Session PP8: Poster Session VI: Shocks, Flows, Dusty and Complex Plasmas; Z Pinches, X Pinches, EOS, and HEDP; Stellarator; FRC’s, Flow Pinch, HBT-EP, Helimak and LDX

Heating and cooling in dusty plasmas

A dusty plasma is a partially ionized gas containing small particles of solid matter, which are typically micron size. These particles gain a large electric charge by collecting electrons and ions from the ambient plasma, so that they interact with a large potential energy, yielding a strongly-coupled plasma. Particles can thereby organize in a crystal, which in our experiment is a single layer of microspheres. We can melt this crystal to form a liquid by heating it with random kicks from moving laser beams. The laser imparts a radiation-pressure force on the particles, which also experience frictional drag simultaneously by gas atoms. At steady state, a balance of laser heating and gas cooling determines a temperature. Results will be reported for an experiment where we disturb this balance with a sudden change in heating power to study the temporal development of melting and freezing.   

Dispersion relation of Dust-acoustic waves in three-dimensional complex plasmas under microgravity

In order to measure the dispersion relation for longitudinal Dust-acoustic (DA) waves in quasi-isotropic 3D complex (dusty) plasmas, a series of dedicated experiments with the PKE-Nefedov [1] setup were performed on board the International Space Station. The waves were excited by applying ac electric modulation of variable frequency to the rf electrodes. The amplitude of excitation was varying with frequency to ensure ``sufficiently linear'' regime of the dust density perturbations. The dispersion relation was obtained by measuring the induced density perturbations, revealing fairly good agreement with a simple multispecies theory of DA waves [2]. [1] Nefedov A P et al, 2003, New. J. Phys., vol. 5, 33.1. [2] Rao N N et al, 1990, Planet. Space Sci., vol. 38, 543.   

Dust Impact Studies in Regard to Dust/Wall Interactions in Fusion Research

Particulate contamination has long been an area of concern within the fusion community. Past research has focused primarily on decreasing dust production as well as placing limits on overall dust retention. Unfortunately, due to the increased surface area and higher operating temperatures proposed for ITER, it is assumed that dust production within this environment will be particularly pronounced. The dynamics (and the underlying physics) for dust particles within such an environment are not yet well understood, particularly the manner in which dust interactions occur with the wall. We will discuss an experimental technique, which applying dust and wall parameters from current fusion devices, provides experimental impact data utilizing a single stage light gas gun. The resulting data will be used to discuss dust production methods, dust accretion on the walls, and dust/wall durability.   

Complex Plasma Studies on Ferromagnetic Dust

Dust particles imbedded within plasma are charged through collisions with free electrons and ions. If the ratio of the inter-particle potential energy to the average kinetic energy is sufficient, the particles form disordered or ordered structures depending on whether short or long range ordering dominates. For dust particles forming crystalline structures residing within two-dimensionally extended lattice planes, various stable crystalline phases have been observed experimentally. The dynamics of this behavior is driven in large part by the charge on the particle. Although the charging process for insulating materials has been examined in detail, conducting materials have not yet been fully investigated. This study presents data for 4.5 $\mu $m ferromagnetic dust examined under several pressure and power conditions within a standard GEC reference cell.   

Sensitivity Analysis on Boundary Conditions for Continuum Regime Probe

In both classic literature on the continuum regime Langmuir probe [1], and recent literature on dust grain charging [2], the assumption is made that the electron and ion densities vanish on the probe surface. This implies a singularity in the respective fluid velocities at the surface under steady state conditions. Our recent kinetic simulations [3] of electrons near the surface of a planar probe, showed that reasonable electron boundary conditions require the electron density at the probe surface be on the order of the equilibrium density times the ratio of the electron drift velocity over the thermal speed. Density does not vanish, nor does temperature remain constant, as the surface is approached. In this poster, a sensitivity analysis on spherical probe current and potential is performed to investigate how changes in electron and ion boundary conditions affect results.\\ 1) C.H. Su and S.H. Lam, Phys. Fluids, Vol. 6, No. 10, 1963; I.M. Cohen, Phys. Fluids, Vol. 6 No. 10, 1963.\\ 2) S.A. Khrapak, G.E.Morfill, A.G. Khrapak, L.G. D'yachkov, Phys. Plasmas, Vol. 13, No. 5, 2006.\\ 3) H.L. Rappaport, presented at APS/DPP 2006.   

Complex Plasma with Multiple Distinct Particle Sizes

Dust particle clouds can be found in most fusion and almost all plasma processing environments including both plasma-etching devices and in plasma deposition processes. Dust particles suspended within such plasmas acquire an electric charge from collisions with free electrons in the plasma. If the ratio of the inter-particle potential energy to the average kinetic energy is sufficient, the particles can form either a ``liquid'' structure with short range ordering or a crystalline structure with longer range ordering. The preponderance of experiments to date have employed monodisperse spheres to form the complex plasma system. In contrast, this paper examines the effect that a size distribution will have on overall particle ordering. Two dimensional (2D) plasma crystals were formed employing mixtures of 8.89 $\mu $m, 6.50 $\mu $m, and 4.57 $\mu $m monodisperse particles in Argon plasma. The pair correlation function was determined at differing pressures and powers and then compared to corresponding measurements obtained for monodisperse spheres alone and vibrational data was examined to determine specific dust and plasma parameters. Multiple experiments were conducted to investigate the manner in which system phase transitions and other thermodynamic properties depend upon the overall dust grain size distribution.   

Dispersion relation for the dust-acoustic wave in a Lorentzian plasma

The electrostatic mode of dust-acoustic (DA) surface waves propagating on the interface between a vacuum and a complex plasma is kinetically investigated by using the dispersion relation based on the Vlasov-Maxwell equations. The complex plasma consists of Lorentzian (kappa) electrons and ions, and cold dusty particles. The results show that in the long wavelength limit ($k_{x}$\textit{$\lambda $}$_{D}\to $ 0), the frequency of the wave is reduced to\textit{ $\omega $ }$\approx $ (\textit{$\mu $}$_{\kappa })^{1/2}k_{x}C_{D}$ where \textit{$\mu $}$_{\kappa }$ is a kappa (spectral index) dependent factor and $C_{D}$ = \textit{$\omega $}$_{pd}$\textit{$\lambda $}$_{D}$ is the well known dust acoustic speed. We see that the frequency increases as the ratio of dust density to ion density increases. Some interesting results of the DA surface waves supported by the Lorentzian plasma are discussed.   

Dispersion properties of the dust-acoustic waves in a Lorentzian plasma containing elongated dust grains.

The dispersion relation for electrostatic waves propagating in an unmagnetized dusty plasma whose constituents are electrons, ions, and elongated charged dust grains is obtained and analyzed. Electrons and ions are assumed to be Lorentzian (kappa velocity distribution) and dust grains are assumed to be cold. We consider the one-dimensional dust grain rotation so that the principal moment of inertia has $z$-component only. In the limit of low frequency, i.e., \textit{$\omega $} $<<$ \textit{kv}$_{e}$, \textit{kv}$_{i}$, the dust acoustic (DA) wave dispersion relation is kinetically derived by employing Poisson-Maxwell equations. The result shows that the dispersion relation can admit complex solutions and the growth rate is proportional to the rotation frequency. The effects of spectral index \textit{$\kappa $} are also discussed.   

Oblique dust density waves

We report on experimental observations of dust density waves in a complex (dusty) plasma under microgravity. The plasma is produced in a radio-frequency parallel-plate discharge (argon, $p=15$Pa, $U=65$V$_{pp}$). Different sizes of dust particles were used (3.4 $\mu$m and 6.4$\mu$m diameter). The low-frequency ($f \approx 11$Hz) dust density waves are naturally unstable modes, which are driven by the ion flow in the plasma. Surprisingly, the wave propagation direction is aligned with the ion flow direction in the bulk plasma but becomes oblique at the boundary of the dust cloud with an inclination of $\approx 60^{\circ}$ with respect to the plasma boundary. The experimental results are compared with a kinetic model in the electrostatic approximation [1] and a fluid model [2]. Moreover, the role of dust surface waves is discussed. \newline [1] M. Rosenberg, J. Vac. Sci. Technol. A 14, 631 (1996) \newline [2] A. Piel et al, Phys. Rev. Lett. 97, 205009 (2006)   

Observations of dust acoustic waves driven at high frequencies

Previous measurements of the dispersion relation of dust acoustic waves (DAW) have been restricted to frequencies less than 35 Hz. We report new measurements of the DAW dispersion relation with driving frequencies up to 200 Hz. The experiments were performed in a dusty plasma produced in a argon DC glow discharge. Although DAWs are spontaneously excited in the dusty plasma, a sinusoidal modulation of the discharge current allows the DAW to be synchronized at the applied driving frequency. For each driving frequency, the average wavelengths of the DAW were determined by recording video images of the scattered light intensity. A comparison of the measured dispersion relation with the theoretical DAW dispersion relation indicates that finite dust temperature effects must be taken into account. A new interesting feature revealed in the experiment is the modulation of the `naturally' excited DAW by the high frequency driven DAW, which appears as a fine structure in the video images of the waves.   

Vertically propagating driven dust acoustic waves in a dc glow discharge dusty plasma

Early experimental and theoretical studies of these dust acoustic waves (DAW) have generally assumed that the kinetic dust temperature is comparable to that of the background ions and, as a result, finite dust temperature effects were not considered to play a significant role. However, a number of studies [e.g., J. Williams, et al., Phys. Plasmas, 14, 063702 (2007)] suggest that the kinetic dust temperature may be as high as tens of electron volts. This experimental study, in combination with work by Fisher, et al. (this session), shows that finite dust temperature effects modify the dust dispersion relation. In this study, monodisperse 1.51-micron diameter, silica microspheres are used to form a dusty plasma in an unmagnetized, argon dc glow discharge. Vertically propagating, driven DAW's are formed by modulating the current applied to the anode. Results will be presented on measurements of the dispersion relation and measurements of zero- and first-order wave components obtained using stereo-PIV techniques.   

Preliminary measurement of ion heating in a weakly-coupled complex (dusty) plasma

In previous [J. Williams, et al., Phys. Plasmas, 14, 063702 (2007)] and ongoing [Thomas, et al. and Merlino, et al. (this session)] experimental studies, it has been observed that the kinetic temperature of the microparticle component of a weakly-coupled complex (dusty) plasma, CDP, is significantly larger than the other plasma components (electrons, ions and background neutrals), a result that is consistent with previous measurements of the kinetic temperature for a plasma crystal in a fluid-like state. While there are no direct theoretical predictions to explain the mechanism responsible for heating the microparticle component to the observed temperatures in a weakly-coupled CDP, there have been a number of mechanism proposed to explain the observations involving the plasma crystal. Among the most promising of these mechanisms is an instability triggered by ions streaming past the dust particles. In this presentation, we present preliminary experimental results examining the possible role played by the ions in heating the microparticle component of a weakly-coupled CDP. This work is supported by NSF Grant PHY-0354938.   

Floating potential and collisionless ion drag force on a spherical grain under weakly magnetized conditions

The interaction of a spherical object with a collisionless plasma under weakly magnetized conditions is investigated by means of the PIC code SCEPTIC [1]. The key features of this 2D3v electrostatic ion kinetic code are a spherical geometry accurately resolving the collector's edge, and a Boltzmann treatment of the electrons, whose current is calculated using a recently developed empirical formula accounting for their magnetization [2]. By asymmetrically reducing the ion and electron fluxes to the collector, the magnetic field (${\bf B}$) has a strong influence on the floating potential ($\phi_f$). The non monotonic dependence of $\phi_f$ on ${\bf B}$ is documented for a wide range of plasma parameters relevant to probes and dust particles. The magnetic field is also shown to reduce the ion focusing effects present in an unmagnetized plasma when the drift velocity is non negligible, thus the electrostatic part of the ion drag force. This effect is compared with the variation of the electron-ion Coulomb collision frequency with the local magnetic field.\\ \\ $[1]$ I.H. Hutchinson PPCF 47, 71-87 (2005)\\ $[2]$ L. Patacchini et al. Phys. Plasma 14, 062111 (2007)   

Observation of melting in a heated, two-dimensional complex plasma

The melting transition in a two-dimensional complex plasma has been studied experimentally. The complex plasma is heated by amplitude modulating the rf discharge power with a square wave at the vertical resonance frequency. The vertical motion couples to an in-plane dust-acoustic instability at one-half the driving frequency, thereby increasing the average in-plane kinetic energy (i.e., the effective ``temperature'') of the system. The ``thermodynamic'' phase of a complex plasma consisting of $\approx3900$ $9-\mu\rm{m}$ diameter particles has been characterized for increasing levels of amplitude modulation at constant neutral pressure (35 mtorr Ar) and constant average rf power using the bond-orientational correlation function, defect densities, the Lindemann ratio and the pair correlation function. A melting transition showing clear evidence for hexatic and liquid phases is observed.   

Ionosphere Dusty Plasma in the Laboratory

We describe an experiment that creates dusty plasma with nanometer-sized particles that is similar to the ionosphere in which there are ``smoke'' particles from the ablation of meteors. The meteoritic smoke layer is global and extends from about 70-100 km. The smoke particles are thought to be the condensation nuclei for noctilucent clouds. The meteoritic particles descend into the polar stratosphere in the winter. A Zn vapor source is used to create a smoky gas of Zn particles that are up to tens of nanometers in size and these are seen both by laser scattering and by collecting them on a substrate viewed by electron microscope. A differential pumping scheme is used to introduce the particles into a hot-filament discharge plasma. Probe methods are used to search for charged nanometer-sized particles in decaying afterglow plasma.   

Theoretical and experimental studies of dust particle charging in the presence of a magnetic field

The physical process of the charging of a dust particle immersed in a plasma with an applied background magnetic field is studied theoretically and experimentally. The theoretical study is conducted by means of a spherical harmonics expansion of the Maxwell-Boltzmann equations. Furthermore, we perform PIC simulations of a single particle immersed in a plasma subject to static background magnetic fields of various magnitudes to obtain characteristic charging curves. From this point, various detailed physics packages are added to the PIC code for more accurate simulations. Experiments are being planned in which single micron-size dust particles are dropped into a magnetized Q machine plasma where they become charged and subsequently fall into a Faraday cup where their charge is measured. Charge measurements will be performed at different values of the magnetic field.   

0-D and 2-D LIF Measurements of Small Coulomb Crystals in a Linear RF Trap

One goal of our ion trap experiment is to clarify the mesoscopic statistical properties of small one-component plasmas. As the beginning phase of the research, we improved the controllability of laser-cooled one-component plasmas, and developed 0-D and 2-D LIF measurement system. Since the temperature of laser-cooled ions is sensitive to the wavelength of the cooling laser in the vicinity of the phase transition, the stabilization of the laser system is necessary to perform systematic experiments. In this experiment, the long-term drift of the laser wavelength was suppressed to several mega hertz or less per 10 minutes by locking to a Fabry-Perot interferometer. 0-D and 2-D LIF measurements were performed using a photomultiplier or an ICCD camera, respectively. Commonly, it is believed that the sudden drop of 0-D LIF signal indicates the crystallization of plasma. However, the 2-D LIF image immediately after the sudden drop of the 0-D LIF signal showed a cloudy image. In this presentation, we will show the detail of the difference between the 0-D and 2-D LIF results.   

Crystallization in mass and charge asymmetric bilayers

We consider Coulomb crystal formation in quantum electron-ion (hole) bilayers. Varying the mass ratio $M$ of ions and electrons between 1 and 100 for a fixed layer separation $d$ at low temperature and high density, one can tune the hole behavior from delocalized (quantum) to localized (quasi-classical) while the electrons remain delocalized all the time. While in 3D plasmas [1], ions crystallize if the mass ratio exceeds a critical value of $M_{cr} \sim 80$, in bilayers $M_{cr}$ can be drastically reduced by properly choosing $d$ and the in-layer particle density. The complicated overlap of correlation and quantum effects of both, electrons and holes, is fully taken care of by performing first-principle path integral Monte Carlo simulations. \newline [1] M. Bonitz, V.S. Filinov, V.E. Fortov. P.R. Levashov, and H. Fehske, Phys. Rev. Lett. 95, 235006 (2005) and J. Phys. A: Math. Gen. {\bf 39}, 4717 (2006). [2] P. Ludwig, A. Filinov, Yu. Lozovik, H. Stolz, and M. Bonitz, Crystallization in mass-asymmetric electron-hole bilayers, Contrib. Plasma Phys. (2007), ArXiv: cond-mat/0611556   

Breathing Mode in Complex Plasmas

The breathing mode is a fundamental normal mode present in Coulomb systems, and may have utility in identifying particle charge and the Debye length of certain systems. The question remains whether this mode can be extended to strongly coupled Yukawa balls [1]. These systems are characterized by particles confined within a parabolic potential well and interacting through a shielded Coulomb potential [2,3]. The breathing modes for a variety of systems in 1, 2, and 3 dimensions are computed by solving the eigenvalue problem given by the dynamical (Hesse) matrix. These results are compared to theoretical investigations that assume a strict definition for a breathing mode within the system, and an analysis is made of the most fitting model to utilize in the study of particular systems of complex plasmas [1,4]. \newline References \newline [1] T.E. Sheridan, Phys. of Plasmas. 13, 022106 (2006)\newline [2] C. Henning et al., Phys. Rev. E 74, 056403 (2006)\newline [3] M. Bonitz et al., Phys. Rev. Lett. 96, 075001 (2006)\newline [4] C. Henning et al., submitted for publication   

Measurement of emission from a radiatively collapsed shock

Radiatively collapsed shocks are systems in which radiation transport causes the shock to ``collapse'' or compress to high densities. Such shocks are present in supernova remnants, passing through interstellar medium, and other such astrophysical systems. With the advent of large laser facilities, conditions can be created so that radiativly collapsed shocks can be studied in quantitative way. Recent experiments have been preformed on the Omega laser at the Laboratory for Laser Energetics to study the dynamics of these shocks. Measurements of radiative emission from the collapsed shock and precursor region have been made using a streaked optical pyrometer from which the temperature of the system can be calculated. Details of the experiment and results will be discussed. This research was sponsored by the NNSA through DOE Research Grants DE-FG52-07NA28058, DE-FG52-04NA00064, and other grants and contracts.   

Plasma Formation on an Aluminum Surface Driven by MG Fields

Experiments on the UNR 1 MA Zebra generator drive magnetic fields of several megagauss on the surface of an aluminum conductor. This physics is important in a number of applications including magnetized target fusion. Several 1-mm diameter load designs were tested. The rod diameter was larger than the skin depth for the 70-ns current rise. Diagnostics included optical imaging to a time-gated intensified CCD camera and a streak camera, magnetic field probes, photodiodes, photomultipliers, and laser shadowgraphy, schlieren, and interferometry. These yielded information on the threshold for plasma formation, the expansion of the aluminum, the temperature at the surface, and the growth of the unstable $m$=0 mode driven by the curvature of the magnetic field. Time-gated images show markedly more uniform light from machined loads than from wire loads. The relatively simple experimental setup was chosen to allow comparison with 1-D and 2-D rad-MHD modeling.   

Numerical Modeling of Megagauss Fields on Aluminum Rods

Metal plasma formation and stability were studied on the surface of aluminum rod in recent experiments driven by the UNR Zebra generator [1]. The surface response to megagauss fields is important for a number of applications, including Magnetized Target Fusion (MTF). Recent radiation-hydro numerical simulations by Garanin et al. show how plasma can be generated on a metal surface [2]. Numerical simulations with codes used at UNR (MHRDR and RAVEN), and codes from other institutions, show luminosity, radial expansion, and plasma formation or lack thereof that can be compared with experimental data. The sensitivity of modeling to various equation-of-state and resistivity models will be discussed. \newline \newline [1] Fuelling et al., this conference \newline [2] S.F. Garanin et al., J. Appl. Mech. Tech. Phys. 46, 153(2005).   

Interaction of laser-produced plasmas with large magnetoplasmas

We will present experiments on the interaction of dense laser-produced plasmas with a large mangetoplasma. A high-energy laser ($>$20 J) coupled to the Large Plasma Device (LAPD) at UCLA allows unique experiments on laser driven shocks that can approach the collisionless regime. Focused laser intensities around $10^{13}$ W/cm$^2$ produce an ablating plasma-plume with expansion velocities of several 100 km/s. Prior to the laser pulse an ambient plasma with a size of 18 m lengths and 50 cm diameter at $4x10^{12}\ cm^{-3}$ and T$_e$=5 eV is created in an axial magnetic field of 600-1800 G. We will present measurements of Alfven waves radiated from the laser-produced plasma, as well as a characterization of the evolution and particle distribution of the laser-produced plasma `piston'.   

Observation of Thermal Effects for Shock Wave Acceleration in Glow Discharge Plasma

Shock waves launched into weakly-ionized plasmas experiences an increased velocity and dispersion. These effects have been primarily attributed to: (i) gas temperature gradient and thermal effects, and (ii) plasma-specific (electron density, temperature, and electric field) effects. In this work, we investigate the thermal effects on the observed shock wave modifications in plasma. At a fixed Mach number, shock waves are launched with an incremental delay from the switch-on of the discharge. It is found that the shock wave velocity in plasma increases as the delay is increased, and reaches a steady-state value at a delay of about 100 ms.   

Self similar nonlocal electron heat flow

The well known self similar heat diffusion solutions of Zel'dovich and Raizer [1], for a heat wave advancing from a boundary at a fixed temperature or a fixed heat flux do not keep the ratio R of the scale length to the mean free path constant. Instead, R increases and the solution becomes increasingly valid because Spitzer-Harm [2] heat flow is increasingly applicable. A self similar solution exists which keeps R constant, if one assumes that the boundary heat flux increases in time. Similarly, for the problem of a uniform density plasma heated by a finite width laser beam, a self similar solution keeping R constant can be obtained by assuming that the beam intensity and width increase in time. Such solutions will be studied with the electron kinetic code FPI [3], and compared to simulations with more usual laser characteristics. \newline [1] Ya. B. Zel'dovich and Yu. P. Raizer, ``Physics of Shock Waves {\ldots}'', Academic Press, New York, 1967. \newline [2] L. Spitzer and R. Harm, Phys. Rev. \textbf{89}, 977 (1953). \newline [3] J.-P. Matte \textit{et al.}, Phys. Rev. Lett. \textbf{53}, 1461 (1984)~; \textit{ibid }\textbf{49}, 1936 (1982).   

Modeling the influence of interelectrode spacing in the Pulsed Discharge Nozzle

The Pulsed Discharge slit Nozzle (PDN) source was designed to produce and cool molecular ions, creating an astrophysically relevant environment in the laboratory. Using a discharge model applied to this system, a parameter study of the influence of the interelectrode distance on the plasma properties is carried out to optimize the yield of molecular ions and radicals in the PDN source. The model describes the electron density and energy, as well as the argon ion and metastable atom number density for various interelectrode distances. The results reveal that, by increasing the interelectrode distance, a positive column forms between the electrodes, thereby confirming the glow-discharge nature of the plasma. The positive column however does not contribute significantly to the formation of metastable argon atoms, and no enhanced molecular ionization is thus to be expected from an increase in said distance. The simulation results show that the PDN source might be less efficient for longer column lengths; they also provide key insight into the characteristics of interstellar species analogs in laboratory experiments.   

Experimental Characterization of Plasma Flow in Reconnection Scaling Experiment.

Reconnection Scaling Experiment (RSX) studies linear and non-linear evolution of up to four interacting current-carrying plasma cords with emphasis on kink instability and magnetic reconnection. During the kink instability, the presence of an axial flow gives rise to a Doppler shifted frequency and rotation of the kink, which makes studying the flow important. The axial velocity, plasma density, and electron temperature in one plasma column were measured on RSX with the miniaturized Mach and triple electrostatic probes installed on 3D positioning systems. Significant plasma flow with the velocity on the order of the ion acoustic speed was detected, with the velocity decreasing downstream. 2D profiles obtained at two axial locations were then employed to estimate the radial profile of the ion viscosity using the integral momentum balance equation. The results show that the ion momentum flux is dissipated by the ion-ion viscosity due to significant radial shear of axial velocity. Chord-integrated ion temperature measurements performed at several radial locations using Doppler broadening spectroscopy show temperature of about 1eV. Comparison of the measured viscosity with Braginskii's theoretical predictions demonstrates a good agreement, which is an important new result useful for both astrophysical jets and magnetoplasmadynamic thrusters. Supported by OFES, and DOE/LANL contract DE-AC52-06NA25396.   

Measuring 3D plasma flow in compact toroids

The TS-3 and TS-4 experiments at the University of Tokyo shoot two compact toroids at each other to form a single compact toroid with strong plasma flows. Up to now, conventional ion Doppler spectroscopy has been used to measure toroidal plasma flows only. The observations identified the ``slingshot effect'' [1], which converts magnetic energy into ion thermal and kinetic energy from the 3D contraction of reconnected magnetic field lines. The ions are however accelerated in both the toroidal and the poloidal direction. This paper presents the implementation of a novel Doppler spectroscopy diagnostic, designed to obtain the full 3D plasma fluid velocity profile by tomographic reconstruction. A simulation of the experimental setup determines the minimum number of line-of-sights (projections) and their optimum locations. The synthetic noisy measurements are then fed into the reconstruction program, which uses a spherical harmonics series expansion to obtain the solenoidal component of the velocity vector [2]. Progress towards experimental measurements will be presented. The diagnostic will help determine the ion self-helicity of a compact toroid in the context of two-fluid MHD relaxation theory [3]. [1] Y. Ono et al, Phys. Rev. Lett., 76, 18 (1996) [2] A.L. Balandin, Y. Ono, J. Comp. Phys., 202 (2005) 52-64 [3] L. Steinhauer, A. Ishida, Phys. Rev. Lett., 79, 18 (1997)   

Evaluation of Kinematic Viscosity of Rotating Cylindrical Plasmas Using Flow Velocity Profile Measurements

Viscosity plays a crucial role in determining plasma flow structures. In torus plasmas, for example, the poloidal plasma flow driven by radial electric field produces the toroidal flow through the effect of viscosity. In a laboratory plasma, spontaneous formation of a stable vortex with a density hole around the central axis has been observed. The vorticity distribution around the central axis is well approximated by Burgers vortex in viscous fluids. The kinematic viscosity estimated from the size of the vortex is three to four orders of magnitude larger than the classical value. Although the importance of viscosity on flow structure formation is well recognized, viscosity measurements in laboratory plasmas have been seldom performed. Here we present and discuss an evaluation method of effective plasma viscosity utilizing flow velocity profile measurement. We consider the azimuthal component of ion fluid equation imposing axisymmetric condition. Then the kinematic viscosity is expressed by known quantities related to the flow profile. The result obtained by applying this method to a rotating argon plasma will be shown in the meeting.   

Dynamics of Magnetic Flux Ropes in a Laboratory Plasma

The behavior and interaction of magnetic flux ropes have long been a topic of interest to solar and space plasma physicists. (Gekelman, et al. IEEE Trans. Plasma Sci. \textbf{20}, 614. Furno, et al. Phys. Plasmas \textbf{12}, 055702.) Very few laboratory experiments have been performed as it is necessary to have a relatively collisionless plasma and currents with significant self-generated fields. Movable lanthanum hexaboride (LaB$_6$) cathodes have been developed to study the 3D dynamics of flux ropes in the Large Plasma Device (LaPD). Each 2.5~cm LaB$_6$ cathode can produce current densities of 5-20 A/cm$^2$ and $\Delta B/B \sim 10\%$. The background plasma ($n \sim 2 \times 10^{12}$ cm${}^{-3}$, $d \sim 60$ cm, $L \sim 18$ m, and $\tau_{\mbox{rep}}= 1$ s) is produced with a DC discharge using a pulsed barium oxide-coated cathode. The two or more current channels are created by biasing the LaB$_6$ cathodes with respect to a grid anode at the opposite end of the chamber. They are emitted parallel to each other and the guide field. $\mathbf{J} \times \mathbf{B}$ forces cause the currents to move across the field and interact. Each cathode can be positioned freely within a transverse plane of the cylindrical LaPD. We plan to make detailed volumetric measurements of the magnetic fields and flows generated by the current channels. Diagnostics include $\dot{B}$, Langmuir, and Mach probes, and laser induced fluorescence.   

Ultracold Plasma Expansion in Magnetic Field

We image the ion distribution of an ultracold neutral plasma by extracting the ions with a high voltage pulse onto a position-sensitive detector. Early in the lifetime of the plasma, the size of the image is dominated by the Coulomb explosion of the dense ion cloud. At about 20 microseconds the image size is at a minimum and then linearly increases, reflecting the true size of the plasma. The ion cloud maintains a Gaussian density profile throughout the lifetime of the plasma. By 2-D Gaussian fitting of the ion image, we obtain the transverse width, perpendicular to an applied magnetic field. The longitudinal width is obtained from the temporal width of the ion current. Without magnetic field, the plasma expansion velocity at different initial electron temperatures matches the result obtained by measuring the plasma oscillation frequency (Killian etc, PRL, 85, 2 (2000)). As we increase the magnetic field up to 70 Gauss, we find that the expansion velocity decreases, roughly scaling as B$^{-1/2}$. This field dependence is unlike expectations from ambipolar diffusion, which has a diffusion constant that scales as B$^{-2 }$. Possible models for the expansion will be discussed.   

Models of low-beta plasma expansion across magnetized vacuum

Detailed understanding of the microphysics associated with dynamic penetration of low-beta plasmas across magnetic fields has important implications for a number of applications including magnetic-fusion-energy (MFE), high-power transmission-lines, and charged-particle-beam diodes. Analytic models providing linear growth rates and characteristic wavelengths and frequencies for unstable modes at the interface between plasma and vacuum regions are presented and compared with detailed particle-in-cell simulations. The simulations treat both collisionless and collisional plasma regimes in a variety of configurations. Results of this combined theoretical analysis are compared with measurements from several experiments including magnetized electron-beam-diodes and high-power, magnetically-insulated transmission-lines. Potential applications of this modeling to MFE are discussed.   

Numerical Modeling of a Magnetic Nozzle

We present computational study of a magnetic nozzle, which is a component of the VASIMR (Variable Specific Impulse Magnetoplasma Rocket) plasma-based propulsion system for a space vehicle. The magnetic nozzle transforms ion gyromotion into directed axial motion, adiabatically accelerating the plasma, and enabling plasma detachment from the spaceship via self-consistent magnetic field modification. VASIMR employs ion cyclotron resonance heating to deposit rf-power directly to the plasma ions created by the low energy plasma source. We have developed a numerical code to model the axisymmetric nozzle within the framework of collisionless MHD with an azimuthal ion velocity spread. The code implements a reduced model that consists of truncated steady-state equations for the velocity space moments of the ion distribution function and takes advantage of the plasma flow paraxiality. This makes it possible to study the conversion of the ion gyro-energy at the nozzle entrance into the energy of the directed flow at the exhaust. The magnetic field in the vacuum, which is not assumed to be paraxial, is calculated using a given magnetic coil configuration in the presence of plasma. From the computed steady-state flow configuration, the code evaluates magnetic nozzle efficiency, defined as the ratio of the axial momentum flux in the outgoing flow to the axial momentum flux in the incoming flow.   

Ambipolar acceleration of ions in a magnetic nozzle

We consider collisionless plasma flow through a nozzle that has a magnetic mirror configuration. The incoming subsonic flow of cold ions is accelerated towards the mirror by an ambipolar electric field resulting from the electron pressure. The flow velocity achieves the speed of sound in the mirror, after which the flow becomes supersonic and further accelerates downstream. For incoming Maxwellian electrons, plasma density upstream from the mirror satisfies the Boltzmann relation, with $n \propto \exp (|e| \varphi / T)$, where $\varphi$ is the electrostatic potential. Downstream from the mirror, the Boltzmann relation is no longer valid as some areas of phase-space become depleted in a collisionless flow. The depletion results from the nonmonotonic nature of the effective potential $U = \mu B - |e| \varphi$ for electrons with sufficiently large magnetic moment $\mu$. We examine how the depletion of the electron population affects the profile of the electrostatic potential, the plasma density profile, and the ensuing ion acceleration.   

Plume Narrowing in a Cylindrical Hall Thruster

The cylindrical Hall thruster features high ionization efficiency, quiet operation, ion acceleration in a large volume-to-surface ratio channel, and performance comparable with the state-of-the-art conventional Hall thrusters [1]. The magnetic field of the cylindrical Hall thruster also differs from conventional annular Hall thrusters in that significant numbers of electrons can be trapped through magnetic-electric mirroring. Recently, by overrunning the discharge current, these thrusters also featured very significant plume narrowing, accompanied by significantly enhanced efficiencies [2]. This plume narrowing may be related in detail to the unusual magnetic configuration of the cylindrical thruster and the populations of electrons that it can support. \newline \newline [1] Y. Raitses and N. J. Fisch, Parametric Investigations of Non-Conventional Hall Thruster, Physics of Plasmas 8, 2579 (2001). \newline [2] Y. Raitses, A. Smirnov, and N. J. Fisch, Enhanced Performance of Cylindrical Hall Thrusters, Applied Physics Letters 90, 221502 (2007).   

Time dependent VISAR current diagnostic for pulsed power loads

B-dot probes, placed in the power feed slightly upstream of the load, are the standard technique of measuring the current delivered to pulsed power loads such as Z pinches. Since current losses may still occur downstream of the probe, the measured signal may not represent the current actually delivered to the load. In this paper, a method is proposed to measure the time dependent current actually delivered to the load with potentially much higher precision than B-dot probes. In this method, the velocity induced by magnetic pressure exerted on a metallic wafer is recorded with a velocity interferometer for any reflector (VISAR) probe located after the load. Then, a parallel optimization code is used to vary the current profile in 1D simulations until the calculated velocity profile matches the experimentally measured velocity profile. Design constraints, sensitivity, and error will be discussed as well as considerations for an intense radiative environment.   

Validation of an ablation model for simulating wire array z-pinches

We have developed a 3D computational model of cylindrical wire array z-pinches. In lieu of simulating individual wires, we have incorporated a steady state model of wire ablation physics [E. P. Yu, B. V. Oliver, P. V. Sasorov et al., Phys. Plasmas 14, 022705 (2007)] into our 3D, radiation MHD code ALEGRA. We present results of a validation study using radiation pulses, currents, and density profiles from experiments with single wire arrays on the Z accelerator. By tuning the ablation rate in 2D and 3D simulations of arrays with different masses, radiation pulses are produced that are within the measurement uncertainty, which indicates how the mass ablation rate scales with wire radius. Azimuthal current paths in 3D simulations of a 60 degree periodic wedge lead to mass and current distributions that are significantly different than in 2D, and are more consistent with observations.   

Two-Dimensional Radiation MHD Modeling of Gas Puff Z-Pinch Implosions

A 2D radiation MHD model was recently developed to investigate large diameter nozzle argon Z-pinch experiments performed on the Decade Quad and Z generators.\footnote{J.W. Thornhill, et. al. Phys. of Plasmas \textbf{14}, 063301 (2007).} This model incorporates into the Mach2 MHD code a self-consistent calculation for non-LTE kinetics and ray trace based radiation transport. Such a method is necessary in order to model opacity effects and the high temperature state of these K-shell emitting plasmas. Here, the model is used to demonstrate that increasing the spatial resolution produces significantly better agreement between calculated and experimental current profiles, implosion times, and K-shell radiative powers than attained previously. The resolution is increased by employing a moving rectilinear grid for which each radial grid line moves with the axially averaged radial Lagrangian velocity. The 2D results are processed to generate axially and temporally resolved spectra. By comparing them with experimental spectra, one can assess the capability of a 2D code to accurately model the multi-dimensional Z-pinch dynamics.   

Lumped-state CRE Modeling of the Ionization Dynamics of O- and N-like Krypton

An often used approximation employed to simplify the problem of modeling the L- and M-shell ionization dynamics of moderate to high atomic number plasmas is to lump the states within each $n\ell$ multiplet of each ionization stage, and historically, this approximation has been applied assuming the multiplet substates are in LTE with respect to one another. In both Fe and W Z-pinch plasmas, this assumption has been shown to break down in ionization stages where the ground state has no multiplet structure \footnote{K. G. Whitney, et. al., J. Phys. B, \bf{40}, 2747 (2007).}. In this talk, we study the subpopulation dynamics in O- and N-like ionization stages where significant amounts of population can be stored in excited states and where ground states have multiplet structure. The non-LTE behavior of the following states is calculated: the ground states, the $\Delta n=0$, and the $2p^33\ell$ or $2p^23\ell$ excited states of O-like and N-like Kr respectively, and used to determine the impact on lumped state excitation and ionization rates and on the MHD of Z-pinch Kr implosions. In particular, the reduction of the Einstein decay rates of the $n=3$ states as a function of ion density is calculated.   

Wire Ablation Plasma Source Studies at Sandia National Laboratories

Experiments are underway to investigate wire ablation plasmas as potentially tunable sources for applications such as intense electron beam transport and focusing. For these studies, one or more fine wires (100 micron diameter) are driven by a microsecond long, capacitive discharge (80kA, 100kV) to generate a plasma. High resolution visible/uv spectroscopy is used to spatially and temporally characterize the plasma throughout the pulse. Measured lineshapes and intensities are compared with time-dependent, collisional-radiative calculations to obtain plasma densities and temperatures. Changes in drive current, wire geometry, and materials are studied to determine the extent to which ablation plasma parameters can be controlled. Results are compared to MHD calculations and scaling laws for plasma mass ablation rates from wires.   

Investigations of stagnated plasma conditions and opacity for K-shell x-ray sources at the Z Accelerator

In recent years, experiments have been performed at the Z accelerator to study K-shell x-ray sources, including Al (1.7 keV), Ar (3.1 keV), Ti (4.7 keV), SS (6.7 keV), and Cu (8.4 keV). K-shell scaling theories have shown that the temperature of the plasma necessary to produce the K-shell varies with atomic number, T$_{e}$ = 0.3*Z$^{2.9}$ eV, where Z is the atomic number and T$_{e}$ is the electron temperature. This suggests that for Cu, T$_{e}$ must be $>$ 5 keV. In this presentation, variations observed in T$_{e}$ and ion densities from the different load materials are presented. These plasma conditions are inferred from time-integrated, spatially-resolved spectra, and spatially-integrated, time-resolved spectra. Measured T$_{e}$ confirm the scaling theory predictions, although in some cases the conditions are achieved only in isolated regions of the pinch. The impact of opacity on the K-shell emissions has been directly observed by comparing the line intensities from optically thin dopant materials with those of the main load constituents. Al loads show significant opacity; by contrast, Cu loads appear to be optically thin. Sandia is a multi-program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under Contract DE-AC04-94AL85000.   

Quantitative investigation of mass ablation rates of wire arrays at current levels from 80kA to 1MA

We present investigations of mass ablation rates in x-pinches and wire arrays at different current levels. Interferometry and radiography are used with x-ray framing cameras to investigate ablation from 80 kA to 1MA. The radial ablation flare structure is studied, along with the formation of precursor plasma structures. Quantitative comparisons will be made to analytical and MHD modeling.   

Quantitative Measurements of Ablation in Wire Array Z-Pinches

The long-time scale ablation of the wires in a wire array z-pinch is crucial in determining its subsequent implosion and X-ray emission. Using a combination of interferometry and Faraday probing, we report on direct measurements of the current and mass density profiles in cylindrical, radial and inverse wire array z-pinches leading up to and during implosion. The results are compared and contracted to the rocket ablation model and to both 2 and 3-D MHD simulations. This research was sponsored by Sandia National Labs and the NNSA under DOE Cooperative Agreement DE-F03-02NA00057.   

Mitigation of end-effects in wire array z-pinches through hardware modification

Symmetry is a crucial factor for various applications of wire array z-pinches, including Inertial Confinement Fusion and K- shell x-ray source development. Previous work has shown that a non-uniformity is initiated near the cathode wire contact of a z-pinch. An imploding bubble expands axially until it stagnates prematurely on axis prior to the main x-ray pulse, leading to regions near the cathode in which no x-ray output is present at peak emission. The effects of such non-uniformities are likely to be particularly significant for the large initial load diameters used to achieve appropriate plasma conditions for K- shell emission from mid-Z elements at facilities such as Z. We discuss experiments on the Saturn accelerator which attempt to mitigate this effect by placing a step on the cathode to obstruct the propagation of the bubble towards the axis, hence preventing the non-uniformity on axis.   

Relative Timing of Coronal Plasma Formation for Individual Wires in a Wire Array Z-Pinch

We are investigating the initial stages of plasma formation around individual wires in low-wire-number wire-array z-pinches using the 1 MA COBRA pulsed power generator.~ The experiments are designed to examine the time-dependence of the current distribution among individual wires and pairs of wires in wire-array z-pinches using 5-10 aluminum or tungsten wires. To accomplish this we inductively isolate the wires, or pairs of wires, from each other using segmented load hardware. Each segment is able to hold one or two wires and is connected to machine ground through its own return current post. Experimental goals include determining the timing of the initiation of coronal plasma around each wire and determination of parameters that affect this timing.~ In addition, we will compare the early time rate of rise of the total currents from the segmented anode experiments to that from conventional arrays in order to make estimates of the temporal spread in coronal plasma formation when the anode is not segmented. *This research was supported by the Stewardship Sciences Academic Alliances program of the National Nuclear Security Administration under DOE Cooperative agreement DE-FC03-02NA00057 and by Sandia National Laboratories contract AO258.   

Time Evolution of the Magnetic Field Topology of Cylindrical Wire Array Z-Pinches

We study the influence of the magnetic field topology and the global field penetration time on the ablation plasma dynamics of individual wires in wire array Z-pinches. Knowledge of the magnetic field configuration is necessary for understanding the ablation plasma acceleration process near the wires and the validity of constant ablation velocity approximation as applied to the 1 MA COBRA pulsed power generator. Three-dimensional resistive MHD simulation results suggest that a change in the global magnetic field topology is critical to initiating inward flow of the ablation plasmas. These simulation results are investigated experimentally by using B-dot probes to track the evolution of the field topology over time for small wire number cylindrical arrays on COBRA. This research was supported by the Stewardship Sciences Academic Alliances program of the National Nuclear Security Administration under DOE Cooperative agreement DE-FC03-02NA00057.   

Studies of the Dynamics of Ablation Stream development in Wire Arrays on COBRA

Wire-array simulations with the 3D GORGON code (see adjoining poster by Martin et al.) show a characteristic evolution in the development of streams of ablated material ejected from the wires toward the array axis. In simulations of aluminum arrays, the fundamental behavior occurs in two steps. The first is the development of coronal plasma that is trapped around the wire core in closed ``local'' magnetic flux. This coronal plasma, together with the closed flux, is then accelerated inward after a certain ``dwell'' time, leaving behind a radially distributed current density with entirely open ``global'' magnetic field lines, producing smooth, distributed acceleration of ablated plasma inward from the wire core until the onset of the final implosion. Interpretation of these dynamics in terms of simple physical modeling will be discussed, and experimental evidence of these phenomena from imaging and magnetic field diagnostics on arrays on the COBRA facility at Cornell will be presented.   

Studies of Hot Spots in Wire-Array Z-Pinches and X-Pinches

Wire array Z-pinches and X-pinches radiate in both the soft (sub-keV) and hard (multi-keV) x-ray ranges. Hot spots are brief and intense x-ray bursts at localized small points within a Z- or X-pinch. Experiments have been carried out on the 1MA COBRA and 0.5 MA XP pulsed-power generators to investigate the temporal development, spatial structure, and x-ray emission structure of the hot spots in X-pinches and Z-pinches made from multiple fine metal wires. A Kentech x-ray streak camera and diamond photoconducting diodes (PCDs) with various filters were used to study the time evolution of the energy distribution emitted from the hot spots. Time integrated self emission pinhole images with various filters and time-gated four frame MCP images were used to study the spatial structure of hot spot x-ray emission.   

X-pinch Wire-number Scan at 1 MA

X pinches driven by 0.2-0.4 MA produce 1 $\mu$m, 10-100 ps, $\sim$1 keV, $\sim$0.1x solid-density plasmas. We consider whether $\sim$1 $\mu$m plasmas are also produced at 1 or 6 MA, since such plasmas could have more extreme properties [e.g., Chittenden et al., Phys Rev Lett (2007)]. A 6 MA X-pinch on SATURN is massive at $\sim$100 mg/cm, requiring either large numbers of wires or a few very thick wires. To understand the issues with such an extrapolation, we studied 3 mg/cm X pinches on the 1 MA COBRA facility. Results from 2- to 64-wire W X pinches will be shown, along with results with novel configurations and large numbers of Ti, Al, and Mo wires. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the National Nuclear Security Administration (NNSA) under DE-AC04-94AL85000. This work was supported by Laboratory Directed Research and Development at Sandia, DOE Grant No. DE-FG03-98ER54496, by Sandia National Laboratories Contract No. AO258, and by the NNSA SSAA program, Cooperative Agreement No. DE-FC03-02NA00057.   

Quantification of axially correlated ablation in z-pinch wire arrays.

Wire array z-pinch experiments were performed on the 1 MA, 100 ns rise-time COBRA facility at Cornell University. Experiments utilized 7-wire-arrays, including one pair of identical 7.5 micron diameter tungsten wires and one pair with a 7.5 and a 5.0 micron wire, both spaced 240 nm apart. X-ray backlighters were used to image the wire cores. Axially correlated ablation regions between wires in the equal-diameter pair were observed. The unequal-diameter pair tested whether ablation regions in the smaller, more quickly ablated wire imprinted into the larger wire later in time. Comparisons will be presented of the fractional-lengths of correlated ablation regions for both cases.   

A higher-dimensional theory of electrical contact resistance

Electrical contact resistance is important to wire Z-pinches, high power microwave (HPM) sources, and carbon fiber field emitters, etc. It determines the amount of current delivered to the Z-pinch wire load, and good rf contacts are critical to HPM source development. The classic theory of Holm [1] assumes that the electrical contact has a finite area, but has a zero thickness in the direction of current flow from one region to the other to which electrical contact is to be made. In this paper, we use a simple geometry to calculate the resistance of an electrical contact that has a finite length in the direction of current flow. An analytic scaling law, to be developed, would then allow an assessment of the change in the contact resistance in response to an external force, whose presence would lead to a change of the contact geometry. This change may be related to the hardness of the materials. This work was supported by Sandia and AFRL. \newline \newline [1] R. Holm, Electric Contacts (Springer-Verlag, 1967).   

Study of Wire Contact Resistance in Single and Multi-wire Z-Pinch Experiments

Contact resistance of single and multi-wire array z-pinch has been measured for aluminum, stainless steel, and tungsten wires; diameters ranged from 7.5 to 30.5 micron. DC contact resistance in these experiments accounted for approximately 80{\%} of load resistance, and resistance measurements varied from wire-to-wire by up to 15{\%}. These DC measurements show that the resistance is highly dependent on both the wire material and the mass of the wire weights (0.8 g to 3.6 g). Marx pulses of 120 kV, 18 kA, 150 ns risetime were applied to the z-pinch. Wire plasma expansion velocity was measured using a streak camera, and expansion profile of the wires was determined using laser schlieren imaging. Electron temperature of individual wire plasmas is being determined by visible/UV spectra. Results will be presented of several methods being explored to reduce the contact resistance. *This work was supported by U. S. DoE through Sandia National Laboratories award number 240985 to the University of Michigan. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under Contract DE-AC04-94AL85000.   

Designs and Plans for MAIZE: a 1 MA LTD-Driven Z-Pinch

We present designs and experimental plans of the first 1 MA z-pinch in the USA to be driven by a Linear Transformer Driver (LTD). The Michigan Accelerator for Inductive Z-pinch Experiments, (MAIZE), is based on the LTD developed at the Institute for High Current Electronics, utilizing 80 capacitors and 40 spark gap switches to deliver a 1 MA, 100 kV pulse with $<$100 ns risetime. Designs will be presented of a low-inductance MITL terminated in a wire-array z-pinch. Initial, planned experiments will evaluate the LTD driving time-changing inductance of imploding 4-16 wire-array z-pinches. Wire ablation dynamics, axial-correlations and instability development will be explored. *This work was supported by U. S. DoE through Sandia National Laboratories award number 240985 to the University of Michigan. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under Contract DE-AC04-94AL85000.   

Measurements of plasma conditions in precursor plasmas at the 1-MA Zebra facility

Precursor plasmas, both the early time precursor flow of mass and the accumulation of this material on axis, were observed on many z-pinch experiments at various facilities, including low current ($<$ 1MA) and high current ($>$15 MA, Z) facilities. The impact of these precursors on stagnated plasmas, and targets such as those used for ICF experiments, is still under evaluation. Experiments were performed at the UNR 1-MA, 100ns Zebra facility to study these precursor plasmas with Cu wire arrays. Significant precursor radiation at photon energies $>$ 1 keV was observed on filtered PCDs. T$_{e}$ and n$_{e}$ of the precursor radiation were obtained from modeling of time-resolved spectroscopy of the Cu L-shell emissions for 6 wires on 12mm diameter loads. The precursor plasma temperatures are consistently $>$250eV. Time resolved pinhole images were also collected, which show bright spots of radiation along the axial length of the pinch. Sandia is a multi-program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the US DOE under Contract DE-AC04-94AL85000. Work was also supported by the DOE/NNSA Coop. agr. DE-FC52-06NA27616, 06NA27588, 06NA27586, and by fellowship from the NPSC with SNL.   

Implosion Dynamics and X-Ray Production in Cylindrical Wire Arrays 1-16 mm in Diameter

Implosions and x-ray production in low wire number cylindrical wire arrays 1-16 mm in diameter were investigated in the 1-MA Zebra generator. Wire arrays 2-5 mm in diameter produce enhanced soft x-ray power in comparison with 12-16-mm diameter loads. Compact cylindrical arrays generate a high power x-ray pulse with a short 6-ns rising edge despite a fall of calculated kinetic energy of imploding plasma. Ablating plasma accumulates faster in volume of compact arrays and small-scale plasma turbulence could be involved to fast plasma heating. In 1-mm 8 wire cylindrical loads radiated power drops and the soft x-ray pulse has a multi-burst structure that is similar to x-ray radiation of the single wire z-pinch. Implosion dynamics and precursor formation are compared in wire arrays of different diameters. Work was supported by the DOE/NNSA under UNR grant DE-FC52-06NA27616.   

Effect of an axial wire on wire array z-pinch dynamics

Conical wire arrays have previously been studied at Imperial College mainly as a source of plasma flows similar to astrophysical jets. The central region of the array itself is well suited to studying the z-pinch stability in the presence of axial flows. Supersonic plasma streams converge on the array axis, where the energy associated with the radial momentum is thermalized and radiated, whilst the axial component is maintained. Placing a wire on axis is expected to introduce a radial profile of the axial velocity and to provide early on a current carrying path for the plasma flowing along the axis. The experiment investigated the effect of a central wire upon Al wire arrays at 1 MA. The results were compared with reference results - conical arrays without central wire and cylindrical arrays with and without central wire. The inclusion of the axial wire significantly affected the dynamics of the conical wire array implosion. Time integrated self-emission pinhole imaging shows that the axial wire allows the stagnated pinch to become significantly more uniform. The broad spectral range radiation measured with bolometers indicates that the presence of the axial wire on axis causes an enhancement in the total energy emitted.   

Investigation of particle beams in 1-MA wire array z-pinches by Faraday cups

A single Faraday cup and a linear array of cups were applied to investigate generation of particle beams in implosions of wire arrays in the 1-MA Zebra generator. The linear array includes five Faraday cups placed on the length of 16 mm and provides measurements of particle beams with spatial and temporal resolution. Cylindrical, nested and star-like arrays were investigated with focus on generation of electron beams. Experimental results are compared with different models of generation of particle beams. Work was supported by the DOE/NNSA under UNR grant DE-FC52-06NA27616.   

Plasma Formation from a Single Solid Conductor Carrying a Multi-Magaampere Current

A number of pulsed-power experiments in which, multi-megaampere currents melt solid conductor surfaces and turn them into hot plasmas in a matter of microseconds or less, report on the critical impact the initial plasma formation process has on the characteristics of the entire discharge. This work investigates the features of the plasma formation in a single solid conductor carrying a multi-megaampere current by means of 2-D magnetohydrodynamic simulations. The simulations employ the state-of-the-art code MHRDR, and are performed for a wide range of conductor radii. An important challenge for modeling is to predict the plasma formation threshold and, the maximum magnetic field on the conductor surface that can be obtained prior to current disruption. The results of this study can be generalized to the more complicated problem of modeling a moving liner driven by a multi-megaampere current.   

Radiography using a dense plasma focus device as a source of pulsed X-rays

Soft and hard X-ray emissions have been studied in the FN-II, which is a small dense plasma focus machine (5 kJ), operating at the Instituto de Ciencias Nucleares, UNAM, using aluminum filtered pin-hole cameras. Their angular distribution has been measured using TLD-200 dosimeters [1]. Their temporal evolution has been observed by means of a PIN diode, and scinltillators coupled to photomultipliers outside the discharge chamber. The X rays source can be concentrated by placing a needle on the end of the electrode. X-rays crossing across a 300 micron aluminum window, through the axis of the machine, can be used to obtain high contrast radiographs, with an average dose of 0.4 mGy per shot. In contrast, the average dose with a hollow cathode is 0.2 mGy per shot. This work is partially supported by grant IN105705 de la DGAPA-UNAM. \newline [1] F. Castillo, J.J.E. Herrera, J. Rangel, I. Gamboa, G. Espinosa y J.I. Golzarri ``Angular Distribution of fusion products and X-rays emitted by a small dense plasma focus machine'' \textit{Journal of Applied Physics} \textbf{101} 013303-1-7 (2007).   

Reconstruction of Neutron and Deuteron Energy Spectra in Z-pinch Experiments

The neutron energy spectra were reconstructed in Z-pinch experiments where deuterium atoms were present in a load. The reconstruction was based on the time-of-flight method in which time-resolved neutron detectors were placed at various distances from the neutron source. There are several theoretical approaches to the development of reconstruction algorithms (Monte Carlo, etc.). The improved Monte Carlo reconstruction technique, which simultaneously used neutron detectors placed on two opposite sites from the source, was applied to process data from experiments on the S-300 generator (Kurchatov Institute, Moscow). Since these experiments contained a small number of neutron detectors in one direction, a specific reconstruction procedure was used. From the reconstructed neutron energy spectra, also the energy distribution function of deuterons producing fusion neutrons could be calculated. The characteristics of the neutron scintillation detector and the influence of scattered neutrons were taken into account to estimate the error in the reconstruction.   

Characteristics of extreme ultraviolet radiation from laser triggered vacuum spark discharge plasma

Comparative experimental studies of the vacuum spark discharge triggered by nanosecond duration laser pulses are performed under differing electrical conditions. A maximum discharge current of about 6 kA with a pulse width of 500 ns was supplied to anode-cathode gap. In our system, after laser was irradiated on electrode surface made of Sn, the main discharge will be triggered and extreme ultraviolet (EUV) radiation will occur from the generated Sn plasma between electrodes. In present study, EUV radiation emitted from laser triggered Sn discharge produced plasma was quantitatively measured using an in-band calorimeter. Both time-integrated visible image and time-resolved in-band source image measurements were also conducted using a pinhole camera system. The details of experimental results will be discussed.   

Soft X-ray emission from plasma channel created by wire explosion in water

This year it was designed and built a new apparatus SHOW-WEX (SHOck Wave -- Wire Explosion), which is designed as a soft X-ray source of coherent radiation with wavelength below 20~nm. The radiation will be produced in a plasma channel created by a wire explosion in a liquid where the proximity of liquid wall stabilizes plasma channel similarly as proximity of solid wall stabilizes a Z-pinch in a capillary. Moreover, if the pressure in a liquid is increased (or locally increased by focused shock wave, which is more efficient and a higher pressure can be reached), then the plasma expansion is slowed down, the stability of plasma is enhanced, and the requirements on the driver can be softened. The first experimental data on wire explosions i.e. time dependences of charging voltage, discharge current, and soft X-ray radiation emission (measured by vacuum photo diode) are presented.   

Improved EOS for Describing Off-Hugoniot States in Epoxy/Foam IC Targets

Hydrodynamic experiments typically rely on pre-shot target characterization to predict how initial perturbations in the material interfaces will affect the late-time hydrodynamic mixing. The condition, particularly temperature, of these perturbations at the time of shock arrival dominates their eventual late-time evolution. Modeling of off-Hugoniot states in an expanding interface subjected to a shock reveals the importance of using a chemically complete description of the materials. In the experiment modeled, an epoxy/foam layered package was subjected to tin L-shell radiation, producing an expanding assembly at a well-defined temperature. The evolution of the shocked epoxy-foam interface was imaged with x-ray radiography. Modeling of the data with the hydrodynamics code RAGE required condensation of the plasma to be explicitly included. EOS were prepared that included formation of polyatomic species in the states present before shock arrival. These EOS improved fidelity of the modeling to measured details of interface behavior.   

Preheat Measurements for Supernova Hydrodynamics Experiments

The use of multi-kilojoule, ns lasers to launch shock waves has become a standard method for initiating hydrodynamic experiments in the field of Laboratory Astrophysics. However, the intense laser ablation that creates moving plasma also leads to the production of unwanted energetic x-rays and suprathermal electrons, both of which can be sources of material preheating. In principle, this preheat can alter the conditions of the experimental setup prior to the desired experiment actually taking place. At the University of Michigan, ongoing Rayleigh-Taylor instability experiments are defined by precise initial conditions, and potential deformation due to preheat could greatly affect their accuracy. An experiment devised and executed in an attempt to assess the preheat in this specific case will be presented, along with the quantitative analysis of the data obtained.   

Exploration of Plasma-Jet Magneto-Inertial Fusion Burn Dynamics

Magneto-inertial fusion (MIF) implodes a conducting liner, compressing a magnetized plasmoid to fusion-relevant temperatures. The target's magnetic field reduces thermal conduction, and the liner's inertia provides transient plasma stability and confinement. The present work explores the burn dynamics of using plasma jets to form the MIF liner [1]. Particular attention is paid to the question of burning the thin inner layer of the liner. This exploration of MIF parameter space yields promising fast shock and long dwell time implosion modes. The investigation uses UW's 1-D Lagrangian radiation-hydrodynamics code, BUCKY, which solves single-fluid equations with ion-electron interactions, PdV work, table-lookup equations of state, fast-ion energy deposition, and pressure contributions from all species. Extensions to the code include magnetic field evolution as the plasmoid compresses plus dependence of the thermal conductivity and fusion product energy deposition on the magnetic field. \newline [1] Y.C. F. Thio, et al., ``Magnetized Target Fusion in a Spheroidal Geometry with Standoff Drivers,'' in Current Trends in International Fusion Research, E. Panarella, ed. (National Research Council of Canada, Ottawa, Canada, 1999), p. 113.   

EMHD Calculations of Plasma Jet Acceleration

The acceleration of plasma jets (density $n_i \sim 10^{16} - 10^{17}$~cm$^{-3}$) by magnetic pressure ($B \sim 1$~Tesla) is characterized by the presence of a thin, non-equilibrium current sheath at the plasma-vacuum interface. The sheath is where the electric fields, both inductive (in the plane of the sheath) and electrostatic (normal to the sheath), that accelerate the plasma are generated. We are using a hybrid numerical model with kinetic ions and a massless electron fluid to simulate this phenomenon. A hybrid treatment is desirable because, on the one hand, it avoids the small time-steps needed by kinetic electrons, and on the other hand, the ion mean free path and ion cyclotron radius can be comparable to the sheath thickness. The latter features are important for the parameters of interest, and are outside the scope of the MHD approximation. The main numerical difficulty is in treating the motion of the thin current sheath, with its discontinuous magnetic field gradient, through the stationary mesh. In 1-D, this has been overcome by solving for the magnetic vector potential. We will present results extending the algorithm to 2- and 3-D calculations.   

Plasma jets merging simulation

The progress on numerical 3D simulations of high density high Mach number plasma jets merging is presented. The modeling was conducted with the particle-in-cell LSP code [1]. A few hypersonic plasma jets (Mach number between 5 and 50) with high density (within the range of 10$^{15}$-10$^{17}$ cm$^{-3})$ were injected for merging in a low density low temperature neutral background gas ($\approx $10$^{13}$ cm$^{-3})$. The dynamics of the merging was studied. Onset of a strong instability, which was observed in the modeling of two, three and five plasma merging jets [2], can essentially affect the front formation and finally can lead to a high turbulent flow. The nature of the instability is discussed. The progress on HyperV plasma accelerator experiment simulation and comparison with a recent experimental data is also reported. \newline [1] T. P. Hughes, S. S. Yu, and R. E. Clark, Phys. Rev. ST Accel. Beams 2, 110401, 1999. \newline [2] S. A. Galkin, I. N. Bogatu, J. S. Kim, to be published in PPPS/ICOP 2007 Conference Proceedings. Work is supported by the US DOE SBIR grant and by US DOE Office of Fusion Energy Sciences.   

Dense Hypervelocity Plasma Jets

We are developing high velocity dense plasma jets for fusion and HEDP applications. Traditional coaxial plasma accelerators suffer from the blow-by instability which limits the mass accelerated to high velocity. In the current design blow-by is delayed by a combination of electrode shaping and use of a tailored plasma armature created by injection of a high density plasma at a few eV generated by arrays of capillary discharges or sparkgaps. Experimental data will be presented for a complete 32 injector gun system built for driving rotation in the Maryland MCX experiment, including data on penetration of the plasma jet through a magnetic field. We present spectroscopic measurements of plasma velocity, temperature, and density, as well as total momentum measured using a ballistic pendulum. Measurements are in agreement with each other and with time of flight data from photodiodes and a multichannel PMT. Plasma density is above $10^{15}~cm^{-3}$, velocities range up to about 100 km/s. Preliminary results from a quadrature heterodyne HeNe interferometer are consistent with these results.   

Probe Measurements on the HyperV Plasma Gun

Final diagnostic measurements are underway on the HyperV plasma gun prior to installation on the Maryland Centrifugal eXperiment (MCX). These measurements will help understand penetration of the plasma jet through the MCX magnetic field. We describe both magnetic and pressure probe data. A downstream fast pressure probe confirms a steep increase in mass density coincident with the arrival of a luminous front. An array of fixed magnetic induction probes are installed in the pinch section. These are used to investigate the current and electromagnetic structures during the final phase of the plasma jet formation and acceleration. Both sets of probe data are compared to the jet's visible emissions and measurements of gun current and voltage. We also outline the design of new movable magnetic probes and access ports for optical diagnostics, to be located in the main acceleration section of the gun.   

Laser-Driven Magnetic-Flux Compression Experiments on the OMEGA Laser

Magnetic-flux compression with lasers relies on the kinetic energy of the target shell to compress magnetic flux frozen in the highly conductive target plasma. It is expected to facilitate implosions where seed fields amplified to multimegagauss levels can reduce the thermal losses in the ICF hot spot by inhibiting the electron thermal transport out of it. This can potentially provide for implosions with higher gain (or lower ignition energy requirements) than what is possible in conventional ICF. The successful generation of very strong magnetic fields can also be used in a variety of non-fusion experiments such as laboratory astrophysics, material science, etc. The main concept and the use of a compact magnetic pulse system to seed a macroscopic magnetic field into cylindrical DD-filled targets, which are radially driven with the OMEGA laser, are described. A Helmholtz-type, single-turn coil provides the $\sim $0.1-MG seed field. Compression of the internal magnetic flux is measured by the proton deflectrometry technique\footnote{ C. K. Li \textit{et al}., Rev. Sci. Instrum. \textbf{77}, 10E725 (2006).} optimized for this application. Results from the initial proof-of-principle experiments are discussed. This work was supported by the U.S. Department of Energy Office of Inertial Confinement Fusion under Cooperative Agreement DE-FC52-92SF19460.   

Development and benchmarking of radiation transport models in LSP.

LSP is a hybrid particle-in-cell (PIC) code widely used to model various plasmas. We report on the recently added improvements to the modeling of radiation and atomic physics within LSP. Multi-group radiation diffusion in 2D Cartesian and cylindrical geometries has been implemented and tested. Also, the ability to utilize detailed opacity and equation-of state tables has been added. We will provide details of the implementation, as well the results of various benchmarks against analytic solutions to the radiation transport problems in multi-dimensions and against one-dimensional hydrodynamics simulations. This work is supported by the U.S. Department of Energy Office of Fusion Energy Sciences.   

Configuration based Collisional-Radiative Model including configuration interaction

Atomic levels mixing through Configuration Interaction (CI) yields important effects. It transfers oscillator strengthes from allowed lines to forbidden lines, and produces strong shift and broadening of line arrays, although the total emissivity is almost insensitive to CI, being proportional to the average wave number. However for hi Z material, like Xe or Sn (potential xuv-ray source for micro-lithography), a non-LTE calculation accounting for all relevant levels wiill be untractable with billions of states. The model we constructed, CAVCRM (caf\'{e}-cr\`{e}me), is a non-LTE C.R.M. where states are configurations but it includes C.I. to give full richness of spectral quantities, using the latest version of the HULLAC-v9 suite of codes and our newly developped algorithm for large set of states with as many as 50,000 states [1]. \newline \newline [1] M.Klapisch et al, this conference   

Benchmarking algorithms for the solution of Collisional Radiative Model (CRM) equations.

Elements used in ICF target designs can have many charge states in the same plasma conditions, each charge state having numerous energy levels. When LTE conditions are not met, one has to solve CRM equations for the populations of energy levels, which are necessary for opacities/emissivities, Z* etc. In case of sparse spectra, or when configuration interaction is important (open d or f shells), statistical methods[1] are insufficient. For these cases one must resort to a detailed level CRM rate generator[2]. The equations to be solved may involve tens of thousands of levels. The system is by nature ill conditioned. We show that some classical methods do not converge. Improvements of the latter will be compared with new algorithms[3] with respect to performance, robustness, and accuracy. \newline [1] A Bar-Shalom, J Oreg, and M Klapisch, J. Q. S. R. T.,65, 43 (2000). \newline [2] M Klapisch, M Busquet and A. Bar-Shalom, Proceedings of APIP'07, AIP series (to be published). \newline [3] M Klapisch and M Busquet, High Ener. Density Phys. 3,143 (2007)   

M-shell transmission measurements of gadolinium in LTE at 30 eV

X-ray transmission opacity measurements provide a stringent test of the modeling of partly-stripped ions in high-temperature plasmas. While good agreement has been reached in studies of n=1 to n=2 (K-shell) and n=2 to n=3 (L-shell) absorption spectra, there remain significant differences between various models' predictions of the n=3 to n=4 (M-band) opacities of lanthanide elements such as gadolinium (Z=64) at temperatures in the range 25-50 eV. For example, spin-orbit splitting, orbital relaxation and configuration interaction all produce measurable signatures in the predicted M-band absorption spectra of gadolinium. Using the Omega laser facility, hohlraum experiments have been performed to study the X-ray transmission of plastic-tamped gadolinium samples in the photon energy range 1200-1400 eV at temperatures around 30 eV. The sample density and temperature were measured independently on the same laser shot. The M-band spectra of Gd are presented and compared with opacity code predictions, and some implications are discussed. This work was performed under the auspices of the U.S. Department of Energy by University of California, Lawrence Livermore National Laboratory under Contract W-7405-Eng-48.   

Overview of HSX Results and Experimental Program Plan

HSX has recently begun operations at B=1.0 T employing fundamental ECRH at 28 GHz. T$_{e0}$ of up to 2.5 keV and $\tau _{E}$ up to 5 ms have been observed with 100 kW of injected power. Significant wall conditioning has been necessary for density control under these conditions. Improvements in confinement due to quasisymmetry are observed, as at B=0.5T operation. Fundamental heating has resulted in increased plasma density (up to $<$n$_{el}> \sim $ 6 x 10$^{18}$ m$^{3}$ ) and a significant reduction in the non-thermal population. The MHD mode which appears driven by the precession of deeply trapped energetic electrons produced by second harmonic heating is no longer observed. The GNET and CQL3D codes are being used to understand the differences in the electron distribution functions between fundamental and 2$^{nd}$ harmonic heating in both QHS and mirror configurations. A key element of the HSX program is investigation into the role of low effective ripple on anomalous transport. Knowledge of the radial electric field is needed to calculate the neoclassical transport. Two systems are in development to provide this data: a CHERS system based on a DNB on loan from MST, and a novel HIBP system on loan from RPI.   

Transport Studies in HSX at 1 Tesla

To further investigate the effect of quasi-symmetry on neoclassical and anomalous transport, the HSX stellarator has recently begun regular operations at a magnetic field strength of 1 Tesla. Transport studies at 0.5 Tesla demonstrate that the electron thermal diffusivity is a factor of two smaller in the core for the Quasi-Helically Symmetric (QHS) configuration as compared to the configuration with the symmetry intentionally degraded (Mirror) due to a reduction in neoclassical transport [1]. Thermal transport analysis was complicated at 0.5 Tesla by the presence of an ECH driven suprathermal electron population, which is reduced in the higher density plasmas possible at 1 Tesla. It has also been observed that, for an identical injected power, the central temperature is double that of Mirror, with the same line averaged density in each case. A transport analysis will be presented showing the effect of higher field strength, density and injected power on electron thermal diffusivity in QHS and Mirror. This work is supported by DOE Grant DE-FG02-93ER54222. \newline \newline [1] J.M. Canik et al., Phys. Rev. Letters 98, 085002 (2007)   

Modeling of Anomalous Transport in ECRH Plasmas at HSX

The Weiland ITG/TEM anomalous transport model [1] is used to predict density and temperature profiles in ECRH plasmas at HSX. The local geometry approximation in [1] is replaced by the local geometry in the low-field, bad curvature region of HSX, where curvature/$\nabla $B scale lengths ($\sim $R/3) and magnetic ripple ($\varepsilon _{H})$ differ from those of a tokamak (R {\&} $\varepsilon _{T}$, respectively). This is justified by GS2 3D [2] calculations, which demonstrate that the dominant linear instabilities (TEM) in HSX are spatially localized in this region. Growth rates from the Weiland model in this limit agree within 30{\%} of growth rates predicted by GS2 for 3D HSX plasmas. Predicted profiles agree with a number of experimental profiles. Predicted confinement times agree within $\sim $20{\%} of experimental confinement times. Confinement times predicted without the local geometry approximation of HSX ($\kappa $/$\nabla $B, $\varepsilon _{H})$ are 2-3$\times $ larger. This work is supported by DOE grant number DE-FG02-93ER54222. [1] H. Nordman et al., Nucl. Fusion \textbf{30}, 983 (1990) [2] E.A. Belli et al., Bull. Am. Phys. Soc. \textbf{46}, No. 8, 232 (2001)   

Measurement of the Pfirsh-Schl\"{u}ter and Bootstrap Currents in HSX

Pfirsch-Schl\"{u}ter (PS) and bootstrap currents in the quasihelically symmetric stellarator HSX are unlike those of a conventional stellarator. The lack of toroidal curvature in HSX results in a helical PS current that rotates with toroidal angle. The PS current is smaller in size than for comparable MFEs by a factor of n-m$\iota $ (=3 in HSX). The bootstrap current in HSX is opposite in direction to that in a tokamak, which reduces the rotational transform but increases the effective transform. An external Rogowski and magnetic pickup coil array measure the currents. The bootstrap current rises throughout the discharge on a 10-50 ms timescale, approaching a maximum value between 0.4-0.5 kA. The PS current rises on a 5-10 ms timescale and exhibits a dipole variation. T$_{e}$ and n$_{e}$ profiles are measured with a 10-chord Thomson scattering system, showing central T$_{e}$ (n$_{e})$ up to 1.6 keV (5x10$^{12}$ cm$^{-3})$. Varying the electron pressure profile and gradients adjusts the equilibration times and maximum values. HSX can spoil the symmetry with a set of auxiliary coils which adds a (n, m) = (4, 0) symmetry-breaking term in the $\vert $B$\vert $ spectrum. This degrades the neoclassical properties of HSX and affects the resulting equilibrium currents. The measured currents will be compared to theoretical estimates. Supported by DOE grant number DE-FG02-93ER54222.   

ECRH at 0.5 and 1 Tesla in the Helically Symmetric Experiment

A 28 GHz gyrotron power (up to 100 kW) is used to heat HSX plasmas. The experiments are done at 0.5 T with the extraordinary wave and 1 T with the ordinary wave. The plasma stored energy, confinement time and electron temperature are studied as a function of the absorbed power and the plasma density in two magnetic configurations - quasihelical symmetric (QHS) one and second with broken symmetry. Energy confinement time is up to 5 msec in QHS configuration at the higher field. Comparisons with the international stellarator transport scaling database will be presented. In the configuration with symmetry, the central electron temperature is higher (up to 2.5 keV) than in configurations without symmetry. The electron cyclotron emission (ECE) diagnostic shows the presence of suprathermal electrons at 0.5 T. At 1 T the plasma is almost thermal. We run the CQL3D code for 0.5 and 1 T plasma parameters. ECE spectrum versus plasma density at different power level is discussed.   

5-D Kinetic Modeling of ECRH Plasmas in the HSX Stellarator

The global transport code GNET is used to model the evolution of the perturbed electron distribution function and radial electron transport due to electron cyclotron heating (ECRH) in the HSX stellarator. GNET solves a linearized drift kinetic equation in 5-D phase space, allowing simulation of 3-D HSX magnetic configurations. ECRH is modeled in GNET via a quasi-linear source term calculated with a separate 3-D ray tracing routine for 2\textsuperscript{nd}-harmonic X-mode at 0.5 Tesla operations and 1\textsuperscript{st}-harmonic O--mode at 1.0 Tesla operations. First low input power simulations ($<$ 50kW) show a slight difference between radial transport in quasihelically symmetric and mirror magnetic configurations. GNET predictions of ECRH driven flux, power deposition profiles, and implications for ECE and X-ray diagnostics will be presented.   

Alfv\'{e}nic Modes in HSX Stellarator

Coherent, global fluctuations in the range of 20-120 kHz are observed for quasi-helically-symmetric, 2$^{nd}$ Harmonic X-mode ECRH produced plasmas in HSX (B$_{T}$=0.5T). Measurements and theory indicate that the mode with helicity m/n=1/1 is likely a global Alfv\'{e}n eigenmode (GAE) driven by nonthermal electrons. Under certain conditions, a satellite mode of same helicity is observed with frequency $\sim $20 kHz higher than the primary mode. Radial structure of both the primary and satellite modes are obtained by inversion of interferometry data showing peaks at different spatial locations. Finite pressure effects, even at low plasma beta, distort the Alfven continuum and mode frequency for these low m,n modes. For HSX operation at B$_{T}$=1T with first Harmonic O-mode ECRH, the fast electron population is reduced and the mode is no longer observed.\textit{ *Supported by USDOE contracts DE-FG03-01ER54615 and DE-FG02-93EE54222.}   

Wall Conditioning for 1T Operation in HSX

The Helically Symmetric Experiment (HSX) routinely runs electron cyclotron resonance heating discharges with 0.5T field on axis with stainless steel walls conditioned with helium glow discharge cleaning. When the main field is increased to 1T, impurity fueling makes density control impossible. Three techniques are explored to sustain 1T plasmas: carbonization, introduction of a limiter, and boronization. Carbonization is performed with a methane glow discharge and shows large recycling but low impurity radiation even for high injected power. A small carbon limiter is placed in the plasma to reduce wall interactions and cuts impurity influx enough to obtain stable dischages. Boronization of the HSX vacuum vessel is carried out with the solid boron precursor o-carborane. This powder is heated to form a vapor that is injected into HSX from four ovens distributed around the machine. A number of collection coupons are inserted at the vessel wall to measure film characteristics. Results are shown including Thomson scattering and spectral measurements for the three wall conditioning methods.   

Ion Temperature Measurements and Impurity Radiation in HSX

Doppler broadening of impurity line radiation from HSX plasmas is measured in order to calculate the temperatures of ions in the plasma. Impurity content and temperature measurements are primarily being used at present to examine the plasma under different wall conditioning methods. When only glow discharge cleaning has been employed to condition the stainless steel first wall iron emissions are observed in 1 T operation, with a lack of density control. The correlation between edge impurity content and density control is examined for both boronized and carbonized wall conditions. Carbonized walls give good control with reduced oxygen signals and generally show lower radiated power than boronized discharges. These temperature measurements can be used as an indicator of the temperature of the primary ion species (typically hydrogen) in various magnetic configurations, and also must be known to correctly measure the plasma rotation velocity using the charge exchange recombination spectroscopy system, which is currently being implemented on HSX.   

Overview of Recent Results from HSX and the Planned Experimental Program

HSX has previously demonstrated that the quasihelical symmetry (QHS) does indeed improve single-particle confinement and reduce parallel viscous damping over a non-optimized 3-D configuration. New neoclassical differences have been observed under the present operating conditions including reduced thermodiffusion and electron thermal conductivity in the QHS case as compared to the mirror case. Current measurements are consistent with bootstrap calculations and show the current flows in a direction opposite to the tokamak. MHD modes have been observed tied to the presence of energetic electrons in the QHS configuration. A new ECRH transmission line now permits operation at full tube power. Our goals are to increase the density, the magnetic field and heating power to accentuate neoclassical transport relative to anomalous. A CHERS system is being implemented to infer radial electric fields for transport analysis. Preparations are near complete for going to B=1.0T for O-mode heating.   

Simulation and Implementation of HIBP Electric Field Measurements for the HSX Stellarator

Understanding the relative roles of neoclassical and anomalous transport in advanced stellarators requires knowledge of the radial electric field. At HSX, work is under way toward measuring the radial electric field using the deflection of a beam of singly charged Cesium ions. In contrast to a typical HIBP, which measures the energy of higher charge state ions created by collisions within the plasma, this technique measures the displacement of the beam due to the plasma electric field. Recent simulations show measurable differences between ion trajectories through the HSX vacuum field and those of a typical HSX plasma with a realistic potential profile. The displacement is a path effect, but scanning the insertion angle of the beam allows the electric field in different radial locations to be diagnosed. Work to map deflected beam trajectories into radial profile scans is also under way. The ion beamline is being tested and optimized.   

Stability of Current-Driven Discharges in the Compact Toroidal Hybrid Experiment

Experiments on stability and disruption avoidance in current-driven stellarator plasmas are in progress on the Compact Toroidal Hybrid (CTH) torsatron (R = 0.75 m, a $\sim $ 0.2 m, B $\le $ 0.7 T, n$_{e} \quad \le $ 10$^{19}$ m$^{-3})$. The edge vacuum rotational transform variable in the range 0.1 $< \quad \iota $/2$\pi \quad <$ 0.5. Ohmic plasma currents of I$_{p}$ $\le $ 40 kA are induced in target plasmas generated by 12 kW ECRH at the fundamental resonance of 18 GHz. The duration of the ohmic phase of the discharge is up to 100msec. During the plasma current rise, hesitations in the rate of current increase and associated MHD instabilities correlated with low-order rational values of the net edge rotational transform are observed. At edge rotational transform values of 1/3 or 1/2, the current usually undergoes repetitive relaxations in which the current rise is arrested, and the value of the total current drops by about 3{\%}. Major disruptions associated with these instabilities have not yet been found to occur. Efforts to operate with an edge transform above a value of $\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} $ with substantial plasma current are ongoing.   

Vacuum Magnetic Field Mapping of the Compact Toroidal Hybrid (CTH)

Vacuum magnetic field mapping experiments are performed on the CTH torsatron with a movable electron gun and phosphor-coated screen or movable wand at two different toroidal locations. These experiments compare the experimentally measured magnetic configuration produced by the as-built coil set, to the magnetic configuration simulated with the IFT Biot-Savart code using the measured coil set parameters. Efforts to minimize differences between the experimentally measured location of the magnetic axis and its predicted value utilizing a Singular Value Decomposition (SVD) process result in small modifications of the helical coil winding law used to model the vacuum magnetic field geometry of CTH. Because these studies are performed at relatively low fields B = 0.01 - 0.05 T, a uniform ambient magnetic field is included in the minimization procedure.   

Soft X-Ray Tomography and Temperature Measurements on the Compact Toroidal Hybrid (CTH) Experiment

Soft X-Rays (SXR) arrays are used on the CTH experiment (R = 0.75 m, a $\sim $ 0.2 m, B $\le $ 0.7 T, n$_{e} \quad \le $ 10$^{19}$ m$^{-3}$, T$_{e}$(est) $\sim $ 300 eV) for tomographic reconstruction of the emissivity profile and for electron temperature measurement. The SXR tomography is done using a 60 chord system viewing the poloidal cross-section with 3 cameras each consisting of a 20-channel AXUV-20EL photo-diode array filtered with 500nm Al foil. A description of the SXR tomography cameras, the tomographic reconstruction technique and results will be given. The SXR electron temperature measurement diagnostic is a 20 chord system viewing a single toroidal cross-section. Each chord is viewed simultaneously in 2 energy bands with 2 photo-diodes. The energy bands are discriminated using filters with different thicknesses. The ratio of the 2 photo-diode signals can be used to infer the maximum electron temperature along that chord. A description of the dual-energy camera will be given as well as calculations that leading to the choice of filter material and thickness. Calibration methods will be discussed and results will be given.   

Density Measurements of Compact Toroidal Hybrid Plasmas and Design of an Interferometer-Polarimeter Diagnostic

A single-channel 4-mm heterodyne microwave interferometer (on loan from ORNL) provides line-integral density measurements of ECRH and current-driven plasmas in the CTH torsatron (R = 0.75 m, a $\sim $ 0.2 m, B $\le $ 0.7 T, n$_{e} \quad \le $ 10$^{19}$ m$^{-3})$. Densities up to the cutoff value n$_{e}$ = 0.4 x 10$^{19}$ m$^{-3}$ are obtained in ECRH only plasmas. Higher densities are observed when ohmic heating is applied to the ECRH plasmas, however the measurement is often compromised due to refraction. The interferometer is presently set up in a double pass Mach-Zehnder configuration using a retro-reflector mounted on the inner wall of the CTH vessel. In addition, a 1mm interferometer-polarimeter system similar to 3-color FIR polarimeters [1] is currently being designed to provide electron density and current density profiles of current-driven CTH discharges in conjunction with V3FIT modeling. Details of the design will be presented. \newline \newline [1] J. Rommers and J. Howard, Plasma Phys. Control. Fusion 38 (1996) 1805   

Triple probe measurements of edge plasma parameters in the Compact Toroidal Hybrid torsatron

Sheared flows arising from transverse electric fields are observed in space, laboratory and fusion plasmas. Experiments to be performed on the Compact Toroidal Hybrid (CTH) device (R = 0.75 m, a $\sim $ 0.2 m, B $\le $ 0.7 T, n$_{e} \quad \le $ 10$^{19}$ m$^{-3})$ will investigate the stability of the stellarator plasma in response to modifications of the radial electric field. In these studies, the radial electric field structure will be modified by means of a biased limiter. As a first stage of this project, measurements are needed of plasma parameters in the edge region of the CTH device. This presentation will give initial measurements of plasma parameters by means of a triple Langmuir probe. Plans for biased limiter studies on CTH will also be presented.   

Calculated Refraction and Cotton-Mouton Effect for a Millimeter-wave Interferometer/Polarimeter on the Compact Toroidal Hybrid (CTH) Experiment

A combined mm-wave interferometer/polarimeter based on the method of Dodel and Kunz$^{1}$ is being developed to measure the density and current profiles of current-driven discharges in the CTH torsatron (R = 0.75 m, a $\sim $ 0.2 m, B $\le $ 0.7 T, n$_{e} \quad \le $ 10$^{19}$ m$^{-3})$. Measurement of the internal magnetic field by Faraday rotation wavelengths is less costly than FIR approaches, but is more susceptible to refraction effects and the Cotton-Mouton (C-M) broadening of the polarization. Computational modeling of Faraday rotation, beam refraction, and C-M effects for wavelengths between 1.0 and 4.0 mm have been performed in 3-D geometry using plasma parameter values relevant to CTH plasmas in order to minimize the undesired refraction and C-M broadening while maintaining an adequate magnitude of Faraday rotation. Study results indicate that a 1 mm system is optimal for the CTH. 1. G. Dodel and W. Kunz, Infrared Phys. \textbf{18}, 773 (1978)   

Fast Particle Loss-Cone Measurements by the Novel Angular-Resolved Multi-Sightline Neutral Particle Analyzer (ARMS-NPA) on Large Helical Device.

The novel diagnostic of fast particles (ARMS-NPA) based on linear AXUV detector has been successfully developed and started measurements on LHD [1]. This is the first time of using AXUV detector for fast particle measurements on plasma devices. ARMS-NPA can provide time-, angular- and energy-resolved measurements of fast particles even in short-time discharges. This diagnostic can be a powerful tool in fast particle physics and confinement studies in such a complex helical plasma geometry like the one of LHD. It can become irreplaceable instrument in the checking of fast particle loss-cones existing in helical devices which were predicted by some theoretical works [2,3] and refuted by another [4]. Measurements were made in the variety of experimental conditions and compared with theoretical simulations. [1] E.A. Veshchev, T.Ozaki, \textit{et al.}, Rev. Sci. Instrum., \textbf{77}, 10F129-1 (2006) [2] H.Sanuki, J.Todoroki and T.Kamimura. Phys. Fluids B \textbf{2 }(9), 2155 (1990) [3] M. Wakatani, \textit{Stellarator and Heliotron Devices }(Oxford University Press, Oxford, 1998) [4] T. Watanabe \textit{et al.}, Nucl. Fusion \textbf{46}, 291 (2006).   

Calculation of a stable path to high beta for the LHD stellarator

In the LHD experiments, good confinement of the plasma has been observed in a magnetic configuration with a vacuum magnetic axis located R\textit{ax}=3$.$6m, where linear ideal interchange modes and Mercier modes were predicted to be unstable. In order to investigate the stabilizing mechanism of the modes, we developed a multi-scale simulation scheme [1] by utilizing the NORM code [2] and the VMEC code [3]. This scheme treats both the equilibrium change in the long time scale and the nonlinear dynamics of the instability in the short time scale simultaneously. We applied the multi-scale scheme to the low beta LHD plasma with $R$\textit{ax}=3$.$6$m$. As beta is increased, we found a self-organization of the pressure profile. The resistive interchange modes flatten the pressure profile at the low order singular surfaces and that induces the stabilization of the Mercier modes. In this way, we find a stable path to a high beta regime. \newline [1] K.Ichiguchi, B.A.Carreras, J. Plasma Phys. 72(2006) 1117-1121. \newline [2] K.Ichiguchi et al., Nucl. Fusion 43(2003) 1101-1109. \newline [3] S.P. Hirshman and O. Betancourt. \textit{J.Comp.Phys.}, \textbf{96},99 (1991).   

Quasi-linear fluxes in heliotron configurations

Quasi-linear particle and energy fluxes by the linear gyrokinetic modes (for example, ITG modes) are investigated in heliotrons. For this purpose, the MHD magnetic configurations to model the LHD like parameters (R/a$\sim $6, L=2, M=10) are considered, which are obtained by using the VMEC. It is well known that the neoclassical ripple transport is enhanced by the helically trapped particles for low collisional regime, while its magnitude is strongly affected by the slight shift of the magnetic axis in the poloidal plane. On the other hand, in the case of quasi-linear anomalous transport, the trapped particles have tendency to make the particle fluxes negative. This tendency is strong in the heliotron configurations due to the effects of the helically trapped particles. The resulting particle pinch will be balanced with the neoclassical particle fluxes to determine the density profiles. The resulting density profiles will then affect the quasi-linear energy fluxes. By considering the different heliotron configurations with or without the neoclassical optimization, the anomalous energy transport and confinement properties will be discussed. The electromagnetic effects (for example, by KBMs), and collissional effects on the fluxes will also be shown, if possible.   

Shear Alfv\'{e}n spectrum and mode structures for 3D configurations

Energetic particle destabilized Alfv\'{e}n modes are observed in a wide range of stellarator experiments. We have developed a code (AE3D) to calculate the full shear Alfv\'{e}n frequency spectrum and associated mode structures for arbitrary stellarator equilibria. This is based on a Galerkin approach using a combined Fourier mode (poloidal/toroidal angle) finite element (radial) representation. It has been applied to an LHD case where Alfv\'{e}n activity and enhanced ion losses were seen. Applications also are underway to other experiments, such as HSX, where ECH-driven Alfv\'{e}n modes were observed. This model can form the basis for stellarator optimization targets, synthetic diagnostics, and reduced linear/nonlinear stability models. It is also applicable to tokamaks with symmetry-breaking effects. By matching observed frequencies with calculated mode structures, improved understanding of the physics mechanisms of AE modes, such as sideband coupling, damping, and enhanced fast particle losses can be developed.   

Magnetic islands and confinement in the H-1NF heliac

Magnetic islands in fusion devices have serious impacts on the confinement properties, including enhancement of radial transport and deterioration of plasma confinement. However, there is experimental evidence that under certain conditions, islands can induce transport barriers and thus improve confinement. Present understanding of the conditions for either deterioration or improvement in plasma confinement due to magnetic islands is far from complete. The H-1NF heliac in the Plasma Research Laboratory, ANU, provides an excellent opportunity to conduct controlled experiments on magnetic islands. The flexible coil system of H-1NF allows the magnetic configurations to vary over a wide range to accommodate or avoid major rational surfaces and islands. Our recent experiments in a low temperature RF-produced Argon plasma indicate that, under our experimental conditions, magnetic islands near the core may serve as pockets of improved plasma confinement regions. In the presence of these islands, the radial electric field near the core jumps to a large positive value, reversing its direction within the island, producing a strong electric field shear layer.   

A Preconditioned Newton-Krylov Code for Calculating 3D MHD Equilibria with Magnetic Islands

We have implemented a Jacobian-free Newton-Krylov method with a Levenberg-Marquardt line-search in the PIES code, which solves for 3D MHD equilibria. The algorithm has performed well in tests on helical equilibria with islands. We are investigating further techniques, such as using an adaptive preconditioner, where the limited subspace information from each linear solve is used to construct a preconditioner for future linear solves.   

V3FIT: Three-Dimensional MHD Equilibrium Reconstruction

V3FIT is a three-dimensional MHD equilibrium reconstruction code, based on the VMEC equilibrium code. V3FIT is a general and easily extensible reconstruction code, designed so that information from many types of diagnostics can be used to determine the equilibrium. The first diagnostics included in V3FIT were magnetic diagnostics. We will present results on reconstruction using microwave interferometers and polarimeters as diagnostics. We will also show comparisons between V3FIT and EFIT reconstructions using experimental data from the DIII-D tokamak. This work is supported in part by US DOE Grant DE-FG02-03ER54692B and a US DOE Postdoctoral Research Fellowship.   

Studies of the neoclassical transport for CNT

The Columbia Nonneutral Torus (CNT) was not optimized with respect to $1/\nu$ neoclassical transport, therefore, such studies are of interest and desirable. For such a task the code SORSSA was adapted to CNT. SORSSA computes a normalized stored energy based on a simple transport model depending on the neoclassical effective ripple $\epsilon_{\rm eff}$. For this purpose $\epsilon_{\rm eff}$ is calculated by following the magnetic field line. Because the magnetic field is computed in real space coordinates directly from coil parameters there is no restriction to the complexity of the magnetic field. First results of computations of the total stored energy are presented. \newline *This work, supported by the European Communities under the contract of Association between EURATOM and the Austrian Academy of Sciences, was carried out within the framework of the European Fusion Development Agreement. The views and opinions expressed herein do not necessarily reflect those of the European Commission. Additional funding is provided by the Austrian Science Foundation, FWF, under contract number P16797-N08.   

Progress in NCSX Construction

The National Compact Stellarator Experiment (NCSX) is being constructed at the Princeton Plasma Physics Laboratory (PPPL) in partnership with the Oak Ridge National Laboratory (ORNL). The NCSX has major radius 1.4 m, aspect ratio 4.4, 3 field periods, and a quasi-axisymmetric magnetic field. The device will provide the 3D plasma configuration flexibility and the heating and diagnostic access needed to study compact stellarator physics. The components have complex geometries and tight tolerances, but the most challenging ones are nearing completion. The vacuum vessel was completed in 2006. Delivery of the 18 modular coil winding forms was completed in 2007 and at least twelve modular coils have been fabricated, satisfying the $\pm $0.5~mm tolerance requirement on the current center position. The toroidal field coils are in production. Installation of tubing and diagnostic loops on the vessel is nearly complete. Preparations for assembly of modular coil subassemblies began in 2007. Plans for completing NCSX construction, including an updated schedule, will be presented.   

Magnetic Flexibility of NCSX.

The National Compact Stellarator Experiment (NCSX), currently under construction, is a modular quasi-axisymmetric stellarator designed to study confinement and stability of high-beta plasmas. It has 18 modular coils, 18 planar weak toroidal field coils, and 6 pairs of poloidal field coils. Each type of coil is powered separately, providing a wide range of 3D shape flexibility. This equilibrium flexibility space has been explored to determine the range available, to identify candidate equilibria for early experiments, and to analyze the expected plasma characteristics. Vacuum equilibria, with well formed flux surfaces are found for iota (magnetic rotational transform) ranging from 0.19 to 0.9 and low effective helical ripple $<$ 1{\%}. The effective ripple can be varied by more than a factor of 10, at fixed rotational transform. At low effective ripple, the ripple generated neoclassical transport is predicted to be negligible. At the maximum ripple, the ripple generated transport reduces the predicted plasma temperature, and this change is large enough to be measurable. The change in transform from the center to the edge can be varied from --0.1 to +0.25. Similar variations have been calculated for finite beta equilibria. Calculations of flux-surface quality and the effect on transport and stability will be discussed.   

Status of the QPS Project

The Quasi-Poloidal Stellarator (QPS) is designed to test key physics issues at plasma aspect ratios 1/2-1/4 of other stellarators. QPS has a quasi-poloidal (linked-mirror-like) rather than quasi-toroidal (tokamak-like) magnetic configuration, which allows poloidal flows and flow shear a factor of $\sim $10 larger than in other toroidal confinement systems, and very low effective ripple to reduce neoclassical transport. It is the only toroidal device stable to drift wave turbulence over a range of temperature and density gradients and has a large fraction of trapped particles in regions of low/favorable field line curvature, which strongly reduces the drive for some trapped-particle instabilities. QPS has highly accurate coil winding forms that are cast and machined, conductor wound directly onto the winding forms, a vacuum-tight cover welded over each coil pack, coils vacuum pressure impregnated, and the winding forms bolted together to form a structural shell inside the vacuum vessel. Nine independent controls on the coil currents permit varying key physics features by a factor 10--30: the degree of quasi-poloidal symmetry, poloidal flow damping, neoclassical transport, stellarator/tokamak shear and trapped particle fraction. The current status of the project will be presented.   

Summary of the Magnetized Target Fusion physics demonstration

We summarize a Magnetized Target Fusion (MTF) effort, whose primary goal is the first integrated liner-on-plasma physics demonstration at Air Force Research Laboratory (AFRL) in 2008. LANL physics, engineering, diagnostic coordination, and hardware at AFRL brings the Field Reversed configuration (FRC) to the liner. To minimize the technical risk, physics questions must be resolved. These require detailed instrumentation not compatible with the AFRL liner on plasma realization of this experiment. The LANL FRXL experiment is thus a separate physics oriented front end with slotted liner, radial access for probes, optical diagnostics, and magnetics. We will measure the trapped flux, plasma entry to the liner region mirror, how well the mirror trapping works, how well the FRC bounces at the end mirror, effects on the FRC lifetime, trade off of translation speed against FRC lifetime, and helicity created with conical theta coils.   

Toroidal Field and Magnetic Helicity in a Translating, High-Density Field Reversed Configuration

The ideal Field-Reversed Configuration (FRC) has zero toroidal field, but finite toroidal field and magnetic helicity have been observed in many translating FRCs, especially those formed via conical theta pinch. The appearance of helicity is believed to depend upon the Hall Effect. Other experiments have also observed a reduction of the toroidal field when a translating FRC is arrested in a magnetic mirror, with a corresponding increase in poloidal flux. This suggests a relaxation process that increases beta. We discuss plans to produce FRCs with varying amounts of helicity on the Field Reversed eXperiment-Liner (FRX-L) by using theta coils with a wide range of cone angles. The FRX-L program emphasizes high-density FRCs for use in Magnetized Target Fusion (MTF). Observations of helicity at higher density will improve knowledge of the role of the Hall parameter. Additional helicity may increase the stability of the translating FRC. Helicity content can thus be used to balance plasma beta against stable lifetime to provide an optimum MTF target.   

Guide and Mirror Magnetic Field Diffusion Calculations for the FRC Compression Heating Experiment (FRCHX) at AFRL

Calculations of the guide and mirror applied magnetic field diffusion were conducted using a commercially available generalized finite element solver. As part of the integrated FRC compression heating experiment (FRCHX), an applied magnetic field captures the translating FRC in the liner region long enough to enable compression. Solenoidal coils inject the necessary magnetic field prior to liner implosion. Since the liner implosion is underway before the FRC is injected, the magnetic flux that diffuses into the liner is compressed, and the calculations must account for the liner motion. A generalized finite element code, using appropriate simplifying assumptions, aided the design of the guide and mirror coils for the FRCHX. The code was used to determine that the Shiva Star return conductor needs to be slotted to permit magnetic field diffusion. In addition the liner motion was approximated to evaluate the field within the liner during implosion. This work is funded by the U.S. Department of Energy Office of Fusion Energy Sciences.   

FRC Adiabatic Compression Heating Experiments

AFRL and LANL are developing Magnetized Target Fusion (MTF). This will use the Shiva Star capacitor bank at AFRL to implode an Al solid liner containing the target plasma to raise density and temperature. The Field Reversed Configuration (FRC) has been chosen for the target because of its stability, translatability, and divertor-like field configuration. The FRX-L experiments at LANL explore FRC formation and translation into the liner. 2D-MHD calculations with MACH2 look at translation, capturing and compressing the FRC. Extended MHD examines FRC rotation. The aforementioned guide the design of the experiment at AFRL, which called FRCHX. Formation and translation tests at AFRL are underway before the first compression heating experiment. Supported by DOE-OFES.   

FRC Rotation in Extended MHD Modeling

Field reversed configurations (FRCs) are observed to develop bulk rotation. The explanation for this behavior from a particle point of view is the preferential diffusion of one sense of angular momentum through the separatrix. We demonstrate that bulk angular momentum is developed in computational simulation of FRCs with extended MHD using the Generalized Ohm's Law and without finite Larmor radius effects and explain how. We analyze the relationship of the fluid model to the hybrid particle model. These simulations are performed in geometries and with fields driven by self-consistent circuits that reflect experiments performed as part of the DoE OFES Magneto-Inertial Fusion program. The fluid point of view clarifies the cause of the rotation and allows development of applied fields to counteract the rotation.   

Power Balance on a High-Density Field Reversed Configuration

An analysis of global power balance has been performed recently on the Field Reversed Experiment with Liner (FRX-L) for a high density ($> 5 \times$ $10^{22}$ ${\rm m}^{-3}$) Field Reversed Configuration (FRC) for the first time. Total radiated power was compared to the total power losses estimated from the power balance zero-dimensional model proposed by Rej and Tuszewski (Phys.~Fluids {\bf 27}, p. 1514, 1984). The percentage of radiative losses versus total loss is an order of magnitude lower than previous lower density FRC experiments. An explanation for the beneficial effect of density is provided by an empirical scaling drawn from the tokamak database. This scaling shows that $Z_{\rm eff}$ has an inverse- squared dependence on density. Assuming that radiated power is due primarily to impurities in the edge plasma, this explanation is sufficient.   

Progress on the Colorado FRC Experiment

Experiments have begun on a new machine for the study of turbulence, flow, stability, and cross-field transport in a field-reversed configuration (FRC). The Colorado FRC Experiment is a high-$\beta$, merged-spheromak device driven by magnetized coaxial plasma guns. A two-point biasing probe will be used to drive $E \times B$ flows. Current efforts are focused on characterizing various components and exploring the operating parameters of the device, as well as developing a diagnostic set for initial fluctuation and flow experiments. Early results and progress toward completion of the machine are presented.   

Diagnostics for the Colorado FRC Experiment

A collection of fast diagnostics is under development for studies on the Colorado FRC Experiment. Current and planned instruments emphasize high spatial and time resolution for detailed measurements of fluctuations and bulk flows. All systems are frequency-limited only by the data acquisition rate ($\geq$ 10 MHz). Diagnostics under development include a compact, 16-position, three-axis magnetic probe, a localized ion-Doppler spectroscopy instrument, a fast ion gauge for measuring transient gas pressure, a seven-channel CO$_2$ quadrature interferometer, a multi-channel Mach probe array, and a multi-frequency reflectometry system. Details of the instruments and preliminary measurements are presented.   

Compression of compact tori by use of efficient drivers

The adiabatic compression of magnetized plasmas has come to the fore in recent times as an interesting hybrid of both inertial and magnetic fusion energy schemes, possibly allowing a means to reach fusion conditions in a compact pulsed system. Here we consider the compression both of the FRC and Spheromak, both with a coil compression [1] and with an imploding liquid liner [2]. Of critical importance in choice of target for compression is the scaling of the confinement with convergence, time-scale for compression and obtainable beta. We present analytic scaling relations for the compression schemes, and MHD simulations of the target plasmas in preparation for the design of a new experiment. \newline [1] P. M. Bellan Scalings for a Travelling Mirror Adiabatic Magnetic Compressor Rev. Sci. Instrum. 53(8) 1214 (1982) \newline [2] P. Turchi, D. J. Book, R. L. Burton, A. I. Cooper Stabilized Imploding Liner Research for High Magnetic Field Plasma Compression J. Magnetisim and Magnetic Materials 11 p373-375 (1979)   

Spectroscopic Diagnostics of the Irvine FRC

A spectroscopic system is developed to resolve the Hydrogen-alpha spectral line of the Balmer series in order to estimate neutral hydrogen temperatures and rotational velocities in the Irvine Field Reversed Configuration (IFRC). Light from the chamber is collected with a system of lenses and relayed via 1mm diameter fiber optic cable to a one-meter Jarrell Ash Czerny-Turner monochromator. An image intensifier is placed in series with a CCD camera at the exit slit of the monochomator to capture the image of the spectral line. The image is focused on the CCD camera with approximately 150 pixels per nanometer of wavelength, which allows a wavelength range of around 4 nm per image. The estimated resolution of the system is presently on the order of 5{\AA} FWHM. The spectral line profile is obtained by deconvolving the measured profile with the instrument profile in IDL.   

Triple Probe Array on Irvine FRC

A new triple probe implementation has been designed and tested on the Irvine Field Reversed Configuration (IFRC). Difficulties occur in normal triple probe measurements on IFRC due to two main reasons: short plasma lifetime and a nonconductive vacuum vessel. The new design addresses these issues by allowing pairs of probe tips to float with the plasma. The signal pairs are coupled across a wide bandwidth isolation transformer. Key features include measurement of the floating potential by capacitive coupling between the primary and secondary of the transformer, and the use of only two probe tips to extract the information necessary to solve for the electron temperature and density. The temperature is measured by differential amplification of the floating potential and capacitively-coupled high side of the double probe pair. The ion saturation current is measured by amplifying the transformer differential voltage. The electronics bandwidth is approximately 0.5 kHz to 2 MHz as tested on the bench. Initial results on IFRC indicate densities of mid 10$^{12}$/cc and electron temperatures of 3 to 5 eV.   

Ion Energy Distribution Function Measurements in the Irvine FRC

A time-of-flight diagnostic has been implemented on the Irvine Field Reversed Configuration (IFRC) to obtain an energy distribution function from charge-exchanged neutral hydrogen. The diagnostic includes a 13cm radius slotted disk rotating at 165Hz in vacuum which chops the emitted neutrals at a rate of 27kHz. In-situ timing verification was performed with a DC xenon discharge lamp with an uncertainty less than 100ns for a 38$\mu$s chopping period. Energy calibration was accomplished with a lithium ion source in the range of 300-1500eV, presently achieving an average energy uncertainty, $\Delta E/E$, of 0.23 prior to further analysis. The diagnostic has measured neutrals in the range of 20-80eV from the Irvine FRC and the corresponding energy distribution function has been obtained.   

Irvine FRC Magnetic Field Structure

Magnetic probe arrays have been used to construct time-evolving images of the magnetic field structure in the Irvine Field Reversed Configuration (IFRC). Two radial arrays, consisting of ten probes each, measure the field in all three directions within the interior of the plasma. Axial field arrays measure field strengths adjacent to inner and outer coils. Magnetic field maps are made by moving the radial probes to different axial and azimuthal positions over a series of shots. The map covers a grid of 30 cm x 50 cm in the r-z plane with grid spacing 2.5 cm x 5 cm. Shot-to-shot variation is small enough ($<$10{\%}) to use data from successive shots to interpolate magnetic field lines as they evolve in time. Reversed fields of $\sim $ 200 gauss have been measured with lifetimes of $\sim $ 40 $\mu $s. These data have been used to estimate essential IFRC equilibrium qualities/quantities such as mid-plane separatrix radii, major radius of the compact toroid, field-null location and azimuthal symmetry. During this process the background fields for shots without plasma also were measured. It has been found that some anisotropy in the background may have been the cause of undesired translational motion of the IFRC. Improvement of the background field symmetry may lead to longer lived equilibria in the desired location.   

Rotating Magnetic Field sustainment of hot FRCs at high zeta

Ultra high vacuum modifications to the TCS device have allowed FRCs to be formed and sustained by Rotating Magnetic Fields (RMF) at temperatures well over 100 eV, without increasing the RMF magnitude, $B_{\omega }$. The higher temperatures result in much higher magnetic fields, $B_{e}$, and significantly higher ratios of $B_{e/}B_{\omega }$. The ratio of average electron rotational speed to RMF frequency, called zeta, approaches unity, resulting in a maximum possible applied RMF torque on the electrons. Power is absorbed by the plasma due to oscillating axial currents (which create the azimuthal torque), proportional to $B_{\omega }^{2}$, and due to the azimuthal FRC currents, proportional to $B_{e}^{2}$. Comparison of torques and powers at high and low zeta conditions shows that at low values of $B_{e}$/$B_{\omega }$, most of the power absorption is due to the axial currents (proportional to $B_{\omega }^{2})$, but at values of $B_{e}$/$B_{\omega }$ exceeding 10, this component becomes insignificant. Under such conditions, the cross-field plasma resistivities are only about one order of magnitude higher ($\sim $20 $\mu \Omega $-m) than necessary for modest sized reactor efficiencies.   

Use of a Magnetized Cascade Arc Source in TCSU to Enable RMF Formation of High Temperature FRCs

TCSU can produce 200 eV FRC plasmas out of a weakly ionized gas by means of an azimuthally rotating magnetic field (RMF) and a steady axial bias field. The seed plasma for the RMF driven FRCs is produced by an ultra-high vacuum compatible, magnetized cascade arc source. The arc source has been constructed to translate into the TCSU end section where it is fired in the presence of $\sim $ 150 mT axial magnetic field. This allows the n$_{e}$=3.3x10$^{19}$ m$^{-3}$, T$_{e}$=10 eV gun plasma to stream along the axial field to the confinement section where, along with a necessary mid-plane puff of neutral deuterium, it can be used to form and sustain the FRC. Final FRC parameters depend on the condition of the gun plasma and deuterium puff parameters, as well as the degree of deuterium recycling from the wall. A fast ion gauge is used to measure the neutral pressure in the confinement section at the moment of FRC formation. The effect of varying plasma gun conditions and neutral puff parameters on FRC performance is currently being studied and results will be shown.   

Density and Impurity Measurements on the TCSU Experiment

TCS-U will have numerous diagnostics for density measurements including Thomson Scattering, Langmuir Probes, and a two-color interferometer. Presently only the two-color interferometer is available. Since temperature is inferred from the magnetic field and interferometer-measured density, the density measurement must be accurate and repeatable. The interferometer system on TCS-U is a two color Mach-Zehnder interferometer with an acoustic modulator to shift the reference beams by 40 MHz. The interferometer setup on TCS-U, as well as data supporting its accuracy and repeatability over a number of shots, will be discussed. Impurity measurements made using the spectrometer system, which includes three monochromators and an intensified CCD camera spectrometer, will also be discussed.   

Two-fluid flowing equilibria of spherical torus sustained by coaxial helicity injection

Two-dimensional equilibria in helicity-driven systems using two-fluid model were previously computed, showing the existence of an ultra-low-$q$ spherical torus (ST) configuration with diamagnetism and higher beta. However, this computation assumed purely toroidal ion flow and uniform density. The purpose of the present study is to apply the two-fluid model to the two-dimensional equilibria of helicity-driven ST with non-uniform density and both toroidal and poloidal flows for each species by means of the nearby-fluids procedure, and to explore their properties. We focus our attention on the equilibria relevant to the HIST device, which are characterized by either driven or decaying \textit{$\lambda $} profiles. The equilibrium for the driven \textit{$\lambda $} profile has a diamagnetic toroidal field, high-\textit{$\beta $} (\textit{$\beta $}$_{t }$= 32{\%}), and centrally broad density. By contrast, the decaying equilibrium has a paramagnetic toroidal field, low-\textit{$\beta $} (\textit{$\beta $}$_{t }$= 10{\%}), and centrally peaked density with a steep gradient in the outer edge region. In the driven case, the toroidal ion and electron flows are in the same direction, and two-fluid effects are less important since the $E\times B$ drift is dominant. In the decaying case, the toroidal ion and electron flows are opposite in the outer edge region, and two-fluid effects are significant locally in the edge due to the ion diamagnetic drift.   

Comparison of Rotamak Plasma Discharges in Cylindrical and Spherical Devices

A new cylindrical chamber rotamak device with one additional magnetic coil added in the middle plane has been built and operated at Prairie View Plasma Physics Lab. A series of experiments in the cases with and without a toroidal field have been performed. The measured plasma current, density and electron temperature are roughly same as those measured in our spherical chamber device operated under the same RF generator power (200 KW / 0.5 MHz) and gas filling pressure (1.3 mTorr). In the case without a toroidal field, the typical plasma parameter for cylindrical device is I$_{p}$ = 2.1 kA, T$_{e}$ = 15 eV, and n$_{e}$ = 1.2 $\times $ 10$^{12}$ cm$^{-3}$; in the case with a toroidal field , I$_{p}$ = 2.7 kA, T$_{e}$ = 25 eV, and n$_{e}$ = 1.4 $\times $ 10$^{12}$ cm$^{-3}$. The results from both devices confirm that configuration with toroidal field is more stable and allows to achieve higher Ip with proper choice of toroidal field. Results from cylindrical chamber device show that total plasma current can be increased from 2.2 KA to 3 KA when 400A current is applied to the midplane coil.   

Magnetic field structure evolution in RMF plasmas

A study of magnetic field structure evolution during 40-ms plasma discharge had been performed in 80 cm long / 40 cm OD cylindrical chamber. Plasma current Ip$\sim $2--3 kA is produced by applied 500 kHz rotating magnetic field. In experiments, the 2D profile of plasma current is changed by feeding a 10-ms pulse current to additional magnetic coil located at the midplane. Using newly developed magnetic field pick-up coils system, we scanned the magnetic field in cross-section of plasma. Two experimental regimes were studied: without external toroidal field (TF), and with TF produced by applied axial current. When a relatively small current ($<$0.5 kA) is applied to the midplane coil, in both cases the total plasma current measured with Rogowski coil experiences a jump (up to 100{\%}), but the profile of current remains almost unchanged. When a larger current (1--2 kA) is applied to the midplane coil, the total plasma current drops; the magnetic structure changes differently in two regimes. In regime without TF, the magnetic field of plasma current is reversed at R$<$a/2, so that two oppositely directed current layers are formed. In regime with TF, the plasma current first extends along Z, and then two rings of current are formed at the edge. At smaller radii, the current layer is still approximately uniform along Z. We also show how the magnetic field evolves during initial 1--3 ms transitional period of plasma formation.   

Studies of Inductively Sustained Compact Toroids in MRX

A central solenoid has been installed in the Magnetic Reconnection Experiment, in order to study the inductive sustainment of compact toroids (FRCs and spheromaks) formed from spheromak merging. Inductive sustainment applied to Argon FRCs extends the lifetime from $\sim $35$\mu $s to 350$\mu $s. The sustainment manifests itself as a balance between an inward pinch and resistive diffusion of flux and particles. In the configuration for these experiments, with neither strong plasma shaping nor nearby stabilizers, FRC sustainment in lighter gasses is difficult due the growth of co-interchange instabilities. The stability in Argon results from limited equilibrium field shaping, resistive diffusion, and finite-Larmour radius effects. When induction is applied to spheromaks, terminal tilt (Helium) or n=2 modes (Neon) typically develop. Induction applied to an Argon spheromak results in conversion to an FRC: the toroidal flux resistively decays while the poloidal flux is sustained by induction. The stability throughout the conversion is provided by resistive diffusion. These results will be related to the SPIRIT oblate FRC concept. Work supported by DOE.   

Occurrence of anomalous resistivity in the inductively current driven FRC

Occurrence of anomalous resistivity in the oblate FRC plasma was measured directly by magnetic probes in the center solenoid current drive (CSCD) experiment in TS-4. After the applied electric field by CSCD penetrated into the core region of the FRC, the resistivity of the FRC increased up to 10-20 times larger than the classical spitzer resistivity. It was found that the resistivity $\eta$ at the magnetic axis scaled as $\eta \propto E$, where E is the electric field at the axis. This anomalous heating was the most probable cause for sustainment of the high-beta FRC under the preferential injection of magnetic energy by CSCD. The FRC plasma is concluded to have the robustness to self-adjust the plasma heating power depending on the magnetic energy injection.   

Overview and Recent Results from the ZaP Flow Z-Pinch

The ZaP Flow Z-Pinch 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. Plasma is magnetically confined for an extended quiescent period where the mode activity is reduced. Doppler shift measurements of impurity lines show 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 radially peaked density profiles during the quiescent period. Density profiles are analyzed to determine equilibrium profiles. Internal magnetic fields have been determined by measuring the Zeeman splitting of impurity emission. Measurements are consistent with a magnetically confined plasma. Plasma lifetime appears to be limited by neutral gas supply.   

Thomson Scattering Measurements on the ZaP Experiment

The ZaP Flow Z-Pinch Experiment is presently studying the effect of sheared flow on gross plasma 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. A better comparison can be made once the pressure profile is known. A single point Thomson scattering system has been installed on the machine 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 design and hardware allow for multipoint measurements that would measure the pressure profile of the Z-pinch. Initial testing showed the charge on the MCP was being depleted. Amplifiers for the MCP have been designed and are being characterized. The design of the system and initial results will be presented.   

Density Profile of the ZaP Flow Z-pinch Plasma using a 4-chord Interferometer

The ZaP experiment focuses on the goal of generating a sheared flow stable Z-pinch plasma. This study investigates the density measurements of ZaP using a 4-chord, Mach-Zehnder configuration, heterodyne quadrature interferometer driven by a HeNe laser with a 632.8 nm wavelength. A single Bragg cell is used to split the laser beam and add a 40 MHz beat to the reference beam. The beams can be as close as 4 mm while the plasma has a 1 cm characteristic radius during the quiescent period. Radial density profiles along the z-axis can be determined using an Abel inversion technique. The axial variation of the plasma can also be determined by distributing the chords axially. These measurements will augment the temperature measurements made by the Thomson scattering system, helping to determine the Z-pinch pressure and current profiles. Experimental density measurements will be presented.   

Results of the ZaP Flow Z-Pinch Inner Electrode Upgrade

The ZaP Flow Z-Pinch is a plasma physics experiment that investigates the stabilization of a plasma column using sheared flows. The experiment consists of a coaxial plasma accelerator coupled to a pinch assembly region. Recently, the 10 cm diameter inner electrode (cathode) of the experiment was replaced by a 15 cm diameter inner electrode with the goal of increasing the temperature of the pinch through adiabatic compression while also increasing the quiescent (stable) period of the plasma through increased control of neutral-gas injection. This increased control is a product of the larger number of neutral-gas puff valves located inside the inner electrode (eight in the present configuration, compared to one in the previous). Results obtained after this inner electrode upgrade will be presented. Special attention will be paid to the temperature, density, characteristic radius of the pinch and the length of the quiescent period. Comparisons will be drawn between the properties of the plasma when using the 10 cm inner electrode and the 15 cm inner electrode. Theoretical calculations have shown an increase in the temperature by a factor of two, a slight increase in number density and a decrease in the characteristic radius of the pinch. Plans for future efforts will also be reported.   

HBT-EP Kink Mode Control Research: Progress and Future Plans

The High Beta Tokamak-Extended Pulse (HBT-EP) kink mode control research program is addressing critical key issues related to the suppression of the kink mode as a performance limiting instability of fusion devices. Current main research thrusts include: (i) studying advanced feedback control algorithms based on Kalman type filters, (ii) the installation of a new resistive wall and feedback coil set to measure ITER relevant internal control coil configurations and their effect on kink rigidity, and (iii) quantification of the role of neutral damping on resistive wall mode (RWM) dissipation mechanism physics using Li gettering to reduce charge exchange losses in the plasma edge. Recent experimental results on the effectiveness of a Kalman filter based feedback controller, design of the new segmented wall and small coverage control coils, a novel Li evaporator design, along with other diagnostic measurement improvements aimed at furthering our understanding of kink mode behavior will be reported and discussed.   

A Kalman Filter for Feedback Control of Rotating External Kink Instabilities in a Tokamak Plasma

A Kalman filtering algorithm is proposed for feedback control of rotating external kink modes on the HBT-EP experiment. The Kalman filter contains an internal model that captures the dynamics of a rotating, growing mode. The filter actively compares the results of its model with real-time measurements to produce an optimal estimate for the mode's amplitude and phase. Numerical simulations using a model for the RWM consistent with experimental observations on HBT-EP show that Kalman filter feedback can suppress the unstable mode more quickly and with less control effort than less sophisticated controller algorithms. The Kalman filtering algorithm has been implemented on a set of low-latency, field-programmable gate array (FPGA) controllers and tested in closed-loop operation with RWM-unstable plasmas. Progress in using the Kalman filter to suppress unstable kink activity in HBT-EP plasmas will be reported.   

Kink Radial Eigenmode Structure Measurements Using a Hall Sensor Array on the HBT-EP Tokamak

A 20 element, 4mm resolution Hall sensor array directly measures the poloidal field and its fluctuations in the edge region of HBT-EP plasmas and in the surrounding vacuum [1]. We describe the calibration of the probe, and discuss measurements of kink mode radial eigen-mode phase and amplitude structure measured in the edge plasma and in the vacuum region nearby a conducting wall. These Hall probe measurements are compared to theoretical predictions of the Fitzpatrick-Aydemir model of kink mode dynamics [2] to derive the RWM and plasma mode eigenvectors describing the measured external fluxes. The model accurately takes into account the presence of the segmented HBT-EP stabilizing wall using finite element VALEN code modeling calculations. In discharges with resistive wall mode (RWM) activity, the measured mode structure in the vacuum region given by the model is consistent with Hall sensor array measurements. The use of these measurements to quantify the magnitude of plasma dissipation affecting the RWM will be reported. [1] Y. Liu, \textit{et al}, Rev. Sci. Instr. \textbf{76}, 9, 93501, 2005. [2] R. Fitzpatrick and A. Y. Aydemir, Nuc. Fusion, \textbf{36,} 11, 1996.   

The Effects of Neutral Damping on Resistive Wall Mode Physics

The physics of the dissipation mechanism responsible for rotational stabilization of the resistive wall mode (RWM) continues to be an object of intense current research. On the High Beta Tokamak -- Extended Pulse (HBT-EP), there is experimental evidence that edge neutral damping is a significant dissipation mechanism that affects tearing mode behavior [1].~ To quantify the possible effect of neutral damping on RWM physics, we have constructed a 15-channel linear photo-detector array to measure D$\alpha $ emission and its fluctuations. These measurements will be used in conjunction with a 1D space and 2D velocity kinetic transport model of the atomic and molecular deuterium penetration to quantify neutral profiles within the plasma [2]. Initial quantification of the neutral damping contribution to RWM rotational stabilization utilizing the measured D$\alpha $~profiles to estimate the edge neutral density will be presented. \newline [1] E. D. Taylor, \textit{et al.,} Phys. Plasmas \textbf{9}, 3938 (2002) \newline [2] B. LaBombard,MIT PSFC RR-00-9, (2000).   

Design and Implementation of a Compact Lithium Evaporator to Minimize Edge Neutral Drag on the HBT-EP Tokamak

A candidate for the dissipation mechanism responsible for rotational stabilization of the resistive wall mode (RWM) on the HBT-EP tokamak is neutral damping via charge exchange reactions with cold Deuterium neutrals in the edge plasma. Lithium has been used successfully on the CDX-U experiment to substantially reduce recycling as a plasma fueling mechanism [1]. To study charge exchange drag and its effect on the RWM we have designed and plan to implement a small, compact Lithium evaporator that will getter neutral recycled Deuterium atoms to minimize the edge neutral population and as a result reduce charge exchange reactions. Evaporator design details, bench measurements of Li effusion rate performance, and plans for implementation of the evaporator during daily tokamak operation will be outlined. \newline [1] R. Majeski, \textit{et al.,} Phys. Rev. Lett. 97, 7, 075002, 2006.   

Real-Time Plasma Rotation Diagnostic for Measuring Small Doppler Shifts on the HBT-EP Tokamak

An optical fast time-scale toroidal velocity measurement has been developed for use on the HBT-EP tokamak [1,2]. A unique aspect of the measurement technique this diagnostic employs is that the Doppler shift is determined from the ratio of the light intensity from two detectors rather than by resolving the emission line with a traditional spectrometer. This is accomplished using an inexpensive, high-throughput measurement of impurity line emission using interference filters as the spectral device. One detector views the plasma through an interference filter whose passband has a negative slope, and the other views the identical volume of plasma through a positive-slope filter. The signal ratio varies as the emission line is Doppler shifted across the filter passbands. Importantly, the measurement technique is not sensitive to changes in plasma emission levels. For interference filters with a linear passband, the ratio is not sensitive to ion temperature, and the shifted He-II wavelength can be reduced to a simple function of the signal ratio, the channel's relative responsivity, and the two filters transmission curves. Diagnostic calibration procedures and edge plasma toroidal velocity measurements will be reported using a 10{\%} Helium impurity seed in standard Deuterium discharges. Supported by U.S. DOE Grant DE-FG02-86ER53222.   

Thomson Scattering on the HBT-EP Tokamak

Thomson scattering can be used as a non-invasive method for measuring local electron density and temperature in plasmas. We describe the HBT-EP Thomson Scattering diagnostic, which is based on a design in use at DIII-D [1]. A five-channel interference filter polychrometer measures incoherent scattered light from an 8ns, 800mJ, 1064nm Nd:YAG laser pulse. A set of pre-amplification circuits designed by Princeton Scientific Instruments [2] has recently been installed for signal detection using avalanche photodiodes. System layout, alignment, and straylight level reduction techniques will be outlined. Rayleigh and Raman scattering calibration procedures have been used to absolutely calibrate the collection optics and detection system. Recent progress on diagnosing different HBT-EP plasmas using the Thomson scattering diagnostic will be presented. \newline \newline [1] T. N. Carlstrom, \textit{et al}, Rev. Sci. Instr. 61, 2858, 1990. \newline [2] D. Johnson, \textit{et al}, Rev. Sci. Instr. 72, 1, 1129, 2001.   

Helimak Turbulence and Simulation

The Helimak is a good realization of a sheared cylindrical slab with open field lines. The plasma is heated by microwaves at the electron cyclotron resonance. The resulting pressure and potential gradients give drift and fluid instabilities that drive fluctuations in density and potential. Simulations of the D'Ippolito-Krasheninikov equations show turbulence produced by a combination of Rayleigh-Taylor and Kelvin-Helmholtz instabilities. We compare the statistical properties of the turbulence in the simulation with the measured turbulence of the experiment. We present improvements to models used in codes to represent the physics of the Helimak more accurately. The two dimensional structures in density and floating potential are compared to those predicted by the simulation.   

Control of SOL Turbulence

The Helimak is an approximation to the infinite cylindrical slab, but the field configuration may be arranged as a simplified SOL with magnetic curvature and shear for realistic connection lengths. The turbulent amplitudes are typical of the SOL in fusion devices. Radially segmented isolated end plates allow application of radial electric fields that drive radial currents. Above a sharp threshold in applied voltage (driven current), the fractional turbulent amplitude is greatly reduced, as is the radial turbulent particle transport. Stabilization is observed for both positive and negative bias. Measurements of the transport reduction will be presented. The spatial relations between the region of applied fields and the turbulence suppression will be described. Extrapolation to fusion devices at higher density will be discussed. Work supported by the Department of Energy Office of Fusion Energy Sciences DE-FG02-04ER54766.   

Heavy Atom Neutral Beam Probe

A Heavy Neutral Beam Probe (HNBP) is being developed to measure the space potential on Helimak. The HNBP will make overlapping potential measurements with an array of Langmuir probes (LP). This will allow a direct comparison of LPs and our HNBP measurements. Helimak is a low temperature (7 to 10 eV) plasma device designed to study turbulence with relevance to fusion devices. Several diagnostic techniques were considered to probe this low temperature plasma. Two new techniques proposed involve photo-ionization of the probing beam, which may be singly ionized or neutral. The HNBP was selected however due to its compatibility with the turbulence measurements desired for Helimak. The primary species that we intend to probe with is sodium, which will be electrostatically accelerated to energies of 8 to 12 keV as an ion and subsequently neutralized. Much of the hardware for this system consists of the original Elmo Bumpy Torus (EBT) Heavy Ion Beam Probe (HIBP). The new photo-ionization techniques are ideal for low temperature nonmagnitized plasmas where continuous time resolution is not required, as in plasma processing of semiconductors.   

Drift-wave Turbulence in the Helimak

We present an experimental characterization of drift-wave turbulence in the Helimak, not only a finite realization of the sheared, cylindrical slab used in turbulence calculations, but also a good approximation for the SOL of a tokamak. Measurements of electrostatic turbulence are made both using an large fixed array of langmuir probes and a moveable array on a motorized probe drive. We examine such non-spatially oriented quantities as turbulence levels, fluctuation frequencies, and phases between density and electrostatic potential fluctuations. Measurements on dispersion relations and coherence lengths in both the radial and vertical directions are used to characterize the turbulence in the plane perpendicular to the magnetic field. In addition to this information, we also present a study of fluctuations parallel to the field lines, including measurements of parallel coherence lengths and parallel wavenumbers. Furthermore, we employ the use of wire coil probes to characterize fluctuations of both radial and vertical magnetic fields. We explore the relationships between density, potential, and magnetic turbulence.   

Simulations of extended MHD Turbulence and Sheared flows in the Helimak Configuration

We investigate the interaction of sheared plasma flows with the ambient turbulence in the Helimak configuration using a magnetohydrodynamic slab model that captures most of the important features present in the Helimak device at the University of Texas. We report 2D and fully 3D nonlinear simulations using magnetic and flow profiles based on experimental data. The experiment is well modeled as a bounded magnetized jet. The extended MHD model includes a gravitational term to account for magnetic field curvature drifts. Important features of the code include the presence of walls, resistivity and viscosity. The nonlinear development of various disturbances will be discussed. Preliminary results show that as the linear modes attain finite amplitude, there is considerable development of multiscale plasma excitation.   

First Flight of the Levitated Dipole Experiment

In the past year, the first levitated experiments have been conducted in the Levitated Dipole Experiment (LDX). LDX, which consists of a 560 kg superconducting coil floating within a 5m diameter vacuum chamber, is designed to study fusion relevant plasmas confined in a dipole magnetic field. In previous plasma run campaigns, conducted with the dipole coil held by thin supports, stable high beta plasma operation were demonstrated where the plasma kinetic energy is contained in population of energetic particles. It is expected that levitated experiments will improve confinement by removing the primary loss of energy and particles along field lines. This in turn will lead to higher plasma density and broader radial profiles which should increase the stable operational space. In February, the first flight of the floating dipole coil was achieved with 40 minutes of continuous levitation and three demonstration plasma shots. This first flight experiment demonstrated the operation of the digital feedback system that provides for stable levitation of the coil. The results from the first plasma experiments, planned for early fall, will be presented.   

Prospects for Driven Particle Convection Tests in LDX

An attractive consequence of the shear-free magnetic field of levitated dipole confinement devices is the possibility of using advanced fusion fuel cycles [Kesner et al., NF 44(2004)193]. When the pressure and density profiles are isentropic, convective interchange mixing transports particles but does not necessarily transport heat. In shear-free magnetic fields, low-frequency convective circulation is interchange-like and the size scale of the largest circulation motion extends to fill the confinement volume. As a consequence, particles may be convected from the hot central region to the edge in times much less than the energy confinement time. One goal of the Levitated Dipole Experiment (LDX) is to investigate the relative energy and particle time scales and also to explore active means to induce rapid particle circulation that do not alter the dipole's highly peaked, and isentropic, pressure profiles. Experiments that are planned include the following: (1) optical measurement of localized density and impurity transport, (2) flux-tube charging with insertable bias probes, (3) the impact of localized field errors on convective cell formation, and (4) the application of a weak toroidal field to limit the radial extent of convection and prevent inward particle transport to the dipole magnet.   

Low Frequency Fluctuations in the Levitated Dipole Experiment

Plasma that is heated by ECRH can be subject to instability that feeds on the free energy of either the hot component or the thermal plasma component. A closed field line confinement system such as a levitated dipole is shear-free and the plasma compressibility provides stability. Theoretical considerations of thermal plasma driven instability indicate the possibility of MHD-like behavior of the background plasma, including convective cell formation and drift frequency (entropy mode) fluctuations. In experiments in LDX (in the supported mode of operation) we create a two-component plasma in which a thermal species contains most of the density and an energetic electron species contains most of the plasma stored energy. In addition to high frequency fluctuations reported elsewhere [Garnier et al., PoP 13(2006)56111] we observe low frequency fluctuations in the kHz range that presumably are driven by the thermal species. The fluctuations become undetectable during strong edge fueling when the density profile broadens. During levitated operation lower fueling rates are required and we will compare the low frequency activity between the levitated and supported modes of operation.   

Density Profile Dynamics in 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 may naturally develop a highly peaked profile characterized by an equal number of particles per flux-tube: $\delta(nV)\sim 0$, where $V \equiv \oint\delta\ell/B$. Accordingly, in a dipole-confined plasma, the density profile is predicted to vary with radius as $n \sim 1/r^4$. A 4-cord microwave-interferometer density diagnostic with a center frequency of 60 GHz has been built and tested. In experiments where the dipole was not levitating but rather suspended by thin supports, the density profile was observed to respond to (1) ECRH frequency, (2) total ECRH power, and (3) neutral gas fueling. Comparison with data from true levitation experiments (Sept. 2007) will allow us to further characterize the density profile dynamics of dipole-confined plasmas.   

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. We report the first results of a larger study to investigate the controlled excitation of particular interchange modes, the nonlinear coupling of these modes, and the effect of driven excitation on plasma convection and transport. In CTX, a large diameter electrostatic probe is inserted at various radii and excites strong, nonaxisymmetric flows by flux-tube charging and driving nonaxisymmetric cross-field currents. We have applied both positive ($\sim$ 10 V) and negative ($\sim$ -1000V) biases. Negative bias has been applied to lower-density plasma, which are dominated by the Hot Electron Interchange (HEI) modes, and to the high density regime dominated by turbulent fluctuations. As an extension of a recently implemented simulation upgrade (see accompanying poster) results including a bias probe will be displayed. We also describe plans for our next step investigations when multiple bias probes will be driven by frequency and phase controlled power supplies to excited resonant, rotating interchange modes.   

Simulating Interchange Turbulence in a Dipole Confined Plasma

The dipole magnetic field is a simple, shear-free configuration. Strong, low-freqency interchange mixing, with $k_\parallel=0$, allows plasma cross-field dynamics to be `bounce-averaged'. When dipole confined plasma is produced with ECRH, fast Hot Electron Interchange (HEI) instabilities appear at low densities, and lower-frequency turbulent fluctuations occur at higher densities. The global mode structure of the HEI and centrifugal interchange are understood, with good agreement between laboratory measurements and nonlinear simulations. However, the turbulent fluctuations are much less understood. They exhibit a power-law like spectrum, and require a spatially refined computational grid. To study the interchange turbulence, a fully parallel simulation has been developed to examine these fluctuations. The simulation includes a distributed Fast-Poisson solver for the ion polarization drift, a particle source and sink, as well as user-inputs to charge individual flux tubes driving interchange mixing. Results of high-resolution simulations and parallel performance will be given.   

Linear Study of Electromagnetic Hot Electrons Instabilities in a Closed Field Line Plasma.

Motivated by the electron cyclotron heating being employed on the Levitated Dipole Experiment, the hot electron instabilities are investigated by considering the simplest closed magnetic field line geometry - a Z-pinch. The linear theory of electromagnetic interchange modes in a plasma of fluid background and a small fraction of kinetic hot electrons was recently studied theoretically [1]. The model assumed that the species diamagnetic drift and magnetic drift frequencies are of the same order, and that the wave frequency is much larger than the characteristic frequencies of the background but much smaller than that of the hot species. We extend the framework outlined in this reference to allow mode frequencies of the same order as typical hot electron frequencies, and relax the large azimuthal wave number and local approximations. The characteristic equation, resulting from the eigenvalue formulation is a highly non-linear, integro-algebric function, and is handled in this work by a fast 1-D generalized Newton-based eigenvalue solver. This tool allows us to study the evolution of the mode frequency as a function of several parameters, such as the background profile steepness and the hot electron fraction. The results are discussed and compared with both theoretical predictions1 and experimental results. \newline [1] N. Krasheninnikova, P. J. Catto, Phys. Plasmas, 12, 32101 (2005).   

Improved Plasma Properties in RT-1 with a Levitated Coil

Ring Trap-1 (RT-1) is a novel device to confine plasmas in a magnetosphere-like configuration generated by a superconducting internal conductor. The ring coil is excited with a permanent current of I$_{c}$=250kAT that is magnetically levitated in the chamber to minimize disturbances to the plasmas. The main scientific objective of RT-1 is to realize self-organized states of flowing plasmas with a very high beta value, where the thermal pressure of plasmas is balanced by the hydrodynamic pressure of a fast flow (S. M. Mahajan {\&} Z. Yoshida, PRL \textbf{81}, 4863 (1998), Z. Yoshida {\&} S. M. Mahajan, PRL \textbf{88}, 095001 (2002)). We have started a series of initial plasma experiments since 2006, and in this study, we focused on the improvements of plasma properties by the coil levitation. Hydrogen plasmas were generated by an 8.2GHz ECH system. When the coil was levitated, a line integrated electron density increased to n$_{e}$=4x10$^{17}$m$^{-2}$ and the peak density was close to the O-mode cut off density of the microwave. The beta value of the plasma was $\sim $3{\%} and the pressure was mainly sustained by a high energy component of electrons. The magnetic surface configuration of RT-1 is also suitable for the confinement of non-neutral plasmas. Experiments on electron plasmas were conducted in RT-1 expanding the previous work in a normal conducting device.   

Wave-induced Helicity Current Drive by Helicon Waves

Investigation of helicity in the dynamo field components of helicon wave, lead to a novel study of wave induced helicity current drive in helicon wave generated plasma. Helicon discharge, produced in a toroidal vacuum chamber of small aspect ratio, shows strong poloidal asymmetry in the wave magnetic field components. Owing to this strong poloidal asymmetry in the wave magnetic field structures, a nonresonant current is driven in plasma by the dynamo electric field, which arise due to the wave helicity injection by helicon waves. Simultaneous rise in wave helicity is observed when the input RF power is increased. Study of parametric dependence of plasma current in very high frequency operating regime, along with numerical estimations of nonresonant components, has been done. Close agreement between the numerical estimations and the experimentally obtained plasma current magnitudes clearly delineates the plasma current due to wave-induced helicity from other possible resonant or nonresonant sources at present parameter regime. Preliminary results of helicon current drive experiments and comparison with the numerical estimations are presented.