Session TP8: Poster Session VII: Reconnection and Non-Neutral II; High Power Microwave and Laser Driven Sources; NSTX Spherical / General Torus; Simulation: HEDP/Plasma Accelerator/Space

Hamiltonian Structure of a Collisionless Reconnection Model for High and Low $\beta$ Plasmas

The noncanonical Hamiltonian formulation of a recently derived four-field model describing collisionless reconnection is presented. The corresponding Lie-Poisson bracket is shown to be a sum of a direct and semi-direct product forms and to possess four infinite independent families of Casimir invariants. Three out of four of these families are directly associated with the existence of Lagrangian invariants of the model. Two of the invariants generalize previously discovered invariants of a two-field model for reconnection in low-$\beta$ plasmas. The variational principle is given for deriving general equilibrium equations and examples of equilibrium solutions are described explicitly. The normal modes of the system are identified, shown to be second variation (energy) stable, and normal canonical (action angle) coordinates are obtained.   

Fast magnetic reconnection regime in double tearing modes

Nonlinear phases of magnetic reconnection in double tearing modes are studied. The first two nonlinear phases of magnetic reconnection lead to the formation of magnetic islands followed by a fast phase to complete the reconnection process with all field lines reconnected and islands vanished. Resistivity dependences for various phases are studied and shown by scaling analysis for the first time. It is shown that after an early non-constant-$\psi $ Sweet-Parker phase with a $\eta ^{1/2}$-scale, the long nonlinear phase is in a Rutherford regime with a $\eta $-scale following by the fast reconnection phase with a very fast $\eta ^{1/5}$-scale. The latter phase is found generated by a process of neighboring magnetic separatrices merging and magnetic islands coupling, with a very fast reconnection rate weakly depended on plasma resistivity. The fast reconnection rate can be understood as a result of the island coupling equivalent to a steadily inward flux boundary driven.   

Effects of a toroidal shear flow on magnetic reconnection

In laboratory plasmas, a toroidal shear flow V$_{z}$ can be generated by neutral beam injections (NBI), and in space plasmas, the shear flow V$_{z}$ perpendicular to the anti-parallel magnetic fields B$_{y}$, such as in the magnetosphere plasma, are also observed often. Nevertheless, though magnetic reconnection with a poloidal shear flow V$_{y}$, i.e., a flow parallel or anti-parallel to the equilibrium poloidal field, has been studied in space and laboratory plasmas for years, the effect of a toroidal shear flow on magnetic reconnection attracts little attention, since in a two-dimensional geometry the out-of-plane toroidal flow V$_{z}$ has been thought no effect on the in-plane reconnection process. However, our study on the problem finds that the toroidal shear flow generates a bipolar structure of the perturbed B$_{z}$ field that excites Alfv\'en waves downstream away from the reconnection region. Also particularly in collisionless Hall MHD reconnection regime that is often the case in space plasmas, the bipolar structure destroys the quadruple distribution of the B$_{z}$ field generated by the low frequency whistler modes. The consequence of the effects to tearing modes in tokamaks and collisionless reconnection in space plasmas is also discussed.   

Current-sheet formation in compressible MHD

Current-sheet formation near a hyperbolic magnetic neutral line in the MHD model is investigated. In this model, the magnetic field lines are swept by the plasma flow toward the X-point. The effects of density variation of the plasma are considered, in particular the case of compressible barotropic plasma.   

Identification of a Two-scale Diffusion Layer During Magnetic Reconnection in a Laboratory Plasma

Recent results from the Magnetic Reconnection Experiment (MRX)$^{1}$ are reported. For the first time in a laboratory plasma, a two-scale diffusion layer in a reconnection region has been identified. Recent 2D numerical simulations predict a thin electron diffusion layer residing inside the broader ion diffusion layer, which has width of approximately the ion skin depth. In our experiments, the electron diffusion layer is also identified inside the ion diffusion region. Demagnetized electrons are found to be accelerated in the outflow, in good agreement with recent numerical simulation data. The measured width of the electron diffusion region scales with the electron skin depth (5-8 c/$\omega _{pe})$, and the electron outflow scales with the electron Alfv\'{e}n velocity. While the electron outflow appears to slow down by dissipation in the electron diffusion region, the total electron outflow remains independent of its width. The ion outflow channel is shown to be much broader than the electron channel. Our results will be compared with recent space data. The effects of guide field on the layer structure will also be presented. 1. M. Yamada et al, Phys. Plasma v.4, 1936 (1997). Research Supported by DoE, NSF and NASA   

Investigation of the 3-D profile of the reconnection layer with and without a guide field

In the reconnecting current sheet in the Magnetic Reconnection Experiment (MRX), the electron diffusion region is verified within the ion diffusion region where the ions become demagnetized. This was confirmed through the appearance of the out-of-plane quadrupole field (QF) during the reconnection process. Because of the QF, the reconnection region is no longer 2-D but is stretched in the out-of-plane direction in a bell shape pattern. This three-dimensional~picture (while still axisymmetric)~is seen with magnetic probes that measure three magnetic field components. Using magnetics data along with mach probe and langmuir probe data will give the profiles of both the ion and electron fluid velocities. Also, the shape of the in-plane magnetic fields are compared with and without the guide field. In null-helicity (without guide field) a narrow and long current sheet is observed, while in co-helicity (with guide~field) a broad O-point type~reconnection region is observed. A bipolar electric field profile has been measured in MRX. As the current sheet passes the probe array, a dip in the floating potential is evident. This bipolar electric field will also be investigated as a function of guide field. Work supported by DoE, NSF, and NASA   

Study of the Effects of Guide Field on Reconnection in MRX

In magnetic reconnection, the presence of the third magnetic field component, or guide field, reduces reconnection rate and tends to form O-shaped diffusion regions~\footnote{M. Yamada et al., Phys. Rev. Lett. 78, 3117 (1997).}. In the Magnetic Reconnection Experiment (MRX), cohelicity merging of two plasma toroids created by a pair of flux cores can produce guide field, however, the magnitude is not easily independently controlled and the field is globally nonuniform. A new toroidal field coil set powered by a 50 kJ capacitor bank capable of producing a uniform guide field with strengths up to 1000 G has been installed on MRX. Other guide field hardware is also described. Initial results of reconnection rate, resistivity, and current sheet tilting and as a function of guide field strength are presented as available. Ion flows are measured with a new Mach probe array, which allows simultaneous measurement of two components of the ion velocity at several points in and near the diffusion region.   

Active Perturbations in the Outflow Region of the MRX Current Sheet

Electromagnetic fluctuations have been observed in the Magnetic Reconnection Experiment (MRX) in frequencies up to the lower hybrid frequency. These fluctuations may cause anomalous resistivity, which could increase the rate of magnetic reconnection. To characterize these fluctuations, a 1cm radius magnetic dipole antenna is used in the MRX current sheet to launch perturbations at a single frequency. Previous work partially characterized propagation in the direction normal to the reconnection plane. When detection is downstream with respect to the out of plane electron flow, the signal is enhanced above the vacuum value within the current sheet, whereas the signal detected upstream is often reduced below the vacuum value [1]. Current work explores propagation in the outflow direction where a signal that grows in time is often observed. Experiments and analysis are ongoing to investigate the cause and propagation characteristics of this perturbation as well as its effect on the reconnection process. \newline [1] S. Dorfman et. al., AIP Conf. Proc. 871, 306 (2006)   

Anomalous Resistivity in a Slab Geometry

A broad spectrum of electromagnetic fluctuations is often observed during fast magnetic reconnection both in nature and in laboratory experiments such as the Magnetic Reconnection Experiment (MRX). While much past work has focused on fluctuations in the lower hybrid range of frequencies\footnote{H. Ji, et al., Phys. Rev. Lett. 92, 115001 (2004)}, the fluctuation amplitudes are higher at lower frequencies below the ion cyclotron frequency. In the present study, we use linear gyrokinetic theory and a simple Krook collision model to examine the conductivity\footnote{H. Qin, Princeton PhD Thesis (1998)} in the presence of a density gradient and constant magnetic field in a parameter regime relevant to the strong guide field case in MRX. A simple Fortran code is used to solve the resulting dispersion relation for the coupled drift and Alfven waves. A robust instability is identified in a broad parameter range. These growing modes are found to have a significant effect on the calculated gyrokinetic conductivity; thus this regime is identified as a promising area for further study with a more complex model. This work was supported by DOE FES Fellowship, DOE, NASA, and NSF.   

Fully Kinetic Simulations of Driven Magnetic Reconnection with Boundary Conditions Relevant to MRX

Many simulations of magnetic reconnection use periodic boundary conditions which limit the physical relevance of the results when comparing with large open systems that occur in nature or with laboratory reconnection experiments. To address this issue, more realistic boundary conditions are employed to model the Magnetic Reconnection Experiment (MRX) using a fully kinetic, two-dimensional code. The simulation is made up of a box with conducting boundary conditions and two current-carrying wires. As the current is ramped down over the time scale of the simulation, a current sheet forms and elongates. Scaling comparisons for the the length and width of the electron layer as well as the reconnection rate are presented. In both the experiment and simulation the thickness of the electron layer scales linearly with the electron skin depth. However, in the experiment, the layer is four to five times thicker [1]. Magnetic islands similar to previous undriven, open-boundary simulations [2] are sometimes observed in the present work but have not been conclusively identified in the experiment. [1] Y. Ren, Princeton PhD Thesis (2007). [2] W. Daughton, et all., Phys. Plasmas. {\bf{13}}, 072101 (2006). This work was supported by DOE FES Fellowship, DOE, NASA, and NSF.   

New results on the perpendicularly propagating electromagnetic lower hybrid drift instability (LHDI)

Motivated by the observation of the magnetic fluctuations in the current layer of the MRX, we developed an {\it oblique} LHDI theory [1]. Applying this local theory to the Harris sheet, we found that this local mode is strongly unstable. However, it has such a large group velocity that it propagates out of the unstable region before it grows significantly. In fact, the larger the drift velocity, the more narrow the unstable region, (because the current thickness decreases). Thus, the oblique mode does not seem to be responsible for the observed fluctuations, or any enhanced resistivity. Therefore, we have concentrated on {\it perpendicular} propagation modes. We have found an unstable mode with a very small group velocity in the gradient direction. this mode has a substantial growth rate and a smaller group velocity so it stays for a longer time in the unstable region. This may be the desired mode. Curiously, it is not made unstable directly by ion Landau damping, but is made unstable by the out-of-phase correction to the perturbed ion density due to the $ {\bf \delta V} \cdot \nabla n_0$ term. \newline \newline [1] H. Ji, R. Kulsrud, W. Fox, and M. Yamada, JGR 110, A08212 (2005).   

Global Two-Fluid Simulations of Magnetic Reconnection

Two-fluid effects are known to influence the magnetic reconnection process through non-MHD communication between the reconnection layer and surrounding magnetic field topology$^1$. To examine the interrelationship between the local reconnection physics and the global magnetic field geometry, we perform two-fluid simulations of the Magnetic Reconnection Experiment (MRX) and the Swarthmore Spheromak Experiment (SSX) using the NIMROD extended MHD code. For MRX, we discuss the effects of toroidicity, the shape of the electron outflow region, and the effect of downstream pressure on the reconnection process. We find that much of the communication between local and global scales is due to the pressure gradients that result from the reconnection outflow. During counter-helicity push reconnection, we observe a radial shift in position of the current sheet and an asymmetric outflow, as seen in experiment$^2$. This asymmetric outflow is examined in terms of separate force-density contributions. For SSX, we present simulations of counter-helicity spheromak merging in both prolate and oblate flux conservers, and discuss the impact of geometry as well as two-fluid effects on the reconnection process.\\ $^1$D.~Biskamp \emph{et al.}, Phys.~Plasmas 4, 1002, (1997).\\ $^2$M.~Inomoto \emph{et al.}, Phys.~Rev.~Lett.~97, 135002 (2006).   

Current Sheet Dynamics in TS-4 Tokamak Reconnection Experiment

The current sheet dynamics have been studied in the TS-4 tokamak mergting / reconnection experiment, revealing quasi-steady, transient and intermittent reconnections. Reconnection speed of two tokamak plasmas was varied by acceleration and separation coil currents. When the inflow flux was set larger than the outflow flux, rapid growth of current sheet was followed by its various dynamics, such as sheet deformation, sheet ejection and island structures of the sheet. In the high-q tokamak merging, the sheet resistivity was almost classical due to the sheet thickness larger than ion gyroradius. Large inflow flux and low current-sheet dissipation caused plasma pileup around the sheet, indicating rapid growth of the current sheet. When the flux pileup exceeded a critical limit, the sheet was ejected mechanically from the squeezed X-point area. The reconnection (outflow) speed was slow during the flux pileup and was fast during the ejection, indicating that intermittent reconnection similar to the solar flare increased the averaged reconnection speed. Right after the ejection, the current sheet was often transformed into several current islands, suggesting that the island size comparable with ion gyrodasius increased the sheet resistivity as well as the reconnection speed. These transient effects caused the fast reconnection as well as the high-power reconnection heating in the merging tokamak experiment.   

Mass dependence of impurity ion temperature in a reconnecting laboratory plasma

Magnetic reconnection is ubiquitous in magnetized plasmas, occurring in the solar corona, the magnetosphere, as well as in laboratory plasmas. In the corona, ion temperatures are correlated with ion mass (Cranmer, SSR 2002), therefore suggesting that the heating mechanism in the corona, most likely reconnection, is more efficient for more massive ion species. This observation motivated a recent laboratory study at the Swarthmore Spheromak Experiment (SSX). Magnetic reconnection occurs as left-- and right-- handed spheromaks merge axially within a cylindrical flux-conserving boundary (counter-helicity merging). Doppler broadened and shifted emission lines from impurity ions (He, C, N, O in majority H plasma) are monitored with a fast, high resolution echelle spectrograph (Cothran, RSI 2006) capable of tracking the lineshape at the MHD timescale of the experiment. The well resolved spectral lines intermittently show a double-peaked shape indicative of reconnection outflow at a substantial fraction of the Alfv{\'e}n speed. Contrary to the results in the corona, however, the He ions appear to be somewhat hotter than the heavier impurity species observed.   

Experiment on two RMF-driven FRCs' magnetic reconnection

Magnetic reconnection experiments in RMF-driven FRC plasma are performed in an 80cm/40cm diameter cylindrical chamber with an additional magnetic coil mounted at the mid-plane. In the experiments, RMF produced by two 500 kHz rf generators drives a plasma current about 2 - 3 kA in the presence of a vertical magnetic field 40 -- 60 G. During a 40 ms, 200 kW power discharge, a 10 ms pulse-current above the threshold value 1500 A is applied to the mid-plane coil to sever the plasma current into two rings and form two FRCs. When the current in the mid-plane coil drops to zero, the two FRCs merge into one FRC again. In the experiments, variations in plasma current, magnetic field profile and H-alpha signal were measured. Both the magnetic field evolution and the change of H-alpha signal show the magnetic reconnection process.   

Coalescence of magnetic flux ropes in a 3D reconnection experiment

The dynamics of magnetic flux ropes are of fundamental importance to the Earth's magnetosphere, solar eruptions, and many other astrophysical phenomena. Understanding the flux rope merging process mainly relies on the spacecraft observation, theory, and numerical simulations while little has been done experimentally. We present experimental results of 3D merging of two flux ropes in the Reconnection Scaling eXperiment (RSX) at Los Alamos National Laboratory. The two flux ropes, or the two current channels embedded in the external magnetic field, are produced by two identical plasma guns. By varying the external magnetic field strength and plasma currents, we study the merging process for strong and moderate guide field. The primary results show the flux ropes undergo a sloshing process in the strong guide field and form a reverse current sheet if one decreases the guide field strength to $\sim $5 times the anti-parallel field strength. The results confirm that the merging rate is slower at higher guide field.   

Scaling of Reconnection and Stability of Current Sheets in Large Systems

The scaling of collisionless reconnection in two-dimensional large systems has been a subject of considerable interest recently. We have carried out a sequence of simulations using the same initial conditions for large systems using resistive MHD, Hall MHD and PIC techniques. It is shown that the dynamics of thin current sheets is sensitive to the mechanism that breaks field lines (spatially uniform resistivity, electron inertia, and/or electron pressure tensor), and that velocity shear along the thin current sheets plays an important role in controlling their geometry and stability. In the resistive MHD model, the long thin current sheet spanning Y-points become near-explosively unstable to secondary tearing, producing plasmoids. In Hall MHD, the nonlinear dynamics changes qualitatively, as the Y-points contract spontaneously to form X-points thwarting the secondary tearing instabilities seen in the resistive MHD study. A steady state is then realized due to a balance between the spatial gradients of the current density and the velocity shear. Collisionless PIC simulations show a very different dynamics, exhibiting the tendency to form extended thin current sheets and secondary tearing instabilities, as found by W. Daughton and coworkers [Phys. Plasmas {\bf 13}, 072101 (2006)].   

Nonlinear evolution of the Resistive Kink Mode and its Nonlinear Stabilization

We use the Magnetic Reconnection Code (MRC) to study the nonlinear dynamics of $m=1$ kink-tearing modes. The MRC a state-of-the art simulation code that implicitly integrates the system of extended MHD equations including a generalized Ohm's law in arbitrary curvilinear coordinates. We employ an inexact Newton method for the solution of the nonlinear implicit equations. The inner linear solve is handled by SuperLU, where the Jacobian matrix is symbolically derived and implemented by a code generator. We demonstrate that nonlinearly the Hall term creates spontaneously an X-point-like reconnection configuration, which enhances the reconnection rate nonlinearly, as does the electron pressure gradient. On the other hand, the electron pressure gradient is also responsible for imposing diamagnetic rotation and its stabilizing effect. We present high-resolution simulations in different regimes that show the impact of the various terms leading to either explosive behavior or nonlinear stabilization. In addition, we will also present first simulation results for the nonlinear evolution of m=1 tearing modes in a reverse field pinch configuration.   

Investigation of Current Sheet Instabilities Using a GKE/FKI Particle Simulation Model

The instability of current sheet under finite guide field ($B_y$) is investigated using our new gyrokinetic (GK) electron and fully kinetic (FK) ion particle simulation code, which resolves wave modes ranging from Alfv\'en waves to lower-hybrid/whistler waves. Compared with full-particle codes, the rapid electron cyclotron motion is removed in this model, while the realistic mass ratio $m_e/m_i$, finite electron Larmor radii, and wave-particle interactions are kept. The computation power is significantly improved. The preliminary simulation of Harris sheet is carried out in the 2D $yz$ plane, with $z$ being along the current sheet normal and anti-parallel $B_x$ perpendicular to the simulation plane. The simulation has been performed with both a linearized ($\delta f$) GKe/FKi code and the nonlinear code, for $B_y/B_x=0.1$-$10$. Under very small $B_y$, our results show LHDI modes at the current sheet edge propagating mainly in the $y$ direction, as seen in previous simulations. As $B_y$ increases, $k_\perp$ and diamagnetic drift direction shift away from the current flow direction $y$. The LHDI modes become weaker while high frequency modes stronger. In the cases with a large $B_y$, the LHDI modes evolve to a globally propagating instability, and multiple ion cyclotron modes are excited. A more complete 3D simulation is planned to investigate the new physics introduced by the large guide field.   

Lower-hybrid-drift instabilities in current-sheet equilibriumin in presence of a guide field

Drift instabilities in one-dimensional current-sheet configuration in presence of a guide magnetic field, with lower-hybrid frequencies, are investigated. Nonlocal two-fluid stability analysis is carried out, and a class of unstable modes with multiple eigenstates are found by numerical means. It is found that the most unstable modes correspond to quasi-electrostatic, short-wavelength perturbations in the lower-hybrid frequency range, with wave functions localized at the edge of the current sheet where the density gradient is maximum. It is also found that there exist quasi-electromagnetic modes located near the center of the current sheet where the current density is maximum, with both kink- and sausage-type polarizations. These modes are low-frequency, long-wavelength perturbations. It turns out that the current-driven modes are low-order eigensolutions while the lower-hybrid-type modes are higher-order states, and there are intermediate solutions between the two extreme cases. Attempts are made to interpret the available simulation results.   

Development of an ion source and plasma injection system for a non-neutral plasma using radioactive ions

We are building an ion trap to study the decay of ionized beryllium-7, an isotope with a 53-day half life (for neutral atoms). Because of the short half life of this isotope it is necessary to frequently change the source. We have designed a modified MeVVA (metal vapor vacuum arc) source which allows us to replace the source target material in a relatively short time so that fresh targets can always be used. We have also designed a quadrupole mass filter/ion injector to transport the desired beryllium-7 ions from the source in a low B-field region into the high-field trapping region while rejecting undesirable ions such as boron and carbon. The design of the source and ion injection system will be discussed and results from testing will be presented.   

Modeling the FTICR-MS signal of a $^{7}$Be Ion Plasma

Beryllium-7 ($^{7}$Be) decays only by electron capture into Lithium-7 ($^{7}$Li) with a half life of 53 days. As a result, changing its electronic structure will affect its decay rate. We desire to study the effect of ionization on its decay rate. We will do this by trapping a $^{7}$Be ion plasma in a Malmberg-Penning Trap and measuring its and $^{7}$Li's concentration as a function of time by using Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS). We use this ratio as a function of time to directly measure the decay rate of the confined ion plasma rather than using gamma detection. We have modeled these signals in a 2-dimensional electrostatic particle-in-cell (PIC) code. The two spectrum peaks coalesce at high densities and at low densities they can be resolved. We also plan to model $^{7}$BeH$^{+}$ and $^{7}$Li at high densities to see if we can differentiate between them. The preliminary results of these investigations will be presented.   

Finite temperature m=0 upper-hybrid modes in a non-neutral plasma, theory and simulation.

Axisymmetric upper-hybrid oscillations have been known to exist in non-neutral plasmas and FTICR/MS devices for a number of years$^{1,2}$. However, because they are electrostatic in nature and axisymmetric, they are self-shielding and therefore difficult to detect in long systems. Previous theoretical studies have assumed a zero temperature plasma. In the zero temperature limit these oscillations are not properly represented as a mode, because the frequency at a given radius depends only on the local density and is not coupled to neighboring radii, much like the zero temperature plasma oscillation. Finite temperature provides the coupling which links the oscillation into a coherent mode. We have analyzed the finite-temperature theory of these modes and find that they form an infinite set of modes with frequencies above $\omega^{2}_{c} - \omega^{2}_{p}$. For a constant density plasma the eigenmodes are Bessel functions. For a more general plasma the eigenmodes must be numerically calculated. We have simulated these modes in our $r-\theta$ particle-in-cell code that includes a full Lorentz-force mover$^{3}$ and find that the eigenmodes correspond well with the theory.\\ $^{1}$ J.J. Bollinger, et al., Phys. Rev. A {\bf 48}, 525 (1993).\\ $^{2}$ S.E. Barlow, et al., Int.\ J.\ Mass Spectrom.\ Ion Processes {\bf 74}, 97 (1986).\\ $^{3}$ M. Takeshi Nakata, et al., Bull.\ Am.\ Phys.\ Soc. {\bf 51}, 245 (2006).   

Collisional Damping of Plasma Waves on a Pure Electron Plasma Column.

Collisional damping of electron plasma waves (Trivelpiece-Gould waves) on a magnetized pure electron plasma column is discussed. Damping in a pure electron plasma differs from damping in a neutral plasma, since there are no ions to provide a collisional drag on the oscillating electrons. A dispersion relation for the complex frequency, $\omega$, is derived from Poisson's equation and the drift-kinetic equation with the Dougherty collision operator. This approximate Fokker-Planck operator conserves particle number, momentum, and energy, and also is analytically tractable. For large phase velocity, where Landau damping is negligible, the dispersion relation yields the complex frequency $\omega \! = \! (k_z \omega_p / k)[1\! + \! (3/2)(k \lambda_D)^2 (1 \! + \! i 10 \alpha / 9) (1 \!+ \! i 2 \alpha )^{-1}]$, where $\omega_p$ is the plasma frequency, $k_z$ is the axial wave number, $k$ is the total wave number, $\lambda_D$ is the Debye length, $\nu$ is the collision frequency and $\alpha \! \equiv \! \nu k / \omega_p k_z$. This expression spans uniformly from the weakly collisional regime $( \alpha \! \ll \! 1 )$ to the strongly collisional regime $(\alpha > 1 )$, matching onto fluid results in the latter limit. For comparison, note that in the weakly collisional regime, the damping rate is given by ${\mathrm Im} (\omega) \! = \! - 4 \nu k^2 \lambda_D^2 / 3$, which is suppressed from the damping rate for the case of a neutral plasma [i.e., ${\mathrm Im} (\omega ) \simeq - \nu $] by the small factor $( k \lambda_D)^2 \ll 1$.   

Collisional and Radiative Relaxation of Antihydrogen.

Antihydrogen is produced in high-magnetic-field Penning traps by introducing antiprotons into a pure-positron plasma at cryogenic temperature $T$.\footnote{G. Gabrielse et al., {\it Phys. Rev. Lett.} {\bf 89}, 213401 (2002).}$^,$\footnote{M. Amoretti et al., {\it Nature} {\bf 419}, 456 (2002).} In the experimental regime, three-body recombination forms highly-excited atoms which exhibit classical guiding-center drift orbits.\footnote{M.E. Glinsky and T.M. O'Neil, {\it Phys. Fluids B} {\bf 3}, 1279 (1991).}$^,$\footnote{F. Robicheaux and J.D. Hanson, {\it Phys. Rev. A} {\bf 69}, 010701 (2004).} Using energy transition rates obtained from a Monte-Carlo simulation, we track the collisional evolution of a distribution of atoms from binding energies near $T$ to $U_c = e^{2} (B^{2}/m_e c^{2})^{1/3}$, where atom dynamics is chaotic. While the flux through the kinetic bottleneck $(U = 4 T)$ is proportional to $T^{-9/2}$, data suggest that the flux at $U_c$ (at a fixed time) does not scale strongly with $T$ or magnetic field $B$. At $U_c$, radiation begins to take over as the principle energy-loss mechanism. Evolution due to radiation is tracked for a typical collisionally-evolved energy distribution to show that a small number of low-angular-momentum atoms radiate to the ground state rapidly, while others drop into slowly-radiating, circular orbits at intermediate energies.   

Theory and Simulation of Field Error Transport.

The rate at which a plasma escapes across an applied magnetic field $B$ due to symmetry-breaking electric or magnetic ``field errors'' is revisited. Such field errors cause plasma loss (or compression) in stellarators, tokamaks,\footnote{H.E. Mynick, {\it Ph Plas} {\bf 13} 058102 (2006).} and nonneutral plasmas.\footnote{Eggleston, {\it Ph Plas} {\bf 14} 012302 (07); Danielson et al., {\it Ph Plas} {\bf 13} 055706.} We study this process using idealized simulations that follow guiding centers in given trap fields, neglecting their collective effect on the evolution, but including collisions. Also, the Fokker-Planck equation describing the particle distribution is solved, and the predicted transport agrees with simulations in every applicable regime. When a field error of the form $\delta \phi (r, \theta , z ) = \varepsilon (r) e^{i m \theta} \sin kz $ is applied to an infinite plasma column, the transport rates fall into the usual banana, plateau and fluid regimes. When the particles are axially confined by applied trap fields, the same three regimes occur. When an added ``squeeze'' potential produces a separatrix in the axial motion, the transport is enhanced, scaling roughly as $( \nu / B )^{1/2} \delta \phi^2$ when $\nu < \omega$. For $\omega < \nu < \omega_B$ (where $\omega$, $\nu$ and $\omega_B$ are the rotation, collision and axial bounce frequencies) there is also a $1/ \nu$ regime similar to that predicted for ripple-enhanced transport.$^1$   

Spatial Landau Damping of Diocotron Modes in Nonneutral Disc Plasmas.

We study the $ {\mathbf E} \times {\mathbf B}$ dynamics of a thin disc of charge confined in a cylindrical Penning trap. The axial extent (thickness) of the disc is assumed to be negligible. An eigenvalue equation for density perturbations of the form $\delta n(r) \exp (im\theta) $ is obtained by linearizing the 2d equations of motion. A complete set of eigenmodes can be found numerically for an arbitrary equilibrium density profile, and were found analytically for the special equilibrium density profile of a flattened spheroid that rotates rigidly. In general, for a given $m$ there are a finite number of discrete (undamped) $ {\mathbf E} \times {\mathbf B}$ drift eigenmodes, which are generalizations of diocotron modes. There is also an infinite continuum of eigenmodes, which can lead to spatial Landau damping of initial density perturbations. We find the damping rate using three methods: Landau contour integration, a conservation of canonical angular momentum argument, and by expressing an initial perturbation as a wave packet of continuum eigenmodes. The results of the three methods match closely. A preliminary analysis of the effects of non-zero temperature and length has also been done, and experiments to observe these modes are in progress.   

Nonlinear Coupling of Plasma Waves Modified by Separatrix Dissipation

Quantitative measurements of the nonlinear coupling of diocotron modes characterize both the expected conservative coupling term and a new term arising from separatrix dissipation. Here, the pure electron plasma columns have a controllable axial trapping separatrix created by an applied $\theta$-symmetric wall ``squeeze'' voltage. Prior experiments\footnote{A.A. Kabantsev and C.F. Driscoll, {\it Phys. Rev. Lett.} {\bf 97}, 095001 (2006).} established that this separatrix 1) enables and damps the ``Trapped Particle'' diocotron mode, and 2) damps $m_\theta \!\! \ne \!\! 0$ $k_z \!\! \ne \!\! 0$ plasma modes; and, in combination with external $\theta$-asymmetries, 3) damps $m \! \ne\!\! 0$ $k \!\! = \! 0$ diocotron modes, and 4) causes enhanced bulk plasma expansion and loss. The present experiments observe the resonant interaction between the traditional $m \!\! = \! \!2$ $k \!\! = \!\! 0$ diocotron mode and the $m \!\! = \!\! 1$ TP diocotron mode. The initial parametric decay of $m\!\! = \!\! 2$ into $m \!\! = \!\! 1$ is adequately predicted by the conservative nonlinearity arising from the continuity equation. However, the late-time evolution clearly requires (and quantifies) a dissipative nonlinear term which is not yet understood theoretically. This same dissipative coupling is also observed for {\it non-resonant} interactions, as in bulk plasma transport from field errors.   

Phase-Coherent Measurement of Particle Distributions in Electron Acoustic Waves.

Phase-coherent velocity distribution functions $f ({\mathrm v}_z )$ are measured by Laser Induced Fluorescence, for standing ``electron acoustic'' waves in pure ion plasmas. These (mis-named) waves are the lower-frequency branch of standard electrostatic plasma waves, with phase velocity ${\mathrm v}_\phi \approx 1.3 \bar{\mathrm v}$. The waves are necessarily nonlinear so as to flatten the distribution at ${\mathrm v}_\phi$, thereby voiding the otherwise strong Landau damping. Our measurements are performed on $m_\theta \! = \! 0$, $m_z \! = \! 1$ waves driven to moderately large amplitude, i.e. $ e \delta \phi \geq \! 0.1 T$. Received LIF photons are accumulated in 8 phase bins, according to the instantaneous received phase of the wall electric field. The phase-coherent $f ({\mathrm v}_z )$ shows 1)~particle sloshing, $\delta \langle {\mathrm v} \rangle$, as expected; 2)~phase reversal of $\delta f$ at ${\mathrm v} \! = \! 0$ and ${\mathrm v} \! = \! {\mathrm v}_\phi$, in general correspondence with the linear perspective of $\delta f \! = \! ( \delta f_0 / \partial {\mathrm v} )/ ( {\mathrm v} - {\mathrm v}_\phi )$; and 3)~plateaux around ${\mathrm v}_\phi$ with velocity widths as expected from wave-trapping theory. Measurements will be compared to traveling wave trapping theory and to standing wave particle simulations.   

Frequency Variability of Electron Acoustic Waves.

``Electron Acoustic Waves'' (EAW) are non-linear electrostatic plasma modes, with a phase velocity comparable to the thermal velocity\footnote{F. Valentini et al., {\it Phys. Plas.} {\bf 13}, 052303 (2007).} ${\mathrm v}_\phi \approx 1.3 \bar{\mathrm v}$. EAWs can be excited in neutralized plasmas,\footnote{Sircombe et al., {\it Plas. Phys. Cont. Fus.} {\bf 48}, 1141 (2006).} pure electron plasmas and pure ion plasmas. Here, we present measurements of the ``thumb shape'' dispersion relation of EAW and Trivelpiece-Gould (TG) plasma modes in a pure magnesium ion plasma. Near the end of the thumb ($r_p / \lambda_D < 3$), modes can be excited at almost any frequency, contrasting with the theoretical dispersion relation. The surprise here is that an ``off-resonant'' drive readily modifies the velocity distribution so as to make the drive {\it resonant}. These plasma modes can also be excited by a chirped down frequency burst, similar to the one described by the Berkeley group.\footnote{Bertsche et al., {\it Phys. Rev. Lett.} {\bf 91}, 265003 (2003).} The chirped excitation creates extreme modification of $f ({\mathrm v}_z )$, and can be tailored to support a plasma mode at almost any frequency. We also observe that the resonant frequency of both EAW and TG plasma modes decreases with mode amplitude, in a fully reversible manner; but this effect has no theoretical explanation.   

Antihydrogen Trapping with the ALPHA apparatus

Cold antihydrogen was first produced in 2002. Precision comparison of hydrogen and antihydrogen, which remains the ultimate goal of these experiments, promises to be the most precise test yet of the CPT theorem. I.e. that hydrogen and antihydrogen must have the same spectrum at any level of precision. To make such tests possible the ALPHA collaboration have decided that the most promising route is to trap the antihydrogen. We describe the current state of the ALPHA endeavour, as well as the most recent results. One issue is whether magnetic traps, which are the key to trap the neutral antihydrogen are at all compatible with the penning traps used to store the charged species that make up the antiatoms. As quadrupole magnetic fields were at best, badly compatible with our envisaged schemes for antihydrogen, ALPHA uses a magnetic octupole to create the transverse magnetic field minimum necessary to trap antihydrogen. We have demonstrated that charged particles trapped in a superposed penning trap are stable in this field, it remains ``only'' to demonstrate antihydrogen formation, and ultimately trapping. The main challenge for the trapping seems at present to be that antihydrogen, using the current methods, tends to be formed at temperatures to high to allow trapping. ALPHA is currently working on a number of schemes to overcome this obstacle.   

Magnetic Priming at the Cathode and Anode of a Relativistic Magnetron

Magnetic priming$^{1,2}$ experiments on the UM/ L-3$\neg $Titan relativistic magnetron (100 MW's in L-band, -300 kV, $\sim $3 kGauss), have shown suppression of unwanted modes and reductions in starting currents for the pi-mode. Data from continuing simulations and experiments on magnetic priming at the cathode will be presented, as well as data on magnetic priming at the cathode and anode. Data show that magnetic priming at the cathode significantly lowers (average factor of 2.5) the starting current for pi-mode generation. The percentage of pi-mode shots was also increased by magnetic priming at the cathode by as much as 60{\%} over unprimed shots. Experiments and simulation results will be reported concerning the effects of magnetic priming at both cathode and anode. References [1] V.B. Neculaes, R.M. Gilgenbach, and Y.Y. Lau, US Patents 6,872,929 (3/29/2005) and 6,921,890 (7/26/2005); Appl. Phys. Lett., 83, 1983 (2003). [2] M.C. Jones, V.B. Neculaes, W. White, Y.Y. Lau, and R.M. Gilgenbach, Appl. Phys. Lett., 84, p1016, (2004) Acknowledgements: This research was supported by AFOSR, AFRL and the AFOSR-MURI Program on Cathode and Window Breakdown for High Power Microwave Sources   

Recent Advances in Magnetron Phase Locking: Effects of Frequency Chirps and Locking of Multiple Magnetrons

Phase-locking is utilized today in many important applications, ranging from small scale devices such as cardiac pacemakers to large scale devices such as radar. We have recently developed a magnetron-specific model [1] to qualitatively explain the various regimes observed in magnetron injection-locking experiments [2], which utilize two continuous wave oven magnetrons; one functions as an oscillator and the other as a driver. We have applied this model to study injection locking when the driver has a frequency chirp. The model has also recently been extended to analyze peer-to-peer locking of two magnetrons of comparable powers and frequencies. The feasibility of locking will be explored in terms of the variations in these parameters of the individual magnetrons, as well as the degree of coupling among them. Locking of a larger number of such magnetrons will be explored. A preliminary experiment is being conducted on the peer-to-peer locking of two oven magnetrons. [1] P. Pengvanich, et al., J. Appl. Phys. \textbf{98}, 114903 (2005). [2] V. B. Neculaes, Ph.D. Dissertation, U. Michigan, Ann Arbor, MI (2005).   

Metal-Oxide-Junction, Triple-Point Cathodes for High Current Vacuum Electron Devices

Recent experiments at the University of Michigan have fabricated metal-oxide junction cathodes consisting of hafnium oxide coatings over stainless steel substrates. High dielectric constant HfO$_{X}$ coatings are deposited by ablation-plasma-ion lithography using a KrF laser at 248 nm and 3-40 J/cm2 fluence. Experiments were performed on a relativistic magnetron driven by the Michigan Electron Long-Beam Accelerator at voltages of -300 kV, currents of 1-15 kA, and pulse-lengths of 0.3-0.5 ms. Experiments tested four patterned arrays of HfO2 islands on stainless steel cathodes. Three baseline comparison cases were run: fully dielectric coated, bare metal, and metal-only islands. Experimental data show initial peak currents for cathodes patterned with HfO$_{X}$ islands, reached an average of 6 kA, 60{\%} larger than uncoated cathodes. Current turn-on and rise time are also significantly faster for the patterned arrays of HfO$_{X}$.   

Electric field and electron orbits near a triple point

Triple point, defined as the junction of metal, dielectric, and vacuum, is the location where electron emission is favored in the presence of a sufficiently strong electric field. In addition to being an electron source, the triple point is generally regarded as the location where flashover is initiated in high voltage insulation, and as the vulnerable spot from which rf breakdown is triggered. In this paper, we focus on the electric field distribution at a triple point of a general geometry, as well as the electron orbits in its immediate vicinity. We calculate the orbit of the first generation electrons, the seed electrons. It is found that [1], despite the mathematically divergent electric field at the triple point, significant electron yield most likely results from secondary electron emission when the seed electrons strike the dielectric. The analysis gives the voltage scale in which this electron multiplication may occur. It also provides an explanation on why certain dielectric angles are vulnerable to electron multiplication over others, as observed in previous experiments [1]. This work was supported by AFOSR. \newline \newline [1] N. M. Jordan et al., J. Appl. Phys. (in press, 2007)   

Electric field distribution on knife-edge field emitters

Of critical importance to advanced High Power Microwave (HPM) generators is the development and understanding of robust cold cathodes with low turn-on electric fields. Recent interesting candidates include ridged metallic cathodes fabricated by either laser ablation or other microfabrication methods [1]. We use conformal mapping to calculate the electric field on a knife-edge cathode. We find that the field enhancement factor scales approximately as the square root of the height-width ratio of the knife-edge [2]. An analytic approximation for the divergent electric field in the immediate vicinity of the sharp edge is derived. A smaller knife-edge placed on top of a larger one demonstrates that the composite field enhancement factor is approximately equal to the product of the field enhancement factor of the individual knife-edges. This proves the conjecture [3] on multiplication of field enhancement factors for one special case. This work was supported by AFOSR/MURI and by AFRL. \newline [1] M.C. Jones, et al, Rev .Sci.Instrum.,75, 2976 (2004) \newline [2] R. Miller, Y. Y. Lau, J. H. Booske, Appl. Phys. Lett., (to be published) \newline [3] W. Schottky, Z. Physik, 14, 63 (1923).   

Effect of Random Circuit Fabrication Errors on Small Signal Gain and Phase in Helix Traveling Wave Tubes

Motivated by the current interest in mm-wave and THz sources, which use miniature, difficult-to-fabricate circuit components, we evaluate the statistical effects of random fabrication errors on a helix traveling wave tube amplifier's small signal characteristics. The small signal theory is treated in a continuum model in which the electron beam is assumed to be monoenergetic, and axially symmetric about the helix axis. Perturbations that vary randomly along the beam axis are introduced in the dimensionless Pierce parameters b, the beam-wave velocity mismatch, C, the gain parameter, and d, the cold tube circuit loss. Our study shows, as expected, that perturbation in b dominates the other two. The extensive numerical data have been confirmed by our analytic theory. They show in particular that the standard deviation of the output phase is linearly proportional to standard deviation of the individual perturbations in b, C, and d. Simple formulas have been derived which yield the output phase variations in terms of the statistical random manufacturing errors. This work was supported by AFOSR and by ONR.   

Two-Dimensional Axisymmetric Child-Langmuir Scaling Law

The classical one-dimensional Child-Langmuir law has been extended to two dimensions by numerical simulation in planar geometries [1]. By considering an axisymmetric cylindrical system with emission radius $r$, outer radius $R > r$, and gap length $L$, we further examine the space charge limit in two dimensions. The ratio of the observed current density limit J$_{CL2}$ to the theoretical one-dimensional value J$_{CL1}$ is found to be a monotonically decreasing function of the ratio of emission area ($r^2$) to gap separation ($L$). This result is in agreement with the planar results, where the emission area is proportional to the cathode width (r) [1]. The simulations were run in the particle in cell code, OOPIC [2]. [1] J. W. Luginsland, Y. Y. Lau, and R. M. Gilgenbach, Phys. Rev. Lett. 77, 4668 (1996). [2] J. P. Verboncoeur, A. B. Langdon, and N. T. Gladd, Comp. Phys. Comm. 87, 199 (1995).   

Effect of abrasive surface roughening on the secondary yield of various metals

The secondary electron yield of metallic conductors plays a critical role in the development of multipactor discharges. These discharges require a secondary yield greater than unity at the appropriate energy level for sustained breakdown. By reducing the secondary yield below unity in the necessary energy range, multipactor and multipactor-induced glow discharges can be eliminated. Surface roughening has been shown to successfully lower the secondary yield to below unity (ref. 1). In addition, abrasive bead blasting has been shown to effectively reduce the secondary yield of copper surfaces while preserving voltage breakdown characteristics (ref. 2). This study investigates the effect of abrasive surface roughening on the secondary yield of materials such as copper, aluminum, and stainless steel. In addition to measuring the change in the secondary yield as a function of abrasive particle size, the multipactor resistance and voltage breakdown characteristics are investigated. In addition, the effect of vacuum conditioning via multipactor and rf plasma cleaning on the roughened surfaces will be discussed. \newline Ref. 1. H. Bruining. Physics and Applications of Secondary Electron Emission. McGraw-Hill, NY, 1954. \newline Ref. 2. T. P. Graves, Ph.D. Thesis, MIT. 2007   

Formation of regular filamentary plasma arrays generated by a 1.5 MW, 110 GHz gyrotron

We report the achievement of self-initiated breakdown of a volume of air at atmospheric pressure with a focused Gaussian beam generated by a pulsed gyrotron. The relevant parameters of the beam are the frequency of 110 GHz, pulse length of 3 microseconds, maximum peak power of 1.5 MW, and peak power density of 2.5 MW/cm$^{2}$. Regular two-dimensional arrays of plasma filaments, similar to those observed in our previous experiments on air breakdown at the surfaces of dielectric windows, were also present in the open-shutter images of volume breakdown. Patterns observed in volume breakdown allowed us to deduce that the formation of the array can be explained as a progressive development of each filament due to diffraction from each existing filament resulting in field enhancement approximately a quarter wavelength upstream of the filament. Electromagnetic wave simulations strongly corroborate this explanation. Further breakdown experiments will be also conducted in different pressures and gases in the near future.   

Initial Operation of a Wideband 140 GHz, 1kW Confocal Gyro-Traveling Wave Amplifier

The present experimental results of a zero-drive stable, short pulse 140 GHz gyro-traveling wave tube amplifier are reported. The amplifier consists of three amplifying sections employing a novel high order HE(0,6) operating mode of a quasi-optical confocal waveguide in order to reduce mode density and achieve circuit loss through diffraction rather than absorption in localized dielectric materials. The confocal waveguide preferentially provides higher loss to the lower order competing modes thus allowing operating in a higher order mode. Two quasi-optical severs are used to suppress backward wave oscillations. At present, the amplifier has achieved a linear gain of 34 dB in experiment, and peak output powers up to 400W have been observed at a beam voltage of 39.5kV, beam current of 1.65A, and beam pitch factor of 0.9. Bandwidths over 1 GHz have been observed.   

A Cusp Gun Gyro-TWA with Helical Waveguide Interaction Region

The latest results of experimental and numerical investigations of an X-band gyro-TWA with a cusp gun and a helically corrugated interaction region are presented. A helically corrugated waveguide radically alters the dispersion relation of the interacting mode such that it matches the electron beam dispersion over a broad frequency range at close to zero axial wavenumber. Gyro-amplifiers require relativistic electron beams with low velocity spread and with a high fraction of the electron energy associated with the cyclotron motion. For harmonic operation and mode control an axis-encircling beam is desirable. A cusp gun was used to produce an axis-encircling beam by passing an annular beam through a magnetic cusp, introducing an azimuthal rotation. The passage of an electron beam through a non-adiabatic magnetic field reversal converted part of the electron beam's axial velocity into axis-encircling transverse velocity. Experiments were carried out using a field emission cathode and proved highly successful with a 120keV, 37A azimuthally rotating annular beam being formed. Microwave radiation in the frequency range of 8.4Hz to 10.4GHz was produced, with an output power 1.1MW at a frequency of 9.4GHz, corresponding to a saturated gain of 35dB and a measured efficiency of 25{\%}.   

A High Power High Frequency Maser Based on a Two-Dimensional Structure

High power millimetre-wave sources operating in the W-band (75GHz-110GHz) frequency range are important for a number of applications. In order to achieve the desired high power coherent radiation, the use of an oversized annular electron beam is suggested. This will allow problems associated with high electromagnetic power density inside the interaction space (such as millimetre-wave pulse shortening) to be overcome. A 2D periodic lattice will be used to synchronize the radiation from different parts of the oversized electron beam as well as to ensure spatial and temporal coherence of the radiation. There are a number of radiation sources capable of generating continuous millimetre-wave radiation at MW power levels. Analysis of different beam-wave interaction mechanisms used to produce the radiation will be presented. Various models will be studied and compared for suitability for single mode operation at high frequency and power. The design of a high power source based on the optimum beam wave interaction mechanism for operation in the W-band frequency region will be presented.   

Development of Multi-Frequency (105-140) GHz Gyrotron

The paper presents last time achievement in the development of a step tunable multi-frequency gyrotron with a megawatt power level. The mock-up of such gyrotron with a new principle broadband electrodynamics system containing Brewster output window was successfully tested. In the frequency range (100-150) GHz the generation of power exceeding 1 MW was demonstrated at 6 frequencies with a very low (about 2{\%}) internal diffraction losses. On the basis of this result industrial gyrotron with a CVD diamond output window was constructed for 10 sec operation. The full time tests are planned for September 2007.   

Vortex structures in relativistic magnetrons

We showed recently the existence of vortex flows in the electron beam equilibria of magnetron structures consisting of a central cylindrical cathode and a periodically corrugated cylindrical anode [J. A. Davies and C. Chen, Phys. Plasmas 13, 012310 (2006)]. In this paper, we present a relativistic treatment of the equilibrium of a planar magnetron consisting of a planar cathode and a corrugated anode. The electron density in the electron layer is assumed to be constant, and guiding-center approximation is employed. Properties of the equilibrium such as the electrostatic potential, flow velocity, and the self-magnetic field are determined analytically. An interesting result of the present analysis is the appearance of vortex structures near the cathode. Test particle studies are carried out to identify the parameter regimes in which the guide-center approximation is valid. Progress in determining if these parameters regimes and our results are relevant to relativistic magnetron operation will be discussed.   

Small-Signal Gain Theory of a Planar Magnetron

A planar magnetron model is developed to analyze the small-signal theory of a magnetron. The analysis includes a full Floquet expansion and fully electromagnetic effects. The present planar model avoids the problem of multiple poles (singularities) and the model is a good approximation, provided that the A-K gap is small compared with the cathode radius. An analytical dispersion relation of such a planar magnetron is derived and the growth rate is calculated based on the dispersion relation. MAGIC2D simulations are performed on the planar magnetron. The simulated growth rate is found in good agreement with the theoretical prediction.   

RF Modes in the Saturated Stage of a Magnetron

Theoretical studies of the cold-fluid model of crossed-field electron vacuum devices such as magnetrons and crossed-field amplifiers have shown that there are two important stages to their operation [1]. First there is the ``initiation stage'' wherein an instability in the rf fields grows. When this instability saturates, the device enters into the ``saturation stage.'' In this stage, there are the two slow modes from the initiaion stage, and three additional fast modes. One of these fast modes is the drift (diocotron) resonance. The other two modes are cyclotron modes. Whence the equations for this system is a fifth order set of ODE's. Theory [1] has outlined the major features of the drift resonance in the saturation stage. However a complete understanding of it and the contributions of the cyclotron modes require a study of numerical solutions. In the saturation stage there are five rf modes; the original two modes of the initiation stage and three additional fast modes with fast vertical oscillations on the order of 100-1000 times that of the initiation rf modes. We will present numerical solutions of these rf modes in the saturation stage, discuss their implications and how these solutions differ from those of the initiation stage. \newline [1] D.J. Kaup, Phys. Plasmas {\bf 13}, 053113 (2006).   

Phase-matched even harmonic generation in relativistic ionization fronts

Relativistic harmonic generation in plasmas is an active field of research. Generating harmonics efficiently is still a challenge, mainly due to the difficulties in guaranteeing phase-matching in the conversion process over long interaction lengths. We present a novel scheme to generate phase-matched even harmonics in relativistic ionization fronts. The magnetic mode induced in the collision of e.m. radiation with relativistic ionization fronts, driven by an ultra-intense laser pulse propagating in a gas target, is used to generate even harmonics of the laser pulse. By controlling the frequency of the incident radiation the conversion process can be phase-matched. This scheme also provides a means of indirect detection and characterization of the magnetic mode, which was never observed experimentally. Our theoretical model predicts the phase-matching conditions and describes the amplitude evolution of the generated even harmonics. In order to check the validity of the model, detailed 1D and 2D PIC simulations were preformed with OSIRIS 2.0. The analysis reveals a good agreement between the theoretical model and the simulation results. The conversion efficiency of the process was also studied, indicating the possibility of achieving controlled highly efficient even harmonic generation.   

Interaction of intense lasers with nanostructured plasmas

Radiation generation from the interaction of intense laser pulses with solid density nanostructured plasmas is analyzed using PIC (two and three-dimensional) simulations performed with OSIRIS 2.0. The role of the relativistic electron dynamics on radiation generation is considered. The influence of the nanostructural design of different targets is studied through simulations, and the generation of radiation is optimized for different target periodicities and densities. Simulations show that the target properties allow for the spectral control of the radiated energy. The simulation results are compared with a theoretical model that takes into account the relativistic electron dynamics in the presence of the laser and the periodic self-consistent fields from the high (ion) charge density regions in the target.   

Soft X-ray radiation measured by four-segment vacuum photodiode

A soft X-ray diode is a strong diagnostic tool for system alignment, among others, in capillary discharge experiments, which generate directional soft x-ray radiation, eventually a laser pulse. In our experimental capillary discharge devices we usually used PIN diode or vacuum photodiode (one-segment). These diagnostics are not suitable, mainly because many shots (more than 50) are necessary to find the optical axis. Last year we designed and manufactured a four-segment soft X-ray vacuum photodiode with a golden photocathode, which detects the soft X-ray radiation emitted from our capillary discharge devices in the axial direction. This new vacuum photodiode is capable to locate the soft X-ray laser axis in a few shots (less than 10). The description and the experimental measurement of the four-segment soft X-ray vacuum diode will be presented.   

Fast capillary discharge facility CAPEX-U as a source of the soft X-ray radiation

Capillary discharges are more perspective resources for lasing in soft x-ray region than other media (free electron lasers, synchrotron sources, harmonic up-conversion of high power visible/IR lasers). After successful experiments on CAPEX device with lasing on Ne-like Ar ($\lambda $ = 46.9 nm) we report on our apparatus CAPEX-U (CAPillary EXperiment Upgrade) with larger transversal dimensions, with transparency along its axis, and with multichannel laser-triggered spark gap, which enables exact synchronization of the detectors and attached experiments. Our motivation for building such new apparatus was not only lasing on Ne-like argon, but also testing a feasibility of amplification at shorter wavelengths (below 20 nm). This paper presents the description of the CAPEX-U apparatus, and the results of axial soft X-ray spectroscopic measurements of the pulsed high-current capillary discharge.   

Possibility of an H-like N recombination laser at 13.39 nm excited by capillary discharge

A capillary discharge soft X-ray laser is fascinating in its high efficiency due to direct energy conversion from the electrical discharge energy and spatial coherence taking advantage of the long plasma column. In order to shorten the wavelength of the laser and to put it into practical use, possibility of the lasing of an H-like N recombination 13.39 nm laser, which can be focused by using a Mo/Si multi-layer mirror, is investigated. Population inversion between principal quantum numbers $n$=2 and $n$=3 might be generated in the expansion phase after the maximum pinch utilizing fast pulsed current amplitude of over 50 kA with pulse width of about 100 ns. Temporal radiation intensity from the nitrogen plasma column is measured using a x-ray photo diode to evaluate optimum plasma parameter required to realize a 13.39 nm laser.   

Relic crystal lattice effects on Raman compression of powerful x-ray pulses in plasmas

Powerful x-ray pulses might be compressed to even greater powers by means of backward Raman amplification in ultradense plasmas produced by ionizing condensed matter by the same pulses. The pulse durations contemplated are shorter than the time for complete smoothing of the crystal lattice by thermal motion of ions. Although inhomogeneities are generally thought to be deleterious to the Raman amplification, the relic lattice might in fact be useful for the Raman amplification. Caused by the lattice, the x-ray frequency band gaps can suppress parasitic Raman scattering of amplified pulses, while enhanced dispersion of x-ray group velocity near the gaps can delay self-phase modulation instability and also enable an extra amplification of x-rays in a way similar to the chirped pulse amplification technique.   

High Power Picosecond Laser Pulse Recirculation for Compton Scattering

Gamma-ray generation by Compton back-scattering laser photons off a relativistic electron beam suffers from a small Thomson cross-section. Recirculating unused laser photons can increase the average gamma-ray flux. Traditional approaches to laser recirculation rely on either resonant coupling of a low-energy pulse train to a cavity or active pulse switching using a pockels cell. Our alternative, passive approach does not require interferometeric alignment accuracy and is compatible with ultrashort, high peak power pulses. Pulse injection is achieved by a thin frequency converter inside the cavity in the path of the incident beam. The cavity consists of dichroic mirrors that transmit the incident but reflect the frequency-converted light. Initial modeling and experiments predict better than 20~times increase in the average brightness of Compton back-scattering sources with our pulse recirculation method.   

Evolution of FEL-produced plasma with photoionized electron two-stream instability

Plasmas created in the interaction of X-ray laser pulse of a free electron laser (FEL) with gaseous medium display a number of specific properties that are substantially different from characteristics of plasmas produced by optical lasers. An electron distribution function in the FEL-photoionized plasma is anisotropic and monoenergetic or multi-monoenergetic depending on the material. These features make these plasmas unstable with respect to photoionized electron two-stream (PITS) instability. In this paper we represent a kinetic non-stationary theory of PITS instability of a weakly ionized plasma which takes into account an electron production due to photo-effect through the interaction of an ultrashort linearly polarized X-ray FEL pulse with a gas jet, growth of unstable quasistatic electric field, and wave damping and electron distribution relaxation due to electron collisions with atoms. Our theory is based on the integral kinetic equation for correlation function of electron density fluctuations. The evolution and relaxation of PITS instability is illustrated by an example of He gas-jet ionized by EUV pulse of FEL with different pulse durations for typical gas-jet pressures.   

Commissioning of a high-brightness photoinjector for Compton scattering x-ray sources

Compton scattering of intense laser pulses with ultra-relativistic electron beams has proven to be an attractive source of high-brightness x-rays with keV to MeV energies. This type of x-ray source requires the electron beam brightness to be comparable with that used in x-ray free-electron lasers and laser and plasma based advanced accelerators. We describe the development and commissioning of a 1.6 cell RF photoinjector for use in Compton scattering experiments at LLNL. Injector development issues such as RF cavity design, beam dynamics simulations, emittance diagnostic development, results of sputtered magnesium photo-cathode experiments, and UV laser pulse shaping are discussed. Initial operation of the photoinjector is described and transverse phase space measurements are presented.   

Design and Initial Operation of a Tunable Compton-Scattering Based Gamma-Ray Source

Tunable, monochromatic gamma-ray sources are currently being developed at LLNL for nuclear photo-science and related applications. These novel systems are based on Compton scattering of laser photons by a high brightness relativistic electron beam produced by an rf photoinjector and offer a path to high-brightness high-energy ($>$ 1 MeV) x-ray {\&} gamma-rays due to their favorable scaling with electron energy. The current demonstration source, called the ``Thomson-Radiated Extreme X-Ray" (T-REX) source, targets photon energies up to 1 MeV. With extensive modeling using PARMELA and well-benchmarked custom Compton-scattering simulation codes, the optimal design parameters for an interaction (including factors such as the collision angle, focal spot size, bunch charge, laser intensity, pulse duration, and laser beam path) can be determined. Here we present the results of this optimization, including early experimental results from the newly commissioned system.   

Overview of NSTX Research Facility and Recent Experimental Results.

The 2007 NSTX experimental campaign yielded significant new experimental results in many science areas. Measurements of the turbulent electron fluctuation spectrum made over a wide range of plasma conditions including H-mode, L-mode, and reversed shear plasmas using the high-k microwave scattering system which is capable of local measurements of electron scale turbulence with MHz bandwidth. RWM feedback control has been explored at high beta with and without error field correction. The upgraded lithium evaporator was used to improve the plasma confinement and increase Te in H-mode plasmas. With lithium evaporation, a significant increase in the Electron Bernstein waves emission was observed in H-mode plasmas at high elongation. For the first time, beta suppression of Alfven cascades was documented and the beta-induced Alfven acoustic eigenmode was observed at high beta. Deuterium puffing has been used to demonstrate partial divertor detachment in highly shaped plasmas with little confinement deterioration. A record electron temperature of 4.7keV was achieved on NSTX using HHFW current drive phasing.   

Effects of Evaporated Lithium Coatings on Plasma-Facing Surfaces in NSTX

An evaporator has been used to apply lithium to the carbon tiles on the lower divertor in NSTX at rates up to 70mg/min. Numerous lithium depositions were performed in the 2007 operating period, ranging from about 10mg to 2g but typically 200 - 300mg of lithium prior to a discharge. The lithium evaporation continued through the 5 - 10 min. of helium glow discharge cleaning usually applied before each shot and during the tokamak discharge as well, which distributed the lithium more widely than line of sight. Examination of the divertor tiles after the experiments showed migration of the lithium away from the strike-points. The effects of lithium were studied over a range of plasma conditions. In 1MA, 0.45T, H-mode plasmas with 4MW NBI, there was an increase of about 20\% in the electron and 10\% in the total stored energy and ELM activity was reduced or suppressed after lithium. This was accompanied by increasing impurity radiation from the core which sometimes limited performance. Contrary to previous experience, the effects of the lithium coating could persist for several discharges after application.   

NSTX conditioning experiment using injected lithium powder

An attempt was made to condition the plasma facing components of NSTX by injecting Li powder. The injection was carried out using the existing lithium pellet injector with a modified sabot design. The 50 micron diameter powder was injected into several discharges while its effects were evaluated on each subsequent discharge. A discussion of the effects of this experiment will be presented. This work was supported by U.S. DOE Contract {\#} DE-AC02-76CH03073.   

Effects of Lithiumization of Electron Temperature and Density Profiles

NSTX conducted an aggressive first wall conditioning campaign during which up to 100~g of lithium was evaporated progressively inside the vacuum vessel. This work will search for change in the behavior of $n_{e}$ and $T_{e}$ profiles measured by Thomson scattering. Casual observation during the earlier phase of the lithiumization did not reveal significant changes, but a systematic search will be done for the preparation of this paper. Contrary to last year's results, the effects of this more aggressive lithiumization appear to last longer; increase in stored energy and reduction of ELM activity have been observed, sometimes accompanied by core impurity accumulation. Further analysis will attempt to correct the part of the Thomson scattering data which was affected by window coating during the last month of plasma operation. This work is supported by United States DOE contract DE-AC02-76CH03073.   

Measurements of radiated power during LiTER operation in NSTX

Lithium vapor was injected into the NSTX vacuum vessel by heating lithium in a stainless steel oven that was placed in close proximity to the plasma facing components during the 2007 experimental campaign. Low-Z coating experiments using carbonization, boronzation, an lithium pellets have been used for many years to improve confinement and performance. Time-resolved radiated power profiles of the total plasma radiation in the mid-plane was measured using a 16-channel tangential bolometer. Results showed that confinement was appreciably affected during the runs with lithium deposition. Generally, ELM's were either reduced or eliminated for hundreds of milliseconds, and the density profiles were peaked, rather than flat as in typical H-mode plasmas. The metallic impurity profiles tended to be highly peaked as well, often accompanied by strong impurity accumulation in the center of the plasma. In the more severe cases, the volume-integrated radiated power would exceed 50{\%} of the total input power and the estimated concentration of metals on axis (modeled using iron as the representative impurity) reached 0.2{\%} of the electron density.   

Spectroscopy of NSTX Plasmas During Lithium Wall Conditioning Experiments

During the 2007 NSTX campaign a lithium evaporation system, LiTER, was used to coat plasma facing components as part of a long term program to explore the potential for lithium to improve plasma and PFC performance. The plasma emission was recorded by vacuum ultra-violet and air wavelength spectrometers and showed significant changes with lithium conditioning. Preliminary results show that the lithium conditioning suppressed oxygen and hydrogen to deuterium ratios. However, with lithium applied, ELM-free H-mode plasmas were achieved, which developed high central radiation containing significant levels of metallic impurities. We will present data on the spectral emission of the plasma both with and without lithium evaporation and compare it to 2006 data.   

XPS studies of NSTX tiles and in-situ analysis of Li exposed graphite simulating plasma-Li surface interactions.

Lithium has been considered a potentially viable plasma-facing surface enhancing the operational performance of fusion devices such as: TFTR and NSTX. In particular, lithium coatings are used in NSTX runs to enhance energy confinement. Questions remain on the role of lithiated surfaces and multi-material interactions at the plasma edge. Processes of interest are the erosion of lithiated graphite surfaces, diffusion of Li into graphite and D-retention of lithium-covered surfaces. These processes consist of spatial scales from a few monolayers at the vacuum/film interface to 100's nm deep. Studies are conducted in the IMPACT experimental facility. IMPACT is designed to study \textit{in-situ} how multi-component surfaces evolve under particle irradiation. Techniques include: low-energy ion scattering spectroscopy (LEISS), direct recoil spectroscopy, X-ray photoelectron spectroscopy and in-situ erosion diagnosis. In this paper detailed LEISS and XPS studies of lithiated graphites surfaces simulating conditions in NSTX are presented.   

UEDGE Simulations of the NSTX Liquid Lithium Divertor Module

The Liquid Lithium Divertor (LLD) module planned for installation in the lower divertor of NSTX will provide a nearly toroidally continuous liquid lithium surface in close proximity to the plasma. The objective of the module is to pump enough deuterium to allow full control of the plasma density thereby permitting high performance H-modes to be held in near steady state and increasing the fraction of non-inductively driven current. A series of UEDGE simulations has been carried out to aid in the determination of the optimal location, which may be inboard or outboard of the CHI insulating break, as well as the width of the LLD. UEDGE's transport coefficients and boundary conditions have been adjusted to match an existing NSTX discharge intended as a prototype of the high performance H-mode experiments planned for the LLD. The effect of the LLD has been incorporated into UEDGE as a reduction in the recycling coefficient over a section of the divertor. With the plasma flux coming of the core held fixed, the liquid lithium's particle absorption results in a reduction in the simulation's plasma density at the core boundary. The primary output of this study is then the variation of this density reduction with the major radius and width of the LLD.   

NSTX High-k Scattering System on NSTX: Status and Plan

A multi-channel collective scattering system was commissioned on NSTX to investigate anomalous electron transport physics related to the electron density turbulence. NSTX plasma parameters with a large gyro-radius ($\rho _{i} \quad \sim $1 cm) facilitate the investigation of the turbulence related physics in the high-k regime (k$_{r}\rho _{s}>$3) which is not readily accessible in other toroidal devices. The system employs a moderate power ($\sim $100 mW) source at $\sim $ 1 mm wavelength as the probe beam and has an excellent spatial and wavenumber resolution. The system consists of 5 discrete channels which primarily measure five radial wavenumbers up to k$_{r} \quad \sim $ 20 cm$^{-1}$ which corresponds to k$_{r}\rho _{e}\sim $0.2 and $\sim $0.7 for the NSTX edge and core parameters, respectively. Initial results from various operating regimes [edge and core of the quiescent OH, L/H modes of the RF and NBI heated plasmas] will be addressed in this paper. The observed high signal to noise ratio at the highest wave-number provides confidence in the future upgrade plan for even higher wavenumbers up to $\sim $50 cm$^{-1}$ (k$_{r}\rho _{e}\sim $2) employing a shorter probe beam wavelength in which the net S/N is comparable (optimum beam power and available detector sensitivity) to the present $\sim $1mm system. Upgrade plans for the tangential and poloidal high-k configuration that can share the same probe beam will be discussed.   

Investigation of electron gyroscale fluctuations in NSTX plasmas

Electron gyroscale fluctuations are studied to reveal the existence and nature of electron temperature gradient (ETG) turbulence in NSTX plasmas. The role of parameters relevant to ETG turbulence, such as $\nabla T_e$, $\hat{s}$, and $T_e/T_i$, are highlighted. Fluctuation spectra are obtained using a multi-channel, microwave scattering system that measures fluctuations with $k_\perp\leq20\mbox{ cm}^{-1}$ and $k_\perp\rho_e\leq0.6$. The system can measure up to five distinct wavenumbers simultaneously, and the $k$-space resolution is $\Delta k_\perp\approx0.7\mbox{ cm}^{-1}$. The probe and receiving beams are positioned nearly on the equatorial midplane and configured for tangential scattering, so measured fluctuations are primarily radial. Steerable optics can position the scattering volume throughout the outer half-plasma from the magnetic axis to the edge. In addition to fluctuation spectra, transport calculations using \texttt {TRANSP} and linear gyrokinetic calculations using \texttt{GS2} are also presented. This work is supported by the U.S. Department of Energy under Contract Nos. DE-AC02-76CH03073, DE- FG03-95ER54295, and DE-FG03-99ER54531.   

In-situ calibration of the high-k scattering system on NSTX

The tangential collective Thomson scattering system which is capable of simultaneously measuring five wave-numbers has been extensively engaged in physics studies during the last campaign on NSTX. In-situ calibration of the scattering parameters as well as the receiver system is essential to quantify the detected scattered power. Calibration of the receiver system will be performed by a power modulation technique and standard hot-cold load method. One of the key scattering parameters of the tangential scattering system is the reduced scattering length due to the improved k-matching condition arising from the tight toroidal curvature and strong magnetic shear on NSTX. Theoretical assessment of the effect of the toroidal curvature and magnetic shear on the scattering length will be experimentally quantified using an acoustic cell which can excite waves with a known frequency, wavenumber and well defined direction of the propagation. In addition, measurement of other scattering parameters such as the wave number resolution and wave propagation direction of the heterodyne detection system will be addressed. This work was supported by the U.S. DOE Contract {\#} DE-AC02-76CH03073, POSTECH BK-21, and NFRC.   

Separation of momentum diffusion and pinch using n=3 non-resonant braking perturbations on NSTX

Perturbative studies of momentum transport have been made on NSTX using n=3 non-resonant braking as a means of perturbing the rotation profile. The braking was applied for 50 ms during a relatively MHD-quiescent phase of the discharge, after which the evolution of the plasma rotation was measured. The non-local torque perturbation created by the n=3 error field created some distortion to the toroidal rotation profile, allowing the separation of momentum flux caused by diffusion (proportional to the gradient in the toroidal rotation) and a momentum pinch (proportional to the toroidal rotation). Preliminary analysis indicates the necessity of a momentum pinch to explain the profile evolution. The effect of off-diagonal terms in the momentum balance equation (eg grad(Ti), grad(ne)) are also considered.   

Beam Modulation Effects on NSTX Ion Power Balance

The coupling between the beam particles and the thermal ions is poorly understood.~ To examine the coupling, the beam power was modulated. The fast particles were then measured using a variety of diagnostics. The neutron rate from beam-target interactions shows the expected behavior, with the signal decreasing to a new steady state value in $<$10 ms.~ The Neutral Particle Analyzer (NPA) shows a presence of fast ions at various pitch angles, but not at others.~ The NPA measurement is compared to other fast ion diagnostics including the Fast Ion D Alpha (FIDA) diagnostic, the Solid State Neutral Particle Analyzer (SSNPA) and the Scintillator Fast Loss Ion Probe (SFLIP) diagnostic.~ Comparison is also made between measured NPA signals and TRANSP calculations.~ The ion and electron temperature were also measured and compared before and after the start of the modulation, and conclusions are drawn about the coupling between the beam and the plasma.   

Fast electron temperature, MHD and transport measurements on NSTX using a multi-energy SXR array

A compact multi-energy soft X-ray array has been developed for fast ($\leq$0.1 ms) time and space-resolved electron temperature, MHD and transport measurements on the National Spherical Torus Experiment (NSTX). The electron temperature is obtained by modeling the slope of the continuum radiation from ratios of the Abel inverted radial emissivity profiles in three energy ranges [1]. The applicability of this diagnostic technique to radio frequency electron heating and current drive experiments, perturbative electron and impurity transport studies, as well as an analysis of the impact of several types of MHD activity such as NTMs, RWMs, ELMs and Fishbones will be discussed. This work supported by U.S. DoE Contract No. DE-AC02-76CH03073 DoE and grant No. DE-FG02-99ER5452 at The Johns Hopkins University. \newline [1] L. F. Delgado-Aparicio, et al., Plasma Phys. Controlled Fusion, \textbf{49}, 1245 (2007).   

Time-dependent measurements of the B, C, N, and O Lyman-$\alpha$ emission

The X-ray and Extreme Ultraviolet Spectrometer (XEUS) has been used to monitor the line emission from various impurity ions on NSTX, in particular the K-shell emission of heliumlike and hydrogenlike B, C, N, and O. While C VI typically dominates the spectrum, unusually strong emission from N VII has been observed in multiple disharges during the past run campaign. In this case, the nitrogen concentration can exceed that of carbon by an order of magnitude. Time-dependent measurements show that the nitrogen concentration builds up over the course of the discharge and coincides with a build up of boron. In a few cases we observed several unknown lines. These are clearly lines from heavy impurities, possibly molybdenum. Some of these lines can be explained by the emission from Ti XIII.   

The Motional Stark Effect Diagnostic on NSTX

This work describes the implementation and recent results from the MSE-CIF diagnostic on NSTX. Due to the low magnetic field on NSTX the MSE diagnostic requires a new approach for the viewing optics and spectral filter. This has been accomplished with a novel optical design that reduces the geometric Doppler broadening, and a high throughput, high resolution spectral filter to optimize signal-to-noise. This MSE diagnostic presently has 16 of a possible 19 sightlines operating, providing measurements of the magnetic field line pitch from the plasma center to near the outboard edge of the plasma. The system operates well at low magnetic field, $\geq$0.3~T, using collisionaly induced fluorescence (CIF) from a deuterium heating beam operating at about $\sim$90~keV. MSE data has been obtained in several regimes, including L-mode, H-mode, and reversed shear. The measurements reveal the development of both monotonic and reversed shear q-profiles depending on the discharge evolution. The presence of MHD is found to have a significant effect on the profile evolution and will be discussed.   

Millimeter-wave measurements of edge electron density profile and fluctuations during NSTX H-mode discharges

The fast evolution of the density profile and the associated changes in turbulence are measured near the plasma edge in NSTX H-mode discharges using millimeter-wave reflectometry. FMCW reflectometry (13-50 GHz) provides fast profile measurements with 20 us resolution, while multiplexed fixed-frequency systems (30, 35, 42, 44.5, 50, 65 GHz) monitor fluctuations at various cutoff densities. A new correlation reflectometer (29-40 GHz) is used to measure the poloidal propagation of turbulence. The bulk poloidal velocity can be inferred from these measurements while the propagation of individual turbulence structures is also visible. In addition to the L-H transition, profile and turbulence characteristics are monitored for the various ELM types (Type I, Type III and Type V) present in NSTX.   

NSTX H-mode measurement in conjunction with gyrocenter shift via FIReTIP system

The Far Infrared Tangential Interferometer/Polarimeter (FIReTIP) which spans the entire plasma is used to measure electron density fluctuations during the low confinement mode (L-mode) to high confinement mode (H-mode) transition on the National Spherical Tokamak Experiment (NSTX). The measured neutral density distribution and the radial electric field evolution are compared to the calculations based on the gyrocenter shift [K. C. Lee, \textit{Phys. Plasmas}\textbf{13}, 062505 (2006)].The statistical analysis of electron density fluctuations measured by the FIReTIP system including data from a newly installed additional channel will be reported. Also, the role of the neutral density gradient on the L to H transition associated with the radial electric field formation and turbulence suppression will be discussed.   

Bandwidth Upgrade for the NSTX FIReTIP System

The multichannel Far Infrared Tangential Interferometer/Polarimeter (FIReTIP) system, installed on the National Spherical Tokamak Experiment (NSTX) which has a great potential to be used as a monitoring system for the density fluctuations spanning from micro-turbulence to coherent MHD activities, is currently limited to a 250 kHz video bandwidth. New electronics under development at UC Davis will extend this to approximately 4 MHz in order to access the high frequency density fluctuation spectra and compressional Alfv\'{e}n eigenmodes (CAE) modes driven by supra-Alfv\'{e}nic neutral beam ions on NSTX. Such instabilities are expected to be important for the performance of the ITER burning plasma, where neutral beam and fusion alpha ions are also supra-Alfv\'{e}nic. Additional electronics will allow the study of high harmonic fast wave (HHFW) induced 30 MHz density fluctuations superimposed on the FIReTIP signals. Technical details regarding the FIReTIP upgrade will be presented.   

Control of asymmetric magnetic perturbation in tokamaks by computation of ideal perturbed equilibria

It is well known that tokamak plasmas are highly sensitive to a small breaking of axisymmetry by external magnetic perturbations. The newly developed Ideal Perturbed Equilibrium Code (IPEC) computes an ideally perturbed equilibrium by the perturbations, thereby yielding the three-dimensional features of the perturbed plasma in high resolution. The application of the code to observations of locked modes in NSTX and DIII-D resolved paradoxical results and revealed the most sensitive mode of external perturbations, whose reduction is most important for the control of field error problems in tokamaks. IPEC has numerous applications, such as error field mitigation in ITER or the plasma response to ELM control coils. IPEC can be extended to compute the perturbed equilibria in the presence of plasma viscous forces due to the toroidal asymmetries in the magnetic field strength and can be compared with measured plasma responses in NSTX.   

Nonlinear Study of Error Field Effects in NSTX

RWM stabilization by plasma rotation in NSTX is impeded by the presence of a time-dependent non-axisymmetric component to the toroidal field [1]. Confinement is improved by active correction of this error field; its exact cause is still under investigation. A numerical study of the effects of the error field on magnetic island formation was conducted with ideal linear codes [2], providing estimates of the island widths based on the amplitudes of the singular current sheets that result from the perturbation. We extend these results by conducting nonlinear, non-ideal studies of these effects using the M3D code [3]. The nonlinear correction to the linear response to a pure m=2, n=1 perturbation is shown, followed by investigations of the effects of toroidal rotation and of mode locking and consequent rotation damping. \newline [1] J.E. Menard, et al., submitted to Nucl. Fus., 2007. \newline [2] J.K. Park, poster presented at Sherwood Fusion Theory Conference, Annapolis, MD, April 2007. \newline [3] W. Park, et al., Phys. Plasmas 6, 1796 (1999).   

MHD Induced Neutral Beam Ion Loss from NSTX

Bursts of MHD activity at $\sim $60 kHz occur commonly in NSTX plasmas, particularly at high beta, and are accompanied by neutral beam ion loss over a range in pitch angles. The pitch angle and energy distributions of these losses have been measured with a scintillator type loss probe viewed by a high speed video camera. The data from one representative burst that causes a 13{\%} reduction in the neutron rate has been studied thoroughly and has several interesting features. At first, the mode has a purely n=1 character, sweeping downward in frequency. There is no change to the underlying prompt loss signal during this interval, indicating there is no phase space transport of fast (80 keV D) ions into the loss cone from the frequency sweeping. Later, a concurrent n=2 mode arises, followed quickly by a concurrent n=3 mode. When multiple modes are present, loss is seen over a wide range of pitch angles, suggesting stochastization of the beam ion orbits. There is no evidence of any sweeping in pitch angle of the loss in either phase of the burst, at least not on the 100 us time scale.   

Neutral Particle Analyzer Vertically Scanning Measurements of MHD-induced Fast Ion Redistribution or Loss in NSTX

Observations of MHD-induced redistribution or loss of energetic ions measured using the vertically scanning capability of the Neutral Particle Analyzer diagnostic on the National Spherical Torus Experiment (NSTX) are presented along with TRANSP analysis. Although redistribution or loss of energetic ions due to low-f $\sim $ 10 kHz continuous kink-type MHD was reported previously [1,2], here the primary goal is to study redistribution or loss due to continuous Alfv\'{e}nic (f $\sim $ 20 -- 150 kHz) modes. Initial indications are that the former drive energetic ion loss whereas the continuous Alfv\'{e}nic modes at most only cause redistribution and the energetic ions remain confined. \newline [1] S. S. Medley\textit{, et al}., Nucl. Fusion \textbf{44}, (2004) 1158 \newline [2] J. E. Menard, \textit{et al.}, Phys. Rev. Lett. \textbf{97}, (2006) 095022   

Effect of halo neutrals on neutral particle measurements

The Neutral Particle Analyzer (NPA) diagnostics including the E$\vert \vert $B type NPA and solid state NPA (ssNPA) array on the National Spherical Torus Experiment (NSTX) measure neutral production in charge exchange reactions between energetic ions and beam primary and halo neutrals. A Monte Carlo simulation code is developed to analyze the effect of primary neutrals and halo neutrals to the NPA flux temporal evolution and energy spectrum. The code is validated by comparing with the TRANSP-simulated NPA signals and an analytical halo diffusion model. The simulation results show that the density of halo neutrals around the beam footprint is comparable to that of primary neutrals. Charge exchange with halo neutrals contribute significantly to the neutral flux measured by NPA diagnostics for typical NSTX conditions. Effect of halo neutrals in quiet plasmas and discharges with beam modulation and vertical NPA scans will be presented.   

Excitation of Beta-induced Alfven-acoustic eigenmodes and q-profile MHD spectroscopy in NSTX.

We report on observations and interpretations of a new class of global MHD eigenmode solutions arising in gaps in the low frequency Alfv\'{e}n -acoustic continuum below the geodesic acoustic mode (GAM) frequency. These modes have been just reported [N. N. Gorelenkov {\em et.al.}, Phys. Letters A, doi:10.1016/j.physleta.2007.05.113 (2007)] are the result of coupling of the Alfv\'{e}n and acoustic continua due to geodesic curvature. We show good quantitative comparison of the theory predictions with recent NSTX experiments on the observations of these modes, referred to as Beta-induced Alfv\'{e}n - Acoustic Eigenmodes (BAAE). They exist near the extrema points of the Alfv\'{e}n - acoustic continuum and can sweep up in frequency from zero value in the plasma frame as q-profile relaxes. We show that the measurements of BAAE frequency can be used to infer $q_{min}$ in both reversed and monotonic q-profile plasmas. In NSTX experiments we see a correlation of the MSE measured q-profile evolution and BAAE instabilities. TRANSP code is used to understand q-profile evolution by comparing it to classical predictions.   

Nonlinear simulations of NBI driven GAE modes in NSTX

Hybrid 3D code HYM is used to investigate beam ion effects on MHD modes in a NSTX, aiming at simulations of NSTX shots where chirping frequency GAE/CAE modes have been observed. Thermal plasma is modeled using the MHD equations, and full-orbit delta-f kinetic description is used for the beam ions. Simulations show that for large neutral beam injection velocities and strong anisotropy in the pitch-angle distribution, many Alfven modes are excited. Unstable GAEs modes for $27$ are observed. Scaling of the growth rate of GAE mode with beam ion density is stronger than linear due to significant modification of plasma equilibrium profiles. Profile modification is due to self-consistent beam ion effects, and it has indirect effect on the stability. It was demonstrated that phase velocity of the unstable GAE mode has opposite sign compared to the beam injection velocity, and the resonant particles satisfy Doppler-shifted cyclotron resonant conditions. Dependence of the growth rate on dissipation parameters is studied. Nonlinear simulations show that the GAE instability saturates at low amplitude.   

Development of a Fast-Ion D-Alpha diagnostic for NSTX

A Fast-Ion D-Alpha diagnostic based on active charge exchange recombination spectroscopy is being developed for NSTX. The first results from the 2007 run, obtained with a prototype setup, indicate that fast ion signals have been successfully detected. The signals show a clear time correlation with the neutron emission from beam-plasma reactions. During modulation of the injected neutral beam power, variations on the fast ion slowing down time-scale are observed. The signal amplitude from different spectral regions scales accordingly with the fast ion D$_{\alpha }$ spectrum. For the 2008 run, sixteen channels will cover the outboard poloidal cross-section with a resolution in space, time and energy of 5cm, 10ms and 10keV. In addition, three dedicated channels will monitor the signal from suprathermal ions on time-scales $\sim $10us at different radii. Each channel includes two views inside the plasma, intercepting/missing the neutral beam for a direct subtraction of the background signal not associated with fast ions.   

Identification and Study of MHD modes on NSTX using Soft X-ray Images

Theory and experiments indicate that MHD phenomena can cause significant fast particle losses which in turn lead to heating power loss and elevated wall power loading in present experiments and possibly future burning plasma devices. It is important for STs, ITER, and ITPA database scaling to understand the dominant MHD modes and their effects on fast particles. We have studied the spatial structure and time behavior of the MHD in NSTX using a unique fast soft x-ray imaging camera with a wide-angle (pinhole) tangential view of nearly the entire plasma minor cross section. The camera provides a 64x64 pixel image, on a CCD chip, of light resulting from conversion of soft x-rays incident on a phosphor to the visible. We have acquired plasma images at frame rates of 1-500 kHz (300 frames/shot), and have observed a variety of MHD phenomena: internal reconnection events, disruptions, sawteeth, fishbones, tearing modes, and ELMs. This is important to ITER due to fast particle ($\alpha $'s,etc.) losses. Modes with frequency $>$ 90 kHz have been observed.   

Numerical Investigations of Instability-Induced Current Redistribution in a Spherical-Torus Plasma

Recent experimental observations suggest that interchange-type instabilities may play an important role in redistribution of the neutral beam injected current in the National Spherical Torus Experiment (NSTX). In our present work, the guiding center orbits of various test particles are integrated in the presence of a prescribed magnetic perturbation using a modified version of the ORBIT code. The perturbation modes are derived from NSTX diagnostic data during periods where instability-induced redistribution is observed experimentally. These results show the possibility of enhanced transport for certain regions of phase space. Simulations are also presented which show the time evolution of the neutral beam injected ion distribution, where the initial profile is obtained using a newly developed component for NUBEAM, part of the TRANSP software package. Ultimately, we hope to develop a self-consistent model for instability-induced current redistribution, including possible self-regulation between the fast-ion current and the core MHD instabilities.   

SOL width scale lengths in NSTX

The SOL T$_{e}$ and n$_{e}$ profiles have been investigated with a mid-plane fast reciprocating probe in NSTX. The SOL plasma consists of two regions; a region close to the LCFS where a steep gradient of the profile is observed (\textit{ie} near SOL region) and a region further away from the LCFS where a flatter profile is observed (\textit{ie} far SOL region). It was observed that the near SOL T$_{e}$ and n$_{e}$ decay lengths ($\lambda _{Te} $ and $\lambda _{ne})$ became significantly longer in L-mode compared to H-mode (a factor of $\sim $2 increase in $\lambda _{Te}$ and $\sim $3 increase in $\lambda _{ne})$. It was found that both $\lambda _{Te}$ and $\lambda _{ne}$ in the near SOL decrease with increasing plasma current (I$_{p})$ in H-mode (from $\lambda _{Te} \sim $3cm to $\sim $1cm and $\lambda _{ne} \sim $2cm to $\sim $1cm with I$_{p}$ variation from 0.8MA to 1MA). Near SOL $\lambda _{Te}$ and $\lambda _{ne}$ in L-mode increased ($\lambda _{Te} \sim $0.7cm to $\sim $1.1cm and $\lambda _{ne} \sim $1.5cm to $\sim $2.1cm) with increasing line averaged density (from 2.7 to 3.1x10$^{13}$cm$^{-3})$ and decreased ($\lambda _{Te} \sim $1.7cm to 0.4cm and $\lambda _{ne} \sim $1.3cm to 0.5cm) with increasing input power (P$_{NBI}\sim $1MW to 4MW). A comparison with Thomson Scattering (TS) data shows a reasonably good match for T$_{e}$ and n$_{e}$ profiles. \textit{This work was supported by U.S. DOE contract {\#} }\textit{DE-FG02-03ER54731 and }\textit{DE-AC02-76CH03073}$.$   

Electrode Biasing Experiment for Local SOL Control In NSTX

A set of small electrodes was installed in NSTX to test a proposal to control the width of the scrape-off layer (SOL) by biasing the electrodes to create a strong local poloidal electric field [1,2]. The electrodes in NSTX were $\sim$ 3 cm outside the separatrix near the outer midplane, and were biased in the range -95 V to +50 V with a poloidal separation of $\sim $ 1 cm. The effect of this local biasing was measured with Langmuir probes between the electrodes, and by the NSTX gas puff imaging (GPI) diagnostic located $\sim$1 m away along the magnetic fields lines intersecting the electrodes. Changes in the local density and potential were seen by the probes in some cases, but little change was seen in the D$_{\alpha}$ profile or the turbulent motions as seen by the GPI diagnostic. Analysis of the perpendicular and parallel penetration lengths of the biasing potential and a comparison with the MAST experiments will be presented. \newline [1] D. Ryutov et al, Plasma Phys. Cont. Fusion 43 (2001) 1399 \newline [2] R.H. Cohen et al, Plasma Phys. Cont. Fusion 49 (2007) 1   

Structure and evolution of ELMs in the edge and SOL of NSTX

Edge Localized Modes (ELMs) are routinely seen during H-mode operation in NSTX. These ELMs have been characterized as large-sized Type I, medium-sized Type III, and small Type V ELMs. Recently, an experiment was dedicated to characterize the structure and evolution of these 3 ELM Types in NSTX utilizing multiple diagnostics. These diagnostics include: fast-framing digital cameras, soft X-ray arrays, edge probes (both tile-embedded and reciprocating), reflectometers and Mirnov arrays. In general, the ELM evolves from a perturbation of the edge topology that quickly develops ($<$30~$\mu $s) into strong filamentation that propagates both radially and poloidally/toroidally in the SOL. This ELM filamentation is then followed by an increased level of edge turbulence (and blobs) resembling, momentarily, that observed during L-mode phases. This later blob filamentation is clearly distinct from the initial ELM structures. The characteristics and differences observed in all 3 ELM Types will be presented.   

Study of statistical properties of edge turbulence in NSTX with the GPI diagnostic

The Gas Puff Imaging (GPI) diagnostic is used to study the edge turbulence of the NSTX spherical tokamak. The statistical properties of the edge fluctuations are characterized as a function of the radial position, using the Continuous Wavelet Transform, showing their lack of self-similarity. Bursts are identified in the signals; the correlation between the electron pressure radial profile and the percentage of bursts is shown. The difference between L and H mode is studied, correlating it with the amount of coherent structures in the edge plasma. In the H-mode discharges the linear density of structures decreases drastically compared to the L-mode case; it is also shown that such observation cannot be accounted for by the difference in the poloidal propagation velocity measured near the separatrix. The spectral properties are studied by measuring the power spectrum as a function of the poloidal wavenumber k: a difference between the two confinement regimes is found.   

Reduced simulations of boundary turbulence in NSTX

We solve a reduced set of equations numerically for the evolution of vorticity, density, temperature and zonal fluid momentum, in the two dimensions orthogonal to the magnetic field, in the edge and SOL of a tokamak. In the simulation plane, the edge region supports the electron drift wave instability, while sheath losses and the grad-Te instability are isolated in the SOL. Curvature- and grad-B-driven charge separation is included everywhere, enabling blob transport of density, temperature and vorticity (charge) from the edge into the SOL. Generic features of boundary turbulence seen in NSTX and other experiments are reproduced by the simulations, including skewed PDFs, power law frequency spectra, skewness vs. distance from the separatrix, and qualitative features seen with Gas Puff Imaging. We will also report on our modeling of divertor disconnection/detachment experiments in NSTX for which blob speed-up and SOL-broadening are predicted theoretically.   

Modeling of Blob Formation in NSTX Edge Turbulence

In tokamak edge turbulence, predominantly electrostatic cross-field nonlinearities are balanced with wavelike parallel coupling that is often electromagnetic. Magnetic field fluctuations affect both the parallel coupling and dissipative properties of the turbulence at perpendicular scales larger than the skin depth. The resulting mathematical structure is discussed as are approaches to, and limitations of, 2D approximations. A specific reduced 2D fluid model appropriate for modeling of ``blob'' formation in the electromagnetic NSTX edge is derived both semi-heuristically and from a systematic projection method. Initial numerical solutions will be presented, and their frequency and wave-number spectra will be compared with experimental results from the gas-puff imaging diagnostic on NSTX.   

Spectroscopic $T_e$ and $n_e$ measurements in a recombining divertor region and in MARFEs in NSTX using D~I and He~II high-$n$ series line emission.

Spatially resolved measurements of Balmer and Paschen series D~I line emission, and for the first time, Pfund and Humphreys series He~II emission, have been performed in the divertor and MARFE regions in 2-6 MW NBI-heated deuterium and helium plasmas in NSTX. We analyze relative intensities and Stark broadening of the ultraviolet, visible and near infrared lines corresponding to the $2-n$, $3-m$ transitions (D~I) and $5-k$, and $6-l$ (He~II) with upper principal quantum numbers $n=$7-13, $m=$5-12, $k=$10-19, and $l=$12-16. Temperatures in the range 0.5-1.5 eV and densities in the range $(0.5-5) \times 10^{20}$ m$^{-3}$ are inferred using collisional-radiative modeling and published tabulated line shape calculations, confirming the important role of the three-body recombination process as an ion momentum loss mechanism in the detachment and radiative instability development. The diagnostic potential of the spectroscopic techniques for a divertor of a burning plasma device will be discussed. This work is supported by U.S. DoE under contracts W-7405-ENG-48 and DE-AC02-76CH03073.   

Recent observations of dust particle behavior in the NSTX

Highly mobile incandescent dust particles are routinely observed on NSTX using fast cameras operating in the visible region. Dust particle trajectories in both the main chamber as well as in the divertor region of NSTX have been derived using two fast cameras, each tracking the same particle from two different locations. A 3-D tracking code has been developed that uses the two-camera system to locate particles to within an accuracy of a few millimeters by correlating the position with monuments on the vessel walls. Velocities between 10-200 m/s have been measured in each region. We will also present the results of simulations on the dynamics of measured dust particles using the 3-D dust transport code (DUSTT). In matching experimental particle trajectories using DUSTT we adjusted the initial particle parameters (radius, birth point, etc) and used a plasma background calculated with UEDGE. Abnormal trajectories containing abrupt changes in direction and velocity will also be discussed.   

Upgrade of the NSTX Plasma Control System*

The plasma control system for the National Spherical Torus Experiment (NSTX) has been upgraded to replace the obsolete SKY computer system. The three main improvements with the new system are 1) higher computer speed, 2) lower latency and 3) a recordable absolute time during the discharge. The eight 333 MHz G4 processors in the Sky system were replaced with four dual core AMD Opteron 880 2.4 GHz processors. This provides approximately 7 times the speed for computationally intensive parts of the control system. The data acquisition and control were previously shared between VME and front panel dataport (FPDP) hardware. Two PCI FPDP cards, one each for data input and output made elimination of the VME hardware possible. Presently, the input data is read directly from the FIFO, this results in a loss of speed compared to the full potential of the vmetro FPDP DPIO2 boards using DMA, nevertheless, the present latency is about 2/3 that of the old system. In the old system, time was computed relative to a start trigger and was calculated based on input data frequency and the real-time cpu clock frequency. A digital input and time stamp module (DITS) was developed to provide a 48 bit absolute timestamp for each input data sample. *This work supported by U.S. DOE Contract {\#} DE-AC02-76CH03073.   

Model-Based Shape Control Design for the National Spherical Torus Experiment (NSTX)

Plasma shape and position control is a challenging problem due to the difficulties associated with real-time shape identification, plasma parameters measurement, and control method selection. The recent implementation of the real-time equilibrium reconstruction code rtEFIT on NSTX allows plasma shaping by controlling the magnetic flux at the plasma boundary. A non-model-based shape controller that exploits this capability has been recently proposed [1]. We describe current efforts to develop a robust model-based multi-input-multi-output (MIMO) controller to provide real-time shaping and position control in the presence of disturbances and uncertainties in the plasma parameters. The control design is based on linear plasma response models derived from fundamental physics assumptions. Computer simulation results illustrate the performance of the model-based shape control method. [1] D.A. Gates, et al., Nucl. Fusion \textbf{46 }(2006) 17--23.   

Supersonic gas jet fueling efficiency studies in NSTX.$^*$

Electron and carbon inventory analysis is used to infer the fueling efficiency (FE) of a pulsed high-pressure supersonic D$_2$ jet, produced by a low field side~supersonic gas injector (GI) at a flow rate $3-9 \times10^{21}$ s$^{-1}$ at distance 5-15 cm from the plasma. In ohmic and 2-6 MW NBI-heated L-~and~H-mode plasmas, the FE of the Mach 4 jet is found to be in the range 0.1-0.4, higher than FE of a conventional GI. During supersonic GI pulses, the pedestal density increases by 5-40~\% suggesting that particles are deposited mainly in the pedestal region. A ``single particle'' model of lower-end pressure supersonic GI fueling is developed using the DEGAS 2 neutral transport code. Details of high-pressure jet interaction with background plasma are not included in the model. The modeling suggests that adding a directed velocity does not guarantee a FE improvement. While the supersonic GI does focus the molecules towards the core, there is a reduction in the number of dissociation product atoms that provide much of the transport for the conventional puff, resulting in comparable FE's of a supersonic and a conventional GI's. $^*$Supported by U.S. DOE under Contracts W-7405-Eng-48 and DE-AC02-76CH03073.   

HHFW Heating and Current Drive Progress on NSTX

Operation of NSTX at B$_{T}$(0) = 0.55 T has increased the core power deposition and heating efficiency of the 30 MHz High Harmonic Fast Waves (HHFW) compared to previous B$_{T}$(0) $\le $ 0.45 T operation, particularly when launching longer parallel wavelengths. This improvement is attributed in part to moving the onset density at which the fast waves begin to propagate into the plasma to a point further from the wall [1]. At this field strength the HHFW power deposition at k$_{\vert \vert }$ = 7 m$^{-1}$ is comparable to that of k$_{\vert \vert }$ = 14 m$^{-1}$, and core heating at k$_{\vert \vert }$ = 3 m$^{-1}$ is now seen, albeit at lower efficiency. Comparisons with power deposition from full-wave models (AORSA) will be made and MSE measurements of driven current will be presented. \newline [1] see Invited Talk by J. Hosea, this conference.   

Numerical Modeling of High Harmonic Fast Wave Heating on NSTX

High harmonic fast wave (HHFW) heating and current drive processes, at frequencies up to 15 times the fundamental deuterium cyclotron frequency, are being studied on NSTX. Recent experiments indicate that the core heating efficiency depends strongly on the antenna phasing and plasma conditions [1]. The wave propagation and absorption characteristics for select NSTX discharges will be analyzed using a variety of rf modeling codes, including both ray tracing and full wave models. Both core power deposition profiles and rf power flow in the edge regions will be considered. The possibility of off-axis mode conversion of the HHFW to shorter wavelength modes and the subsequent impact on power deposition will be explored. \newline [1] See invited talk by J. C. Hosea this meeting for details   

Recent EBW Emission Results and Plans for a 350 kW, 28 GHz EC/EBW Heating System on NSTX

Electron cyclotron heating (ECH) and electron Bernstein wave EBW heating (EBWH) can assist plasma startup on the low aspect ratio NSTX device and provide sufficient electron heating to allow effective high harmonic fast wave (HHFW) coupling during current ramp up. EBW current drive (EBWCD) can also provide off-axis current to stabilize solenoid-free NSTX plasmas at $\beta >$20{\%}. Efficient coupling of externally launched electromagnetic waves to EBWs is required for EBWH and EBWCD. The prospect for EBWH and EBWCD is supported by EBW emission studies on NSTX that show efficient EBW coupling for some edge conditions. A 350 kW 28 GHz ECH/EBWH system is being installed on NSTX to support solenoid-free startup, HHFW current ramp up and initial EBW coupling and heating studies. This system will provide on-axis second harmonic ECH/EBWH in NSTX. Fundamental on-axis heating may also be possible by operating the gyrotron at 15.3 GHz.   

Investigation of collisional EBW damping and its importance to EBW emission from NSTX

Collisional damping of electrostatic electron Bernstein waves (EBWs) can play an important role in EBW applications for tokamaks. Electron temperature in the vicinity of the EBW-X-O mode conversion region may be low enough ($T_{e} \alt 15\; {\rm eV}$) to give rise to a significant collisional damping of EBWs, which have rather low group velocity. This can partially block EBW emission or EBW heating. Collisional damping has been investigated by ray-tracing and full-wave simulations, using various collisional terms in the dielectric tensor. The theory of collisional effects for wave propagation in hot magnetized plasmas is still incomplete and different models yield different results. Model results using NSTX experimental data are compared and importance of collisional damping to EBW emission from NSTX is discussed.   

Mode conversion coupling to electron Bernstein waves

In NSTX, and generally in spherical tori, the emission of electron Bernstein waves (EBW) from the interior of the plasma can be observed in the vacuum region after mode conversion to the X mode and/or the O mode. The same mode conversion process comes into play when exciting EBWs through externally launched power. We consider the mode conversion process that couples the O mode to EBWs via the X mode. It is shown that density inhomogeneity can change the mode conversion efficiency significantly from that obtained analytically in [1]. Results obtained from a comprehensive model [2] are found to differ from the analytical result as the gradient scale length decreases. A detailed analysis comparing the analytical and computational results will be presented. \newline [1] E.\ Mj{\o}lhus, {\it J.\ Plasma Phys} {\bf 31}, 7 (1984). \newline [2] A.\ K.\ Ram and S.\ D.\ Schultz, Phys.\ Plasmas {\bf 7}, 4084 (2000).   

Nonlinear Collisional Absorption of High-Harmonic Relativistic Electron Bernstein Modes in the Princeton Spherical Tokamak Plasma.

It is shown that an efficient control of anomalous absorption in the Princeton Spherical Tokamak is possible, leading to a favorable convective R-EB harmonics excitation. In this model the driver pump in the electron cyclotron range of frequencies, O- or X-mode, excites relativistic Electron Bernstein Mode\footnote{V. Stefan, Anomalous Absorption of High-Harmonic Relativistic Electron Bernstein Modes in Spherical Tokamak Plasmas (Abstract ID: BAPS.2007.APR.S1.23; The American Physical Society, April-2007 Meeting, April 14-17, 2007, Jacksonville, Florida.} harmonics (R-EB harmonics) in the edge region of ST plasma. Nonlinear relativistic EB harmonics, in turn, propagate toward the central region of the ST, whereby they are effectively absorbed in the electron cyclotron resonance region via nonlinear collisional damping. The scaling laws for the thermonuclear yield, ratio of the thermonuclear power to the external power, for the case of excitation of EB harmonics, n(EB) + (n-1) (EB), n= 5,6 harmonic number, and for the excitation of n(EB) + (UH), (UH) the upper hybrid mode, are obtained. The plasma-ignition criterion is analyzed in terms of O- and X-Mode power.   

Overview of the Pegasus Experimental Program

The Pegasus Toroidal Experiment is exploring plasma stability at near-unity A and developing non-solenoidal startup tools. Several techniques have been developed to suppress deleterious tearing modes by modifying the current profile, including toroidal field ramps and noninductive current drive via washer-stack current sources. These techniques have allowed access to I$_{N}$=14 MA/m-T without the appearance of performance-limiting instabilities. Filamentary structures have recently been observed near the edge of almost all ohmic discharges; large values of j$_{\vert \vert }$/B in this region suggest that these may be the result of peeling modes. Non-inductive startup via washer-stack current sources has produced plasmas with toroidal currents up to 50 kA. Plasmas have been produced using two geometries: with sources in the lower divertor region, and with a source on the outboard midplane producing moderate-A targets intended for PF induction. Plasmas produced with both geometries have been successfully coupled to Ohmic drive.   

Operations at High I$_{N}$ in the Pegasus Toroidal Experiment

In efforts to define the operating space of a near-unity aspect ratio ST, the external kink boundary is explored by operating at high normalized current (I$_{N})$ and toroidal field utilization (I$_{P}$/I$_{TF})$. Recent experiments have accessed I$_{N}$ up to 14 MA/m-T (I$_{P}$/I$_{TF} \quad \sim $ 2.3) through current profile manipulation. Three techniques are employed to access high I$_{N}$. The first two involve electrostatic current sources for helicity injection, while the third uses TF rampdowns. Equilibrium reconstructions indicate that two techniques are allowing dramatic changes in the current profile and the third is accessing high I$_{N}$ through greater experimental flexibility. Mode analysis during the current manipulation experiments shows no consistent mode activity. The MHD activity that is observed appears to coincide with reduced shear at rational flux surfaces destabilizing tearing modes at higher m. This is opposed to earlier experiments with ohmic-only current drive where low-order tearing modes were universally observed, limiting I$_{N}$ ($\sim $ 6-8 MA/m-T) and I$_{P}$/I$_{TF}$ to unity. There has yet to be evidence of ideal MHD mode activity during these experiments giving encouragement than further gains in I$_{N}$ can be made.   

Nonsolenoidal startup of Pegasus plasmas using DC helicity injection and poloidal field induction

The central solenoid of a spherical torus (ST) offers limited Ohmic flux, which exacerbates the limitations of this heating and current drive technique. The design of a scalable non-solenoidal (NS) startup technique is desired to expand the operating space of the ST and to provide a path to NS operation for STs and tokamaks. Pegasus employs a two-part NS startup technique of DC helicity injection and poloidal field induction. DC helicity injection is used to create a target plasma at the outboard midplane by injecting current along helical field lines. The current filaments relax to a tokamak-like magnetic topology with I$_{p}$ determined by magnetic helicity conservation. A prototype system capable of injecting up to 2 kA has been used to create target plasmas with toroidal current up to 20 kA. Poloidal field induction has been used to ramp the target to 30 kA and provide a target suitable for coupling to other CD techniques.   

Global energy confinement studies on the Pegasus Toroidal Experiment

Recent studies have shown that low-recycling walls significantly enhance L-mode energy confinement [1]. Discharges on Pegasus suggest a low-recycling regime is obtained using titanium gettering and cryogenic pumping. When the external gas supply is terminated during an established discharge, tangential H$_{\alpha }$ and visible light signals drop to 5{\%} of their initial levels within 5 ms. Wall recycling is measured using the density decay rate, and its effect on particle and energy confinement on Pegasus is explored. Initial global energy confinement times of $\tau _{E}$ = 2 -- 4 ms were calculated for I$_{P} \quad \sim $ 0.15 MA L-mode discharges. Scans of plasma current and line-averaged density are used to benchmark $\tau _{E}$ measurements against empirical L-mode scaling laws. These initial $\tau _{E}$ measurements indicate the H-mode power threshold as given by the ITPA04 scaling [2] can be exceeded in diverted Ohmic discharges on Pegasus. \newline [1] Majeski, R. \textit{et al.} Phy. Rev. Lett. \textbf{97} 2006 075002 \newline [2] Takizuka, T. \textit{et al.} Plasma Phys. Control. Fusion \textbf{46} 2004 A227   

Initial Edge Stability Observations in the PEGASUS Toroidal Experiment

Edge stability is an important consideration for design of fusion experiments, as transient heat loads generated by edge instabilities may damage the first wall. Such instabilities are now believed to include peeling (current driven) and ballooning (pressure driven) components. Peeling instability may be expected for high values of edge j$_{\vert \vert }$/B and low edge pressure gradient. This matches the operating space of Pegasus, with typical $<$j$_{\vert \vert }$/B$> \quad \sim $100 kA/m$^{2}$, $\vert $B$\vert \quad \sim $ 0.01 T, and an L-mode edge. A new camera system has observed filamentary structures in the edge of nearly all ohmically-heated discharges. Ideal stability analysis of these discharges with DCON indicates marginal stability to resistive interchange for $\psi _{N} \quad \ge $ 0.95. Modification of triangularity during startup is observed to delay instability onset. A plasma control system based on that used on DIII-D will allow study of the influence of plasma shaping on mode stability characteristics. An array of magnetic probes capable of insertion into the scrape-off layer and plasma edge is being developed to provide a local constraint on the edge current profile.   

An Upgraded Soft X-ray Pinhole Camera for Current Profile Measurements on the Pegasus Toroidal Experiment

An improved soft X-ray pinhole camera for current profile measurement has been installed on Pegasus. With an optical CCD camera and P43 phosphor scintillator that responds to X-ray energies in the range of 100 eV-5 keV, it provides a 240-fold throughput improvement over the prototype (Tritz et al, Rev. Sci. Instrum., \textbf{74}, 2003, 2161). The 4k x 4k back-illuminated CCD has a 200 mm diameter active area, giving a spatial resolution of $\sim $3 cm at 1 m and a temporal window of 2 ms. The current profile is obtained iteratively. Abel inversion of the measured intensity is used to obtain an emissivity profile across the plasma midplane. This profile is then used as constraint on an equilibrium reconstruction program, which generates a set of potential current profiles and associated intensity contours. $\chi ^{2}$ minimization during the equilibrium fitting identifies the best intensity map. This non-invasive current profile measurement technique offers improved understanding of MHD mode evolution and has potential applications for large scale fusion experiments.   

The Lithium Tokamak eXperiment (LTX) - Status and Plans

The LTX is the first toroidal device with a fully non-recycling wall almost completely surrounding the plasma. Such a plasma- facing component (PFC) is expected to lead to a new plasma regime with flat T$_{e}$ profiles, and the LTX goal is to explore its confinement and stability. The LTX is a spherical tokamak designed to have R=40 cm, a=26 cm, B$_{t}$=3.4 kG, I$_{p}$=400 kA, T$_{e}$=1 keV, and T$_{i}$=200 eV, for discharges of 100 ms or more. It contains a shell with four segments, each made of 0.375$''$-thick copper and a 0.0625$''$-thick stainless steel liner. A lithium layer, up to 100 nm thick, will be vapor deposited on the liner between shots. For a non- recycling PFC, the lithium will be kept chemically active with a shell temperature above the lithium melting point. The first tokamak experiments with large area liquid lithium PFC's used a toroidal liquid lithium limiter in the Current Drive eXperiment - Upgrade (CDX-U). To compare with CDX-U results, initial experiments will be performed with a toroidal liquid lithium ``pool'' in the lower half of the LTX shell. Assembly of LTX is complete, and preparations for plasma operations are in progress.   

Plasma Performance with Lithium PFCs in CDX-U and Projections to LTX

Use of a large-area liquid lithium limiter in the CDX-U tokamak produced the largest enhancements in ohmic tokamak confinement ever observed [R. Majeski, et al., Phys Rev. Lett. 97, 075002-1- 075002-4 (2006]. Simulations of CDX-U have now been performed with the ASTRA code, utilizing a model with neoclassical ion transport and boundary conditions suitable to a nonrecycling wall, with fueling via edge gas puffing. This transport model reproduces the experimental values of the energy confinement, loop voltage, and density for a typical CDX-U lithium discharge. The model has been used to project the performance of the new Lithium Tokamak eXperiment (LTX), with fueling via edge gas puffing, and with the addition of core fueling via neutral beam injection (NBI). Core fueling with NBI in LTX, with a low recycling wall of liquid lithium, is predicted to result in core electron and ion temperatures of 1 - 2 keV, and energy confinement times in excess of 50 msec.   

Thomson Scattering Measurements on the Lithium Tokamak Experiment (LTX)

Experiments are beginning on the Lithium Tokamak Experiment (LTX). The goal of LTX is to investigate tokamak plasmas that are almost entirely surrounded by walls coated in liquid lithium. Past results have shown that liquid lithium coatings on plasma facing components may behave as low-recycling boundary surfaces, which can fundamentally alter the behavior of the confined plasma. On CDX-U, results with lithium limiters indicated a reduction in the overall recycling coefficient and an increase in the confinement time. On LTX, it is expected that liquid lithium will result in higher temperatures at the plasma edge, flatter overall temperatures profiles, density profiles peaked near the plasma center, and an increase in confinement time. To test these predictions, the temperature and density profiles in LTX will be measured by a multi-point TVTS Thomson scattering system, in conjunction with microwave interferometry for density. Presently, the TVTS system for LTX offers up to 12 diagnostic channels to measure plasma conditions between the plasma edge and the plasma center. In the future, Thomson scattering measurements focusing on the edge conditions will be made at higher spatial resolution. *Supported by US DOE contract {\#}DE-AC02-76CH-03073 and the ORISE Fusion Postdoctoral Fellowship   

Effects of Liquid Lithium Plasma Facing Components in the Lithium Tokamak eXperiment

The LTX (Lithium Tokamak eXperiment) will investigate magnetically confined plasmas with liquid lithium walls, the first experiment of its kind.~This unique first wall condition is expected to dramatically enhance confinement, stability, and discharge control, and virtually eliminate recycling.~The LTX is currently under construction, with first plasma scheduled in late 2007.~An extensive array of diagnostics will be available, including flux loops, Rogowskii coils, Mirnov coils, Thomson scattering, interferometry, and deposition monitors. This research project will focus on reconstructions of the LTX equilibrium, using magnetics measurements to constrain plasma modeling in the Equilibrium and Stability Code (ESC). This is the first code capable of equilibrium reconstructions using magnetic signals dominated by eddy current contributions from the surrounding walls. Of particular significance will be changes in the current profile as recycling is lowered, and its effect on the confinement time's dependence on plasma current, toroidal field, density, and temperature. In addition, this research will further knowledge of liquid metal walls for chamber technology in both inertial and magnetic fusion.   

Building a Lyman-$\alpha$ detector for measurement of recycling rates in LTX

The measurement of the particle recycling rate is essential for understanding the performance improvements of lithium PFC devices like CDX-U and LTX. Recycling is usually measured by using atomic H-$\alpha$ (Balmer-$\alpha$) emission, but the signal can be difficult to interpret because H-$\alpha$ has a high reflectivity for many wall materials including lithium. In contrast, Lyman-$\alpha$ is known to have a low reflectivity at a lithium wall. To measure recycling rates for LTX, a Lyman- $\alpha$ detector with a photodiode and a directly deposited 117-131nm pass-band filter has been developed. The detector has been tested with collisional beam excitations with a background of hydrogen gas. Based on known inelastic collision cross sections of a hydrogen beam, the relative intensity of Lyman- $\alpha$ collisionally induced fluorescence (CIF) to H-$\alpha$ CIF has been calculated. By comparing the theoretical ratio with the measured one, the detector can be calibrated.   

Recycling Coefficient Calculation for Discharges with Lithium Plasma-facing Surfaces in CDX-U

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

Spherical tokamak plasma startup by use of a washer gun

Startup without a center solenoid(CS) coil is an important subject for spherical tokamak(ST) plasmas due to their narrow center coil space. The new spherical tokamak device UTST in University of TOKYO was designed to form ultra high beta STs using their axial merging. The CS-less startup for each ST was studied by the toroidal electric field induced by external poloidal field(PF) coils. We used a seed of plasma made by a washer gun together with PF coil current whose frequency is a few kHz, in order to make low q and high density ST. The washer gun was installed on the bottom of the vacuum vessel of UTST. A fast piezo valve was used to feed the working gas to the gun. The gas flow from it was as small as 500sccm and discharge time of the gun was as short as 1$\sim $2ms. So the gun discharge started after gas was filled in the vacuum vessel. However a plasma from the gun was supplied to the bottom 1/3$\sim $1/2 of the total volume because of recombination process. A new fast solenoid valve is being installed. Using a video camera, we observed a spiral light line from the gun. The plasma light was observed in large region of vacuum vessel and now proceeded to rogowsky coil measurement during the plasma formation.   

2-Dimensional Imaging Measurement for Pressure-Driven Instability in High Beta Spherical Tokamak

We have been forming ultra-high-beta Spherical Tokamaks (ST) using reconnection heating of their axial merging in the TS-4 experiment, University of Tokyo. The produced ST was observed to have the maximum beta 50-60{\%} right after the reconnection. An question is whether the pressure-driven instability dangerous for high-beta STs appears or not. Using two dimensions image camera, we detected line-shaped emission parallel to magnetic line at the plasma surface. These results agree with a characteristic of the ballooning instability that grows up locally with magnetic line. The two dimensions magnetic probe measurement enabled us to study s-alpha diagrams for the produced ST plasmas using the ballooning stability code. The line-shaped emission was found to appear only when its s-alpha parameters is located in unstable region for ideal ballooning mode. No line-shaped emission was detected when its s-alpha parameters is located in the stable regime. Further magnetic measurement will be made to clarify the localized mode in the high-beta state in addition to the imaging camera measurement.   

Computational Efficiency and Parallelization Issues in ICF Calculations

The advent of commodity cluster computers has put a premium on being able to map physics codes onto the computer hardware efficiently. Here we discuss the issues surrounding a distributed memory implementation of NRL's radiation transport code, FASTRAD3D. FASTRAD3D includes hydrodynamic transport, inverse Bremsstrahlung laser energy deposition, real equation of state through table lookup, implicit thermal diffusion, and a multi-group variable Eddington diffusion radiation transport model. Parallelization is accomplished through domain decomposition, but the data dependencies in some of the physics models can influence the type of domain decomposition. Load balancing issues arise in the implementation of the equation of state, where multi-material regions can take longer than single material regions. Implicit solvers and pre-conditioners associated with the elliptic solvers can impact the parallel efficiency. Finally, effective cache management can improve performance.   

DRACO Development for Modeling 3D Instabilities

Additional features have been included in the DRACO Lagrangian radiation hydrodynamics code enabling realistic 3D simulation of laser driven ablation, shocks, and fluid instabilities in low-Z plasmas. Since last reported (Fatenejad and Moses, Bull. APS \underline{51}, 209(2006).), DRACO now includes 3D laser ray tracing to model laser absorption and hydrodynamic restoring forces to counteract artificial grid distortions. Two temperature (electron and ion) flux-limited thermal transport has been included. DRACO is now being used to model the acceleration of a slab of Cu-doped Be into liquid deuterium via laser ablation. The slab has single mode perturbations imposed on it both at the ablation front and at the D-Be interface. Preliminary simulations of fluid instability growth will be presented using the improved DRACO 3D modeling. These simulations are motivated by similar recent experiments performed at the OMEGA laser facility.   

Experiments to validate self-consistent beam-gas-electron code

The WARP-POSINST model tracks beam ions and secondary particles (ions, electrons, gas molecules) in a self-consistent manner with techniques developed for heavy-ion fusion and e-cloud studies in high-intensity accelerators. We have developed simple experiments to exercise the code. Heavy-ion beams striking a surface cause gas desorption and electron emission, both of which can limit beam performance. Subsequent beam ions can ionize the gas, producing additional electrons. Two parallel plates, on either side of the beam and orthogonal to the end wall, are biased as a dipole: one grounded and the other biased to $\pm$ 10 kV. The electron current to a positive plate jumps to the electron emission value; then ramps slowly due to ionization of desorbed gas. This is a rigorous test of the particle dynamics of the model and constrains the secondary particle production coefficients.   

Simulation of the Spectral Properties of Materials with PrismSPECT

PrismSPECT is a collisional-radiative spectral analysis code designed to simulate the atomic and radiative properties of LTE and non-LTE plasmas over a wide range of conditions. For a grid of user-specified plasma conditions, PrismSPECT computes spectral properties (emission and absorption), ionization fractions, atomic level populations, and line intensity ratios. PrismSPECT can compute the properties of plasmas irradiated with external radiation fields, and plasmas with non-Maxwellian electron distributions, and is capable of simulating inner-shell (e.g., K-alpha and K-beta) satellite line emission. PrismSPECT has been used in the analysis of spectra spanning a wide range of conditions. We will present results from the analysis of high-temperature Fe opacity data obtained in dynamic hohlraum experiments at Sandia National Laboratories, as well as spectra obtained from low-temperature laser-produced plasma experiments.   

Collision Models for Plasma Simulation of Thermonuclear Burn: Comparison of Models and Applications

There is renewed interest in examining plasma physics issues related to thermonuclear burn in inertial confinement fusion (ICF) and fast ignition (FI): e.g., the rate of temperature equilibration of electrons and ions, the formation and/or depletion of high energy tails of ion velocity distributions of ions, the slowing of energetic ions in dense plasmas, etc. To address these types of questions, we have developed a new particle-in-cell (PIC) plasma simulation capability, embodied in the code VPIC. To model TN-burn problems in dense plasmas, we have developed a new Coulomb collision model, based on the use of stochastic differential equations and well-known Spitzer rates to describe the collision process, which was presented at last year's meeting. Here we extend the model to included arbitrary weighting of individual simulation particles, rather than just separate weights for each plasma species, which is a feature intrinsic to VPIC. We compare test cases for plasma relaxation and slowing of fast beams using the new collision model with results obtained from an extension of standard particle-pairing collision models to weighted particles for parameter regimes of interest to ICF and FI.   

Tests for Krook model for nonlocal heat transport in laser produced plasmas

A Krook model has recently been proposed [1] for solving the problem of electron energy transport in laser produced plasmas. In this work, we report on comparisons of this model with 1) a more complete Fokker-Planck model and 2) an experiment performed at NRL [2]. A simple test problem solved with a Fokker-Planck code was first considered by Matte and Virmont [3]. It consists of a pure heat transport problem in a uniform plasma slab between two thermostatic walls at different temperatures. The normalized slab length (L/$\lambda$ where $\lambda$ is the average electron mean free path) varies from order 1 to a few hundreds. The comparison with experiment involves the back side temperature measurement behind a 58 $\mu$m plastic foil after the passage of a laser-produced shock wave. Results from these two comparisons will be presented and outline for further work will be discussed. \newline [1] W.Manheimer, D.Colombant and V.Goncharov, submitted to Phys. of Plasmas \newline [2] E.McLean et al., Optics Comm. 166, 141 (1999) \newline [3] J.P.Matte and J. Virmont, Phys. Rev. Letters 49, 1936 (1982)   

Generation of nonadiabatic laser pulse front from an overdense plasma

We suggest utilizing the interaction of an overdense plasma and an ultraintense laser pulse to generate extremely sharp (nonadiabatic) ramping-up of the pulse front. Due to the relativistic mass increase, the overdense plasma becomes partially transparent. As the boundary between the transparent and opaque region moves with a slow velocity, the laser pulse keeps being reflected by the boundary. After propagating through a couple of microns, the initial Gaussian pulse shape results in half-Gaussian shape. The different characteristics between the linear and circularly polarized pulse are discussed.   

Plasma Heating by Intense Electron Beams in Fast Ignition

Collisionless electron beam-plasma instabilities are expected to play an important role in fast ignition. Such beams are produced by the short high power ignition laser interacting with long scale length plasmas. Here we present results from a one dimensional Vlasov-Poisson code used to investigate different electron beam temperatures and background plasma conditions. The simulations demonstrate that the beam-plasma instabilities drive large amplitude electrostatic waves that undergo the parametric decay instability driving backwards propagating electrostatic waves and much lower frequency ion acoustic waves. Saturation of the beam-plasma instability creates a plateau in the electron distribution function consistent with quasi-linear theory. We observe the creation of high energy tails in the electron and ion distribution functions, formed by the trapping of particles in the waves formed during the collapse of the beam. At the highest electron-beam temperatures we observe the formation of coherent phase-space structures - a direct consequence of the cascade nature of the parametric instability. These simulations are clearly beyond a simple quasi-linear treatment and demonstrate the transfer of energy from an incident beam to the ion population via collisionless effects. Implications of these mechanisms to the fast ignition scheme will be discussed.   

Using Mixtures of Ion Species to Control Stimulated Brillioun Scattering

Predicted plasma conditions in ignition targets, planned for the National Ignition Facility (NIF), have the potential to produce stimulated Brillouin Scattering (SBS) of the incoming laser light. Large SBS reflectivity is predicted from some NIF ignition designs. The SBS interaction takes place in hot (T$_{e} \sim $ 5keV) gold plasma a few hundred microns long in which ion acoustic waves are weakly damped. We show that adding a small fraction of low atomic mass material, $e.g.$ Boron, increases the calculated damping significantly and reduces the predicted SBS reflectivity dramatically without affecting the radiation temperature. SBS in mixtures of low-atomic-number species plasmas is well understood both experimentally and theoretically. We will discuss some of the additional effects that collisions in high-Z plasma have on linear and nonlinear ion wave response.   

Mitigation of Ion Motion in future Plasma Wakefield Accelerators

Simulation and analysis of the ion motion in a plasma wakefield accelerator is presented for the parameters required for a future ILC afterburner. We Show that although ion motion leads to substantial emittance growth for extreme parameters of future colliders in the sub-micron transverse beam Size regime, several factors that can mitigate the effect are explored. These include synchrotron radiation damping, plasma density gradients and hot plasmas.   

Laser wakefield simulation using a speed-of-light frame envelope model

Simulation of laser wakefield accelerator (LWFA) experiments is computationally highly intensive due to the disparate length scales involved. Current experiments extend hundreds of laser wavelengths transversely and thousands in the propagation direction, making explicit PIC simulations enormously expensive and requiring massively parallel execution in 3D. We can substantially improve the performance of laser wakefield simulations by modeling the envelope modulation of the laser field rather than the field itself. This allows for much coarser grids, since we need only resolve the plasma wavelength and not the laser wavelength, and therefore larger timesteps. Thus an envelope model can result in savings of several orders of magnitude in computational resources. Secondly, coherent transition radiation (CTR) from an electron bunch exiting the plasma region of an LWFA is a useful experimental diagnostic, and we wish to investigate the dependence of CTR properties on the bunch properties. Modeling the laser envelope separately from the fields due to the plasma particles allows examination of the CTR, making systematic studies possible. Finally, previous simulations evolving the envelope in the lab frame showed distortions when the laser pulse was propagated over long distances in a plasma. By propagating the laser envelope in a Galilean frame moving at the speed of light, these distortions can be avoided and simulations over long distances become possible. Here we describe the model and its implementation, and show simulations of laser wakefield phenomena such as trapping, acceleration, and CTR using the model.   

Numerical simulation of microwave transmission in the presence of an electron cloud

Electron cloud effects on the transmission of microwaves through beam pipes in the CERN SPS experiment and the PEP-II Low Energy Ring (LER) at SLAC have been recently observed. Electrons within the vacuum chamber generated primarily via secondary electron emission have been observed to cause a phase shift in microwaves injected into the vacuum chamber. Understanding this effect may provide a useful diagnostic tool for measuring electron cloud densities in accelerators. We present numerical simulation results generated by the electromagnetic Particle-In-Cell (PIC) code VORPAL, which predicts this phase shift. We also measure the effects of non-uniform electron cloud density and externally applied magnetic fields on the transmission properties, and compare our predictions to recent experiments at the PEP-II LER.   

High order methods for electromagnetics simulation

Higher order methods in electromagnetics are of interest to the PIC community in modeling electromagnetic wave propagation in cavities. It is believed that high order numerical methods have advantages over lower order methods as they can produce equivalently accurate solutions at lower resolution and thus potentially at lower computational cost. In this paper we present the algorithm and result of electromagnetic simulations of the crab cavity using a higher than second order numerical wave propagation algorithm. Ultimately this high order scheme will be implemented in the plasma code VORPAL where it will be tested on a variety of computational plasma problems.   

Advances in electron emission from conformal boundaries in the VORPAL code

Simulations of high-power microwave devices (HPM) involve the interaction of electrons with complex metal boundaries. Particle-in-Cell (PIC) methods are often used to model electrons when the velocity distribution is non-Maxwellian. The interaction of the PIC particles with the surfaces and the associated surface fields can be very challenging. We present recent advances in modeling electron surface effects at complex boundaries using the VORPAL code. These include accurate interpolation of the fields in cut cells on the boundary, secondary electron emission from conformal surfaces, and field emission of electrons from these surfaces. Discussion of the relevance to simulations of HPM devices with also be presented.   

Benefits of Higher-Order Particle Shapes in the Electromagnetic PIC Code VORPAL

Noise is one of the largest hurdles that particle-in-cell (PIC) codes must overcome in order to resolve such phenomena as particle trapping in laser wakefield acceleration (LWFA) and laser-solid interactions in fast ignition fusion scenarios. Using higher-order particle shapes has been shown to substantially reduce this noise. We present results of the implementation of higher-order particle shapes in the electromagnetic and electrostatic PIC code VORPAL, showing the benefits in application to LWFA and laser-solid interactions.   

Designing an RF thruster booster unit with TOPICA

Electromagnetic (RF) plasma-based propulsion systems have gained increasing interest, as able to yield continuous thrust and controllable and wide-ranging exhaust velocities. An RF plasma thruster essentially features a plasma source, a booster unit and a magnetic nozzle. The usual choice for the booster is the ion-cyclotron resonance heating (ICRH), a well-established technology in fusion experiments to convey RF powers to magnetized plasmas. To help design the booster unit, TOPICA was extended to deal with magnetized cylindrical inhomogeneous plasmas [1]. The latter required a new module in charge of solving Maxwell's equations within the plasma to obtain the pertinent Green's function in the Fourier domain, i.e. the relation between the transverse magnetic and electric fields at the air-plasma interface. Calculating the antenna impedance---and hence the plasma loading---relies on an integral-equation formulation and subsequent finite-element weighted-residual scheme to evaluate the current density distribution on the conducting bodies and at the air-plasma interface. In this work the design of an ICRH stage with TOPICA is discussed. \newline [1] V. Lancellotti\textit{ et al.} (2007) \textit{Proc. Joint Propulsion Conf.} AIAA-2007-5129   

Numerical Model of a Spacecraft Shielding against High-Energy Particles

Galactic Cosmic Rays are composed of predominantly GeV protons and $\alpha $-particles coming uniformly with $\sim $1 (m$^{2}$ sr sec MeV/nucleon)$^{-1}$ flux. Despite very low particle {\&} power fluxes delivered, they pose a major continuous hazard for subjects, biological materials and sensitive equipment in space. A self-consistent adaptive kinetic model is being developed to simulate different strong magnetic, electrostatic and hybrid shielding schemes. The model includes relativistic transport of particles, calculation of internal electromagnetic fields, ambient and incidental plasma responses to the applied strong fields. Numerical method uses unstructured adaptive grids in 3D, enabling automatic capturing of important physical details of the shield and plasma. The numerical method applications using shared and distributed architectures will be discussed. Results of the kinetic simulations of a spacecraft shielding against high-energy particles and possible macro-particles will be presented.   

Numerical Study of Energy Release in Magnetized Corona Driven by Continuous Footpoint Motions

The solar corona is a highly conducting plasma (Lundquist number $S \sim 10^{10-13}$). As such, Ohmic dissipation is negligible except within thin current filaments. In his coronal heating model, Parker suggests that thin current filaments can be induced in a magnetized corona via the shuffling of the field lines driven by continuous footpoint motions. One of the major difficulties in assessing the feasibility of Parker's mechanism is that the realistic parameters are way beyond the reach of current computer simulations. One possible approach is to establish the parametric dependence of the dissipation rate through simulations of attainable parameters. We study the Parker's model in two settings: (1) time independent footpoint twisting, and (2) footpoint shearing in alternating directions with random phases. Thin current filaments are created in both cases, and the system finally settles to a statistical steady state in which the Poynting power influx balances the viscous and resistive dissipation. Both configurations have only three relevant dimensionless parameters : Lundquist number, the aspect ratio, and the ratio between the Alfven transit time and the eddy turnover time. The parametric dependence of the dissipation power, as well as the similarities and differences between the two settings are discussed.