compressible Hall MHD equations. The results of our simulations bring out surprising features, not captured in previous simulations based on reduced equations. It is well established that the reduced resistive MHD equations typically show a regime of linear exponential growth followed by a slower nonlinear regime of algebraic growth (Waelbroeck regime). We show that the fully compressible resistive MHD equations admit another possibility whereby the linear exponential growth regime is not followed, even transiently, by the Waelbroeck regime. Instead, a regime of super-exponential or near-explosive growth occurs due to the phenomenon of flux pile-up, which is not realized in reduced MHD. When the Hall current and the electron pressure gradient is included via a generalized Ohm's law, the near-explosive tendency persists even though the pile-up effect is reduced. In both resistive and Hall MHD simulations, the geometry of the current sheet is seen to change from Y-points to near X-points, accounting for the impulsive transition to near-explosive growth. Nonlinear diamagnetic effects can thwart this near-explosive tendency.   

Stability of a resistive Sweet-Parker reconnection layer and onset of fast reconnection in Hall MHD.

Evolution of a two-dimensional system from a perturbed tearing- unstable Harris equilibrium through to saturation is studied using the implicit adaptive spectral element code SEL. Within resistive MHD, a small localized perturbation to a long Harris sheet (so called, large $\Delta'$ limit) is observed to non- linearly form a long and thin Sweet-Parker resistive layer. In a quiet plasma, such layer is observed to self-similarly expand and remain stable until either the stored energy of the initial equilibrium is dissipated or the boundary of the computational domain prevents further expansion of the resistive layer. However, additional small localized perturbations of sufficient magnitude are shown to be capable of triggering secondary tearing instabilities within the expanding resistive layer before the boundary effects become important. Onset of fast reconnection is investigated within the Hall MHD model in a regime where the ion skin depth ($c/ \omega_{pi}$) is much smaller than the width of the equilibrium Harris sheet and of the order of the resistive layer width. Nonlinear formation and subsequent elongation of a quasi- resistive reconnection layer with some two-fluid characteristics is observed. It is shown that as the layer evolves, it continues to elongate until either the boundary effects with associated layer growth stagnation and secondary tearing instability take over, or the very fast current layer collapse to an X-point is triggered by an explosive onset of fast reconnection.   

Improved Boundary Model for Particle Simulation of Collisionless Driven Reconnection

To clarify the relationship between particle kinetic effects and anomalous resistivity due to plasma instabilities in collisionless driven reconnection, we develop a three-dimensional Particle Simulation code for Magnetic reconnection in an Open system (PASMO). Recently, we have improved a model of upstream boundary to satisfy sufficiently the frozen-in condition both for ions and electrons. From the condition, plasma inflow is driven by ${E}\times{B}$ drift due to a driving electric field. In the previous model, particles are supplied into the system each time step, based on the particle flux through upstream boundary. The number density changes in proportion to magnetic field. In the improved model, particles in a cell near upstream boundary are newly loaded so as to satisfy shifted Maxwellian rigorously every time step. Using this model, the frozen-in condition is satisfied near the boundary both for electrons and ions. We will discuss the relationship between excitation of instability and mechanism of magnetic reconnection in the meeting.   

Formation of non-Maxwellian distribution and its role in collisionless driven reconnection

The dynamical evolution of collisionless driven reconnection is investigated by using a newly developed electromagnetic particle simulation code in a microscopic open system (``PASMO''). The plasma inflows, which are described by the shifted Maxwellian, are symmetrically driven from two upstream boundaries by imposing the external electric field in the z direction. The plasma flows into the current sheet while modifying the current density profiles. Since charged particles are not magnetized near the neutral sheet, their motions change from magnetized gyration to unmagnetized thermal motion called meandering motion as they approach the neutral sheet. The existence of unmagnetized meandering motion in the current sheet modifies particle distribution function from the shifted Maxwellian to an anisotropic one. An ion hole appears at the center of current sheet in the phase space, where distribution becomes two-peaked and no ions exist in low velocity region between two peaks. The strong modification of distribution function leads to the generation of off-diagonal components of pressure tensor term, which is one of major causes to violate frozen-in constraint and trigger collisionless reconnection.   

Open Boundary Kinetic Simulations of Collisionless Magnetic Reconnection

Kinetic simulations of magnetic reconnection typically employ periodic boundary conditions that limit the duration in which the results are physically meaningful due to the artificial recirculation of particles and magnetic flux. To address this issue, a new model was recently developed\footnote{Daughton, Scudder and Karimabadi, {\em Phys.~Plasmas} {\bf 13}, 072101, 2006} that is open with respect to particles, magnetic flux and electromagnetic radiation. This new model is used to examine both {\em driven} and {\em undriven} reconnection in neutral sheet geometry. In both cases, the electron diffusion region does not remain microscopic, but expands in time to form an extended current layer. As a consequence, the electron diffusion region forms a bottleneck and the reconnection rate is substantially reduced. Periodically, the electron layer becomes unstable and produces a secondary island, breaking the diffusion region into two shorter segments. After growing for some period, the island is ejected and the diffusion region again expands until a new island is formed. These results indicate that reconnection in a neutral sheet may be inherently unsteady and raise serious questions regarding the standard model of Hall mediated reconnection.   

Finding ``The'' Electron Diffusion Region: EDR

The diagnostic properties of the EDR are now realistically resolved with full PIC codes using open boundary conditions [Daughton et al. 2006]. Previously, periodic boundary conditions permitted significant unphysical recirculation of electrons along the separatrices through the diffusion region. This paper describes an operational approach to find the distinguishing \textit{observable} properties and/or correlations of observables of the plasma within and outside the EDR. This work represents the ``forward'' problem for the ``inverse'' problem facing experimentalists using spacecraft data. The EDR: (i) is \textit{not} rectangular, (ii) on its inflow side meets the separatrices where they are kinked, (iii) contains distinct patterns of strongly enhanced perpendicular electric fields and electron pressure agyrotropy, and (iv) is permeated by low levels of parallel electric fields. The strong perpendicular electric fields that can directly demagnetize the thermal electrons and the parallel E also occur \textit{outside} the EDR; accordingly, detection of these signatures by spacecraft do not necessarily place the spacecraft in the EDR. Incontrovertible \textit{in situ} detections of the EDR will hinge on both correlations between observables in one locale and the simultaneous multipoint measurement of critical plasma parameters of the electrons as planned on the US MMS mission or the ESA CrossScale concept. [Daughton et al, Phys. Fluids, 13, 072101, 2006]   

Experimental Study of Two-fluid Effects on Magnetic Reconnection

This paper describes the recent findings on two-fluid effects on magnetic reconnection in plasmas with variable collisionality in the MRX (Magnetic Reconnection Experiment)[1]. After the recent upgrade, our experimental operation regime has moved from the collisional to the collision-free, two-fluid effects have become more evident. It is observed that the 2-D profile of the neutral sheet is changed significantly from the rectangular shape of the familiar Sweet-Parker type to a double wedge shape as the collisionality is reduced and the reconnection rate increases. Two-fluid analysis is presented to illuminate the physics of Hall MHD in a collision-free reconnection layer for a variety of modes of operation. It is important to note that the Hall effect, which occurs due to 2-D laminar flows of electrons in the reconnection plane, is observed together with the presence of low and high frequency magnetic turbulence, which often has 3-D structures. In particular, the relationship of magnetic fluctuations[2] with the observed Hall field has been intensively studied in the MRX neutral sheet, where the sheet width is comparable to the ion skin depth. 1) M. Yamada et al, Phys. Plasmas 13, 052119 (2006) 2) H. Ji et al, Phys. Rev. Letts. 92, 115001 (2004)   

The Hall Effect and Magnetic Fluctuations during Fast Reconnection in MRX

Recent breakthroughs show that non-MHD effects, including the Hall effect and electromagnetic fluctuations, can facilitate fast magnetic reconnection. A quadrupole out-of-plane magnetic field in the diffusion region is the hallmark of the Hall effect [1]. This quadrupole magnetic field has been clearly observed in the Magnetic Reconnection Experiment (MRX) [2,3]. The experimental results show good agreement with simulation results. The Hall effect is found to be more significant in the collisionless regime and becomes small as the collisionality increases. Along with the Hall effect, magnetic fluctuations in the lower-hybrid frequency range have also been observed during magnetic reconnection in MRX. These fluctuations are found in the out-flow region as well as the current sheet center [4]. The interrelationship between the non-MHD effects and fast magnetic reconnection will be discussed along with comparison to space observations. [1] J. Birn et al., J. Geophys. Res., 106, 3715, 2001 [2] M. Yamada et al., Phys. Plasmas, 13, 052119, 2006 [3] Y. Ren et al., Phys. Rev. Lett., 95, 055003, 2005 [4] H. Ji et al., Phys. Rev. Lett., 92, 115001, 2004   

Active Perturbation of the Reconnecting Current Sheet in MRX

Electromagnetic fluctuations are thought to provide anomalous resistivity, speeding up the magnetic reconnection process\footnote{H. Ji, et all., Phys. Rev. Lett. {\bf{80}}, 3256 (1998).}. Such fluctuations have been previously observed in MRX in a broad spectrum up to the lower hybrid frequency\footnote{H. Ji, et all., Phys. Rev. Lett. {\bf{92}}, 115001 (2004).}. In order to characterize these fluctuations in detail, a magnetic dipole of $\sim$1mm radius is used to produce a field at a single frequency in the reconnecting current sheet of the Magnetic Reconnection Experiment (MRX). The field from this active probe is picked up by a three component fluctuation probe a few centimeters upstream or downstream with respect to electron flow within the current layer. With detection downstream, the signal is enhanced within the current sheet. By contrast, the signal detected upstream within the layer is often reduced below the vacuum value. Ongoing experiments and analysis will more fully explore the propagation characteristics and their implications on the reconnection process; this includes use of a $\sim$1cm radius coil that may better couple to plasma modes\footnote{C.L. Rousculp, et all., Phys. Plasmas. {\bf{2}}, 4083 (1995).}.   

Mach probe measurements in the context of the Hall effect at MRX.

MRX clearly observes the quadrupole out-of-plane field, which is the most significant signature of the Hall effect. This effect appears when we go from the collisional to the collisionless regime where the one-fluid MHD formulation not longer holds and the separation of the electron and ion motions give rise to in-plane currents. These currents can be calculated from the measured quadrupole field. We used a Mach probe to measure the axial (along current sheet) profile of the ion flow velocity in the outflow region of the current sheet. We have calculated a calibration factor to overcome the difference in the effective area of the Mach probe electrodes. We have written a code to filter and analyze the data and we have used the unmagnetized model by Hutchinson to extract the Mach numbers from the raw signals. The ion outflow speed is at most 0.2V$_{A}$, which is much less than the maximum electron outflow speed of 2-3 V$_{A}$ in the same region. These measurements confirm the separation between electron and ion motions, which is the basis of the Hall effect. Y. Ren, M. Yamada, S. Gerhardt \textit{et al.,} Phys. Rev. Lett. \textbf{95}, 055003 (2005). M. Yamada, Y. Ren, H. Ji \textit{et al}., Phys. Plasmas \textbf{13, }052119 (2006).   

On the saturation of plasma instability responsible for anomalous resistivity in the MRX

Both enhanced resistivity and electromagnetic fluctuations have been identified in the MRX. In order to understand the origin of this fluctuation, the linear theory has been developed.\footnote{H. Ji, R. Kulsrud, W. Fox, and M. Yamada, JGR 110, A08212 (2005).} Determining the resultant anomalous resistivity from theoretical calculation, the wave amplitude has to be known.\footnote{R. Kulsrud, H. Ji, W. Fox, and M. Yamada,PoP 12, 082301 (2005).} To predict the amplitude and understand the underlying wave-particle interaction mechanism, we need to calculate non-linear saturation of the waves. The non-linear effect can be broken down into the sum of independent interactions between unstable and stable modes, which propagate in different directions. We consider a single pair of unstable and stable modes, and the beatwave determined by them. The interaction is a generalization to 3-D EM modes of the usual non-linear Landau mechanism for energy exchange between unstable and stable modes. We have calculated the energy exchange rate between any two pairs of modes. We use this to arrive at scaling for the amplitude (and the resultant resistivity), that can be applied to large space and astrophysical systems. We benchmark this calculation by comparing with observations of the fluctuation in the MRX.   

Effects of Global Boundary and Local Collisionality on Magnetic Reconnection in MRX

The magnetic reconnection process is generally thought to be determined by both global constraints and local plasma dynamics. However, how exactly the reconnection depends on both these aspects is under heated debates. For example, in numerical simulations the reconnection rate can be independent [1] or dependent on the system size [2] or even on whether the boundary is open or closed [3]. In this poster, we report a systematic study of reconnection dependence on global boundary conditions (the distance between two flux cores) and local plasma parameters in the MRX device. It is found that the reconnection rate is a function of both local plasma collisionality and global boundary conditions. At a given flux-core distance, the current sheet length is inversely proportional to the effective resistivity, depending on the plasma collisionality. As a result, the reconnection is accelerated by both the resistivity enhancement and the current sheet shortening. At a given collisionality, the current sheet length increases with the flux-core distance, slowing down the reconnection rate. The observed rate dependance can be explained by the generalized Sweet-Parker model [4] which approximates the diffusion region shape by a rectangular box. Implications to large space and astrophysical systems will be discussed. This work is supported by DoE under contract \#DE-AC02-76- CH03073. [1] Shay et al. JGR (1999). [2] Wang et al. PRL (2001). [3] Daughton et al. PoP (2006). [4] Ji et al. PRL (1998).   

NIMROD Simulations of Reconnection in MRX and SSX

Two-fluid effects are known to influence magnetic reconnection rates through non-MHD communication between the current sheet and the surrounding magnetic field topology [1]. To examine the interrelationship between the physics of the reconnection layer and the global magnetic field topology, we perform simulations of the Magnetic Reconnection Experiment (MRX) and the Swarthmore Spheromak Experiment (SSX) using the NIMROD extended MHD code. Two-fluid simulations clearly show the development of the out-of-plane quadrupole field signature associated with whistler-mediated reconnection with features similar to experiment. We discuss the tilting of the current sheet that occurs when an imposed guide field is present. For SSX, we show simulations of spheromak formation and merging. Comparisons with experimental line-of-sight velocity measurements are made. For both experiments, we discuss the contributions the geometry of the problem makes on the reconnection process. In order to investigate the impact of communication with the global field on the reconnection process, we compare simulations of these experiments to simulations of reconnection in a simplified domain.\newline [1] D.~Biskamp, E.~Schwarz, and J.F.~Drake, Phys.~Plasmas 4, 1002 (1997).   

Laboratory observations of spontaneous magnetic reconnection

Detailed measurements of spontaneous magnetic reconnection are presented. The experimental data, which were obtained in the new closed VTF magnetic configuration, document the profile evolution of the plasma density, current density, magnetic flux function, reconnection rate and the current density during a spontaneous reconnection event in the presence of a strong guide magnetic field. The reconnection process is at first slow, which allows magnetic stress to build in the system while the current channel becomes increasingly narrow and intense. The onset of a fast reconnection event occurs as the width of the current channel approaches the ion sound Larmor radius, $\rho_s$.   

Experimental studies of magnetic and electrostatic fluctuations on the VTF reconnection experiment

We present studies of magnetic and electrostatic fluctuations observed during reconnection in the new closed magnetic configuration of the VTF experiment at MIT [1]. We have observed fairly steady magnetic fluctuations near the lower hybrid frequency ($\sim$~10~MHz) punctuated by bursts of higher frequency fluctuations in the Buneman range, $(m_e/m_i)^{1/3}f_{pe}$, $\sim$~200~MHz. Experiments are underway to study tip-tip correlations on the RF probes and also between fluctuation level and reconnection rate. In addition, the higher frequency modes may indicate the creation of superthermal electron populations during reconnection; we are now installing detectors for soft x-ray Bremsstrahlung. Finally, we present conclusions of previous studies of electron momentum balance during driven reconnection for the open field line configuration of VTF [2]. \newline \newline [1] J. Egedal, et al. (2006) Laboratory observations of spontaneous magnetic reconnection. Submitted to {\it Phys. Rev. Lett.} \newline [2] J. Egedal, et al. (2000) {\it Rev. Sci. Instrum.} 71, 3351.   

Plasma Blobs in VTF

We investigate the large-scale motion of plasma blobs in the Versatile Toroidal Facility (VTF) using Langmuir probe arrays. Blobs, or ‘intermittent plasma objects’, have been used to model plasma fluctuations in the scrape-off layer of tokamaks and other devices [1-3]. These fluctuations, which are interchange modes driven by magnetic field curvature, display a convective or ‘bursty’ character and can sometimes form large coherent structures. We use VTF, a well-diagnosed basic plasma physics experiment, to create plasma blobs reproducibly. The experiments are designed to investigate how the average blob speed scales with various experimental parameters. We find that charge exchange collisions with neutrals play a significant role in the non-linear evolution of the plasma structures. \newline [1] Krasheninnikov S, {\it Phys. Lett. A} {\bf 283}, 368 (2001) \newline [2] Zweben S et al, {\it Nucl. Fusion} {\bf 44}, 134 (2004) \newline [3] Garcia O et al, {\it Phys. Plasmas} {\bf 12}, 090701 (2005)   

Current sheets and reconnection at 3D null points

The evolution of the magnetic field in the vicinity of a single isolated three-dimensional (3D) magnetic null point is discussed. Such 3D magnetic nulls may be important sites of magnetic reconnection in both solar coronal plasmas and the Earth's magnetosphere as well as some laboratory experiments. The formation of large current density at 3D nulls as a result of boundary driving is described. It is demonstrated by means of resistive MHD simulations that shear boundary perturbations which act to close up the angle between the null point spine and fan separatrices result in strong growth of the current density. Locally, the null point magnetic field collapses to form a 3D-localised current density structure, which has a Y-type appearance in the plane perpendicular to the boundary shear, resembling that of a Sweet-Parker current sheet. The qualitative and quantitative properties of the current sheet with respect to the driving parameters, the domain size, and the plasma parameters are discussed. Accompanying the current growth is the development of a significant component of the electric field parallel to the magnetic field. This parallel electric field is an indicator of the breakdown of ideal MHD, and of magnetic reconnection.   

Driven magnetic reconnection evolution in an X-point magnetospheric plasma

The nonlinear evolution of a plasma typical of the earth magnetosphere is studied, in the configuration of a neutral X-point with a guide field, which would be relevant for the day-side magnetosphere. For magnetospheric parameters, the electron inertial skin depth is smaller than the ion-sound gyroradius ($d_e < \rho_s$) while $\beta< 1$ and the resisitivity is negligible. The ensuing magnetic reconnection driven by a plasma flow due to the incoming interplanetary plasma is studied using a reduced model derived for the relevant collisionless regime (Kuvshinov et al., J. Plasma Phys. (1998) {\bf 59}, 727). This model is first analyzed in an asymptotic regime for long times, following Ramos et al. (Phys. Rev. Lett. (2002) {\bf 89}, 055002) who made a study based on a linear analysis, valid when the forcing is small. Then a numerical solution is performed in order to verify the validity of the linear results and analyze the spatial structure of the magnetic configuration as it evolves to long times. The numerical solution gives also results valid for strong forcing, as in class-X solar flares, which turn out not to be very different from the small forcing. In particular, the reconnected magnetic flux approaches a constant value as $t \to \infty$, and the spatial variation scale length is of the order of $d_e$.   

Detection of Magnetic Nulls in Toroidal Geometry

The importance of magnetic nulls in toroidal geometry has long been recognized in the fusion community as an important component to understand plasma transport. Most methods for numerically calculating the magnetic nulls use as their basis Taylor expansions about the singular points in ``flux space.'' The difficulty of these methods is that they require a mapping from physical space (X,Y,Z) into flux space (flux, theta, phi) and doing this mapping accurately is very difficult. As a consequence, these methods are not robust, especially in the complicated geometries of modern experiments. In this work, we present methods that are purely geometric, local in nature, and geared for parallel computations. Emphasis is on robustness and speed and ``sufficiently accurate'' methods, which are more suitable for visualization. The application of these methods to data from the NIMROD and M3D codes will be presented.   

Study of Current Sheet Formation and Forced Reconnection Based on the Newton Challenge.

Through the rapid acceleration of a boundary, or supersonic injection, it is possible to generate a shock wave within a plasma. It was the intention of this work to simulate shocks in both a fluid and a kinetic model of a plasma. The particular codes used were Graale, in the fluid case, and CELESTA3D for the kinetic case. It was necessary to verify the validity of the codes first. This was achieved by setting the B-field of Graale to zero, and consequently reducing this plasma code into a gas dynamic code. From here the code was compared against Rankine-Hugonoit jump conditions, and it was found that there was agreement to within 3.6{\%}. Once the fluid case was confirmed accurate, the kinetic case was compared with the fluid case, by comparing the point at which the shocks initially collide. So long as the fluid and kinetic model shocks collide at the same point in time and space, then the shocks speeds are identical and one can presume that the kinetic code is accurate. A noteworthy finding, was the kinetic simulation showed a bifurcated current profile, where as the fluid case did not.   

Whistler wave bursts near a reconnection region in the magnetotail

Bursts of right-hand polarized electromagnetic waves with frequencies around 100 Hz (a few times less than the local electron cyclotron frequency) and a bandwidth ~100-200 Hz are observed near a reconnection site in the magnetotail by the Cluster spacecraft. The waves are interpreted as propagating whistler waves. The burst duration ranges from a few to ~10 seconds. The waves have a typical wave length of about 1 electron inertial length (~20 km). The strongest burst is observed right before the magnetic field curvature peaks negatively and then reverses sign. The curvature reversal coincides with ion flow reversal, and is interpreted as due to the traversal of the reconnection X-region by the spacecraft. The strongest whistler burst occurs in association with the enhancement of energetic electrons up to 100 keV, and with a strong electron temperature anisotropy. We explore the possibility of inferring information about the reconnection dynamics and the stability of thin current sheets from these wave characteristics.   

Electron and DC electric field signatures near a magnetotail reconnection region: Comparison between Cluster observations and PIC simulations

A collisionless magnetic reconnection event, which occurred in the magnetotail during a substorm, is studied based on data from the Cluster spacecraft and the results from a 2D PIC simulation. The focus is on the structure of DC electric fields and electron distribution functions within an ion inertial length of the reconnection site, including the electron diffusion region. The simulation shows the formation of an electrostatic potential well, with the electric field peaking near the separatrices and the thin current sheet. The existence of such an electrostatic potential well has been previously reported by J. R. Wygant and coworkers [J. Geophys. Res., 110, doi: 10.1029/2004JA010708, 2005]. Electric field structures (~80 mV/m, peak ot peak) of the order of a few electron inertial lengths are observed by multiple spacecraft at times separated by a few minutes, indicating the persistence of the structure. Observed electron distribution functions exhibit very similar features as those obtained from the simulations. The comparison between observations and simulations enables us to see the extent to which 2D PIC simulations capture observed collisionless reconnection signatures, and to locate the spacecraft relative to the reconnection site.   

Momentum transport from current-driven reconnection

In rotating toroidal plasmas in both laboratory and astrophysical settings, toroidal angular momentum is observed to be transported radially outward. In both cases the transport is much greater than can be explained by collisional viscosity. In the reversed field pinch (RFP), the toroidal rotation profile flattens abruptly during a reconnection event. Here we evaluate momentum transport that arises from current-driven reconnection, in particular from tearing instabilities in the RFP. Through quasilinear calculation of Maxwell and Reynolds stresses, we find that a single tearing mode, in the presence of equilibrium flow, can indeed produce momentum transport in the vicinity of the reconnection layer. However, nonlinear, resistive MHD computation of the full, multi-mode nonlinear dynamics reveals an additional effect. In the presence of multiple tearing modes, nonlinear coupling strongly enhances the torques and broadens their radial width. Theoretical results will be compared to the momentum transport measurements in the MST experiment. Preliminary computational results of momentum transport from current-driven reconnection in an accretion disk (a possible mechanism in addition to the transport from flow-driven instabilities) will also be reported.   

Two Fluid Dynamo in Reversed Field Pinch

In the Madison Symmetric Torus reversed field pinch experiments, tearing instabilities are observed to generate magnetic field, flow velocity and current density fluctuations that follow a temporally cyclic sawtooth behavior. One of the consequences of these instabilities is the production of dynamos, fluctuation-induced mean electromotive forces in the generalized Ohm's law, that surge during sawtooth crashes. In two-fluid theories, the dynamo is produced from the combination of the MHD (\textbf{v}$\times $\textbf{B}) and Hall (\textbf{j}$\times $\textbf{B)} contributions to Ohm's law. We report new results on the physics of two-fluid dynamos with particular focus on edge-resonant m=0 tearing modes. The two fluid quasilinear theory that was originally derived for a sheared slab [1] is generalized to cylindrical geometry and illuminates the effects of current gradient and field line curvature. The key results are: \textbf{(1)} two fluid effects are important for dynamo through their influence on the phase between the fluctuations; \textbf{(2)} two-fluid theory yields a non-zero flux surface averaged Hall dynamo that is absent in resistive MHD; \textbf{(3)} the two fluid version of the NIMROD code confirms analytic results during the linear stage of the instability but exhibits significant broadening of the Hall dynamo profile on the longer time scales of nonlinear evolution. *Work supported by the USDoE and NSF. [1]V.V.Mirnov, C.C.Hegna, and S.C.Prager, Plasma Physics Report\textbf{ 29}, 612 (2003)   

Effect of neoclassical toroidal viscosity on error-field penetration thresholds

A model for error-field penetration relevant to ohmic tokamak plasmas is introduced that accounts for both resonant and non-resonant magnetic field perturbations. The non-resonant components produce neoclassical damping of the toroidal flow velocity throughout the plasma volume. For simplicity, a single resonant harmonic is considered which produces an electromagnetic torque localized on a particular resonant magnetic surface. A governing equation for the velocity profile is derived extending a recently developed drift-MHD model for error-field penetration [A.~Cole, R.~Fitzpatrick, \emph{Phys.~of Plasmas}, \textbf{13}, 032503 (2006)] by including the neoclassical physics. The model predicts a value for the critical error-field threshold. As in previous theoretical models, extrapolating a scaling of the critical threshold with engineering parameters---such as device major radius, electron density, and toroidal field strength---involves a detailed knowledge of the momentum confinement time scaling in an ohmic plasma discharge.   

Effects of the Perpendicular Electron Spatial Diffusion on the Excitation Properties of the Drift-Tearing Mode*

Contrary to relevant experimental observations, the linear theory of the drift-tearing mode[1] predicts that the mode should not be excited in the high temperature regimes in the presence of a finite perpendicular gradient of the electron temperature[2]. In particular, the values of the stability parameter $\Delta'$ (the jump in the first derivative of the perturbed magnetic field across the reconnection layer) for the modes observed in experiments are well below the linearized theory threshold $\Delta'_{\mathrm crit}$. We have proposed that the interaction of the drift-tearing mode with a background of microscopic modes reduces $\Delta'_{\mathrm crit}$. In particular, such effects as a local depression in the electron parallel thermal conductivity, or local flattening of the electron temperature profile, destabilize the mode. The limit, where the role of the background is only to create perpendicular electron spatial diffusion is investigated considering the collisionless regime[3], where such diffusion acts to mostly affect the thermal energy transport by modifying Landau resonances. For reasonable values of the perpendicular diffusion coefficient, the reduction of $\Delta'_{\mathrm crit}$ is rather small. Therefore other effects of a background microturbulence that can further decrease $\Delta'_{\mathrm crit}$ are analyzed. [1] B. Coppi, {\em Phys. Fluids } {\bf 8}, 2273, 1965; [2] J. Drake {\em et al.} {\em Phys. Fluids} {\bf 26}, 2509, 1983; [3] G. Bertin {\em et al. Annals of Physics} {\bf 119},371, 1979; *Supported in part by U.S. D.O.E.   

Kinetic Simulation of the Island Coalescence Challenge of Magnetic Reconnection

We study the full kinetic simulation of the island coalescence instability as an internal driven reconnection problem with CELESTE3D, which is an implicit particle-in-cell code developed by Brackbill and Lapenta et al at LANL. The simulation starts from the standard Fadeev island chain equilibrium of a small length scale and an initial perturbation. We will study the dependence of the maximum reconnection rate on the driven amplitude and other factors. The simulation results in different geometry scales will be compared. The decoupling of electron and ion flows is observed. We will also look into the effect of a guide field. A guide field does not change the reconnection rate here, and the currents rotate after reconnection. Comparing to resistive MHD simulations, one interesting result here is that the coalescence time, and hence the reconnection rate is independent of driving amplitude, meaning reconnection is an intrinsic process. We will test this conclusion in simulations of the Newton reconnection challenge as well.   

Coalescence of Magnetic Islands in the low resistivity Hall MHD Regime.

We revisit the well-known problem of the coalescence of magnetic islands in the context of Hall MHD. Unlike previous work, we focus on regimes of small resistivity ($S \sim 10^6$) and where the ion skin depth $d_i \ll L$ (system size). These conditions are of relevance, for instance, in the solar corona and the earth's magnetotail. We aim to address under which conditions such systems can exhibit fast reconnection. First, we revisit the resistive MHD problem to further understand the well-known sloshing result.\footnote{D. A. Knoll, L. Chac\'on, {\em Phys. Plasmas}, {\bf 13} (3), p.032307 (2006).} Next, the interaction between the ion inertial length, $d_{i}$, and the dynamically evolving current sheet scale length, \(\delta _{J}\), is established.\footnote{D. A. Knoll, L. Chac\'on, {\em Phys. Rev. Lett.}, {\bf 96}, 135001 (2006).} Initially, $d_{i} \ll \delta_{J}$. If $\eta$ is such that \(\delta _{J}\) dynamically thins down to $d_{i}$ prior to the well-known sloshing phenomena, then sloshing is avoided. This results in peak reconnection rates which are $\eta$-independent and scale as $\sqrt{d_i}$. However, if $d_{i}$ is small enough that resistivity prevents \(\delta _{J}\) from thinning down to this scale prior to sloshing, then reconnection (and sloshing) proceeds as in the resistive MHD model. Finally, we discuss our development of a semi-analytical model to describe the well-known sloshing result in the resistive MHD model,\footnote{A. Simakov, L. Chac\'on, D. A. Knoll, {\em Phys. Plasmas}, accepted (2006)} and our plans to extend it to Hall MHD.   

Stellarator studies of magnetic reconnection

Vacuum magnetic fields in a stellarator can be controlled to give a magnetic island of desired width on any selected rational magnetic surface, which makes stellarators uniquely suitable for reconnection experiments. In a pressureless ideal plasma, a delta function current arises to prevent changes in the island width. The magnetic field produced by this current can be measured outside of the plasma. As the current decays due to plasma dissipation, the time and spatial structure of the resulting field give a non-invasive diagnostic of reconnection. Important parameters include the Alfv\'en speed, the ion gyroradius using the sound speed, the electron collisionless skin depth, the plasma rotation, which can give a trigger-like phenomenon, and the width of the saturated, or vacuum, island. Plasmas can be produced in a given stellarator device over a broad range of densities, temperatures, and species types, and the saturated island width can be adjusted to any size up to a large fraction of the plasma radius without causing a plasma disruption. Consequently, various regimes of magnetic reconnection can be systematically studied.   

Gyrokinetic simulations of magnetic reconnection

We present linear and nonlinear simulations of magnetic reconnection in a simple slab geometry using the GS2 code. The GS2 code treats both the electrons and the ions gyrokinetically, and includes effects such as trapped particles and the out-of-plane magnetic field perturbations due to finite plasma beta. We show numerical convergence studies in both the linear and nonlinear cases, and compare the GS2 results to those obtained using a simple two-fluid model. We address the dependence of the reconnection rate on the ion-to-electron temperature ratio, the plasma beta, the simulation box geometry, and the mass ratio.   

Reconnection studies under more realistic conditions

Reconnection is a fundamental process in plasmas in Nature and in the laboratory. Its complication arises both from the complex processes developing on large scales and involving daunting topological changes in the magnetic fields and from the plethora of microscopic processes underlying the large scale evolution. The research has typically been most successful when the problem is reduced in complexity both from the standpoint of the equilibria where reconnection is allowed to develop and for the range of processes present (as can be obtained simplifying the physics studied or the dimensionality of the problem). In our past work we have removed the second limitation introducing a fully kinetic implicit PIC approach that treats concurrently large scale processes and the whole range of microscopic physics at a fully kinetic level. The present work addresses the first issue. We present our most recent results where more realistic equilibria are studied including more realistic models of the relationship between the system and its surrounding with appropriate boundary conditions.   

Modeling the Interaction between Fluid and Kinetic Scales

An understanding of magnetic reconnection often requires the self-consistent description of the interaction between internal layers and plasma flows in open domains. For example, changes in the global topology of a magnetic field and collision-less reconnection in a thin current sheet may be strongly coupled. The challenges in modeling such problems are the incommensurable time and space scales involved, and the differences in basic assumptions and dependent variables between the kinetic description of the thin current sheet and the magnetohydrodynamic (MHD) model for the surrounding flow. These make imposing flux balance or Marshak conditions across an interface between fluid and kinetic regions much more difficult. To meet these challenges, we explore the special properties of implicit simulations, which allows us not only to extend kinetic simulations to much longer time and space scales, but also to formulate the MHD equations in a form that shares field equations and dependent variables with the kinetic simulations. The cost, of course, is increased computational complexity of the MHD equations, but the gain in range of applicability is significant.   

An iterative semi-implicit scheme for KAW-mediated magnetic reconnection

Recent results in the field of magnetic reconnection have come to emphasize the importance of going beyond the single fluid MHD description. In particular, the Hall term and/or finite Larmor radius (FLR) effects have been shown to be crucial in obtaining the long sought speed-ups of the reconnection rate. From the numerical point of view, these effects originate new difficulties as they introduce dispersive waves into the system [whistler, kinetic Alfven wave (KAW)] which have dispersion relations where the frequency $\omega\sim k_\perp^2$ , i.e., extremely fast when compared to the macroscopic dynamics of the system. Explicit integration schemes show great difficulty in coping with these waves, yielding timesteps which are impractically small. In this work we discuss how semi-implicit methods can be adapted to deal with the KAW. The main idea resides in deriving a wave-like operator which mimics the real wave operator in the linear and nonlinear regimes, while being analytically invertible. Timestep enhacements by factors of $\sim$100 are obtained, with computational time per timestep roughly the same as with an explicit scheme. An error control method is derived and used to determine the timestep. This approach is thus both unconditionally stable and accurate. Comparisons with a purely explicit integration are found to be in excellent agreement.   

Numerical Methods for Real-Geometry Simulation in SUMMIT/PG3EQ\_NC

SUMMIT/PG3EQ\_NC is a nonlinear gyrokinetic $\delta f$-PIC code for turbulence simulations in realistic axisymmetric geometry, which uses the quasiballooning representation for the field quantities. The key algorithms, their motivation, properties, and implemention are summarized. Sample code results, both using real DIII-D equilibria, as specified by EFIT, ONETWO, and PLOTEQ analyses, and using simplified noncircular equilibria will be shown. A central component of PG3EQ\_NC is the field solver. This uses a first order Pade representation of the multispecies quasineutrality equation to enable it to work with spatially dependent equilibrium coefficients as occur in global simulations. Optimization of (the coefficients in) the Pade fit makes it highly accurate for the wavenumber range of interest over a wide range of species concentrations and temperatures. Our graphical package, including recent real-geometry upgrades, for plotting PG3EQ\_NC field quantities on sections in real space will be described, and sample plots will be shown.   

Hybrid Simulation of Plasma Boundary Problems

New hybrid kinetic algorithms for the simulation of plasma systems that span a wide range of collisionality are being developed. An algorithm that is an adaptation to a fully ionized plasma of the ``interpolated-fluid-Monte-Carlo'' (IFMC) method,\footnote{L. Pareschi and R.E. Caflisch, J. Comput. Phys. {\bf 154}, 90 (1999).} successfully used in rarefied gas dynamics (RGD), is investigated. The distribution function is split into a fluid component and a kinetic component. The latter is represented with a particle-in-cell (PIC) method. Particles that undergo sufficient collisional velocity deviation are ``thermalized,'' i.e. they are removed, and their mass (and charge), momentum, and energy are added to the fluid variables. An evaluation of the algorithm, with various possible options for the thermalization criteria, through simulations of a collisional electrostatic sheath and other plasma-boundary relevant problems, will be presented.   

Accelerated Monte Carlo Methods for Coulomb Collisions

A Monte Carlo particle simulation method for Coulomb collisions in a plasma was derived by Takizuka and Abe (J. Comp. Phys, 1977) based on the Landau-Fokker-Planck equation. We investigate two accelerated methods for Coulomb collisions. The first method, developed by Nanbu (PRE 1997), combines many Coulomb collisions into a single step. We present results from a comparative study of the accuracy and computational time for the methods of Takizuka and Abe and of Nanbu. The second method relies on a thermalization approximation, developed in the context of rarefied gas dynamics by Pareschi and Caflisch (J. Comp. Phys, 1999). We apply this approximation to Nanbu's method. For both methods, the simulations are performed for several simple spatially homogeneous problems.   

Application of GEM Code for Experimentally-Realistic Tokamak Cases

The GEM code is a gyrokinetic electromagnetic nonlinear particle-in-cell simulation code[1]. It has recently been extended to be radially global[2], using the Miller toroidal MHD equilibrium[3]. In recent work, the GEM code has been interfaced with the TRANSP experimental data system[4]. I n particular, the GEM code calculations can now include experimentally-derived TRANSP density and temperature profiles for the electron and background ion species, as well as for an impurity species and a hot beam ion species, with trapped electrons and electron collisions, and including self-generated and externally-driven flow. Preliminary results will be presented for tokamaks such as NSTX and DIII-D.\\ {[1]} Y. Chen and S. Parker, J. Comput. Phys. \textbf{189}, 462 (2003).\\ {[2]} Y. Chen and S. Parker, J. Comput. Phys., in press (2006).\\ {[3]} R.L. Miller, \textit{et al.}, Phys. Plasmas \textbf{5}, 973 (1998); R.E. Waltz, \textit{et al.}, Phys. Plasmas \textbf{6}, 4265 (1999).\\ {[4]} R. Goldston, in \textit{Basic Physical Processes of Toroidal Fusion Plasmas}, Varenna Proceedings, (Monotypia Franchi, Citt\'a di Castello, 1985), Vol. 1, p. 165.   

Noise driven diffusion in gyrokinetic PIC simulations

The detailed statistical analysis of discrete particle noise in global gyrokinetic PIC simulations has been carried out. Based on the correlation function of electrostatic potential fluctuations, the diffusion coefficient is calculated, using the simple expression with no resonance broadening effects. It's value is compared with the one obtained directrly from the simulations. The theoretical tool deployed in this study is useful for monitoring the physics fidelity of gyrokinetic PIC simulation of turbulent transport in magnetized plasmas.   

Development of XGC-RF for Global Guiding-Center Particle Simulation of minority ICRH heated Plasmas in a General Tokmak Geometry

A global guiding center particle in cell code (called XGC-RF) has been developed for kinetic simulation of minority ICRF heating on multi-species tokamak plasmas. The code can treat arbitrary axisymmetric toroidal equilibrium and limiter geometry given by GEQDSK data format. A prescribed RF wave field form provided by TORIC full wave solver is used for the RF heating model in the simulation. With these new features of the code, generation of radial electric field, plasma rotation, and energetic particle distribution are studied self-consistently in realistic geometry. By comparing these with the results from simplified circular geometry and homogeneous RF wave field, the effects of the plasma shaping and the detailed form of RF field distribution are studied. The code coupling of XGC-RF and full wave solver for more realistic simulation will be discussed. Also the status of coupling of XGC-RF derived capability to the NTCC NUBEAM fast ion module will be described.   

Implicit formulation of the relativistic Vlasov-Maxwell system

High energy particles of many of astrophysical phenomena and laboratory experiments are relativistic. One can study the complexities and long-time behavior of such a problem by using collisionless particle-in-cell (PIC) methods. However, the smallest timescale needs to be resolved in the explicit schemes, and no implicit relativistic scheme have yet been formulated. We present a new relativistic implicit PIC formulation, and compare numerical results with analytical solutions and results from the explicit code. We also extend CELESTE3D into relativistic, and test the new scheme on the magnetic reconnection problem.   

Semi-Lagrangian methods for gyrokinetic delta-f particle-in-cell turbulence simulation

It is well-known that the particle weights in the $\delta\! f$ method continue to grow in turbulence that has apparently reached a stationary-state, due to test particle diffusion and phase-space granulation. The granulation process is eventually limited due to finite collisionality, but the distribution of particle weights at a phase-space point continues to broaden. This so-called growing weight problem has received attention in the simulation of the ETG turbulence, where long-time simulation is needed to obtain an accurate estimate of the saturated flux. Many questions arise: Does a stationary-state exist in (nearly) collisionless turbulence? Is the long-time simulation noise-dominated? Are these fine structures in the distribution caused by turbulent diffusion important? We investigate these questions by using an algorithm to reset the particle weights periodically, so that the integral of the particle weights at a phase-space location is unchanged (so is $\delta \! f$), but the spread of those particle weights is reduced. By adjusting the size of the phase-space grids used in the resetting scheme, the importance of various scales in the distribution will be assessed. The GEM code \footnote{Y.~Chen and S.~E.~Parker, J. Comp. Phys. 189 (2003) 463; \ \ J. Comp. Phys., 2006, in press} will be used to carry out this study.   

Developing MultI-timescale in 3D PIC CODE OSIRIS

An idea of advancing the beam and plasma with different time scales is proposed in this paper. Because beam particles usually respond much more slowly than plasma particles, large time steps can be used to update beam particles to save computation time. We will describe how to apply this multi-timescales method in 3D particle-in-cell (PIC) code OSIRIS. Optimized parameters for preserving fidelity and saving computation time are discussed. The code is applied to modelling the energy gain in the SLAC E167 experiment and shows an energy gain of 40GeV for 75cm plasma length. The limitations of this method are also studied, such as trapped particles and hosing.   

Scaling for high-end HPC systems: New features in OSIRIS 2.0

The OSIRIS 2.0 framework [1] is an integrated framework for particle-in-cell (PIC) simulations. This framework is based on a three-dimensional, fully relativistic, massively parallel, object oriented particle-in-cell code, that has successfully been applied to a number of problems, ranging from laser-plasma interaction and inertial fusion to plasma shell collisions in astrophysical scenarios. One-to-One modeling of ongoing and future experiments require state of the art computer systems, with a number of computing nodes going up to tens of thousand. To make efficient of such systems it is crucial to maintain an evenly balanced load on all computing nodes. We describe the dynamic load balancing algorithm that we implemented in OSIRIS to allow for near perfect scaling up to tens of thousand of computing nodes. Details on the partition selection scheme and simulation space repartition routines are given. We present the results on the performance impact for simulation using large number of nodes. Some details on other issues pertaining efficient use of large computer systems, such as parallel I/O and hardware tuning, are also shown. [1] R. A. Fonseca et al., LNCS 2331, 342-351, (Springer, Heidelberg, 2002)   

A collision module for OSIRIS

Standard PIC ``collisions'' occur between finite sized particles. It is an inherent property of the PIC algorithm that collisional effects therefore are not properly reproduced in a standard implementation. Present day problems in plasma physics on the other hand require full scale modeling and collisions can no longer be neglected (for instance in fast ignition scenarios). In order to deal with collisional effects, we have implemented a binary collision module in osiris 2.0. The implemented algorithm is fully relativistic, and different weights for different particles are allowed without violating the conservation of energy and momentum. The plasma to be simulated can have properties with a strong spatial dependence - relevant quantities for the collisions (density, temperature, collision frequency) can be calculated locally. The collision module is benchmarked against the theoretical thermalization rates and the distribution function properties in equilibration for non-relativistic and relativistic conditions. The influence of the numerics (particle weights, time step, particles / collision cell) is also explored in detail.   

Reducing Undersampling Noise in PIC Codes Using Advanced Multiresolution Analysis Techniques

We show results from the implemention of a number of new ideas stemming from the multiscale, multiresolution analysis arena where Poisson noise, or under-sampling noise, is adequately treated via a series of more and more geometrically sophisticated objects going from elementary 2D Haar wavelets, to isotropic undecimated wavelet transforms (in 2D), to biorthogonal Haar bases with multiscale nonlinear transforms that convert Poisson distributions to Gaussian ones where noise estimation (thresholding) is much easier, to curvelets, where orientation information (resolving coherent structures in phase space, detecting and respecting anisotropy) is vitally important. This suite of new techniques allows the accurate extraction of phase space densities with fidelity impossible to achieve with naive or trivial interpolation or smoothing techniques. We will demonstrate the relative strengths and detection capabilities of these techniques. The examples we treat are the Beam-Plasma Instability (BPI) and ponderomotively driven KEEN waves. These allow intricate phase space structures to coexist with chaos and turbulence. The former has a simple single mode linear limit which is unstable, but the latter gives rise to pure multimode nonlinear phenomena.   

A New Coulomb Collision Model for PIC Codes

We develop a Coulomb collision algorithm for PIC codes based on a Langevin particle pusher that incorporates velocity sensitive collision rates. According to the algorithm, every time step of the simulation each particle collides with all other particles in a cell where the latter are modeled as one or more drifting Maxwellians. Thus, the collisional particle advance is order N where N is the number of particles in the cell. Particle-Maxwellian collisions reproduce the usual Spitzer velocity diffusion rates. Each particle-Maxwellian collision conserves momentum exactly and energy statistically. Energy conservation can be made exact with a linear velocity shift. Furthermore, the time step can be either very large or very small compared to equilibration time scales. We apply a zero-dimensional version of the algorithm to standard equilibration test problems and compare the results to other (order N$^{2}$ and particle pairing) algorithms exercised on the same problems.   

A Distributed Memory Grid Enabled GPU Implementation of the Boris Particle Pusher Algorithm

The Boris pusher is a numerical algorithm to advance charged particles in an electromagnetic field. It is widely used in numerical simulations in Plasma Physics. This poster explains the implementation of the Boris pusher algorithm on stream processors, in particular on a modern Graphics Processor Unit (GPU) with programmable shading capabilities, and explores the parallelization of the code on several GPUs. A GPU Grid node was developed and the code was deployed there, as first step for the use of PIC code in a Grid environment.   

Three Dimensional Particle-in-Cell Simulation of Device for Plasma Processing

For development of high-efficiency device for plasma processing it is important to investigate plasma characteristics in the device. The device has wafers, some structural objects inside and external electrodes for RF discharge. Plasma characteristics such as density distribution, temperature distribution and potential profile are influenced by structure of inside objects and external electrodes. In order to investigate plasma characteristics in the device and the effect of additional objects inside, we have developed a three-dimensional Particle-in-Cell simulation code with Monte Carlo collision. Simulations are performed under the condition in which plasma is produced by capacitive discharge with 13.56MHz RF power supply. Plasma behavior and effect of additional objects are investigated.   

Simulation of Plasma Jet Dynamics using Hybrid Particle-in-Cell Methods

High-energy plasma jets have potential applications in both magnetic and inertial fusion$^*$. Because of the high plasma densities ($10^{17}$--$10^{19}$~cm$^{-3}$), and long timescales (several $\mu$sec), it is not practical to treat the bulk electrons as kinetic PIC particles. We are applying hybrid methods, including Electron Magnetohydrodynamics (EMHD), where the electrons are treated as an inertialess fluid, and an electron-fluid method, where the electron inertia is retained. The main difficulty in the EMHD method is due to discontinuous field derivatives across the moving plasma-vacuum interface. We solved this by using the vector potential $\mathbf{A}$ instead of the $\mathbf{E}$ and $\mathbf{B}$ fields. We have derived stability conditions for the algorithm: a conventional diffusion-equation constraint, and a constraint on the grid magnetic Reynolds number (ratio of convective to diffusive transport of the magnetic field over one cell). We show results of $\theta$- and $z$-pinch benchmark calculations in 1D and 2D, and preliminary results applying the algorithm to the HyperV plasma jet experiments.\footnote{F. D. Witherspoon and F. Y. Thio, ``Dense Hypervelocity Plasma Jets for Fusion Applications'', Bulletin of the American Physical Society, Vol. 50, No. 8, Oct. 2005. (http://www.hyperv.com/projects/pic/)}   

Real geometry gyrokinetic PIC computations of ion turbulence in tokamak discharges with SUMMIT/PG3EQ{\_}NC

The PG3EQ{\_}NC module within the SUMMIT Gyrokinetic PIC FORTRAN90 Framework makes possible 3D nonlinear toroidal computations of ion turbulence in the real geometry of DIII-D discharges. This is accomplished with the use of local, field line following, quasi-ballooning coordinates and through a direct interface with DIII-D equilibrium data via the EFIT and ONETWO codes, as well as Holger Saint John's PLOTEQ code for the (R, Z) position of each flux surface. The effect of real geometry is being elucidated with CYCLONE shot {\#}81499 by comparing results for growth rates and diffusivities from PGEQ{\_}NC to those of its circular counterpart. The PG3EQ{\_}NC module is also being used to model ion channel turbulence in DIII-D discharges {\#} 118561 and 120327. Linear results will be compared to growth rate calculations with the GKS code. Nonlinear results will also be compared with scattering measurements of turbulence, as well as with accessible measurements of fluctuation amplitudes and spectra from other diagnostics.   

Investigation of Long Wavelength ETG Modes

Simulations of ETG turbulence suggest that the greatest energy transfer is through long wavelength modes ($k_\theta \rho < .1$) The effect of curvature as a cutoff on long perpendicular wavelength electron turbulence is investigated. Analytic calculations are presented along with simulations from the gyrokinetic code GYRO.   

Dynamic sub-grid scale modelling: a wave action approach

Modelling disparate scale interactions remains an ongoing theoretical and computational challenge. In order to facilitate computation, high Reynolds number systems are often described via the introduction of phenomenological dissipation coefficients as a means of modelling stresses exerted by the unresolved scales. The temporal and spatial evolution of these phenomenological coefficients are usually described via heuristic turbulence models. As the dynamics of the unresolved scales play a crucial role in the evolution of the overall system, especially in cases where inverse cascades are present, a simple dynamic sub-grid scale model for the unresolved turbulent scales, that is rigorously derivable from the original fluid equations, is clearly desirable. In particular, systems which possess strong uniform magnetic fields or under go rapid rotation exhibit quasi 2-D behavior which may lead to an inverse cascade of energy. Here a self-consistent model describing nonlocal interactions between the large resolved scales and the small unresolved scales is discussed. The unresolved scales see the resolved scales as a slowly evolving background, allowing for the use of wave kinetics and adiabatic theory. The stresses exerted by the self- consistently evolved wave population density on the large scale flows are calculated by mean field methods. This model has the advantage of being both systematically derivable from the fundamental fluid equations without introducing any free parameters, as well as being simple to implement.   

Entropic Lattice Boltzmann Simulations of Turbulence

Because of its simplicity, nearly perfect parallelization and vectorization on supercomputer platforms, lattice Boltzmann (LB) methods hold great promise for simulations of nonlinear physics. Indeed, our MHD-LB code has the best sustained performance/PE of any code on the \textit{Earth Simulator}. By projecting into the higher dimensional kinetic phase space, the solution trajectory is simpler and much easier to compute than standard CFD approach. However, simple LB -- with its simple advection and local BGK collisional relaxation -- does not impose positive definiteness of the distribution functions in the time evolution. This leads to numerical instabilities for very low transport coefficients. In Entropic LB (ELB) one determines a discrete H-theorem and the equilibrium distribution functions subject to the collisional invariants. The ELB algorithm is unconditionally stable to arbitrary small transport coefficients. Various choices of velocity discretization are examined: 15, 19 and 27-bit ELB models. The connection between Tsallis and Boltzmann entropies are clarified.   

Development of a Grid-Based Gyro-Kinetic Simulation Code

A grid-based semi-Lagrangian code using cubic spline interpolation is being developed at CRPP, for solving the electrostatic drift-kinetic equations [M. Brunetti \textit{et. al}, Comp. Phys. Comm. \textbf{163}, 1 (2004)] in a cylindrical system. This 4-dim code, CYGNE, is part of a project with long term aim of studying microturbulence in toroidal fusion devices, in the more general frame of gyro-kinetic equations. Towards their non-linear phase, the simulations from this code are subject to significant overshoot problems, reflected by the development of negative value regions of the distribution function, which leads to bad energy conservation. This has motivated the study of alternative schemes. On the one hand, new time integration algorithms are considered in the semi-Lagrangian frame. On the other hand, fully Eulerian schemes, which separate time and space discretisation (method of lines), are investigated. In particular, the Essentially Non Oscillatory (ENO) approach, constructed so as to minimize the overshoot problem, has been considered. All these methods have first been tested in the simpler case of the 2-dim guiding-center model for the Kelvin-Helmholtz instability, which enables to address the specific issue of the $\mathbf{E} \times \mathbf{B} $ drift also met in the more complex gyrokinetic-type equations. Based on these preliminary studies, the most promising methods are being implemented and tested in CYGNE.   

Collisionless Trapped Electron Mode Turbulence

Collisionless Trapped Electron Mode (CTEM) turbulence is a likely canidate for explaining anomolous transport in tokamak discharges that have a strong density gradient relative to the ion temperature gradient\footnote{D. R. Ernst {\it et. al.}, Phys. Plasma 11 (2004) 2637; T.~Dannert and F.~Jenko, Phys. Plasma 12 (2005) 072309; R. Gatto {\it et. al.}, Phys. Plasma 13 (2006) 022306;}. Here, CTEM turbulence is investigated using the Gyrokinetic $\delta f$ GEM code.\footnote{Y.~Chen and S.~E.~Parker, J. Comput. Phys. 189 (2003) 463; Y.~Chen ad S.E.~Parker, accepted, to appear in J. Comput. Phys. (2006)} GEM is electromagnetic, includes full drift-kinetic electrons, generaly axisymmetric equilbria, collisions and minority species. Here, the flux-tube limit is taken and $\beta$ is so small that the simulations are essentially electrostatic. Linear theory\footnote{J. Wesson (1997) {\it Tokamaks}, Oxford Science} predicts that the instability occurs at $\frac{\sqrt{2\varepsilon}R}{L_n}>1$, which agrees very well with the simulation results. With increasing density gradient, it is observed that the most unstable mode transitions from a CTEM to drift wave mode and the short-wavelength modes are most unstable ($ 2 > k_\perp \rho_i > 1$). Nonlinear simulations are underway to address the parametric dependence of particle and energy transport. The importance of zonal flows for CTEM turbulence, is still not well understood and is under investigation.   

Transport and discrete particle noise in gyrokinetic simulations

We present results from our recent investigations regarding the effects of discrete particle noise on the long-time behavior and transport properties of gyrokinetic particle-in-cell simulations. It is found that the amplitude of nonlinearly saturated drift waves is unaffected by discreteness-induced noise in plasmas whose behavior is dominated by a single mode in the saturated state. We further show that the scaling of this noise amplitude with particle count is correctly predicted by the fluctuation-dissipation theorem, even though the drift waves have driven the plasma from thermal equilibrium. As well, we find that the long-term behavior of the saturated system is unaffected by discreteness-induced noise even when multiple modes are included. Additional work utilizing a code with both total-f and $\delta f$ capabilities is also presented, as part of our efforts to better understand the long- time balance between entropy production, collisional dissipation, and particle/heat flux in gyrokinetic plasmas.   

Current Status of the Gyrokinetic-Electron and Fully-Kinetic Ion Particle Simulation Model

A novel gyrokinetic (GK) electron and fully kinetic (FK) ion particle code has been developed for the investigation of dynamics in collisionless plasmas, e.g., magnetic reconnection. In this model, the rapid electron cyclotron motion is removed, while keeping realistic mass ratio $m_e/m_i$, finite electron Larmor radii, wave-particle interactions, and off-diagonal components of electron pressure tensor. In such model, the wave modes ranging from Alfv\'en waves to lower-hybrid/whistler waves can be handled on an equal footing. The computation power is significantly improved over that of the existing full-particle codes, and thus the microscopic physics and the global dynamics of reconnection are expected to be solved simultaneously. Following the successful code benchmark for 1-D uniform plasma, the code has been further benchmarked for (1) linear waves in uniform plasmas in 2-D and 3-D simulations against the analytical GKe/FKi dispersion relation and (2) a 2-D current sheet with a strong guide field against the eigenmode theory of tearing mode. Our numerical results agree very well with the linear theories. Furthermore, the GKe/FKi code has also been benchmarked for (3) the lower-hybrid drift instability (LHDI) in a 2-D current sheet. The results are compared with the linear theory as well as previous kinetic simulations of LHDI. The detailed results and comparisons will be presented. *Supported by DOE grant DE-FG02-05ER54826.   

Gyrokinetic Secondary Stability Theory For Toroidal ETG Modes

Secondary stability theory has been invoked to explain the large disparity in the non-linear behavior of Ion Temperature Gradient (ITG) and Electron Temperature Gradient (ETG) driven turbulence. In particular, the existence of persistent ``streamer'' structures in ETG turbulence indicates a significant weakening of the secondary instabilities which tend to isotropize ITG tokamak turbulence. We use the electrostatic non-linear gyrokinetic equation to solve for the secondary stability of the local two-dimensional ``toroidal'' branch of the Electron Temperature Gradient (ETG) mode. We address the issue of stable streamer structures and relate our findings to recent ETG simulations.   

Gyrokinetic simulations of turbulent transport in a closed fieldline geometry

Plasma turbulence due to small scale entropy modes is studied with gyrokinetic simulations in a simple closed field line geometry, the Z-pinch, in low-beta parameter regimes that are stable to ideal interchange modes. We find an enormous variation in the nonlinear dynamics and particle transport as a function of two main parameters, the density gradient and the plasma collisionality. This variation is explained in part by the damping and stability properties of spontaneously formed zonal flows in the system. As in toroidal systems, the zonal flows can lead to a strong nonlinear suppression of transport below a critical gradient that is determined by the stability of the zonal flows.   

Implementation of Large Scale $E \times B$ Shear Flow in the GS2 Gyrokinetic Turbulence Code

GS2 is a 5-D gyrokinetic flux-tube code for studying turbulence in general geometry plasmas. It has always self-consistently included small-scale zonal flows (with radial wavelengths smaller than the simulation domain) that are driven by the turbulence, but for simplicity it neglected equilibrium-scale zonal flows (which are not radially periodic on the simulation scale) that can be driven by beam injection, neoclassical effects, etc. Shearing rate estimates of corrections due to equilibrium-scale flows could be made based on earlier gyrofluid and gyrokinetic nonlinear simulations by Waltz et al.\ and Dimits et al. Large-scale sheared flows can be implemented directly in a flux-tube code by transforming to moving coordinates where the physical radial wavenumber $k_x$ is related to the radial wavenumber $k_x'$ in shearing coordinates by $k_x(t) = k_x' - k_y' \gamma_{E \times B} t$, where $\gamma_{E \times B}$ is the shearing rate. Direct implementation of this is challenging in GS2's implicit algorithm, as that would require a large overhead of recalculating the implicit response matrices every time step. By discretizing the effective $k_x$, we can avoid this large overhead, and yet still be effectively 2cd order accurate (similar to how Godunov splitting is effectively 2cd order accurate) and it converges well for typical parameters. Examples and tests of the GS2 implementation will be presented.   

Collisional Physics in GS2

Collisions are an important component of gyrokinetic systems, even in the long mean-free-path limit. In this poster, we recall the role of collisions in several interesting test cases (kinetic Alfven waves, reconnection, zonal flow damping, and neoclassical transport). Upgrades to the GS2 collision operator that proved to be necessary to obtain expected results in each area have been implemented and will be described.   

Resolution Issues in Continuum Gyrokinetic Simulations

In the absence of collisions, particle distribution functions quickly develop fine scales in velocity-space. This makes it very difficult for kinetic codes to resolve weakly-collisional plasma processes. For many basic processes in gyrokinetics, few systematic numerical studies exist. We present results from a study on resolution requirements for a number of important problems in weakly-collisional plasmas using the continuum gyrokinetic code GS2. The problems considered include: long-time limit of Landau-damped ion acoustic waves; long-time limit of Barnes-damped kinetic Alfven waves; and neoclassical ion thermal conduction in a tokamak as a function of collisionality. For each problem, we compare the numerically generated distribution functions with theory and suggest useful measures of the quality of numerical results. The insight gained from this study is then used to propose a series of test problems applicable for a generic gyrokinetic solver. Additionally, we consider neoclassical transport in stellarator equilibria and the velocity space structure of microinstabilities in tokamaks, with and without equilibrium ExB shear.   

Spectral characteristics and coherence in plasma turbulence

Direct numerical simulations of plasma turbulence have become an important tool for interpreting experimental data from tokamaks. There is, however, relatively little exploration of the fluctuation data that is produced by gyrokinetic simulations in the literature. In preparation for more detailed experimental validation of predictions from gyrokinetic simulations of plasma turbulence, we present studies of turbulence that is well described by simpler models: Hasegawa-Mima (with and without including the field-line-averaged potential term associated with parallel electron dynamics, and with and without strong background velocity shear), and reduced MHD. Numerical results from a spectral fluid code will be compared to the results obtained with a gyrokinetic code for each problem studied. To study coherent structures, the data is projected onto an orthogonal wavelet basis and a nonlinear thresholding is applied to the wavelet coefficients. The denoised data is then reconstructed in physical space. Using this procedure we analyze the spatial and frequency spectra and test them against theoretical expectations. We will also discuss the importance of conserved quantities in these systems.   

A Gyrokinetic Benchmarking of Electron Temperature Gradient Turbulence

A suitable operating point for benchmarking numerical simulations of electron temperature gradient (ETG) turbulence is presented together with a linear analysis of the unstable ETG modes at this operating point. Convergence studies in time step, spatial grid, and velocity-space resolution demonstrate well-converged results from both continuum and particle-in-cell gyrokinetic simulations codes at the chosen benchmark point. Simulation results from four gyrokinetic simulations codes demonstrate excellent agreement ($\pm $10{\%}) in the electron heat flux. Comparison of potential fluctuations between these codes demonstrates similar agreement in the correlation functions, spectral density, and \textit{rms} flow shear due to the self-generated zonal flows. A parameter scan in which the magnetic shear, $s$, is varied reveals dramatic increase in both the ETG turbulent intensity and the transport as the magnetic shear is increased from $s=0.3$ to $s=0.4$.   

The Influence of Noise on Turbulent Transport.

Recently there have been considerable discussions and contradictory conclusions about the possible influence of numerical noise on measured turbulent fluxes.\footnote{W. M. Nevins, G. W. Hammett, A. M. Dimits, W. Dorland, and D. E. Shumaker, Phys.\ Plasmas \textbf{12}, 122305 (2005); W. W. Lee, Bull.\ Am.\ Phys.\ Soc., {\tt http://www.aps.org/meet/APR06}, abstr.I16.00004 (2006).} In the present work, some of the conceptual and analytical foundations of noise-related calculations are reconsidered, and some paradoxes are resolved. An elementary model involving coupled random processes shows that extra noise (e.g., related to numerical sampling errors in $\delta f$ particle simulations\footnote{G. Hu and J. A. Krommes, Phys.\ Plasmas \textbf{1}, 863 (1994).}) can reduce total transport. (Intuition to the contrary stems from oversimplified models involving independent, additive, and passive advection velocities.) This result is interpreted in terms of the structure of the steady-state spectral balance equation for turbulence in the presence of discreteness-induced noise.\footnote{H. A. Rose, J. Stat.Phys.\textbf{20}, 415 (1979).} The relationship of the Fluctuation-- Dissipation Theorem to general nonequilibrium statistical balances is also discussed.   

Noise as a turbulent decorrelation mechanism in Reaction-Diffusion equation like transport models

Simple dynamical models of transport have been able to capture much of the dynamics of the transport barriers found in many devices. However, these models, which have many similarities with the classic reaction-diffusion equations, have wave like structures that can propagate in certain regimes near transition points. This propagation, while being realistic in a reaction diffusion model, is probably limited in a turbulent plasma due to the turbulent decorrelation. In order to investigate methods for correcting this, noise is added to the system to simulate the intrinsic decorrelations. The wave propagation characteristics are studied as a function of the noise amplitude and compared to similar studies in reaction diffusion systems in which propagation can actually increase in the presence of noise.   

Fractional calculus phenomenology in two-dimensional plasma models

Transport processes in confined plasmas for fusion experiments, such as ITER, are not well-understood at the basic level of fully nonlinear, three-dimensional kinetic physics. Turbulent transport is invoked to describe the observed levels in tokamaks, which are orders of magnitude greater than the theoretical predictions. Recent results show the ability of a non-diffusive transport model to describe numerical observations of turbulent transport. For example, resistive MHD modeling of tracer particle transport in pressure-gradient driven turbulence for a three-dimensional plasma reveals that the superdiffusive ($\sigma^2 \sim t^{\alpha}$ where $\alpha > 1$) radial transport in this system is described quantitatively by a fractional diffusion equation \footnote{D. del Castillo Negrete, et al, Phys. Rev. Lett. 94, 065003 (2005)}. Fractional calculus is a generalization involving integro-differential operators, which naturally describe non-local behaviors. Our previous work showed the quantitative agreement of special fractional diffusion equation solutions with numerical tracer particle flows in time-dependent linearized dynamics of the Hasegawa-Mima equation (for poloidal transport in a two-dimensional cold-ion plasma). In pursuit of a fractional diffusion model for transport in a gyrokinetic plasma, we now present numerical results from tracer particle transport in the nonlinear Hasegawa-Mima equation and a planar gyrokinetic model. Finite Larmor radius effects will be discussed.   

Equation Free Projective Integration for Plasma Systems

``"Equation free projective integration'' has the potential to allow global simulations of phenomena including relevant kinetic physics. In our algorithm, the global plasma variables stepped forward in time are not integrated directly from differential equations -- hence the name ``equation free.'' Instead, these variables are represented on a microgrid by a kinetic simulation, which is used to estimate the time derivatives of the variables for a large projection step. We present three examples. (1) An ion acoustic wave with strong Landau damping, with wavelets to represent f(x,v). (2) A large-scale MHD wave using a non-ideal fluid code as the micro-simulator. A key aspect of this problem is demontrating that the global time step is not limited by the nonideal wave speeds (such as the whistler). (3) Magnetic reconnection. We focus here on the use of nonlinear wavelet approximation schemes (thresholding and shrinkage). The resulting wavelet coefficients are projectively integrated. We study the effecs of various level-dependent threshold selection criteria based on statistical inference rules. We also discuss how to choose optimal decomposition bases with wavelet and more general lifting schemes.   

Fine Scale Zonal Flow Suppression of Electron Temperature Gradient Turbulence

Simulations converged with respect to particle number run for long times are presented using the GEM code[1], which is a global electromagnetic gyrokinetic delta-f particle simulation with general axisymmetric geometry. Higher flux results, similar to those found from flux-tube codes, are obtainable[2]. A low electron heat diffusivity [3] (normalized by the temperature gradient) is obtained by reducing the temperature gradient in the flux-tube limit. It is found that, while zonal flows are weak at early times, the zonal flows continue to grow algebraically in time. Eventually, the zonal flows grow to a level that suppresses the turbulence due to ExB shearing. The algebraic growth of the zonal flow can be explained via the Rosenbluth-Hinton random kick mechanism[4]. High phase-space resolution simulations are underway to investigate if zonal flow suppression takes place at larger temperature gradients. Simulations with realistic electron-ion collisionality indicate collisional damping of the zonal flow is important and can cause the zonal flows to saturate at lower levels. [1] Y. Chen, S. Parker, available on line, J. Comput. Phys. (2006). [2] W. Dorland, et al., Phys. Rev. Lett. (2000). [3] Z. Lin, et al., Phys. Plasmas (2005). [4] M. Rosenbluth and F. Hinton, Phys. Rev. Lett. (1998).   

Arc discharge for carbon nanotube synthesis

The arc discharge is one of the most practical methods for single wall nanotube (SWNT) synthesis. This method yields highly graphitized tubes, because the~ manufacturing process occurs at a very high temperature. Arc-produced carbon nanotubes have fewer structural defects than those produced by low temperature techniques such chemical vapor deposition (CVD). Most likely this is due to fast growth that prevents defect formation. The most important arc process for SWNT synthesis is the anode erosion. It is shown that the dependence of the anode erosion rate on arc current and background pressure can be strongly affected by the~ magnetic field. The effect of the magnetic field on the SWNT properties and SWNT production yield is investigated. A theoretical model suggests that a magnetic field may lead to longer nanotubes.   

Numerical Modeling of Atmospheric Dielectric Barrier Discharge in a Single-hole Spray Structure

A numerical model of the spray-type DBD (dielectric barrier discharge) plasma is developed to understand discharge and chemical characteristics of spray etching plasma for TFT-LCD production. In this numerical work, elementary chemical reactions in nitrogen plasma are included at atmospheric condition to find out the amounts of metastably-excited species which are important factors of the LCD etching process. The calculation domain is limited to a single-hole region among the array of DBD spray holes in the etching equipment, and is represented with a two-dimensional axi-symmetric configuration. This single-hole region consists of discharge and spray regions. In the discharge region, a set of continuity equations of charged particles and metastably-excited species is considered, and Possion's equation coupled with continuity equations is used for the calculation of electric field. In the spray region, fluid dynamic equations are taken into account for spatial distributions of metastably-excited species. The discharge characteristics depending on operating condition and the spatial uniformity of metastably-excited species are discussed on the basis of calculated results. This numerical study will be further extended to the numerical simulation of the entire DBD spray region with a multi-hole structure.   

A new method to find the electron distribution function from cylindrical probe data

Druyvesteyn's method finds the distribution of electron speeds from the second derivative of probe data using the assumption that the distribution is spherically symmetric. For the disk probe, the data are more directly related to the velocity distribution projected onto the direction normal to the probe surface. The projected distribution is less sensitive to noise because it is related to the first derivative of the disk probe data rather than the second. For the cylindrical probe, the data are more directly related to the distribution of energies projected onto the plane perpendicular to the probe axis. A method is developed for recovering this projected distribution from digitized probe data. The method is mathematically more complex than Druyvesteyn's method, but has the advantage of being less sensitive to noise. The methods are compared using noise-free simulated data and using noisy data from a double-plasma device with multidipolar magnetic confinement.   

Development of microprobes at UCLA to measure f(\textbf{v}), \textbf{E} and \textbf{B}

Electric field, magnetic flux, and velocity-analyzer probes sized on the order of a Debye length (30 microns) are being developed using microelectromechanical systems (MEMS) technology, through a joint effort between the UCLA Basic Plasmic Plasma Science Facility and the UCLA Electrical Engineering Department. The electric-field probe has square tips, 8 microns on a side and separated by 20 microns [1]. A probe, now being tested, will have a frequency response of 100 MHz to 12 GHz, and should be able to access events at the plasma frequency (9 GHz) and the electron-cyclotron frequency (1 to 6 GHz) in the Large Plasma Device (LAPD) at UCLA. Differentially wound magnetic flux probes with diameters of 100 to 500 microns are also being fabricated. Finally, we are building velocity-analyzer probes have 2-micron-wide holes and a grid spacing of 15 microns, which yields an angle of acceptance that is less than 10 degrees. Details of the fabrication processes, calibration, and operation of these devices will be presented. [1] P. Pribyl et al,``Debye Size Microprobes for Electric Field Measurements in Laboratory Plasma,'' accepted for Publication in Review of Scientific Instruments, (2006).   

Laser Induced Fluorescence Diagnostic for the ASTRAL Plasma Source.

A Laser Induced Fluorescence (LIF) diagnostic is presented in this poster. The ion temperature measurements are made in the ASTRAL (\textbf{A}uburn \textbf{S}teady s\textbf{T}ate \textbf{R}esearch f\textbf{A}ci\textbf{L}ity) helicon plasma source using a diode laser based LIF diagnostic. ASTRAL produces Ar plasmas with the following parameters: n$_{e}$ = 10$^{10}$ to 10$^{13}$ cm$^{-3}$, T$_{e}$ = 2 to 10 eV and T$_{i}$ = 0.03 to 0.5 eV. A series of 7 large coils produce an axial magnetic field up to 1.3 kGauss. Operating pressure varies from 0.1 to 100 mTorr and any gas can be used for the discharge. A fractional helix antenna is used to introduce rf power up to 2 kWatt. A number of diagnostics are presently installed on the plasma device (Langmuir Probe, Spectrometer, LIF system). The LIF diagnostic makes use of a diode laser with the following characteristics: 1.5 MHz bandwidth, Littrow external cavity, mode-hop free tuning range up to 16 GHz, total power output of about 15 mW. The wavelength is measured by a precision wavemeter and frequent monitoring prevents wavelength drift. For Ar plasma, a new LIF scheme has been developed. The laser tuned at 686.354 nm, is used to pump the 3d$^{4}$F$_{5/2}$ Ar II metastable level to the 4p$^{4}$D$_{5/2}$ state. The fluorescence radiation between the 4p$^{4}$D$_{5/2 }$and the 4s$^{4}$P$_{3/2 }$terms (442.6 nm) is monitored by a PMT.   

Generation of Ionic Plasma without Electrons using Alkali Salt

Accommodation of various dopant atoms, molecules, and compounds is available for modifying intrinsic electronic and mechanical properties of single-walled carbon nanotubes. For alkali metal and halogen atoms encapsulation, an alkali-halogen plasma is generated by a dc magnetron discharge under a uniform magnetic (B) field. Spiral and linear thermionic cathodes of tungsten wire are set at the central axis of a grounded cylinder, and they are negatively biased to form an electric field E perpendicular to the B field lines. Alkali-salt vapor is introduced from an oven, filling the cylinder. Thermal electrons drift in the azimuthal (ExB) direction and the electrons collide with alkali-salt vapor, dissociating and ionizing it. As a result of this process, alkali positive ions, halogen negative ions, and electrons are produced. A magnetic-filter region is situated at the exit of the cylinder and the electrons are removed from the plasma. The electron emission, the E and B fields, and the length of the magnetic-filter region are optimized, resulting in the alkali-halogen plasma with the ion density 10$^{8}$ cm$^{-3}$ at B = 0.2 T.   

An RF Driven, Ferroelectric, Atmospheric-Pressure Plasma Source

The ferroelectric atmospheric plasma source generates plasma at atmospheric pressure and functions with a wide variety of gases. Research on the source extends from research on a ferroelectric plasma thruster (FEPT) being developed for microspacecraft. The ferroelectric plasma source is driven by oscillating high voltage at RF frequencies. The ferroelectric plasma source produces plasma at a surface partially covered by an electrode when the spontaneous polarization vector is reversed. At the University of Missouri-Columbia, research is focusing on using the FEPT under atmospheric pressure conditions. Goals of this research are to find optimum device parameters for plasma generation, including but not limited to gap width, electrode height, applied voltage, frequency dependence, and ferroelectric ceramic materials.   

Compact Multitube Helicon Source with Permanent Magnets

In spite of their efficiency, helicon sources are not readily adopted by industry because they require a large, heavy electromagnet and its power supply. Annular permanent magnets can create the B-field compactly and cheaply, but only if the plasma is placed outside the magnet in its remote field, so that the internal field lines do not carry the plasma into the wall. An 8-tube array of such sources has been constructed and tested. The size and shape of each tube was optimized by computation. The source can be extended to provide uniform densities of order 10$^{12}$ cm$^{-3}$ over an arbitrarily large substrate. This source, which requires only six inches of height above the processing chamber, would be useful for web-coating, optical coating, and etching of flat-panel displays and solar cells.   

Spectroscopy Study of Ar + CO$_{2}$ Plasmas in ASTRAL.

A spectroscopy study of the ASTRAL (\textbf{A}uburn \textbf{S}teady s\textbf{T}ate \textbf{R}esearch f\textbf{A}ci\textbf{L}ity) helicon plasma source running Ar + CO$_{2}$ gas mix is presented. ASTRAL produces Ar plasmas: n$_{e}$ = 10$^{10}$ to 10$^{13}$ cm$^{-3}$, T$_{e}$ = 2 to 10 eV and T$_{i}$ = 0.03 to 0.5 eV. A series of 7 large coils produce an axial magnetic field up to 1.3 kGauss. A fractional helix antenna is used to introduce rf power up to 2 kWatt. A spectrometer which features a 0.33 m Criss-Cross monochromator and a CCD camera is used for this study. Very different plasmas are produced following the relative importance of CO$_{2}$ in the gas mixture. At low CO$_{2}$ concentration, the plasmas are similar to those obtained with pure Ar with weak CO$_{2}$, CO$_{2}^{+}$, CO and CO$^{+}$ bands. The usual blue plasma core associated with intense Ar II transitions is observed with however a significant white glow coming from the outer plasma regions. At higher CO$_{2}$ concentration, the plasma becomes essentially molecular and can be described as an intense white plasma column. Molecular dissociative processes associated with the production of strong C and O atomic lines are observed under specific plasma conditions. The atomic spectral lines are compared with ADAS modeling results. This study indicates the possible advantages of using a helicon source to control the CO$_{2}$ plasma chemistry for industrial applications.   

New laser based X-ray source at 100 Hz repetition rate for ultrafast XAS

X-ray absorption techniques allow studying the atomic environment and the electron structure of specific atoms in complex material. Using ultrafast x-ray sources produced by femtosecond laser combined with optical pump and x-ray probe geometry, these techniques can be extended in the time domain with an ultrafast resolution. We present here our most recent progress in the development of a femtosecond time resolved x-ray absorption spectroscopy (XAS) system based on a broadband soft x-ray source produced by an ultrafast 100 Hz repetition rate laser system. This femtosecond XAS is designed to probe the electronic dynamics ocurring during the vanadium dioxide (VO2) semiconductor to metal phase transition following excitation by a femtosecond laser pulse. In the present experiments, broadband spectra near the vanadium L edge (511 eV) and the oxygen K edge (525 eV) have been generated and measured. Static VO2 absorption spectra in the metallic an the semiconductor phase will be presented.   

Ion Energy Distributions for a High Power Helicon Plasma Source

The high power helicon source, developed at the University of Washington is capable of depositing up to 100 kW of peak power into the plasma. Measured source electron densities using argon are near 2x10$^{20}$ m$^{-3}$ with electron temperatures of 5-7 eV. The HPH system has been operated in a pulsed manner with shot durations ranging from 30 $\mu $s to several milliseconds and ambient magnetic field strengths (B$_{0})$ ranging from 60 to 500 G. Langmuir probe measurements, at the exit of the helicon source and further downstream, show a peaked spatial profile. Both the time of flight and Mach probe measurements indicate a supersonic axial flow. Ion energy distributions as a function of axial distance away from the source region have been obtained using a retarding field analyzer. The distributions show a dually peaked population flowing downstream away from the discharge. The special profile of the energy distributions show increasing directed ion energies several centimeters downstream of the helicon coil region. Maximum sustained directed ion energies using argon are near 55 eV. Detailed results of the helicon source and ion energy distributions will be presented.   

High Power Helicon Plasma Source Characteristics as a Function of Input Neutral Density Distributions

A high power helicon source has been developed at the University of Washington, which is capable of tens of kilowatts power transfer into the plasma. Measured source electron densities in Argon are near 2x10$^{20}$ m$^{-3}$ with electron temperatures of 5-7 eV. The system is capable of operation with different types of neutral input gases with argon, xenon, nitrogen and hydrogen having been investigated. Unlike typical helicon coil experiments, which usually use a low-pressure backfill to start and maintain the discharge, neutral gas is injected into the center of the helicon coil region just prior to the creation of the discharge. Several neutral gas injectors have been designed and tested allowing for an investigation of source performance with different neutral pressure distributions and flow rates. Results show that differing profiles for the neutral gas density distribution and flow rates can have a significant impact on the downstream plasma characteristics as measured with both an ion energy analyzer and Langmuir probe. Detailed results of the helicon source and downstream election densities and ion energies, as a function of neutral gas injection parameters will be presented.   

Kinetic Model of Anomalous Transport for Hall Effect Thrusters

Recent experimental and numerical studies indicate existence of a transport barrier at the end of a Hall Effect Thruster channel, which is characterized with a strong shear of magnetic field. We have developed a numerical procedure allowing inclusion of a self-consistent Bohm coefficient calculation into our fully kinetic 2D3V model of the discharge. The model is used to simulate operation of a Stationary Plasma Thruster (SPT) with Xe gas and Near-Vacuum Hall Thruster (NVHT) with Kr propellant. Simulation results are compared with available experimental data for SPT and NVHS, and discussed.   

Application of Spectroscopic Measurements to Electrical Propulsion

Many plasma propulsion systems do not allow direct measurement of important operational conditions such as electron temperature in the discharge region and rate of wall erosion using common invasive diagnostics. To overcome these limitations we are trying to deploy visual spectrum line emission measurements using a portable optical system with $\sim $0.01-0.02~A spectral resolution in the broad UV-VIS to VIS-IR range. Experimental results for Hall Effect and RF-Driven Thrusters will be presented. Those will include line spectra for argon, xenon and nitrogen gases, and also impurities. We will discuss measurements of neutral and ionic lines intensity, broadening and shift, and possibility of plasma parameters derivation using relevant collisional-radiative models of the gas discharges.   

Development of a Plasma Cathode Electron (PCE) source for use in a plasma thruster

At Los Alamos National laboratory, we are in the process of developing a new plasma thruster system that employs a Plasma Cathode Electron (PCE) source. By biasing an ECR source chamber to high voltages, we can drive out a highly energetic electron beam that ionizes a propellant in a downstream chamber. This is a more efficient ionization mechanism than conventional electric propulsion concepts since we do not have lifetime issues that normally come with the presence of grids as in other plasma thruster systems. In this presentation we outline the thruster concept, in particular, the generation of the electron beam in a Plasma Cathode Electron (PCE) source. Our PCE source was created using 1.5kW of microwave power at 2.45GHz delivered in a static magnetic field of 875Gauss. We were able to drive electron beams of greater than 100A in our source with very high beam efficiencies by biasing the ECR source chamber to -120V.work was funded by DARPA.   

Spectroscopic Diagnostics of a Plasma Cathode Electrode (PCE) source

The EBIT experiment at Los Alamos National Laboratory is a new idea using a plasma cathode electron source to generate a highly energetic electron beam for ionization in a downstream chamber. The physics of plasma cathodes is well known and has already been utilized for electron beam generation in other capacities [1], [2]. We employ an ECR source at 2.45GHz, (described in detail in another presentation at this conference) by biasing a conducting plasma chamber to negative voltages up to -140V. We have a small aperture of 2cm in diameter through which an electron beam is extracted into a downstream Pyrex glass chamber with magnetic coils for plasma confinement. The plasma-electron beam system was diagnosed using three methods: a Langmuir probe (for electron temperatures, space potentials and electron densities), spectroscopy (for electron temperatures) and a retarded electron potential energy analyzer (for electron energies and space potentials). In this presentation we will focus on the spectroscopy diagnostics of the EBIT experiment. We will go into the different plasma equilibriums that we can work on and compare the results with the other 2 diagnostics we have in place. \newline [1] Yu. E. Kreindel, \textit{Plasma Cathode Electron Sources }$\sim $Atomizdat, Moscow, 1977, p. 144. \newline 2] E. M. Oks, Plasma Sources Sci. Technol. \textbf{1}, 249 $\sim $1992.   

Effects of secondary electrons on properties of a Hall thruster

Thermalization of cold secondary electrons in Hall thrusters (HT), if it occurs, limits the HT electron temperature. Plane geometry particle-in-cell simulations resolving the radial direction in HT reveal that almost all electrons emitted from one wall of coaxial HT channel reach the opposite wall without thermalization. The reasons for high penetration of emitted current are the low collision frequency and the depleted non-Maxwellian electron velocity distribution function preventing the two-stream instability. With 100\% penetration, the secondary electron emission (SEE) does not affect the electron temperature in HT, which qualitatively agrees with experiments. However, the role of SEE in HT cannot be neglected. Secondary electrons acquire energy in crossed electric and magnetic fields and produce intense energy flux to the walls. These electrons increase the axial electron mobility in HT via the near-wall conductivity effect. Oscillation of kinetic energy of secondary electrons along their trajectories may impose a certain condition on the plasma potential.   

Experimental studies of wall material effects on the Hall thruster discharge

The effects of secondary electron emission (SEE) properties of the channel wall material on the electron temperature and the electron cross-field current are studied for a conventional annular geometry Hall thruster. The linear growth of the maximum electron temperature with the discharge voltage, observed in the channel with a low SEE yield, suggests that SEE is responsible for the electron temperature saturation in the thruster with the channel walls having a higher SEE yield. The temperature saturation is directly associated with a decrease of the Joule heating, rather than with the SEE-enhanced electron energy loss at the walls [Raitses et al., Phys. Plasmas \textbf{12}, 073507 (2005)]. The reduction of the Joule heating is due to the decrease of the electric field, which, in its turn, occurs because of a local increase of the electron cross-field mobility. These results may support the recently predicted kinetic regime of plasma-wall interaction with counter-streaming beams of secondary electrons from the opposite walls of the thruster channel [Sydorenko et al., Phys. Plasmas \textbf{13}, 014501$^{ }$(2006), and I. Kaganovich, invited talk, this conference].   

Experimental demonstration of plasma detachment from a magnetic nozzle

We have demonstrated the detachment of a magnetized plasma from a magnetic nozzle, that is, the plasma has expanded from a region of high magnetic field to a location where the plasma kinetic energy is higher than the local magnetic field pressure. Interferometers, Mach probes, Langmuir probes, flux probes and magnetic field probes follow the flow of the plasma as it expands in the magnetic nozzle. Experimental results will be compared with theoretical models.   

Spectroscopic diagnostics on the VX-50

We have used hydrogen spectra to estimate electron temperature on VX-50, a 20 kW helicon plasma with a 20 KW ICRF acceleration section, using absolutely calibrated spectroscopic measurements of the Balmer series. The time evolution of the hydrogen spectra shows a transition from an ionizing plasma to a recombining plasma and back during a shot. We used a collisional radiative mode to estimate electron temperatures along with electron density measurements from an interferometer.   

Optimization of the Performance of Cylindrical Hall Thrusters

Cylindrical Hall thrusters have lower surface-to-volume ratio than conventional (annular) design Hall thrusters and, thus, seem to be more promising for scaling down.\footnote{Y. Raitses and N.J. Fisch, \textit{Phys. Plasmas} \textbf{8}, 2579 (2001). }$^{,}$\footnote{Artem Smirnov, invited talk, this conference.} We present the results of the performance study of the cylindrical Hall thrusters with channel outer diameters of 2.6 cm and 3 cm. The effect of the magnetic field distribution and segmented electrodes on the thruster discharge characteristics and efficiency is investigated. The experimental results demonstrate a substantial flexibility in the thruster magnetic field configuration, which is a key tool in achieving the high-efficiency operation. The electron confinement and ion acceleration can be optimized over a family of realizable magnetic field distributions.   

Measurement of ion temperature and flow velocity by using LIF and electric probe methods in K2H and DiPS propulsion simulators

Ion temperature, plasma flow velocity and plasma density are measured in DiPS (Diversified Plasma Simulator) and K2H (KBSI-KAIST-Hanyang University) propulsion simulators by a laser induced fluorescence (LIF) method and a fast scanning electric probe system, which consists of an rf-compensated single probe and a Mach probe. In both devices helicon plasmas were stably generated with m=+1 right-helical antenna at 13.56 MHz with powers of 1 - 3kW (DiPS) and 0.5 - 1kW (K2H), and open ended magnetic configurations are utilized. The measured plasma parameters are as follows: plasma densities of 10$^{11}$ -- 10$^{13}$ cm$^{-3}$ (K2H) and 10$^{12}$ -- 10$^{13}$ cm$^{-3}$ (DiPS), electron temperatures of 3 -- 9 eV (K2H) and 2 -- 4 eV (DiPS), ion temperatures of 0.14 -- 0. 17 eV (K2H) and 0.05 -- 0.2 eV (DiPS) and drift velocities of 0.8 -- 1.6 km/s (k2H) and 0.2 -- 0.5 km/s (DiPS).   

A parallel finite-volume MHD code for plasma thrusters with an applied magnetic field

The Princeton Code for Advanced Plasma Propulsion Simulation (PCAPPS) is a recently developed parallel finite volume code that solves the resistive MHD equations in axisymmetric form. It is intended for simulating complex plasma flows, especially those in plasma thrusters. The code uses a flux function to represent the poloidal field. It allows for externally applied magnetic fields, necessary for efficient operation of magnetoplasmadynamic thrusters (MPDT) at low power. Separate electron and heavy species energy equations are employed, and model closure is achieved by a multi-level equilibrium ionization equation of state. We provide results from various validation tests, along with solver accuracy and parallel efficiency studies. Preliminary numerical studies of a lithium-fed MPDT are also presented.   

Design of an ICRF plasma thruster antenna by TOPICA

A typical RF plasma thruster is comprised of an RF plasma source, an open-ended magnetic confinement device, an RF acceleration unit and a magnetic nozzle. The usual choice for the acceleration is to employ the Ion-Cyclotron resonance frequency (ICRF), a well established technology in fusion experiments for transferring large RF powers to magnetized plasmas. To help design RF thruster ICRF antennas, TOPICA (Torino Polytechnic Ion Cyclotron Antenna) code [1] has been recently extended to handle cylindrically symmetric plasmas. The latter entailed developing a wholly new module of TOPICA charged with the task of solving Maxwell's equations in cylindrical magnetized warm plasmas and yielding the Green's function$\underline{\underline {\tilde {Y}}} (m,k_z )$, i.e. the relationship at the air-plasma interface between the transverse magnetic and electric fields in the spectral (wavenumber) domain. The approach to the problem of determining the antenna input impedance relies on an integral-equation formulation for the self-consistent evaluation of the current distribution on the conductors. This work reports on TOPICA evolution and presents the design of an RF thruster ICRF antenna. \begin{enumerate} \item V. Lancellotti et al., Nucl. Fusion, \textbf{46} (2006) S476-S499 \end{enumerate}   

Dynamics of low-density coronal plasma in low current x-pinches

A series of experiments have been performed to study the low-density coronal plasma formation in x-pinches driven by a current generator capable of producing an 80 kA current with a rise time of 40 ns. Various wire materials including: aluminum. copper, nickel, stainless steel, molybdenum and tungsten were used. Simultaneous optical probing techniques, (schlieren, interferometry) and gated XUV imaging were used to record information in various density ranges. X-pinches consisting of aluminum, copper and molybdenum showed the coronal plasma streams towards the mid plane, where it converges. It then forms a sheath on either side of the cross-point, which moves with a velocity 6 x 10$^{5}$ \textit{cm s}$^{-1}$ towards the electrodes. The coronal plasma dynamics were significantly different in tungsten x-pinches, where no such sheath formation was observed. Experimental results quantitatively agree with 2D MHD simulations.   

Dielectric flashover testing results and application to a study on magnetic flashover inhibition

Magnetic flashover inhibition (MFI) is being considered as a method to increase hold-off at water vacuum barriers. This technique would reduce the size and therefore inductance and cost of pulsed power machines. Self-generated MFI conditions are being tested at the Missouri - University Terawatt Test Stand (MUTTS). Although dielectric flashover tests have been performed many times, non-magnetic field flashover characteristics were obtained for future comparison to self-generated magnetic field experimentation. The non-magnetic field testing included effects from shielding triple points on zero degree and 45 degree insulators. A discussion of the status of the insulating barrier flashover testing at MUTTS will be presented. Future flashover tests will be conducted on the upgraded MUTTS facility. The new facility will be capable of producing high currents necessary for self-generated MFI experiments. An overview of the design for the MFI experiments on the new facility will be presented.   

UV Characterization of an SF6 Filled Laser Triggered Gas Switch

Incident ultra-violet (UV) light is being considered as a contributor to dielectric flashover of acrylic insulators on high voltage, high current switches. At the University of Missouri-Terawatt Test Stand (MUTTS), a Rimfire laser triggered gas switch (LTGS) has been modified in order to study UV induced flashover. UV irradiation on the insulator of a single gap switch is studied. Various methods for UV characterization of the switch are being considered. Time resolved measurements and spectral analysis of the incident UV light are currently being performed.   

Plasma Characterization of a Magnetically Triggered Plasma Opening Switch Using Optical Techniques$^1$

Plasma opening switches have been studied for many years and much is known about them. Interferometry, spectroscopy, etc. are among the many techniques that have been used to quantify characteristics of the plasma. 120GHz microwave and 10.6$\mu $m laser interferometry techniques are currently being used to characterize the plasma density in the Sandia National Laboratories Magnetically Controlled Triggered Plasma Opening Switch (MCTPOS) experiment. Corroborative density measurements using Moir\'{e} deflectometry are planned. Of particular interest are the early time (as compared to $d_{drift} /(\tau _{rise} \upsilon _{drift} )\approx 0.5)$ density gradients that illustrate the trapping of charged particles into the magnetic field. Methods such as laser Schlieren and Zernike (phase contrast) imaging are planned to illustrate the gradients of the magnetically confined plasma using a 532nm doubled Nd: YAG laser with a pulse width of 5ns. The plasma source itself is a ring of carbon-coated flashboards (16 total, 8 per side) concentrically aligned with a `slow' ($\sim $500$\mu $s) magnetic field coil.\newline $^1$Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company for the USDoE's National Nuclear Security Administration under contract DE-AC04-94AL85000.   

Design and Initial Development of the Divertor Erosion and Vapor shielding eXperiment (DEVeX)

The focus of the DEVeX project is to experimentally measure the erosion of Plasma Facing Components (PFCs) under pulsed plasma loads indicative of a disruption in a large fusion device. DEVeX is planned to produce plasmas of similar density and temperature to disruptions in fusion machines like those reported previously [P.D. Rockett, et al. Jour. Nucl. Mat. Vol. 220-222. (April 1995) 785-789.]. DEVeX will also provide a suite of diagnostics to analyze both the incident plasma flux and the erosion mechanisms during the disruption event. The design of the DEVeX plasma source will be presented in addition to the models used to predict the source behavior. Likewise, the planned diagnostics and their responses to predicted erosion rates [A. Hassanein. Fusion Eng. and Design. Vol. 60. (2002) 527-546.] will be shown. This work is supported by ALPS/DOE Contract: DEFG02-99ER54515.   

New research initiative for Ion/surface Interaction Experiment (IIAX) at University of Illinois: lithium coated graphite studies

The Ion/Surface Interaction Experiment (IIAX) at the University of Illinois is beginning a new research initiative into the study of lithium coated graphite. With NSTX coating graphite tiles with lithium, IIAX could be a valuable tool to aid in their research. With the project still in the planning phase, an overview of the possible design and experiments is presented. The design will be similar to the present IIAX design with an ion beam system, a movable carriage for sample holder, beam diagnostics, and a Quartz Crystal Microbalance (QCM) to measure sputtered and evaporated materials. In addition to these, there will be an in-situ evaporator to coat the graphite films with lithium, and a calibrated leak system to determine the saturation rate of gasses into the Li. Possible experiments include measuring the intercalation rate of Li on C and measuring the sputtering yield of the Li coated C films with varying levels of Li concentration.   

Solid-Liquid Lithium Divertor Experiment: SLiDE

Liquid lithium has been proposed as a material for the first wall and divertor/limiter of a fusion device. One objection raised against the use of liquid lithium is the high vapor pressure at modest temperature increases. Recent experiments on the CDX-U device show however, that lithium absorbs a surface heat flux of greater than 40 MW/m$^{2}$ with negligible evaporation. Observation of a focused electron beam hitting solid lithium in the CDX-U lithium tray saw melting of a large section of the tray. Macroscopic liquid flows were observed which redistributed the incident power. Surface tension effects caused by temperature gradients have been proposed as a mechanism for this convection. These flows were insensitive to MHD effects in fields up to 600G [1]. This paper presents a design of an experiment which will diagnose the flows induced by an intense heat flux onto a lithium pool and measure the maximum heat flux lithium can absorb in an incident magnetic field. A number of diagnostics are considered and evaluated with the goal of being minimally invasive to the induced flows. These results are the first step in the creation of an experimental facility to study the heat transfer capabilities of free-surface liquid lithium at the University of Illinois. [1] Majeski, \textit{et al}., Final results from the CDX-U lithium program, \textit{Presentation at} \textit{APS-DPP05}, Denver, Colorado. 2005.   

Magnetized plasma flow injection for a dynamo drive in a TPE-RX reversed-field pinch

In a reversed-field pinch (RFP) plasma, the poloidal current is sustained through dynamo activity, which is the consequence of mainly tearing (MHD) instabilities. To control the dynamo activity, the method using magnetized plasma flow (MPF) with a large degree of magnetic helicity and dense particle content was proposed and a series of experiments have been performed. The MPF is generated by a magnetized coaxial plasma gun which has capacitor banks of 367mF with a maximum charging voltage of 800V and 20$\mu$F, 15kV. In the response to the MPF injection, excited specific mode (m = 1/n=5, 6) of magnetic dynamo activity has been observed. While the intensity of these modes is sustained, other modes of magnetic fluctuation keep lower intensity. During the period of MPF injection, increased toroidal magnetic flux has also been observed. This may indicate driven poloidal current through the exited dynamo activity and/ or result of increase confinement because of reduced stochasticity of magnetic field.   

Generation of micro-jet atmospheric pressure plasmas and study of their characteristics

Low temperature micro-plasmas of about 360 $\mu $m in radius and were produced in the ambient air at tens of kHz using a pin electrode with and without a plane electrode. A pin electrode was placed in a pyrex tube, through which a helium gas was supplied. In the case of a pin electrode to a dielectric-covered plane electrode set up, a cone-shaped plasma was generated due to the presence of the dielectric material. It was shown that the discharge mode, plasma size, and gas temperature could be controlled not only by operational parameters such as gas flow rate, voltage, frequency, but also by geometrical parameters such as electrode position. The plasma radius was up to 5.5 mm at the dielectric surface and up to 8 mm in length. The rotational temperature was varied between 310 K and 490 K. In the case of the single pin electrode only, a needle-shaped jet plasma was generated of which length was as long as 60 mm. The plasma size was varied as the operational parameters were changed. The measured gas temperature was less than 310 K under all experimental conditions. Due to the advantageous features of the plasmas, they can be applied to treat small area, thermally sensitive surfaces.   

Numerical Simulation and Design of Dense Hypervelocity Plasma Jets for Fusion Applications

We report on the results of design studies to determine optimal configurations for coaxial pulsed plasma jets. Dense hypervelocity plasma jets have a variety of promising uses including momentum injection, plasma refueling, and as drivers for magnetized target fusion. Previous studies showed that the tendency of coaxial plasma guns to develop a blow-by instability can be effectively offset by shaping the accelerating section. A plasma jet incorporating these concepts was designed and built by HyperV Technologies Corp. for the Maryland MCX experiment. Further studies of the next generation of plasma jets will be reported. Numerical simulations were performed using the Mach2 2 $\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} $-D MHD code. To maximize performance, each stage of the pulse discharge, including armature formation, acceleration and detachment from the inner electrode, must be optimized. Plasma jet designs have been found that are predicted to perform well over a range of parameters and that are capable of accelerating plasma masses exceeding 200 $\mu $g to greater than 200 km/s without onset of the blow-by instability.