Session UP1: Poster Session VII: DIII-D II; MHD and Plasma Flows; Turbulence and Transport; Fast Ignition, Short Pulse, Ion Beams, and Laser Coupling

Tokamak MHD Stability at High Beta and Low Plasma Rotation,

Recent high-beta DIII-D experiments with the new capability of balanced neutral beam injection show that the resistive wall mode (RWM) remains stable even with significant reductions in the neutral beam torque relative to pure co-injection. Previous DIII-D experiments showed a higher plasma rotation threshold ($\sim 1-3\%\,\,\Omega_A$) for RWM stabilization when resonant magnetic braking was used to lower the plasma rotation. We speculate that the previously observed rotation threshold corresponds to the entrance into a forbidden band of rotation that results from torque balance including the resonant field amplification by the stable RWM. Previous and recent experimental data show a bifurcation taking place when the plasma rotation is reduced to half its unperturbed value, consistent with theory [1]. This hypothesis may have implications for both RWM stability and error field tolerances in ITER. \par\vskip4pt\noindent [1] R. Fitzpatrick, Nucl. Fusion \bf{33}, 1049 (1993).   

Feedback Control of Resistive Wall Modes in Slowly Rotating DIII-D Plasmas,

In slowly rotating plasmas on DIII-D, the requirement of RWM control feedback have been identified, using a MHD code along with measured power supply characteristics. It was found that a small time delay is essential for achieving high beta if no rotation stabilization exists. The overall system delay or the band pass time constant should be in the range of 0.4 of the RWM growth time. Recently the control system was upgraded using twelve linear audio amplifiers and a faster digital control system, reducing the time-delay from 600 to \mbox{100 $\mu$s}. The advantage has been clearly observed when the RWMs excited by ELMs were effectively controlled by feedback even if the rotation transiently slowed nearly to zero. This study provides insight on stability in the low- rotation plasmasw with balanced NBI in DIII-D and also in ITER.   

Non-Axisymmetric Equilibrium Measurements in DIII-D,

Stationary non-axisymmetric states may arise spontaneously in a tokamak plasma, or they may be driven by external magnetic perturbations (intrinsic or applied). Examples include distortion of the plasma shape by field errors, non-rotating magnetic islands, resonant response of wall-stabilized kink modes at high beta, and stochastic boundary layers generated by shorter-wavelength perturbations. Despite the small amplitudes of typical magnetic perturbations, the effects on plasma performance can be significant. DIII-D$\rq$s new capability for balanced beam injection allows experiments at low plasma rotation where magnetic asymmetries can penetrate the plasma more easily; these conditions may also be relevant to ITER plasmas. We will discuss the impact of non- axisymmetric states on plasma performance in DIII-D, the experience with measurement of these states using the present magnetic diagnostic set, and the requirements for a full three-dimensional equilibrium reconstruction.   

Recent EFIT Developments and 3D Extension,

Recent developments of the equilibrium reconstruction code EFIT and its 3D extension to model toroidally asymmetric effects due to error and externally applied perturbation magnetic fields are presented. These include a new more complete uncertainty matrix for magnetic diagnostics based on detailed knowledge about their fabrication, installation, calibration, and operation. A new algorithm to efficiently compute high bootstrap-fraction equilibria that explicitly separates out the Pfirsch-Schluter and bootstrap contributions to the poloidal current stream function is also being developed. Other on-going and planned developments include a new computational structure based on Fortran 90/95 with a unified interface that can conveniently accommodate different tokamak devices and grid sizes, as well as a computational link that allows easy integration with transport and stability physics modules for integrated modeling. EFIT reconstruction capability is also being extended to 3D based on perturbation solutions to the 3D Grad-Shafranov equilibrium equation.   

GATO Code Modification to Compute Plasma Response to External Perturbations,

It has become increasingly clear that the plasma response to an external nonaxiymmetric magnetic perturbation cannot be neglected in many situations of interest. This response can be described as a linear combination of the eigenmodes of the ideal MHD operator. The eigenmodes of the system can be obtained numerically with the GATO ideal MHD stability code, which has been modified for this purpose. A key requirement is the removal of inadmissible continuum modes. For Finite Hybrid Element codes such as GATO, a prerequisite for this is their numerical restabilization by addition of small numerical terms to $\delta$\,W to cancel the analytic numerical destabilization. In addition, robustness of the code was improved and the solution method speeded up by use of the SuperLU package to facilitate calculation of the full set of eigenmodes in a reasonable time. To treat resonant plasma responses, the finite element basis has been extended to include eigenfunctions with finite jumps at rational surfaces. Some preliminary numerical results for DIII-D equilibria will be given.   

Measurement of Plasma Displacement Due to Resonant Field Amplification in High Beta DIII-D Plasmas Using CER Spectroscopy

In a plasma with beta above the no-wall limit, externally applied magnetic perturbations can couple to the rotationally stabilized RWM via resonant field amplification [1]. This phenomenon is routinely exploited in the technique of active MHD spectroscopy to test the stability of the RWM [2]. We utilize measurements of the ion temperature from charge exchange recombination spectroscopy at two toroidal locations during MHD spectroscopy experiments to obtain a direct measurement of the $n=1$ plasma fluid displacement due to the RFA. The displacement profiles are compared with those expected for the stabilized RWM. \par\vskip6pt\noindent [1] A.M. Garofalo, et al., Phys. Plasmas 10, 4776 (2003).\par\noindent [2] H. Reimerdes, et al., Phys. Rev. Lett. 93, 135002 (2004).   

Magnetic Field Error Correction in DIII-D After Reduction of TF-Coil Error,

A new current feed at the DIII-D toroidal field (TF) coil 210 deg feed point reduced this feed\rq s magnetic error field at the plasma by $\sim$10-fold, but other error sources remain unchanged. The modified DIII-D intrinsic error, in addition to requiring that a new empirical algorithm be developed for routine error correction by the DIII-D C-coil, offers a rare opportunity to study the effects of magnetic error field geometry on plasmas in the same tokamak. Initial results show a moderate $\sim$30$\%$ improved locked mode avoidance in the standard, low-density, Ohmic, locked-mode test plasmas used in the past. The C-coil makes further improvement, as in the past, and the DIII-D I-coil, used alone for error correction for the first time, makes even more improvement. A search for large spatial scale (not TF coil “ripple”) TF coil errors is underway and will be reported. The combined correction and error fields will be analyzed to identify the error field features that are most and least deleterious to the plasma.   

Overview and Plan of FAR-TECH RWM Identification Via Kalman Filter and Implementation of Model-Based Feedback Control,

FAR-TECH is developing, implementing, and validating real-time resistive-wall-mode (RWM) identification algorithms and model-based RWM feedback algorithms on DIII-D. For RWM identification, a numerically simulated spatial pattern of the sensor signals (matched filter) can be matched to the measured sensor signals in real-time. Temporal behavior of the RWMs is further utilized by a Kalman filter in the identification to discriminate them from other noise/modes, i.e. edge localized modes. We will present modeling of the RWM signals at sensor locations by FARVAC, implementation of RWM identification algorithms on DIII-D, internal RWM mode structure identification, feedback controller algorithms, and ongoing validation results. Our new effort on identification of RWMs with toroidal modes for $n>1$ will be discussed.   

Modeling of High Kinetic Energy Plasma Jets for Fusion Applications

We used semi-analytical models for high velocity ($>$200 km/s) and density ($>$10$^{17}$ cm$^{-3})$ plasma jets to describe the acceleration in coaxial electrodes geometry, the collision, and plasma liner implosion, assuming that jets have merged into a spherical or cylindrical shell. The results are compared with experimental data and are being used for guiding LSP and MACH2 codes simulation and for optimization. The simplest model which uses the adiabatic invariant for oscillator revealed the basic relation between the velocity and the parameters of the plasma accelerator. Plasma slug model was extended for including friction and mass addition by electrode erosion. A simple model of blow-by instability by using the canting angle of the plasma current was formulated. As plasma jets collision at high interfacial Mach number generates shock fronts, we analyzed their possible consequences on the merging process and liner formation. The structure of the spherical shell liner during adiabatic implosion and the effect of the shock wave generated at void closure on the confinement time were also investigated.   

Resistive Wall Mode (RWM) Identification and Feedback Control Using Eigenmode-Based DIII-D/RWM Model,

Recent DIII-D experiments demonstrated that a model-based dynamic Kalman filter scheme, in which the wall is modeled as composed of “picture frames,” was effective in discriminating edge localized modes (ELMs) from resistive wall mode (RWM). A newly developed DIII-D/RWM model using a “wall surface current eigenmode” approach was predicted to be not only more effective in RWM identification but also more efficient in the feedback control [1]. Specifically, this eigenmode approach helps to identify RWMs more accurately with fewer wall states than in the picture frame model, reducing computation time without sacrificing the accuracy. Several controllers are under development based on this eigenmode approach. \par\vskip6pt\noindent [1] Y. In et al., Phys. Plasmas \bf{13}, 062512 (2006).   

$n>1$ Resistive Wall Mode (RWM) Identification,

Resistive wall mode studies in DIII-D demonstrated the effectiveness of $n=1$ RWM feedback control beyond $n=1$ no-wall $\beta$ limit, where $\beta$ is the ratio between plasma pressure and magnetic pressure. However it is predicted that, as $ \beta$ increases, not only $n=1$ RWM but also $n>1$ RWM may become unstable. The presence of $n=3$ mode on top of $n=1$ mode has been observed in some recent DIII-D RWM shots. In order to accurately identify $n>1$ RWM, a set of matched filters associated with $n>1$ RWM is under development using the same method as developed for $n=1$ matched filter [1]. Specifically, based on the magnetic perturbations of each toroidal mode on plasma surface, the FARVAC code calculates the estimated signals for magnetic sensors to construct $n>1$ RWM matched filter. Along with the $n=1$ RWM matched filter, we plan to use these $n>1$ RWM matched filters to provide a more complete RWM identification to achieve higher $\beta$ operation. \par\vskip3pt\noindent [1] D.H. Edgell, et al., Rev. Sci. Instrum. \bf{73}, 1761 (2002).   

Control of Resistive Wall Mode Using a Matched Filter Eigenmode Approach

One of the major non-axisymmetric instabilities under study in the DIII-D tokamak is the resistive wall mode (RWM), a form of plasma kink instability whose growth rate is moderated by the influence of a resistive wall. The Far-Tech RWM model represents the plasma surface as a toroidal current sheet and represents the wall using an eigenmode approach [1]. Although the plasma surface deformation cannot be directly measured in real time, the magnitude and direction of the deformation can be deduced from measurements by a set of 22 magnetic field sensors and saddle loops. An array of 6 control coils can then be used to return the plasma to its original shape. Using an estimator for the two orthogonal components (related by quadrature in toroidal angle) of the assumed n=1 mode, the resultant plant is reduced from a 22 by 6 system to a simple 2 by 2 system. Several control techniques are considered to stabilize this system. The various approaches are compared for their individual advantages and disadvantages. Implications for experimental implementation and use are discussed. [1] Y. In, et al, ``Model-based dynamic resistive wall mode identification and feedback control in the DIII-D tokamak,'' Phys. Pl. \textbf{13} (2006) 062512   

Fast Ion Profiles in Plasmas With Alfv\'en Instabilities,

Fast-ion redistribution is observed in plasmas with many different types of Alfv\'en eigenmode (AE) activity: toroidicity-induced (TAE), reversed shear (RSAE), elongation induced (EAE), and beta-induced (BAE). AE wave fields calculated by the NOVA code and benchmarked against experimental measurements are used to predict the modification of the fast-ion distribution function. These predictions are compared with profiles measured by the fast-ion $D_\alpha$ diagnostic, as well as fast-ion profiles inferred from the equilibrium. Neutron, neutral particle, and beam-ion loss detector diagnostics are also employed. In cases with strong AE activity, the central fast-ion profile is often flat.   

Fast-Ion Profiles in MHD-Quiescent Plasmas

The fast-ion distribution is measured using the fast-ion $D_\alpha$ (FIDA) diagnostic [1,2], which has spatial resolution of $\sim$5 cm, time resolution of $\sim$1 ms, and energy resolution of $\sim$10 keV. This paper focuses on the measurements under quiescent discharge conditions (i.e. in the absence of MHD activity and collective particle effects). A weighted Monte Carlo simulation code allows direct comparison of classical calculations of the fast-ion distribution function using either the TRANSP code or a Fokker-Planck code with the FIDA measurements. Pitch angle scattering and slowing down of fast ions are studied by varying the injection energy, beam angle, plasma density and electron temperature; the FIDA signals vary as classically expected in these MHD-quiescent plasmas. In addition, the fast-ion profiles are compared during co- and counter-injection of neutral beam. Neutral particle and neutron diagnostics corroborate the FIDA measurements. \par\vskip6pt\noindent [1] W.W. Heidbrink, et al., Plasma Phys. Control. Fusion \textbf{46}, 1855 (2004). \par\noindent [2] Y. Luo, et al., Rev. Sci. Instrum. \textbf{75}, 3468 (2004).   

Measurements of Escaping Fast Ions at the DIII-D Vessel Wall,

The loss of fast ions is detected by two pairs of thin foil Faraday collectors [1] that are installed just behind the graphite first wall in a vacuum port. Collimating apertures select fast ions that have energies $>$10 keV and that travel either with or against the plasma current. The strong correlation of beam-ion loss detector (BILD) signals with neutral beam modulation shows that, under appropriate conditions, prompt losses from nearly every beam source are detected. Orbit calculations indicate that the correlation occurs when injected neutrals are deposited at a location that “connects” with an orbit observed by the detector; as expected, these correlations depend strongly on plasma current. In addition to these classical effects, enhanced signals sometimes occur during ion cyclotron heating (presumably due to parametric decay instabilities) and during Alfv\'en activity (due to transport by the instabilities). \par\vskip6pt\noindent [1] F.E. Cecil, et al., Rev. Sci. Instrum. \bf{74}, 1747 (2003).   

Absorption of Fast Waves at Moderate to High Ion Cyclotron Harmonics: Experimental Results and Theoretical Models,

Strong absorption of fast Alfv\'en waves (FW) by ion cyclotron damping has been observed in DIII-D at the 4th and 5th harmonic of an injected beam while only weak absorption is observed at the 8th harmonic. The experimental results are compared with three different theoretical models; differences between the predictions of the models suggest the possible importance of finite-width orbit effects at high harmonics. In a linear model, it is found that damping on fast ions from neutral beam injection can be significant even at the 8th harmonic under experimentally relevant conditions. This is tested in experiments in DIII-D with FW power at 60 MHz and at 116 MHz. A novel $D_\alpha$ charge exchange recombination diagnostic is used to observe interaction of the FW power with beam ions. The results are compared with modeling with quasilinear and with orbit-following codes.   

Fast-Ion Profiles During Ion Cyclotron Heating,

Fast wave heating at the 4th-8th harmonic is combined with neutral beam injection. For 60 MHz heating at the 4th-6th harmonic, an energetic deuterium tail is observed by the fast-ion $D_\alpha$ (FIDA) diagnostic [1,2]. FIDA profiles are compared with the fast-ion profiles inferred from the equilibrium, as well as neutral particle data. Under some conditions, enhanced losses of fast ions at the vessel wall occurs during the rf. The fast-ion tail is largest near the resonance layer. For 116 MHz heating at the 8th harmonic, little evidence of a fast-ion tail is observed, even in higher density plasmas where fast-ion absorption was originally predicted. The FIDA spectra and profiles for cases with and without fast-ion heating are compared with calculations of the expected fast-ion acceleration. \par\vskip6pt\noindent [1] W.W. Heidbrink et al., Plasma Phys. Control. Fusion \textbf{46} (2004) 1855. \par\noindent [2] Y. Luo et al., Rev. Sci. Instrum. \textbf{75} (2004) 3468.   

DIII-D Studies of Massive Gas Injection for Disruption Mitigation,

Experiments with massive ($\approx 3\times 10^{22}$ particles) argon injection in the DIII- D tokamak have shown that neutral delivery rate is the crucial jet parameter. Nozzle aiming is not crucial, as the neutrals are stopped at the plasma edge. This was demonstrated over a range of plasma thermal energies from $W_{th}\approx 1.0$ MJ down to $W_{th}\approx 0.02$ MJ. Calculations suggest that magnetic field pressure is contributing to the observed neutral jet stopping. The subsequent core radiative thermal collapse is greatly accelerated by the onset of low-order ($m=1,2/n=1$) MHD modes; this was demonstrated by shutting down target plasmas with different \mbox {$q$-profiles} and observing a delay in the collapse onset as the low order ($q=1$ and 2) rational surfaces were buried deeper in the target plasma. Experiments using a new large valve with a 10x higher flow rate will also be presented.   

Analysis of Major Disruptions With Extremely Rapid Current Quenches in DIII-D and C-Mod

Major disruptions are characterized by a prompt loss of stored energy before any loss of position, and followed by a rapid current quench (CQ). The CQ often produces an uncontrolled loss of vertical position, leading to plasma-wall contact. A rapid CQ at this time can induce large destructive eddy currents in surrounding structures. Without motion, the CQ time is proportional to the pre-disruption plasma area, among other dependencies. CQ times are often normalized by plasma area for cross-machine comparisons, but this ignores the role of vertical motion in accelerating the CQ rate. Some major disruptions in DIII-D have unusually rapid vertical motion and a normalized current decay time less than 1 ms/m2, which would present a challenge to ITER's engineering design. C-Mod provides examples of plasmas similar to DIII-D's but with different CQ dynamics. We describe comparative analyses of C-Mod and DIII-D disruptions in order to determine whether extremely rapid CQ times are likely to occur in ITER.   

New Valve for Massive Gas Injection in DIII-D

Previous experiments on DIII-D have demonstrated the efficacy of using massive gas injection for disruption mitigation. The new valve has an orifice diameter of 22.3~mm vs 5~mm for the previous valve used from 1998 through 2005. Flows in argon greater than 2$\times$10$^6\,$Torr-l/s were measured on a mockup of the injection line. The original valve produced flow of $\sim$1$\times$10$^5\,$Torr-l/s when mounted on DIII-D. The new valve is intended to increase the effective risetime of particles delivered to the plasma rather than the total number of particle delivered. It is now on DIII-D undergoing testing under actual tokamak operating conditions to check the opening time in the presence of a magnetic field. Initial experiments of injection into the DIII-D plasma are scheduled for the summer of 2006.   

Proposed Next-Generation Thomson Scattering Diagnostic on DIII-D

The present paper describes the next generation Thomson scattering system developed at DIII-D. It is motivated by the need of increased time resolution to determine electron density and temperature evolution over the discharge lifetime as well as to replace obsolete hardware no longer commercially available. The new system includes a new overall low noise amplifier detector system that incorporates a TEC cooling circuit to reduce the systematic errors incurred due to temperature fluctuations in the APD detectors. The amplification circuitry incorporates a sample-and-hold branch for the dc signal and an integrating circuit for the pulsed signal offering an integrating gate smaller than 45 ns. The new system will have a new digitizing system that will replace the existing CAMAC data acquisition crates. The overall system's time resolution will be enhanced by a new laser system with individual laser beams capable of delivering 1 Joule, 10 ns pulses at a 100 Hz repetition rate. This represents a factor of 5 increase in the time resolution over the existing system.   

Periscope Design and Testing for Remote Viewing Inside DIII-D

Spectroscopy and imaging are key diagnostics for studying transport and edge physics in tokamaks. However, high neutron flux in environments such as ITER will degrade the performance of optical diagnostics. Optical fibers are particularly susceptible to neutron damage because of their extended length. For example, in existing tokamaks optical fiber damage has been observed for neutron fluences of order 10$^{16}$~cm$^{-2}$, while ITER is expected to produce a neutron fluence of order 10$^{21}$~cm$^{-2}$. Thus, optical fibers are not a viable option for remote viewing of ITER, and alternative methods need to be pursued. As part of disruption mitigation studies at DIII-D, we have designed a periscope system comprised of mirrors and a series of Nikon 100 mm f/2.8 camera lenses that relay an image of the plasma viewed through a window flange to a fast-framing CMOS camera detector. We present preliminary measurements of image quality and light throughput of the optical system.   

MSE Analysis Techniques for Determining Local Current Profile Features, New Calibration Tools, and an Update on the New DIII-D Counter-Beam MSE

We critique analysis techniques that seek to reconstruct the maximum spatial detail regarding the current density profile from the magnetic field pitch angles measured by motional Stark effect (MSE) polarimetry. Local features of interest include the missing bootstrap current in neoclassical tearing modes (NTMs), current drive from electron cyclotron waves, current holes, and neoclassical current in the H-mode pedestal. These techniques rely on either more detailed spline fitting in a reconstruction or direct evaluation of Ampere’s Law using discrete MSE measurements of $B_z^i$. The level of detail and resulting uncertainty in $j$ depend on the type of curve fit (or interpolation) to the $B_z^i$. For example, placing a current density extremum at a MSE channel location is tantamount to taking spatial derivatives of the $B_z^i$ measurements using spline interpolation. We also discuss a new technique to improve channel-to-channel calibration in the edge MSE array and report the status of the new counter-beam MSE on DIII-D.   

Approaches to Alpha Knock-On Tail Measurements on ITER,

Possible approaches to measuring the energetic DT neutron tail resulting from collisions between confined alphas and plasma fuel ions are discussed. Knock-on measurements on ITER require neutron detectors with both sufficient detection efficiency and energy resolution to measure the small fraction ($\sim 10^{-4}$ to $10^ {-3}$) of DT neutrons in the alpha collision-induced tail. The use of neutron activation detectors with energy thresholds above 15.5 MeV appears attractive if radiochemistry techniques can be employed to reduce the background decays from impurities or competing neutron-induced reactions in the activation targets. The use of bubble detectors with neutron energy thresholds between 15 and 20 MeV is being re- examined in light of the recent development of gel bubble detectors with higher detection efficiency and a reduced chance of the problematic below-threshold response observed in our earlier experiments. The use of proton recoil tracks produced by neutron collisions in nuclear emulsions or in track etch detectors is also discussed.   

Second Harmonic Electron Cyclotron Pre-Ionization in the DIII-D Tokamak

Second harmonic pre-ionization, i.e. the production of plasma before the application of a toroidal electric field, $E_\phi$, has been successfully demonstrated in the DIII-D tokamak using both the previously installed 60 GHz gyrotrons ($B_\phi \leq\,$ 1.05~T) and the present 110~GHz system ($B_\phi \approx\,$1.9~T). Pre-ionization and electron cyclotron (EC) assisted startup may be important in future devices such as ITER (at reduced toroidal magnetic field) and K-STAR where thicker vacuum liners and superconducting coils limit the maximum $E_\phi$ to values which are marginal for plasma initiation and burnthrough. In the DIII-D experiments the X-mode 2nd harmonic pre-ionization was reproducible, initially occurred at the 2nd harmonic EC resonance, and then filled the vessel volume. We will present the characteristics of these pre-ionized plasmas and parameter scans of EC power, neutral pressure, and toroidal field. The pre-ionization scenario will be discussed including modeling of single electron collisionless heating.   

Waveguide Pellet Accelerator

DT fuel pellets placed in a straight ($\sim$1~m) section of a waveguide can be accelerated to high velocity ($>$3~km/s) by using millimeter microwave power to vaporize a composite ``pusher medium'' and convert it to high-pressure propellant gas [1]. Wave absorption in the pusher medium occurs by joule dissipation of eddy currents induced in micron sized conducting particles (Li, Be) uniformly dispersed in a slug of solid D$_2$ between the fixed window and the DT pellet. Formulae are derived for the absorption coefficient of waves propagating through the pusher medium in rectangular and circular waveguides. The wave damping distance elongates exactly in proportion to the length of the propellant gas, such that wave absorption remains constant in time. As the absorption coefficient doesn't depend on the wave power, a bench test experiment utilizing small-signal microwaves can be used to measure the absorption coefficient of the TE$_{01}$ mode in a cylindrical waveguide for combinations of absorber species and host media. Results are compared with theoretical predictions.\par \vskip6pt \noindent [1]~P.B.\ Parks and F.W.\ Perkins, Nucl.\ Fusion {\bf 46} (2006) 770.   

Optimizing Fueling Profiles in ITER and DIII-D by a Gyrotron-Powered Pellet Injector (GPPI)

The fueling system is an essential element in a tokamak reactor and control of its thermonuclear reactions. Pellets, accelerated by gyrotron-driven pellet injector [1], will provide sources of plasma density and energy. Subsequent evolution of density profiles depends strongly on toroidicity and position within a magnetic surface. We report the studies of ITER experiments for optimizing fueling profiles. With modest modifications, a scaled demonstration of GPPI is possible on DIII-D. For the ITER example, a GPPI has been designed to maximize four pellet properties: speed (V$>$3$k_{km}$/s), barrel bore (d$\leq$10.0mm), launch position (inside magnetic midplane), and launch trajectory (orthogonal to separatrix). The speed anticipated for the GPPI is more than a factor-of-10.0 above the limit of 300 m/s for a conventional guide-tube. The penetration of ablation ionization source increases a factor-of-6.0 with an order-of-magnitude increase in V. Previous models with V$^{1/3}$ scaling, predicted just a factor-of-2.2. Breakdown limitations will also be addressed.\par \vskip6pt \noindent [1]~P.B.\ Parks and F.W.\ Perkins, Nucl.\ Fusion {\bf 46}, 770 (2006).   

Installation and Testing of a 110 GHz Gyrotron With Depressed Collector Potential on the DIII-D Tokamak

A single stage depressed collector gyrotron has been installed for testing on the DIII-D tokamak. The tube has operated at the 1.25~MW level at 44\% efficiency for short pulses and at 0.5~MW for 10~s pulses at CPI and now is being tested to full parameters at DIII-D. A two-stage mode conversion dummy load has been built to handle the higher ultimate power from this gyrotron for pulses up to 5~s in length. Modifications to the high voltage power supply system were required to provide 30~kV depression and sequencing of the application of the voltages.   

Improved Collector Sweeping for Megawatt Gyro\-trons

Failure of the collectors on several high power gyrotrons in the DIII-D installation due to cyclic fatigue has prompted a study of power loading in the collectors. Thermal analysis showed that power loading needed to be reduced to below 600~W/cm$^2$ from the previous limit of 1~kW/cm$^2$ to obtain acceptable service life. Remedial measures taken to reduce the loading included use of stronger sweeping of the spent electron beam in the collector, raising the beam to reduce the footprint, use of a sawtooth waveform for the sweep coil current to reduce the dwell at extremes of the sweep, increasing the sweep frequency and tightening the rf dropout interlock window. With these measures in place, the target power loading is met and the predicted service lifetime exceeds 50,000 pulses 5~s in length.   

Design and Analysis of a 60 MHz Antenna Array for DIII-D

A long pulse (10s) four-element antenna array design is being developed and evaluated as a possible replacement for the present 285/300 DIII-D ICH array. Each array element will be poloidally segmented to reduce the strap voltage and the electric field in the near-plasma region, with the goal of improving reliability at high power levels. The single frequency (60 MHz) operation will allow the use of an internally self-resonant design, which will reduce the peak voltages in the antenna structure and the unmatched sections of transmission line. The present 285/300 antenna array, which recently had its single-tier, open Faraday shield replaced with its original double-tier, opaque Faraday shield, is also being modeled with the Microwave Studio 3D EM code. The modeling results will be used as a reference case for evaluating the new design.   

An Implicit Method for Magnetic Fusion MHD Calculations using Adaptive, High-Order, High-Continuity Finite Elements

Many aspects of the physics of toroidal magnetic fusion experiments can be described by a set of ``Extended Magnetohydrodynamic'' (E-MHD) equations for the evolution of the fluid-like quantities describing the high-temperature plasma and the magnetic field. Because of the multiplicity of time and space scales that develop, it is now recognized that adaptive higher-order finite elements with an implicit time integration scheme offer significant advantages. An ongoing effort to solve these E-MHD equations with finite elements with $C^{1}$ continuity is described. This leads to a compact representation and efficient solution algorithm. The method builds on a formalism for representing the velocity in a potential/stream-function form, and the magnetic field in an intrinsically divergence-free form. We report on solution characteristics of the full 8-field E-MHD equations in slab geometry. Recent applications on 2-fluid magnetic reconnection will be discussed, in particular the effect of a guide magnetic field on the onset of fast reconnection.   

Finite element implementation of Braginskii's gyroviscous stress with application to the gravitational instability

A general coordinate-independent expression for Braginskii's form of the ion gyroviscosity in the two-dimensional potential field representation is presented, and is implemented in a full two-dimensional, two-fluid extended magnetohydrodynamic (MHD) numerical model. The expression for the gyroviscous force requires no field to be differentiated more than twice, and thus is appropriate for finite elements with first derivatives continuous across element boundaries ($C^1$ finite elements). From the extended MHD model, which includes the full gyroviscous stress, are derived linear dispersion relations of a homogeneous equilibrium and of an inverted-density profile in the presence of gravity. The treatment of the gravitational instability presented here extends previous work on the subject. Linear and nonlinear simulations of the gravitational instability are presented. Simulations are shown to agree closely with the derived dispersion relations in the linear regime. The ``gyroviscous cancellation'' effect is demonstrated, and some limitations of the $\vec{v}_*$ approximation are discussed.   

Compression of Magnetohydrodynamic Simulation Data Using Singular Value Decomposition

Numerical calculations of magnetic and flow fields in magnetohydrodynamic (MHD) simulations can result in extensive data sets. Particle-based calculations in these MHD fields, needed to provide closure relations for the MHD equations, will require communication of this data to multiple processors and rapid interpolation at numerous particle orbit positions. To facilitate this analysis it is advantageous to compress the data using Singular Value Decomposition (SVD, or Principal Orthogonal Decomposition, POD) methods. As an example of the compression technique, SVD is applied to magnetic field data arising from a dynamic nonlinear MHD code. The performance of the SVD compression algorithm is analyzed by calculating Poincar\'e plots for electron orbits in a three-dimensional magnetic field and comparing the results with uncompressed data.   

Asymmetry of magnetic islands in sheared flow

In the present day tokamak plasma discharges, the plasma confinement and maximum operational plasma beta are strongly limited by the destabilization of neo-classical tearing modes (NTMs). These modes, stable at low beta, are excited by the bootstrap current loss within the island as a result of a local pressure flattening. The problem of islands stabilization has been largely investigated using schemes based on the electron cyclotron current drive. On the other hand, variations of the plasma pressure along the magnetic field may induce stabilization effects due to the ion neoclassical viscous forces for finite heat conductivity and inertial ion drift off the magnetic surfaces. Asymmetric deformation of magnetic islands may arise due to the effect of torque associated with the sheared viscous flow and are equivalent to an additional source of the longitudinal current. The deformation is described by a dependence of the island helical phase on the distance x from the rational surface. We reconsider reconnection, in rotating plasmas, allowing for deformed islands. Modifications of the Rutherford evolution equations are obtained taking into account the nonlinear ion inertia and the neoclassical viscosity that affect the longitudinal current and the island rotation frequency. As a consequence the critical island width for NTM onset changes and leads to significant effects on the estimate of value of the added rf power needed for the island control.   

Physics of supersonic two-fluid islands

Simulations of a magnetic island in a diamagnetic plasma are performed with the four-field equations, but with the magnetic flux-function specified. The ions are assumed to be cold. The island frequency is determined by adjusting the equilibrium E cross B velocity until there is no net electromagnetic torque acting on the island. Our simulations cover the ``unmagnetized" regime $W\ll\rho_s$, the supersonic regime $\rho_s\ll W\ll \rho_s\,(L_s/L_n)$, and the subsonic regime $\rho_s\,(L_s/L_n) \ll W$, where $W$ is the island width. In the``unmagnetized" regime, we expect the ions to flow straight through the island, and for the island to be convected by the electrons. Conversely, in the subsonic regime, we expect the density to be flattened across the island, and for the island to be convected by the ions. In both cases, we do not expect a substantial polarization current. However, in the intermediate supersonic regime, we expect the density to only partically flatten, and the island to be only partially convected by the ions. In this case, there is likely to be a substantial polarization current. We find that this current is {\em stabilizing}.   

Axisymmetric equilibrium with flow and pressure anisotropy in Hall MHD

Effects of the Hall current and pressure anisotropy on ellipticity of axisymmetric toroidal MHD equilibrium with strong poloidal and toroidal flow are studied. In MHD, the equilibrium equation so-called the generalized Grad-Shafranov equation can be both elliptic and hyperbolic partial differential equation depending on poloidal flow velocity and velocities of MHD waves. It has been shown that the model equations extended from Hall MHD equations to include pressure anisotropy obtain the linear dispersion relation that exactly coincides with the kinetic one for cold ions and adiabatic electrons. A set of equilibrium equations has been derived and its ellipticity has been examined. An ellipticity criterion for poloidal flow velocity has been found for tokamaks. It is the poloidal sound speed in the small wave length limit modified by pressure anisotropy. The ellipticity condition for general axisymmetric configuration would be obtained from nonexistence of real roots of fourth-order algebraic equation for characteristics.   

Validation of 2-Fluid and Gyro-Viscous Terms in Nimrod

Drift effects in modern tokamak plasmas can cause stabilization of modes that are otherwise unstable within the resistive MHD model. In the context of fluid modeling, these effects appear as additional terms in the ion and electron momentum equations. These terms account for the fact that ions and electrons flow as distinct and separate fluids (diamagnetic and polarization drifts), and that the small but finite size of the ion gyro-radius can cause a reversible (non-dissipative) flux of fluid momentum (FLR, or gyro-viscous effects). It is well known [1] that these effects become stabilizing for interchange instabilities when $\omega _\ast =2\gamma _{MHD} $, where $\omega _\ast $ is the drift frequency and $\gamma _{MHD} $ is the single-fluid (MHD) growth rate. We use this result to validate the implementation 2-fluid and gyro-viscous terms into the NIMROD code [2]. For model problems, we demonstrate excellent agreement with analytic predictions. Linear and non-linear results relevant to edge localized modes (ELMs) are also presented. [1] K. V. Roberts and J. B. Taylor, Phys. Rev. Lett. \textbf{8}, 197 (1962). [2] C. R. Sovinec, A. H. Glasser, T. H. Gianakon, et al., J. Comp. Phys. \textbf{195}, 355 (2004).   

Applying Asymptotic Approximations to the Full Two-Fluid Plasma System to study Reduced Fluid Models

Simulations are performed using the full two-fluid plasma system. The two-fluid model is investigated for its capabilities of capturing physics that is lost with simpler fluid models such as Magnetohydrodynamics (MHD). Asymptotic approximations are applied to the two-fluid equation system, both individually and collectively, to obtain reduced fluid models. These asymptotic approximations involve ignoring electron inertia, setting the speed of light to infinity and ensuring charge neutrality. Applying all three approximations together gives Hall MHD. The results obtained by applying the asymptotic approximations are compared to the two-fluid plasma model to determine what physics is lost by the application of each approximation. Simulations of electromagnetic plasma shock and collisionless reconnection will be presented to demonstrate the various physical effects.   

Numerical Implementation of the 10-Moment Two Fluid Model

The set of 10-moment fluid equations for the two fluid plasma model is examined and numerically implemented. The equation set is derived by taking the first three moments of the Vlasov equation. A 1-D harris current sheet equilibrium is explored, using the MacCormack algorithm. For an equilibrium, the pressure tensor for both fluids must be isotropic. If the current is carried only by electrons, an E-field is required to provide ion confinement. Simulations performed reveal whether the plasma maintains isotropic pressure in the absence of collisions. The results are compared to five moment two fluid simulation results.   

Low Collisionality Orderings for Extended MHD

A fluid theory of collisionless magnetized plasmas can be based on a single expansion parameter, namely the ratio ``delta'' between the ion gyroradius and the macroscopic lengths perpendicular to the magnetic field [J.J. Ramos, Phys. Plasmas, 12, 052102 (2005)]. The generalization of this theory to the fusion-relevant regimes of low but finite collisionality involves two more independent small parameters, namely the ratio between the electron and ion masses and the ratio between the ion collision and cyclotron frequencies. Such generalization is carried out assuming that these two ratios are comparable to or smaller than the square of ``delta.'' These conditions are well satisfied over a wide range of fusion-relevant plasma parameters, thus providing the basis for an attractive low-collisionality extended MHD model. The first significant order FLR equations for the flow velocities, the stress tensors and the heat fluxes are derived, with a detailed analysis of the collisional terms that need be taken into account. The analysis is valid for general magnetic geometry and fully electromagnetic non-linear dynamics with arbitrarily large fluctuations. It is also valid for strong anisotropies, does not require the distribution functions to be close to Maxwellians and assumes Fokker-Plank collision operators in their complete, quadratic form. Both the fast (sonic or Alfvenic motions) and slow (diamagnetic drift motions) orderings are considered.   

Initial Plasma Experiment in the Levitated Ring Trap RT-1

Studies on toroidal flowing plasma have started in a superconductor levitated coil device, Ring Trap 1 (RT-1) [1]. RT-1 generates a magnetosphere-like dipole magnetic field configuration that enables various kinds of experiments related to flowing plasmas. The main purpose of the Ring Trap Experiment is to explore a new high-b relaxation state of plasmas predicted by two-fluid relaxation theory of flowing plasmas [2]. Magnetic surface configuration of RT-1 also enables stable pure-magnetic trap of non-neutral plasmas [3], which is potentially suitable for the confinement of charged particles including anti-matters. As an initial experiment, hydrogen plasma is produced by electron cyclotron heating using 8.2GHz microwave generated by a klystron with the maximum power of 100kW for 1s pulse operation. The high-Tc superconductor (Bi-2223) ring with a total coil current of 250kAT is magnetically levitated in a vacuum chamber using a PID feedback control system. The field strength in the trap region is 0.03T to 0.3T. Diagnostics for the RT-1 experiment includes spectroscopy, soft X-ray pulse-height analysis with Si (Li) detector, magnetic probes, and Langmuir probes for edge plasma measurement. The initial experimental results and basic plasma parameters of RT-1 will be presented in the meeting. 1. Z. Yoshida et al., Plasma Fusion Res. \textbf{1}, 008 (2006). 2. Z. Yoshida and S. M. Mahajan, Phys. Rev. Lett. \textbf{88}, 095001 (2002). 3. Z. Yoshida, et al., in Nonneutral Plasma Physics III, IV.   

Radial Force Balance in Plasma Hole and Role of Centrifugal Force

A large-scale monopole vortex has been observed in a cylindrical magnetized plasma produced in the HYPER-I device at National Institute for Fusion Science, Japan. It is spontaneously formed with a deep density hole in its core and is referred to as \textit{plasma hole} from the impression of the end-view image taken by a CCD camera. The flow-velocity field of the plasma hole exhibits two characteristic features: a supersonic azimuthal rotation caused by a strong radial electric field and an inward radial flow. Since the latter is not driven in axisymmetric collisionless invicid plasma, it implies finite viscosity of the plasma. It is revealed that quasi-neutrality breaking ($\delta n/n\sim 10^{-3})$, which is the source of strong electric field, occurs in the hole region. To develop a deeper understanding on the structure of the flow-velocity field, we have analyzed the radial force balance including the nonlinear terms, i.e. the dynamic pressure due to radial flow and the centrifugal force. It is found that the centrifugal force dominates the radial electric field in the hole region, giving rise to a rigid rotor equilibrium which is similar to the fast rotation mode realized in pure electron plasmas.   

Flowing Magnetized Plasma experiment

Results from the Flowing Magnetized Plasma experiment at Los Alamos are summarized. Plasmas are produced using a modified coaxial plasma gun with a center electrode extending into a cylindrical vacuum tank with 0.75 m in radius and 4.5 m long. The basic diagnostics are Bdot probes for edge and internal magnetic field, Mach probes and Doppler spectroscopy for plasma flow in the axial and azimuthal directions, and Langmuir probes for plasma floating potential, electron density and temperature. We have found two different plasma flow patterns associated with distinct IV characteristics of the coaxial plasma gun, indicating axial flow is strongly correlated with the plasma ejection from the plasma gun. Global electromagnetic oscillations at frequencies below ion cyclotron frequency are observed, indicating that familiar waves at these frequencies, e.g. Alfven wave or drift wave, are strongly modified by the finite plasma beta. We eliminate the possibility of ion sound waves since the ion and electron temperatures are comparable, and therefore, ion sound waves are strongly Landau damped.   

An Experimental study of the non-ideal effects of the radial Ohm's law in the Flowing Magnetized Plasma experiment

The radial ideal Ohm's law in the Flowing Magnetized Plasma (FMP) experiment is studied experimentally. Two probes are designed and built to measure all terms in the radial ideal Ohm's law, plus electron temperature and density to estimate the importance of the non-ideal effects in the Ohm's law. The experimental data shows the ideal Ohm's law is not fully satisfied, the Hall effect is the most important effect, and the importance of the Hall effect is correlated to the ion skin depth.   

Two-dimensional MHD simulations of tokamak plasmas with poloidal flow

It has been shown [1] that, according to the ideal MHD equilibrium theory, poloidal flow in a tokamak can give rise to a pedestal structure with the pressure, density and velocity developing sharp discontinuities in their radial profiles. Such a pedestal arises when the poloidal velocity exceeds the poloidal sound speed. Since the poloidal sound speed vanishes at the separatrix, it is conceivable that evena rather slow poloidal flow can become transonic near the plasma edge, thus inducing a pedestal in the hydrodynamic profiles. While equilibrium calculations [1-4] of such a pedestal are well established, only a few two-dimensional time-dependent simulations have been carried out [5]. Here, we show the preliminary results from a two dimensional MHD code that simulates the formation of the pedestal starting from a poloidal velocity profile that becomes supersonic at the plasma edge. This work was supported by US-DOE under Contract DE-FG02-93ER54215. [1] Betti and Freidberg, Phys. Plasmas 7, 2439 (2000). [2] Guazzotto, Betti, Manickam and Kaye, Phys. Plasmas 11, 604 (2004). [3] Guazzotto and Betti, Phys. Plasmas 12, 056107 (2005). [4] Thyagaraja and McClements, Phys. Plasmas 13, 062502 (2006). [5] Gardiner, Betti and Guazzotto, Bull. Am. Phys. Soc. 46, No. 8, 166 (2001).   

Evaluation of Ion Specific Heat Ratio in a Transonic Plasma Flow

Dynamics of a fast-flowing plasma in a magnetic field are important to clarify a variety of MHD phenomena in space-, fusion- and also in electric propulsion-plasmas. Although an ion specific heat ratio $\gamma_i$ is one of the key parameters in plasma dynamic behaviors, it has not been measured yet in laboratory plasmas. In a high density plasma with a weak magnetic field, electrons are magnetized and restricted by a magnetic field, besides ions are not magnetized and behaves as ion fluid surrounded by the field-restricted electrons. In this case, ion Mach number changes according to the one-dimensional (1D) isentropic flow model. When a compressible flow passes through a Laval nozzle, Mach number becomes unity at the nozzle throat. We measured an ion Mach number $M_i$ by a Mach probe in a transonic plasma flow passing through a Laval type magnetic nozzle. The ion specific heat ratio $\gamma_i$ was evaluated for the first time by comparing the spatial profile of $M_i$ with 1D flow model.   

Large transport induced operational limits in tokamak plasmas

Recent observations on Alcator C-Mod by LaBombard et al.\footnote{B. LaBombard et al., Nuclear Fusion, \textbf{45}, 1568 (2005). } of various confinement regimes in the phase space identified by Rogers et al\footnote{B. Rogers et al. Phys. Rev. Lett. \textbf{81}, 4396 (1998).\par }, is found to be in very good agreement with their simulation results$^{2}$. In this phase space, they both identified a boundary at high collisionality (related to the empirical `density limit') which defines a region that is inaccessible due to very large transport in the edge region of the tokamaks. Simulations indicate that the generation of secondary zonal flows saturates the primary instability (drift-resistive ballooning or dissipative curvature driven drift waves). If, however the zonal flow becomes unstable below an amplitude necessary to saturate the primary instability, the transport can become prohibitively large and can lead to disruption of the plasma. Using this basic idea, a stability curve in the two-dimensional phase-space has been determined which provides a plausible explanation of the boundary between the accessible and inaccessible regions identified both in the simulations of Rogers et al. and the observations on Alcator C-Mod reported by LaBombard et al.   

Investigation of Intermittent Turbulence and Turbulent Structures in the Presence of Controlled Sheared Flows

Convective `blobs' (polarized filamentary structures) are observed in the boundary of a wide variety of magnetically confined plasmas -- in both laboratory and fusion devices. Intermittency in the fluctuations and particle flux has also observed near sheared flow layers internal to the plasma. However, while blob dynamics and blob transport have been investigated by a number of researchers, the mechanism of the formation of these structures has not received much experimental attention. Sheared flows are typically found at the plasma boundary and may play an important role in convective structure generation. Experiments are being conducted in both the LAPD (UCLA) and HELCAT (UNM) linear devices with the goal of elucidating the physics of the formation of intermittent structures at shear layers, as well as studying their dynamics. ExB flow shear is controlled by both biasing and the use of physical limiters. Initial measurements suggest that the correlation length inside the shear region depends strongly on magnetic field, while blob scaling with B is weaker.   

Turbulent flow and energy transfer in the RFX-Mod device

In the edge region of fusion devices $\mathbf{E}\times\mathbf{B}$ sheared flow and turbulence tend to organize themselves near marginal stability, and the role of fluctuations in driving sheared flow through Reynolds stress mechanism has been proved. This self-regulation process suggests the existence of an energy transfer between fluctuations and mean flow. A new set of insertable probes, installed in the RFX-mod Reversed Field Pinch device, allow the study of the quantity $P=\left[-\frac{\langle\tilde{b}_r\tilde{b}_{\phi}\rangle}{\overline{\rho}\mu_0} +\langle\tilde{v}_r\tilde{v}_{\phi}\rangle\right]\partial_r\overline{V}_{\phi}$, which provides the energy transferred between fluctuations and mean flow, and also the determination for the first time of the quantity $T=\frac{\langle\tilde{v}\times\tilde{j}\rangle}{\overline{\rho}}\cdot\overline{B}$, which represents the energy exchanged between electrostatic and magnetic fluctuations at small scales. Both the radial profiles and the temporal evolutions of these quantities have been measured supporting the existence of a continuous energy exchange between fluctuations and mean flow and among the fluctuations themselves.   

2D imaging of the edge turbulence in RFX-mod

In the reversed Field Pinch Experiment RFX-mod a Gas Puffing Imaging Diagnostic (GPID) is used to investigate the turbulence of the edge plasma. The system consists of a gas puffing nozzle and 32~optical channels to measure the HeI (668 nm) line emission from an area normal to the main magnetic field. A method based on Fourier expansion is developed to obtain a 2D tomographic reconstruction of the light emission pattern from the line integrals. The high time resolution allows to obtain a 2D image every 0.1 $\mu $s; moreover the time evolution of the turbulence can be analysed for the whole discharge duration (350~ms). Emission structures (``blobs'') that move along the \textbf{E x B} flow emerge from the background turbulence and they are characterised by computing energy and phase of the Fourier modes. A comparison is carried out between the structures identified by this 2D reconstruction and the intermittent events detected in the line-of-sight signals with a method based on the continuous wavelet transform. Furthermore, density structures detected with an array of Langmuir probes located in a different toroidal position are comparable with the ones reconstructed by the GPID.   

H-Mode Pedestal Width and Neutral Penetration

ITER confinement depends sensitively upon the \textit{width} of the H-mode pedestal, the physics of which remains poorly understood. Here we report on analytical studies of a simple model of the L$\to $H bifurcation in heat and particle transport, with central heating and edge fueling. A simple change-of-variables enables the reduction of this coupled system to simpler one field systems, \textit{without} any ad-hoc assumptions concerning the transport coefficients in L and H mode. Results indicate that a transition occurs locally if the product of heating and fueling lies within an interval set by the transport parameters. Thus, the pedestal width is inexorably linked to the neutral penetration depth, and an exponentially increasing amount of power is required to push beyond it. The major unknown is the particle diffusivity in H-mode. Implications for ITER, where neutral opacity is thought to be high, will be discussed.   

Dynamics of L-H transition and hysteresis in a spatially averaged transport model

A zero-dimensional L-H transition model suggested by Kim and Diamond (2003) is studied analytically and numerically in detail. The dynamical system consists of three equations coupling the drift wave turbulence level, zonal flow speed and the pressure gradient. The fourth component, the mean shear velocity is slaved to the pressure gradient. The bursting behaviour characteristic for predator-prey models of the drift wave - zonal flow interaction is recovered near the transition to the quiescent H-mode. It occurs as strongly nonlinear relaxation oscillations. The latter, in turn, arise as a Hopf bifurcation (limit cycle) of an intermidiate (between the L and H modes) fixed point. The system is shown to remain at the H-mode fixed point even after the heating rate is decreased below the bifurcation point ( hysteresis, subcritical bifurcation) but the basin of attraction of the H-mode shrinks rapidly with decreasing power. The shrinkage of the H-mode basin at the back-transition suggests that the hysteresis at the H-L transition may be less than what is often thought.   

Low-frequency turbulence and non-diffusive cross-field plasma transport in mirror systems

Low-frequency (LF) turbulence and the resultant cross-field plasma transport in mirror-based systems are studied on the basis of direct numerical simulations of nonlinear plasma dynamics. Under the low-beta assumption the nonlinear dynamics can be described in a frame of adiabatically reduced one-fluid MHD model (Pastukhov and Chudin, JETP Lett. 82(6), 2005). Simulations of self-consistent plasma evolution have shown formation of large-scale flute-like stochastic vortex structures, which have broad-bend frequency and wave-number spectra and are similar to the intermittent vortex-like structures observed in GAMMA 10 experiments (Cho et al., Phys.Rev.Lett. 94 (8),2005). The simulations were performed both for the conventional tandem mirror configurations and for axisymmetric non-paraxial configurations with a diverter-like separatrix as well. Various regimes of plasma confinement with sheared plasma rotation have been modeled and analyzed. The results obtained show a complex influence of sheared flows on the nonlinear plasma dynamics and the resultant cross-field plasma transport in mirror systems. The ability to control profiles of plasma rotation and sufficiently high dynamic vorticity of sheared flows can lead to turbulence reduction, modification of dominant vortex vorticity structures and transport barrier formation.   

Characteristics of Turbulence dominated by Zonal Flows and Large Scale Structures

In order to better understand the feature of turbulent transport in tokamak plasmas, characteristics of turbulent plasmas dominated by nonlinearly excited large scale structures (LSS),such as zonal flows, streamers, and generalized Kelvin- Helmholtz mode, are investigated by gyro-fluid simulations of electron/ion temperature gradient modes. It was found that the zonal flows change the characteristics of turbulence from ``homogeneous'' to ``inhomogeneous,'' in which disintegrated micro- scale vortices and nonlinearly excited macro-scale vortices appears at different radial zones, exhibiting a two-scale nature in turbulence. It is also found that the reduction of the heat flux by zonal flows results from the synergetic interplay of two exclusive mechanisms, i.e. the reduction of coherence and the phase synchronization between the poloidal electric field and the pressure perturbation. The effects of LSS on mode couplings will be also shown by bispectral analysis.   

Fractional diffusion models of non-local transport

A class of non-local models based on the use of fractional derivatives (FDs) is proposed to describe non-diffusive transport in magnetically confined plasmas. FDs are integro-differential operators that incorporate in a unified framework asymmetric non-Fickian transport, non-Markovian (``memory'') effects, and non-diffusive scaling. To overcome the limitations of fractional models in unbounded domains, we use regularized FDs that allow the incorporation of finite-size domain effects, boundary conditions, and variable diffusivities. A numerical method is proposed to solve the fractional model. An anomalous fractional pinch is observed, accompanied by the development of an up-hill transport region where the ``effective'' diffusivity becomes negative. The fractional flux is in general asymmetric and has a component towards the core that enhances confinement and a component that increases towards the edge and leads to poor confinement. The model exhibits the anomalous scaling of the confinement time, $\tau$, with system's size, $L$, $\tau \sim L^\alpha$, characteristic of low-confinement mode plasma where $1 < \alpha <2$. Numerical solutions of the model with an off-axis source show that the fractional inward transport gives rise to profile peaking reminiscent of what is observed in tokamak discharges with auxiliary off-axis heating. Also, cold-pulse perturbations to steady sates in the model exhibit fast, non- diffusive propagation phenomena that resemble perturbative experiments.   

Chaos generated subdiffusion and related convection in toroidal confinement devices

Transport in toroidal devices is usually described as the sum of diffusion and convection, $\Gamma = - D \nabla n + v \cdot n$, and $v$ is interpreted as the spatial variation $\partial D/\partial r$ of $D$. When the magnetic field is chaotic and it is near the stochastic threshold (as it is the case for the reversed-field pinch, RFP), the assumption that particles moving along chaotic field lines diffuse in the system is not valid. Instead, in such a condition, a convective velocity term appears quite naturally due to the streaming motion of particles with velocity nearly parallel to the magnetic field (i.e., with pitch $\lambda = v_{\parallel}/v$ close to 1), while particles with small pitch diffuse collisionally through the magnetic field. The convective term is a consequence of the intrinsic, non-diffusive character of the transport. Diffusive motion is recovered when the configuration consists of closed nested flux surfaces, such as in the ideal single helicity (SH) condition \footnote{D. F. Escande \textit{et al.}, Phys. Rev. Lett. \textbf{85 (15)}, 3169 (2000).}. The study is carried on calculating magnetic field lines and particle orbits with the code \textsc{Orbit} for a typical multiple helicity (MH) chaotic field, provided by a 3D MHD numerical simulation (SpeCyl) of the RFP.   

Non-local Heat Flow in a Sheared Slab with a Single-helicity Island

In this work, we review the derivation and implimentation of non-local closures\footnote{E. D. Held, J. D. Callen and C. C. Hegna, Phys. Plasmas 10, 3933 (2003).} for $\vec{q}_\|$ in the electron and ion plasma temperature equations which are valid in all geometries and for plasmas of all collisionalities. We then apply the closures to a plasma embedded in a magnetic field with a single-helicity perturbation. We compare quantities such as effective radial thermal diffusivity ($\chi_r$) and on-axis plasma temperature with those obtained using a flux-limiting and a local diffusive form for the closure. Calculations are made in sheared-slab geometry using new algorithms for rapid approximation of the heat-flow integrals. A description of the algorithms will be presented along with results from validity and convergence tests.   

Intermittent dynamics originated from geodesic acoustic modes (GAMs) near critical gradient regime

Dimits shift phenomenon, namely, the nonlinear upshift of stability threshold of ITG fluctuations, has been well recognized through understanding the suppression role of zonal flows. Here we present a novel intermittent dynamics of zonal flow and ITG turbulence system near the critical gradient regime by performing 5-filed Landau fluid global toroidal ITG turbulence simulation. It is identified that the intermittency originates from the coupling between the zonal flows and GAMs, where the latter can effectively damp the zonal flows. This process seems to be similar to the well-known collisional damping of zonal flows, which also cause an intermittency of ion heat transport. However, the observed bursting process here due to the coupling with GAMs can locally promote the energy accumulation of the stationary zonal flows so that ITG turbulence is quenched after several bursty periods. The details of the GAMs dynamics near the critical gradient regime will be reported.   

Nonlinear electromagnetic gyrokinetic particle simulations with the electron hybrid model

The electromagnetic model with fluid electrons is successfully implemented into the global gyrokinetic code GTC.\footnote{Z.~Lin, {\it et al.}, Science {\bf 281}, 1835 (1998).} In the ideal MHD limit, shear Alfven wave oscillation and continuum damping is demonstrated. Nonlinear electromagnetic simulation is further pursued in the presence of finite $\eta_i$\footnote{F.~Zonca and L.~Chen, Plasma Phys. Controlled Fusion {\bf 30}, 2240 (1998); G.~Zhao and L.~Chen, Phys. Plasmas {\bf 9}, 861 (2002).}. Turbulence transport in the AITG unstable $\beta$ regime is studied. This work is supported by Department of Energy (DOE) Grant DE-FG02-03ER54724, Cooperative Agreement No. DE-FC02-04ER54796 (UCI), DOE Contract No. DE-AC02-76CH03073 (PPPL), and in part by SciDAC Center for Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasmas.   

Simulation of Finite-Beta Effects in Gyrokinetic Plasmas

A generalization of the original split-weight scheme for finite-beta plasmas [W. W. Lee, J. Lewandowski, Z. Lin and T. S. Hahm, Phys. Plasmas {\bf 8}, 4435 (2001)] to multi-dimensional plasmas is developed. The scheme is based on the concept of perturbative particle simulation, where only the non-adiabatic response of the electrons, $\delta h$, is followed in time, where $\delta h = F- (1+\psi) F_0$, $F$ is the electron dunstibution function, $F_0$ is the background electron distribution function, $\psi =\phi + \int A_\parallel d x_\parallel/c$, and $\phi$ and $A_\parallel$ are the perturbed potentials. The procedure involves the Poisson solvers for $\phi$, $A_\parallel$, $\partial \phi / \partial t$, $\partial A_\parallel /\partial t$, and $\partial^2 A_\parallel / \partial t^2$, which, in turn, need up zeroth, first, second and third velocity-space moments for input. The use of the scheme for turbulence and MHD studies [Lee and Qin, Phys. Plasmas {\bf 10}, 3196 (2003)] will be presented.   

Electron Transport Driven by Short Wavelength Trapped Electron Mode Turbulence

An outstanding issue in tokamak confinement studies is the origin of the anomalous electron thermal transport in internal transport barriers (ITB), where the ion transport is reduced to the neoclassical level. As the density gradient steepens in barrier regions, the electrostatic trapped electron mode (TEM) is often driven unstable. The key issue is whether TEM turbulence is capable of driving a large electron heat flux without driving significant ion heat and particle fluxes. In global gyrokinetic particle simulations using the GTC code, we find that the TEM mode has a wide spectrum with a large linear growth rate for k$_{\theta }\rho _{i}$ ranging from $\sim $0.2 to $\sim $1. The short wavelength modes drive a large electron heat flux, but a smaller ion heat flux and particle flux. The longer wavelength modes drive a large ion heat flux and particle flux. Since the formation of the ITB is often accompanied by the generation of equilibrium sheared flows, these longer wavelength fluctuations can be easily suppressed or broken up into smaller eddies by the strong flow shear, while the short wavelength fluctuations can survive the shearing effects. Therefore, the small scale TEM turbulence is a viable candidate for driving the electron thermal transport in the ITB regions.   

Gyrokinetic theory and simulation of toroidal ETG turbulence and zonal flow

Electron temperature gradient (ETG) turbulence is considered as a plausible cause that is responsible for producing the anomalous electron heat transport in magnetic confinement fusion plasma. While linear mode properties of the electrostatic ETG and ITG (ion temperature gradient) instabilities are isomorphic, their different nonlinear saturation processes are associated with zonal flows. Here, the linear response of the zonal flow in the toroidal ETG system is analytically studied, and then, is verified by the gyrokinetic-Vlasov (GKV) simulation. While the residual zonal flow level has higher normalized amplitude than that in the ITG case, the nonlinear excitation of zonal flows by ETG turbulence is much weaker. Nonlinear saturation process of the toroidal ETG turbulence is also investigated by means of the GKV simulation performed on Earth Simulator. Large modulation of streamer-like potential structures of nonlinearly excited mode is clearly found in case with a wide flux tube simulation box. *Numerical simulations are carried out by means of Earth Simulator under the support by JAMSTEC and of Plasma Simulator at NIFS. This work is supported in part by grands-in-aid of the Ministry of Education, Culture, Sports, Science and Technology (No. 16560727 and 17360445) and by NIFS collaborative research programs.   

Isotope Effects due to Ion Temperature Gradient Drift Instabilities in Global Gyrokinetic Particle Simulation

Ion temperature gradient (ITG) drift instabilities using the global Gyrokinetic Turbulence Code (GTC) [Z. Lin et al., Science $<$281$>$, 1835 (1998)] have been carried out using different hydrogen species (H+, D+ and T+) to study the isotope effects. Since it is commonly believed that, in the GyroBohm regime with $\chi_i \propto \sqrt{M}/B^2$, the ion thermal diffusivity should increase for heavier hydrogen isotopes. On the other hand, in the Bohm regime with $\chi_i \propto 1 / B$, the ion thermal diffusivity is independent of the mass. To test these hypotheses, we have carried out simulations with different minor radii to insure that we are indeed in both of the regimes [Lin et al., Phys. Rev. Lett. (2002)]. In these simulations, both the ${\bf E} \times {\bf B}$ nonlinearity and the parallel velocity space nonlinearity have been included, since both of them are closely related the zonal flows dynamics. Preliminary results have indicated that favorable isotope effects are always present. However, it is not as prominent as those reported earlier [W. W. Lee and R. A. Santoro, Phys. Plasmas $<$4$>$, 169(1997)]. Initial theoretical understanding will be presented.   

On the effect of a non-uniform longitudinal ion flow on the linear ITG mode stability.

A one-dimensional model for slab ion temperature gradient (ITG) modes, in the presence of an inhomogeneous equilibrium plasma velocity along the main magnetic field direction, has been formulated in the frame of a two-fluid guiding-center approximation. The physical effects of a magnetic field gradient and of the line curvature are included by means of a gravitational drift velocity. The magnetic shear across the plasma slab is also taken into account. The linear stability of slow plasma dynamics, under the assumptions of quasi-neutrality and adiabatic electrons, is described by means of a third-degree dispersion relation. Generally speaking, the presence of a sheared longitudinal ion velocity leads to the linear destabilization of the ITG modes, especially for flat equilibrium density profiles. Transverse quasi-linear fluxes of ion thermal energy and longitudinal momentum are calculated for different equilibrium profiles of the density, temperature, momentum, and magnetic shear. Plasma configurations leading to zero transverse (or even negative) momentum fluxes are exploited and discussed in the light of their experimental implementation.   

Models for fast ion tails and ion orbit loss in the moments formulation of neoclassical theory

We present models for the inclusion of strongly anisotropic fast ion tails and orbit losses in the moments formulation of neoclassical theory [1], and implemented in the NCLASS code [2]. Anisotropic fast ion tails (e.g. from NBCD or RFCD) provide a torque, which induces poloidal as well as toroidal flows in the thermal species. Ion orbit losses at the plasma edge also provide a torque, and may drive the L-H transition [3,4]. One of the most challenging computational aspects of this work has been the extension of the friction and viscosity tensors to arbitrary order in order obtain converged solutions to the resonant perturbation to the electron distribution when the fast ion velocity is finite relative to the electron thermal velocity. The velocity moments then yield a converged solution for the flows (which can be measured directly for non-hydrogenic ions), as well as particle and heat fluxes and currents. [1] S.P. Hirshman, D.J. Sigmar, Nucl. Fusion 21 (1981) 1079 [2] W.A. Houlberg et al, Phys. Plasmas 4 (1997) 3230 [3] K.C. Shaing et al, Phys. Fluids B 2 (1990) 1492 [4] R. Hiwatari et al, Plasma Phys. Control. Fusion 44 (2002) A445   

Comparing the Fluid and the Kinetic Approaches to Collisional Angular Momentum Transport

Collisional transport of tokamak plasmas can be investigated using a fluid or a kinetic approach, both of which start from the kinetic equation, but employ differing orders of expansions in the small parameters of gyro-radius over scale length and collision frequency over gyro-frequency. In the fluid approach, a closed description is first obtained for local moment equations. The kinetic approach achieves closure only for flux surface averaged moment equations, but has the advantage of being applicable to long mean-free-path regimes. It was noted recently [1] that although the two approaches yield identical results for particle and heat fluxes in the Pfirsch-Schluter regime, they do not for the angular momentum flux, mainly because of incompleteness in the kinetic approach. The work being reported revisits both approaches and attempts to reconcile the difference in the results if any, and casts the angular momentum flux into a closed form involving flux averaged density, temperature, and electric potential.\par \vskip6pt \noindent [1]~P.J.\ Catto and A.N.\ Simakov, Phys.\ Plasmas {\bf 12}, 012501 (2005).   

Modification of turbulent particle transport and intermittency by biased rotation in LAPD

The edge plasma in LAPD is rotated through the application of a bias voltage between the plasma source cathode and the vacuum vessel wall. As the bias voltage is applied and increased past a threshold value, the measured density profile steepens dramatically (from $L_n > 10 \rho_s$ to $L_n \sim 2 \rho_s$) at a radius near the peak of the flow shear. Turbulent transport flux measurements in this region show that the flux is reduced and then suppressed completely as the threshold is approached. The amplitude of the density and azimuthal electric field fluctuations is observed to decrease during biased rotation, the product of the amplitudes decreasing by a factor of 5. However the dominant change appears in the cross-phase, which is altered dramatically, leading to the observed suppression and reversal of the turbulent flux. Detailed two-dimensional turbulent correlation measurements have been performed. During biased rotation, a dramatic increase in the azimuthal correlation is observed, however there is little change in the radial correlation length. An investigation of the modification of intermittent (or ``blobby'') transport due to the shear flow is underway and initial results will be presented.   

Incentives for and Developments of the Accretion Theory of Spontaneous Rotation*

Since the ``accretion theory''\footnotemark[1] of the spontaneous rotation phenomenon was introduced, the body of observations supporting this theory has grown considerably. Accordingly, angular momentum is ejected from the toroidal plasma column by modes excited at its edge while angular momentum in the opposite direction resulting from the associated ``recoil'' force is transported from the outer region of the plasma column toward its center by another kind of mode. In the H confinement regime, the inward transport of angular momentum is associated with ``VTG modes''\footnotemark [2] that involve the gradients of both the ion velocity $V_\parallel (r)$ and temperature $T(r)$ and have a phase velocity in the direction of $v_{di}$. The frequency of these modes, which depends on the combined effects of the (quasi- linear) ion transverse thermal conductivity and viscosity, vanishes if d$V_{\parallel}/$d$r=0$. Given the formation of a steep density gradient at the edge of the plasma column in the H-regime, resistive ballooning modes\footnotemark[3] that have a phase velocity in the $v_{de}$ direction, are the best candidates for the ejection of angular momentum in this regime and are consistent with observations. In the case of a colder edge with smaller electron pressure gradients, characterizing the L-regime, the relevant unstable mode acquires a phase velocity\footnotemark[3]$^,$\footnotemark[2] in the direction of $v_{di}$. *Sponsored in part by the US DOE. \vspace{3pt}\\ \small{$^{1}$B.~Coppi, {\sl Nucl.\ Fusion} \textbf{42}, 1 (2002) and B.~Coppi, Paper IAEA-CN-\hspace{15pt} 94-TH/P1-02, (Lyon, 2002) and MIT-RLE Report PTP02/05 (2002) and B.~Coppi, {\sl et al.}, Paper IAEA-F1-CN-TH3/7 (Yokohama, 1998).\\ $^2$B.~Coppi {\sl et al.}, Paper 04.017,\ Proceedings, 2006 EPS Meeting P.P.\\ $^3$B.~Coppi and M.~N.~Rosenbluth, {\sl Plasma~Phys.~Control~Fus.~Res.}~\textbf{1}, 617 (1966).}   

Angular Momentum Ejection and Transport Equation for the ``Spontaneous Rotation'' Process*

a process of ejection of angular momentum, from the edge of the plasma column [1,2]. This is attributed to modes driven by the local (edge) plasma pressure gradient. The unstable mode associated with the effect of finite resistivity, is characterized by a phase velocity direction that changes from that of the electron diamagnetic velocity [3] to the opposite as the temperature and the electron pressure gradient decrease. The recoil angular momentum is transported towards the center of the plasma plasma column by collectives modes (V.T.G.modes [4]) that the gradient of both the ion temperature and the longitudinal (toroidal) velocity. A smplified angular momentum equation that includes an inflow term associated with the ion temperatue gradient has been employed to reproduce velocity profiles available from current experiments as well as past experiments [5] on rotation induced by neutral beam injection. [1]B. Coppi, {\em Nucl. Fusion} {\bfseries 42}, 1 (2002) and B. Coppi, Paper IAEA-CN-TH/P1-02, (Lyon, 2002) and MIT-RLE Report PTP02/05 (2002).[2]B. Coppi, {\em et al.}, Paper IAEA-F1- CN-TH3/7 (Yokohama, 1998). [3]B. Coppi and M.N. Rosenbluth, {\em Plasma Phys. Control Fus. Res.} {\bfseries 1}, 617 (1966). [4]B. Coppi, {\em et al.}, Paper 04.017, Proceeding of the 2006- E.P.S. Meeting on Plasma Physics. [5]{K. Nagashima, Y. Koide, H. Shirai, {\em Nucl. Fusion} {\bfseries 34}, 3 (2002)}. *Supported in part by the U.S. D.O.E.   

Equilibrium Profiles in the Helimak

The Helimak is a good approximation to the infinite cylindrical slab, and the end plates allow application of radial electric fields that drive radial currents. The plasma is produced by ECH, but the profiles are much broader than the ECH resonance. The high level of turbulent density fluctuations allows an upper hybrid resonance for a range of magnetic fields below the ECH resonance (larger radii). The density fluctuations can be greatly reduced by application of radial bias. The self-consistent equilibria over the range of operating conditions will be described. Work supported by the Department of Energy Office of Fusion Energy Sciences DE-FG03-00ER54609.   

Turbulent Transport Studies in the Helimak Experiment

Measurements of turbulent fluctuations and the associated transport have been made in the Helimak experiment, a device possessing a simple, helical confinement geometry. We have found there to be a strong dependence of the character of both the turbulence and transport on the connection length along the magnetic field lines, which we find to be an appropriate stability parameter. There appears to be a strong correlation between density and electric field fluctuations when the particle flux reaches is maximum value, a hallmark of drift wave turbulence driven transport. Local particle fluxes are also investigated as a function of neutral gas pressure, input ECRH power, ion mass, and radial position inside the vessel.   

Structure of Helimak Turbulence

The Helimak is a good realization of a sheared cylindrical slab with open field lines. The plasma is heated by microwaves at the electron cyclotron resonance. The resulting pressure and potential gradients give drift and fluid instabilities that drive fluctuations in density and potential. Both density and potential structures are studied by two dimensional arrays of Langmuir probes placed in the cross field plane. The structures observed are compared to those predicted by simulations of the D’Ippolito-Krasheninikov equations. The simulations show turbulence produced by a combination of Raleigh-Taylor and Kelvin-Helmholtz instabilities. In addition we compare our statistical characterization of turbulence to the predictions of drift turbulence. Finally we will look at the change in the two dimensional structures as we drive flows that shear the turbulence and stabilize the fluctuations in the Helimak plasma.   

Suppression of Weibel Instabilities by High Harmonic Electron Bernstein Modes in Advanced Fast Ignition Laser Fusion Pellets

A novel mechanism for the suppression of Weibel instabilities$^{\ast }$\footnote{$^{\ast }$ E. S. Weibel, Phys. Rev. Lett., 2,83 (1959)} in the core of advanced fast ignition pellets$^{\ast }$\footnote{$^{\ast }$ M. Tabak, J. Hammer, M.E. Glinsky, W.L. Kruer, S. C. Wilks, J. Woodworth, E. M. Campbell, and M.D. Perry, Phys. Plasmas 1 (5), 1626 (1994).} is addressed. The propagation of generated suprathermal electron beam toward the core may lead to the appearance of colossal ($\sim $10MG), small scale (L$\sim $c/$\omega _{pe}$, c---velocity of light, $\omega _{pe}$---local electron plasma frequency)$^{\ast }$\footnote{$^{\ast ,a,b}$ V. Stefan, (a) Quasi-Stationary B-Fields due to Weibel Instability in FI Laser Fusion Pellets; (b) Pellet Core Heating Via High Harmonic EB Modes in FI Laser Fusion. 35th Annual A.A.C, 2005, \textit{Puerto Rico}\par }$^{,a,b}$ magnetic fields. The suppression synergy of high harmonic electron Bernstein, (EB), modes and Weibel modes, (WB), in the cone-attached laser fusion pellets is based on nonlinear mode-mode coupling. EB modes are excited by ignition, a cone guided, or implosion laser beams. High harmonic EB modes easily propagate to the core of the pellet whereby they nonlinearly interact with, and suppress, the WB. The suppression synergy is maximized at the simultaneous action of ignition and implosion lasers.   

Stopping of Relativistic Electrons in Partially Degenerate Electron Fluid

The stopping mechanisms of relativistic electron beams in superdense and partially degenerate electron fluid targets are investigated in framework of the fast ignitor concept for ICF. We focus attention on target partial degeneracy parameter Theta=Te/Tf. The target electron fluid is thus accurately modelled with a RPA dielectric function. Stopping is seen as steadily increasing with Theta. For electron projectile energies below 2-4 MeV, according to target densities, stopping power decays a la Bethe i.e in 1/Vp$^2$, with Vp, projectile velocity. At higher energies, stopping increases steadily with Vp in a quasi- logarithmic fashion, characteristic of the ultra-relativistic regime.   

Oblique Electromagnetic Modes for a Hot REB in a Hot and Magnetized Plasma

A temperature-dependent fluid model[1]is used to explore the linear and oblique EM instabilities suffered by a hot REB entering a hot, dense and magnetized plasma. Temperatures are nonrelativistic. In the weak beam approximation, the magnetic field reduces every instabilities except the 2-stream one.In the high beam density regime, highly unstable oblique modes appear due the magnetic field. In both cases, temperature effects are overcome by the magnetic field and uniform stabilization all over k space cannot be obtained. \newline \newline [1]A. Bret and C. Deutsch Phys Plasmas, 13, 042106(2006).   

Collision effects on the filamentation instability

In the fast ignitor scenario the MA current carried by the forward laser driven beam MeV electrons, beyond the Alfv\'{e}n limit, can be transported only by the presence of a plasma return current. This system is subject to collisionless filamentation (Weibel) instability in the coronal region. The effects of collisions in inner regions of the fusion pellet change the features of the filamentation instability and have to be considered. Simulations performed with PIC code osiris 2.0, including binary collisions, are presented, analyzing the filament behavior due to the collisional filamentation instability. As the collision frequency increases, the instability occurs at larger typical wavelengths compared to the collisionless case. Hence, only larger filaments can form, eventually becoming comparable to the typical beam size, and whole beam instabilities can be driven. These features are theoretically recovered using relativistic kinetic theory, including space charge effects, warm species and collisions through the BGK model. Furthermore, it is shown that collisions lead to small but not negligible growth rates even at temperatures for which the collisionless instability is completely stabilized by thermal effects.   

Issues in assembling fuel for Fast Ignition

Optimized Fast Ignition designs require that the fuel must assembled into a compact mass with little separation from the critical surface. In addition, the fuel must be assembled with good hydrodynamic efficiency and with low entropy. The cone-focus targets have been designed that meet some of these criteria. In this poster we discuss requirements to optimize targets with and without cones. Specific designs are suggested. This work was performed under the auspices of the U.S. Department of Energy by University of California, Lawrence Livermore National Laboratory under Contract W-7405-Eng-48.   

Target size and boundary condition effects in PIC simulations of fast ignition

Due to the amount of computation involved the current PIC simulations on fast ignition have to be performed with reduced sizes and dimensions. The relevant physics could be significantly affected by the size and boundary conditions used in these reduced simulations. Compared to other particle boundary conditions such as the periodic one the thermal boundary condition which reemits particles with their initial temperatures can maintain a relatively small hot electron population even under constant laser irradiation, a situation closer to that in the actual laser-plasma interface region where hot electrons leave and cold background electrons flow in. We will present a study on effects of different boundary conditions on electron distributions and current filament and merge process.   

PIC Simulation of Fast Ignition Targets with OSIRIS

Understanding transport of fast electrons generated by the ignition laser pulse at the critical surface to the target core is essential to the success of fast ignitor concept. Results of 2.5D PIC simulations of scaled fast ignition targets along with code modifications made to the massively parallel PIC code OSIRIS for fast ignition relevant regimes are presented. We look at the effect of target density profiles on the laser envelope and how it affects electron transport. We also look at how feedback from a resistive core affects electron transport. Diagnostics show electron energy flux as a function of position and particle energy. Code modifications include deposition and interpolation schemes that have significantly better energy conservation, a mock up of target (resistive) core, and specialized diagnostics. The improved energy conservation is particularly important for the large range of densities necessary for simulation of fast ignition targets.   

Multi-Scale Kinetic Model of Ultrafast Laser-Matter Interaction

Interaction of ultrafast laser pulses with solid density targets is characterized with multiple temporal and spatial scales. Predictive simulation with traditional methods (e.g. PIC) is restricted due to computational costs and high statistical noise. A hybrid multi-scale approach combines moving adaptive mesh, which automatically follows physical parameters such as electro-magnetic fields, target density, their gradients, etc. with dual representation of the distribution functions by discrete particles and continuous grid-function in velocity space. These elements allow us to control computational cost while providing required accuracy of simulations. For instance, an ablation of a micron-size droplet in a cm-sized domain can be simulated on a desktop computer. We present results of simulations, discuss code parallelization, and interfacing with molecular dynamics at nano-scale and fluid codes at macro-scale.   

Generation of Hot Dense Matter in High Intensity Laser Plasma Interaction Experiments

We have studied the heating to T$_{e}>$100 eV of tamped Ti foil targets at near solid density, conditions which are found in inertial confinement fusion and laboratory astrophysics plasmas. The experiments were conducted at the Vulcan Laser Facility at the Rutherford Appleton Laboratory (UK) using a 100 J, 1.5 ps laser beam focused to a 10 micron spot onto Al or CH coated Ti flat foils. The Ti inner-shell spectra (4--5 keV) have been measured both from the front (i.e., the laser side) and back of the target. The data from the back show a large shift in the K-alpha emission compared to cold metal, suggesting a high degree of heating. Simulations using collisional radiative and 1-D radiation hydrodynamics codes were used to study opacity effects on the emitted spectra. This allows us to infer the average electron temperature and ionization state.   

Electromagnetically induced transparency at Ion Acoustic Frequency in Dense Plasmas

Electromagnetically induced transparency (EIT) is a technique where an electromagnetic wave controls the refractive index of a plasma\footnote{ S.E.Harris, Phys. Rev. Lett. 77, 5357 (1996)}. It enables us to create a passband for low frequency electromagnetic wave in a dense plasma even if the plasma is opaque for the electromagnetic wave. This technique will be used to prove the ion acoustic wave since the ion acoustic frequency is lower than the plasma frequency. Then by using the EIT technique, we have investigated feasibility of electromagnetic radiation at THz region corresponding to the ion acoustic frequency from a dense plasma. Based on calculations, we demonstrate that a passband is created at about 10THz corresponding to the ion acoustic frequency in the plasma (10$^{21}$ cm$^{-3})$ with a Ti:S laser (800nm, 10$^{17}$W/cm$^{2})$.   

Theoretical limit for attosecond Raman compression of powerful x-ray pulses in plasmas

We examined the possibility to improve both the longitudinal compression and focusing of intense x-ray pulses by means of resonant backward Raman amplification (BRA) of laser pulses in plasmas. The method features conventional Raman compression and beam-cleaning techniques in which the output can be made much shorter and better focusable than the pump. However, the plasma-based BRA deals with laser intensities that would be too high to handle efficiently otherwise. Similar method was applied earlier to optical laser pulses. We found the theoretical limit of about 1 nm for the shortest laser wavelength at which this method can be applicable to x-ray pulses. The respective shortest possible duration of output x-ray pulses is about 10 attoseconds.   

Absorption of Ultra-Short Intense Laser Pulses and Particle Transport in Solid Density Targets

A new version of the numerical code KALOS [1] has been developed to solve the Vlasov-Fokker-Planck equation for the electrons and ions as well as EM wave propagation. KALOS represents the electron distribution function in momentum space by an expansion in spherical harmonics. Its unique features make possible simultaneous investigations of fast electron generation and transport and the collisional evolution of thermal particles, including the return current of cold electrons, without the usual `hybrid' approximation. We report here on results obtained in 1D3P. Absorption of short ($\sim $100fs) laser pulses has been studied over a range of intensities (10$^{14}$-10$^{18}$ W/cm$^{2})$ at normal incidence in sharp-edged dense plasmas. We have studied the effect on absorption of energy transport into the target as well as the deviation of the electron distribution function from Maxwellian. The role of kinetic effects has been assessed by comparing the full kinetic KALOS calculations with the hydro code MULTI-FS [2] and theoretical predictions of absorption and transport. [1] A. R. Bell, \textit{et al.}, Plasma Phys. Control. Fusion \textbf{48}, R37 (2006). [2] K. Eidmann, \textit{et al.}, Phys. Rev. \textbf{E62}, 1202 (2000).   

Spherical nanoplasmas irradiated by intense x-ray sources

Clusters exposed to ultra-short ultra-intense infra-red laser pulses can undergo a Coulomb explosion. Using two sequential pulses it is possible to control the dynamics of the explosion, and to produce multibranch structures in the phase space (shock shells). In x-ray irradiated clusters, the electron excursion length in the radiation field is shorter than the typical cluster dimension, and a pure Coulomb explosion is difficult to achieve. The initial cluster dynamics is mainly determined by the electron distribution function generated by ionization. Using particle-in-cell simulations performed with OSIRIS 2.0 coupled with an x-ray ionization code, we have studied the role of ionization in the expansion dynamics and shock shell formation in clusters irradiated by intense x-ray pulses (e.g. XFEL and LCLS sources). Our results show that under suitable conditions, the dynamics of the cluster expansion can be controlled, and shock shell formation with intense x-ray sources is possible using pulse sequences with different intensities, thus opening the way to phase space control of the expansion of nanoplasmas with x-ray sources.   

Relativistic ionization fronts in gas jets

A high-power ultra-short laser pulse propagating through a gas jet, ionizes the gas by tunnelling ionization, creating a relativistic plasma-gas interface. The relativistic ionization front that is created can be used to frequency up-shift electromagnetic radiation either in co-propagation or in counter-propagation configurations. In the counter-propagation configuration, ionization fronts can act as relativistic mirrors for terahertz radiation, leading to relativistic double Doppler frequency up-shift to the visible range. In this work, we identified and explored, the parameters that optimize the key features of relativistic ionization fronts for terahertz radiation reflection. The relativistic ionization front generated by a high power laser (TOPS) propagating in a supersonic gas jet generated by a Laval nozzle has been fully characterized. We have also performed detailed two-dimensional relativistic particle-in-cell simulations with Osiris 2.0 to analyze the generation and propagation of the ionization fronts.   

Simulation of Foil Heating Using Short Pulse Lasers for Strongly Coupled Plasma Experiments

Laser facilities can now generate high-contrast picosecond-regime temporal pulses having peak intensities of $\sim $10$^{18}$ W/cm$^{2}$ with pre-pulse intensity levels below the ionization threshold of a solid target. This allows for the generation of high laser intensity gradients at the surface of the target. In turn, these gradients ponderomotively produce hot electrons that penetrate into the target substrate and heat it. The utility of using this mechanism to quickly heat a thin $\sim $10 micron thick target into an inertially-confined strongly-coupled plasma is examined using the radiation-hydrodynamics code LASNEX. Results for various material targets and laser parameters will be shown.   

Time Resolved K$_{\alpha}$ Measurements in laser-solid interaction at relativistic laser intensities

We present the time-resolved K$_{\alpha}$ emission measurement in short pulse laser-solid interactions using a picosecond time-resolved x-ray spectrometer for laser intensities at 10$^{17}$, 10$^{18}$ and 10$^{19}$ W/cm$^{2}$. Our measurements indicate that most of the K$_\alpha$ radiation is generated several ps after the laser pulse is over. This suggests that the electrons responsible for the underlying process originate in an ionization cascade initiated by the hot electrons. This can be explaned by a simple model based on collisional coupling, plasma expansion and M-shell ionization that can reproduce the characteristics of the K$_\alpha$ history.   

PIC Simulations of Short-Pulse, High-Intensity Light Impinging on Structured Targets

The production of energetic electrons in short-pulse, high-intensity laser-plasma interactions is a key component of the fast ignition concept. In present day scenarios this short-pulse high intensity laser propagates down a cone to produce the hot electrons near the compressed core. PIC simulations with our code, Z3, are used to study the laser plasma interaction in such irradiations. We investigate whether shaping the laser beam interaction surface aids in the production of high energy electrons with the desired characteristics for fast ignition. In these idealized simulations, this surface is taken to be a series of `divots' whose dimensions are of the order of several laser wavelengths. Determining an optimum `divot' shape is one area of investigation. We also report on simulations of cone irradiations more closely guided by experiment in which we use more realistic beam spatial profiles and consider the effect of (expected) beam pointing inaccuracies. The cone shapes are also varied. In all these simulations presented here, the main metrics are the energetic electron distribution functions.   

SPECT3D Post-Processing of LSP PIC Simulations: Application to Short-Pulse Laser Experiments

In the fast ignition concept for inertial fusion energy, high-intensity short-pulse lasers (SPL) are used to create energetic particles (protons and relativistic electrons) that propagate to the fuel within a compressed capsule. To achieve a good understanding of energetic particle transport through dense plasmas, a combination of well-diagnosed experiments and high-quality simulation tools is required. In this study, we utilize the SPECT3D simulation package to post-process the results from LSP particle-in-cell (PIC) simulations to generate images and spectra that can be directly compared with experimental measurements. In doing this, we have updated the multi-dimensional collisional-radiative SPECT3D package to include the effects of both relativistic electrons and energetic proton beams that are generated in SPL experiments. Energetic particle effects are included in computing non-LTE atomic level populations, emergent spectra, and images for the target plasma. This procedure allows us to study diagnostic signatures arising from energetic particles. We will present example results from simulations and comparisons with available experimental data.   

Ballistic radial energy transport in micron-scale plasmas under high energy density conditions.

In this work we apply fs microscopy to solid targets (Al, Cu) irradiated at relativistic intensity ($I_{pu} \ge 2 \times 10^{18}$ W/cm$^{2}$) by high-contrast (better than $1:10^{-10}$), obliquely-incident ($\theta^{inc}_{pu} = 45^{\circ}$ and $70^{\circ}$), \textit{P}- and \textit{S}-polarized pump pulses ($\lambda_{pu} = 0.8$ $\mu$m, 34 fs) focused to a {\it wavelength-scale} spot size ($w_0 = 0.8$ $\mu$m). Under these conditions, radiation and hot electrons are the dominant carriers of energy out of the initially photo-excited volume. The mean free paths governing both transport processes exceed the spot size $w_0$, opening the study of ballistic transport of energy into surrounding target material. Our fs microscopy experiment, with $\lambda_{pu}^2$ pump spot, is well-suited to observe the initial stages, and the radial dimension, of such non-local transport directly on any target material. The physics of this transport is relevant to fast ignition of laser fusion, to generation of ultrashort pulsed x-rays and relativistic proton and ion beams, and to astrophysics. Our interaction volume may be small enough that the entire experiment is amenable to large-scale particle-in-cell simulations.   

Time resolved inner-shell spectroscopy of laser produced plasmas using a HOPG crystal in Von Hamos geometry

Time resolved heat transport in warm dense matter, an essential component of the Fast Ignition concept, has been studied using inner-shell spectra from Ti and Al/Ti/Al foils. Thermal emission is generated by irradiation with either 527 nm and 1ns or 1053 nm and 5 ps pulses using the Vulcan laser at RAL. Fluorescence emission was recorded with a ZYA grade HOPG crystal used in mosaic focusing mode and Von Hamos geometry. The crystal was coupled with a Kentech Low Magnification Streak Camera, fitted with a fluffy CsI photocathode, providing a temporal resolution of about 50 ps. Although the small dynamic range of the streak camera restricts measurement of the full duration of He-alpha emission, our data indicates that the FWHM duration of the resonance line is approximately 1.5 ns when the Ti foil is irradiated with 1 ns pulses.   

Extremely Nonsinusoidal Emissions from Strong Laser Pulses Obliquely P-Incident on Sharp-Edged Plasmas

Extremely high laser harmonics emissions [1] emerge from the Vulcan petawatt laser's sub-picosecond laser pulses obliquely incident on slab targets with extremely low pre-pulse energy. Similar studies are to be made using the ALLS 200 TW Ti-Saph laser (24 fs at 10 Hz with 10$^{-10}$ contrast even without plasma mirrors). We discuss our 2-D PIC simulations using the OSIRIS code with a view to (a) understanding the basic mechanism(s) for the production of the harmonics and (b) establishing the effect of density gradients. Typical results resemble those of Naumova et al. [2], including the presence of a very large and asymmetric electromagnetic ``spikes'' which account for the high harmonic content. \newline [1] B. Dromey, M. Zepf, A. Gopal, K. Lancaster, M. S. Wei, K. Krushelnick, M. Tatarakis, N. Vakakis, S. Moustaizis, R. Kodama, M. Tampo, C. Stoeckl, R. Clarke, H. Habara, D. Neely, S. Karsch and P. Norreys, Nature Phys. Lett., 2, 456-459 (2006) \newline [2] N. Naumova, I. Sokolov, J. Nees,1 A. Maksimchuk, V. Yanovsky, and G. Mourou Phys. Rev. Lett. 93, 195003 (2004)   

Modeling High-Energy Backlighters Produced by Intense Laser-Matter Interaction

The utility of reasonably monoenergetic, high frequency backlighters for radiographic use in high energy density physics experiments has been understood for a long time. A reasonable approach to generating these xrays is to use a high-intensity laser incident on suitable (typically mid-z) elements. The deposition produces hot (non-thermal) electrons and ions, which ionize and excite inner shell electrons in a highly non-LTE environment. Resulting xray generation often occurs in only a few bound-bound transitions. Because the hot electrons have substantial range, the lines can be optically thick. In this presentation, I use the radhydro code Lasnex to deposit both a prepulse and a main pulse of order 10$^{18}$---10$^{19}$ watts/cm$^2$ onto Ag and Sn substrates. The physical situation is then postprocessed using Plaspp, with an embedded DCA package to produce spectra. A unique feature of these simulations are the multiphoton inverse- bremstrallung and photoionization physics for deposition near the critical surface, as well as non-thermal collisional physics for the non-LTE spectra.   

Ion acceleration by hot electrons in micro-clusters

Neutron yield, observed in experiments with laser-irradiated deuterium clusters [1], is associated with fast multi-keV ions. Such ions are produced by large clusters that contain a population of stochastically heated electrons [2]. Our work deals with a first-principle theory of ion acceleration to multi-keV energies. We present a semi-analytical description for collisionless expansion of a fully ionized cluster with a two-component electron distribution function. The problem is solved for a ``water-bag'' distribution function of the hot electrons with self-consistent treatment of ion acceleration and electron cooling. The solution involves a cold core of the cluster, a thin double layer at the cluster edge, and a quasineutral flow with a rarefaction wave. The asymptotic energy spectrum of the accelerated ions contains a substantial number of particles with energies greater than the maximum electron energy. \newline \newline [1] T. Ditmire et al., Nature \textbf{398}, 489 (1999). \newline [2] B. N. Breizman, A. V. Arefiev, and M. V. Fomyts'kyi, Phys. Plasmas \textbf{12}, 56706 (2005).   

Physical properties and potential applications of plasma focus ion beams.

Plasma Focus (PF) discharges are known to produce pulsed high energy ion beams. We have performed an experimental study on the spatial distribution of the ion emission from a 1.8 kJ PF device operating in different gases. We have also conducted preliminary investigations on the interaction of these ion beams with different substrates. Simultaneous measurements at different angular directions for operation in methane indicate that the dominant charge states are H$^{+}$, C$^{+4}$ and C$^{+5}$, irrespective of the angular positions. The fluxes are maximum for the energy ranges 10--40 keV, 30--100 keV and 60-200 keV, for H$^{+}$, C$^{+4}$ and C$^{+5}$, respectively. Similar results are obtained with different gas fillings. The interaction of carbon ion beams with a silicon surface results in the formation of a surface layer of hexagonal silicon carbide, with embedded step/terraces structures. The result of the interaction of PF ion beams of different compositions with additional substrates will also be reported.   

Flexible Simulation Tools for Modeling Ion-Driven HEDP Experiments

We are developing new software libraries to assist in the simulation of planned ion-driven high energy density physics (HEDP) experiments. These libraries are designed to be cross-platform and multi-language so that they may easily be incorporated into multiple simulation packages running on various architectures and written in different languages. Relevant to the production of HEDP states, recently we have implemented models of electronic and nuclear stopping of ions in cold targets. We show how these new stopping algorithms allow us to predict that a beam of 2.82 MeV lithium ions could heat an aluminum foil to 2-3 eV. Such a beam is under consideration for the NDCX II experiment at Lawrence Berkeley National Laboratory. We also discuss modification to these stopping powers for warm targets.   

Beam-Background Gas Total Cross-Section Measurements with a Retarding Field Analyzer

The High-Current Experiment (HCX) at LBNL is a driver scale single beam injector that provides a 1 MeV K$^{+}$ ion beam current of 0.2 A during 5 $\mu $s for high energy density physics and heavy ion fusion. We developed a new technique to measure the beam-background gas total cross-section in a high-current accelerator using a retarding field analyzer. The beam-background gas interaction will produce cold ions by ionization and charge exchange. The ions are radially expelled in few hundreds of microseconds by the space-charge beam potential of $\sim $2000 V. Due to the lack of data in the literature at the energy range of interest (1 MeV K$^{+})$, we intentionally leaked different gases and measured the total cross-sections. The experimental data will be compared with theoretical predictions.   

Ion-driven warm dense matter target studies

In developing the use of ion beams to heat matter to warm dense matter conditions to infer the equation of state and other transport properties, numerous hydrodynamic calculations are being carried out by both the Heavy Ion Fusion Science Virtual National (HIFS VNL) Laboratory (a collaboration between LBNL, LLNL and PPPL) and the HEDgeHOB collaboration (a multi-institutional project carrying out experiments at GSI, Darmstadt, Germany). As a result of the different ion energies of the two different proposed facilities the target geometries will be different. In the HIFS VNL experiments planar target foils illuminated normal to the face of the foil will be used. In the HEDegHOB collaboration, cylindrical targets illuminated along the axis, and planar targets illuminated parallel to the face of the target are employed. A comparison of simulations for all three types of targets will be shown, using codes being used by researchers in the the HEDgeHOB and HIFS VNL collaborations. The effects of different assumptions made in the simulations (e.g. differences in equation of state, including assumptions concerning equilibrium (Maxwell) construction vs. non-equilibrium constructions) will be explored.   

Kinetic Effects on the IFE Ion Energy Spectra$^*$

During an ICF post-burn expansion, ion collisional mean free paths can become significantly larger than the shock thickness, limiting the maximum momentum and energy transfer from the shock to the background plasma. For one potential ICF target of the high average power laser (HAPL) fusion reactor conceptual design study [J.D. Sethian, et al., Nuclear Fusion 43, 1693 (2003)], the University of Wisconsin's 1-D radiation hydrodynamics code, BUCKY, predicts that, at 34.592\ ns, the primary shock wave occurs in the zones at the plastic(CH) DT interface just outside of the pure DT zones, and another shock occurs at the interface where the plastic impacts the gold. The dense core inside r$\simeq$10\ mm remains well described by hydrodynamics. The mean free path in the primary shock's frame for slowing down of CH ions on the shock DT ions and electrons approximately equals the shock thickness. The purely radiation hydrodynamic calculation also predicts that at this time the shock thickness where the CH ions impact the Au ions is nearly 1000 times smaller than the mean free path, implying that kinetic effects alter the dynamics at a much earlier time. Results of addressing this problem by implementing energy deposition for moderate-to-large mean free paths using zone-by-zone differential masses and velocities will be reported.\hfil\break * Research supported by the Dept.\ of Energy under the High Average Power Laser Study.   

Modeling of a 1-D spherically symmetric experiment on conversion efficiency and thermal transport.

Recently experiments were performed at the Omega laser at URLLE by a joint CEA/LLNL experimental team. Spherical targets, 1 mm in diameter, were coated with high Z materials, such as gold and cocktails, and were spherically illuminated at irradiances that varied from 10$^{14}$ W/cm$^{2}$ (10 kJ / 3 ns) to 10$^{15}$ W/cm$^{2}$ (30 kJ / 1 ns). Conversion efficiency of this laser light to x-rays was measured. Spectral information on the 1 keV thermal x-rays, as well as the multi-keV M-band were obtained. Crucial additional constraints on the modeling were provided by temperature measurements, via Thomson scattering, at 2 different radii in the blow-off, and at various times throughout and after the laser pulse. We compare various modeling tools (e.g. flux limiters, non-local transport models, and a variety of non-LTE atomic physics packages) to all of these well-constrained data. The spherical symmetry allows us to model all of this in 1-D, thus allowing very good zoning to fully resolve the radial variations. In particular, the narrow radial region where the density drops and the temperature rises, and in which most of the conversion to x-rays take place, is well resolved. Implications for how to model NIF ignition hohlraums will also be discussed.   

Stimulated Raman backscatter leading to electron acoustic Thomson scatter

1-D Eulerian Vlasov-Maxwell simulations of stimulated Raman backscatter show kinetic inflation due to electron trapping in the plasma wave, as previously reported. Trapping distorts the electron distribution, which results in new electrostatic modes, including beam acoustic modes (BAMs) [L. Yin et al., PRE \textbf{73}, 025401 (2006)] and an electron acoustic wave (EAW). Light from pump scattering off the EAW is also observed, similar to experimental measurements interpreted as stimulated electron acoustic scatter [D. S. Montgomery et al., PRL \textbf{87}, 155001 (2001)]. However, parametric interaction of BAMs excites our EAW, and the laser scatters off subsequent fluctuations (electron acoustic Thomson scatter). Linear analysis using the Gauss-Hermite projection of $f_e$ reveals BAMs, sometimes unstable \textit{without coupling to light waves}, and a heavily-damped EAW. This linear EAW differs from the nonlinear, undamped EAW due to trapping discussed by others. We explore the role in kinetically-enhanced Raman backscatter of inhomogeneity, ion dynamics, and transverse sideloss. Work performed under Dept.\ of Energy Contract No.W-7405-Eng-48. UCRL-ABS-222958.   

Investigation of Stimulated Raman Scattering Using a Short Pulse Single Hot Spot at the Trident Laser Facility

A new short-pulse version of the single-hot-spot configuration has been implemented to enhance the performance of experiments to understand Stimulated Raman Scattering. The laser pulse length was reduced from $\sim$200 to $\sim$4 ps. The reduced pulse length improves the experiment by minimizing effects such as plasma hydrodynamics and filamentation of the interaction beam. In addition, the shortened laser pulses allow full length 2D particle-in-cell simulations of the experiments. Using the improved single-hot-spot configuration, a series of experiments to investigate k$\lambda_{D}$ scaling of SRS has been performed. Details of the experimental setup and initial results will be presented.   

Kinetic saturation of stimulated Raman scattering in a fluid code

We have implemented a saturation model for backward stimulated Raman scattering (BSRS) based on kinetic nonlinearity of the driven Langmuir waves into pF3d. The parametric coupling of BSRS leads to a daughter Langmuir wave (LW) whose wave number \textit{k$\lambda $}$_{D}$ depends on plasma conditions and determines the level of LW dissipation via Landau damping. It is accepted that more strongly damped waves lead to a reduced BSRS response, which was the motivation for shorter wavelength laser drivers in ICF. However, an increase in \textit{k$\lambda $}$_{D}$ increases the likelihood of electron trapping in the LW. Trapped particles in a wave change the character of Landau damping, causing the damping to decrease with time, and also leading to a time-dependent frequency shift. This decrement in Landau damping leads to an inflation of BSRS levels beyond those predicted by linear convective theory, and has been observed in previous RPIC simulations and in experiments. A model for inflated BSRS was recently developed and tested in a 1-d fluid-type three-wave code to reproduce RPIC simulations with a rapid rise of BSRS levels by orders of magnitude with a small change in incident intensity. This work is extended to 3-d by adding the trapping physics model to pF3d. We will show results from using the modified pF3d code to examine SRS issues at NIF relevant conditions.   

Driven Plasma Waves Relevant to Stimulated Raman Scattering

In fully self-consistent particle-in-cell (PIC) simulations the saturation of Stimulated Raman Scattering (SRS) is quite complicated. To better understand, we study the excitation of plasma waves by imposing an external ponderomotive force in 1D electrostatic PIC simulations. By varying the phase velocity, the drive frequency (detuning), and the amplitude of the driving wave, several saturation mechanisms are explored, including fluid and kinetic nonlinear frequency shifts, sideband generation, and particle trapping. The simulations indicate that simple frequency shift models are inadequate in describing the wave saturation. Wave harmonics are also observed and these can contribute to the non-linear frequency shift. In addition to these ``fluid'' (harmonics) frequency shift effects the distribution function changes during the growth and saturation of the wave, indicating that kinetic frequency shift calculations (Morales and O'Neil PRL \textbf{28} 417 (1972)) depending only on the initial distribution function $f_{0}$ need updating. Sidebands will also be discussed along with comparisons to electromagnetic OSIRIS PIC simulations.   

Two features in the numerical modeling of Raman backscattering : boundary condition for an infinite homogeneous system and test particle method for the kinetic effects

We investigate two issues in the computational modeling of Raman backscattering in a plasma. The first one is on the effect of boundary condition in the infinite homogeneous Raman backscattering system. It was found that the periodic boundary condition for the electrostatic potential, which is commonly used in an infinite homogeneous plasma, induces a numerical frequency shift of the plasma wave. Though the frequency shift is small (typically one or two percent) for a non-relativistic plasma wave, the Raman backscattering is significantly changed due to its sensitivity to the frequency detuning. A corrected version of boundary condition based on the Ampere's law is presented. Second, we treat the kinetic effects in the Raman backward laser amplification. The envelope-kinetic model of the plasma wave is numerically closed by calculating the kinetic term from test particles. The benchmarking results of the test particle method against the full kinetic simulation are presented.   

Particle-in-cell Simulations of Stimulated Raman Scattering

Using the full-PIC code OSIRIS, we have studied stimulated Raman scattering (SRS) over a wide range of parameters relevant to NIF. The role of beat-wave damping as a saturation mechanism is explored, as well as its relationship to other nonlinear effects which have previously been used to explain SRS behavior in NIF-relevant plasmas. Vu et al., have proposed that a nonlinear frequency shift due to the trapped particles detunes the instability, Brunner and Valeo argue that the trapped-particle instability is one of the dominant saturation mechanisms, while L. Yin et al., claim that electron beam acoustic modes are important. We will discuss the role played by each of these effects in OSIRIS simulations, as well as the importance of plasma wave convection on the recurrence of SRS reflectivity. We will also discuss how SRS behavior changes as the electron density and temperature are varied.   

Investigation of High Z dopants to Mitigate Stimulated Raman Scattering in Gas Filled Hohlraums

Gas bag experiments at the Helen laser showed that the addition of a small amount of high Z dopant could significantly reduce Stimulated Raman Scattering (SRS). Understanding this mechanism could provide a method to mitigate stimulated Raman scattering energy losses in NIF ignition hohlraums. Efforts at Los Alamos National Laboratory have provided a theoretical basis for the reduction in SRS backscattered laser light. Thermal filamentation of the laser results in beam spray that in turn helps to reduces SRS. Since thermal effects depend strongly on Z$^{2}$, a small amount of a high Z dopant, 1-2{\%}, can have a large effect. Experiments are underway at the Omega laser to validate the theory by varying the amount of Xe dopant in neopentane gas filled hohlraums. Using a 3$\omega $ Transmitted Beam Diagnostic, the beam spray of an interaction laser beam can be monitored along with the SRS backscattered light as Xe dopant is added to the gas fill looking for a correlation between the two. Details of the experiments and the results will be presented.   

Mitigation of Laser Plasma Instabilities in Hohlraum Targets

Additional techniques to control laser plasma instabilities would enlarge the parameter space for ignition target designs on the National Ignition Facility. A possibility recently suggested [1] is to engineer coherence disruptions in NIF hohlraums, say, by modulations in the liner composition or by manipulation of the plasma flow. Hohlraum simulations using striped liners look promising. We also explore other effects leading to instability mitigation, including re-absorption of Raman-scattered light, instability gain reduction by strong refraction of the Raman-scattered light in transverse density gradients, and preheat reduction associated with a diminishment of the Raman-heated electron distribution function beyond an energy of about 4-5 times the hot electron temperature. Finally we note that it is also important to minimize seeding the laser-driven instabilities, which can happen in various ways, and to avoid intensity enhancement due to focusing of laser light by transverse density gradients in the hohlraum. \newline [1] William L. Kruer, et. al., UCRL-SR-220853 (2005)   

Kinetic-Ion Simulations of Stimulated Brillouin Backscattering in Ignition Target Plasmas and Reduced Models for Nonlinear Saturation

1D and 2D simulations with the BZOHAR$^{2,3 }$hybrid code (kinetic PIC ions and Boltzmann fluid electrons) are being used to investigate the saturation of stimulated Brillouin backscatter (SBBS) instability for plasma conditions in ignition campaign experiments in the National Ignition Facility. Ignition targets must be designed so that backscatter is not severe. BZOHAR can simulate ion kinetic and fluid nonlinearities affecting SBBS.$^{2-4 }$A reduced model that captures the physics of two-ion-wave-decay instability, ion trapping effects (nonlinear frequency shift and reduction of ion Landau damping$^{4})$, and pump depletion has been synthesized in coupled-mode equations that are being implemented in the pF3d fluid simulation code used for macroscopic 2D and 3D simulations of laser-plasma interactions. Progress will be reported including studies of whether ion trapping can ``inflate'' SBBS reflectivities by reducing ion Landau damping. Refs.: $^{ 2}$B.I. Cohen, B.F. Lasinski, A.B. Langdon, and E.A. Williams, Phys. Plasmas 4, 956 (1997). $^{3}$B.I. Cohen, L. Divol, A.B. Langdon, and E.A. Williams, Phys. Plasmas \textbf{12}, 052703 (2005) and Phys. Plasmas 13, 022705 (2006). $^{4}$L. Divol, et al., Phys. Plasmas 10, 1822 (2003).   

Stimulated backscattering in speckled laser beams

High power lasers used for laser-plasma interaction experiments are commonly equipped with phase plates, which create high intensity speckles in their far field. Independent speckle models for stimulated backscatter have been proposed in which the reflectivity is determined by a convolution over the speckle intensity distribution. Such models should apply when the resonant amplification region extends over no more than a characteristic speckle length. By a variational approach, we show how these results are modified if the amplification region extends over multiple speckle lengths, reducing the contrast of the effective intensity distribution. We compare these results with those obtained using our laser-plasma interaction code pF3D.   

Particle In Cell Simulations of the Two Plasmon Decay Instability For Plane Waves in Inhomogeneous Plasmas

A particle-in-cell code (OSIRIS) is used to investigate the two-plasmon decay instability in nonuniform plasmas of various density profiles. We find good agreement between the simulation and linear theory by Afeyan and Williams (Phys. Plas. {\bf{4}}, 3827, 1997.) under a variety of laser and plasma conditions relevant to ICF. So far the theory has been tested for linear density profiles and parabolic density profiles where the perfect phase matching condition (PPMP) is at the parabolic peak density. We will also test the theory’s predictions concerning growth rates and eigeneconditions when the PPMP is in the transition region between the peak density of the parabolic profile and down on the flanks where strictly linear profile behavior is recovered. These simulations allow a check on linear theory, and also demonstrate the ability of PIC codes to study this instability in small regions of ICF relevant targets. P-Polarized obliquely incident lasers will also be considered where the theory predicts a non-equal ratio between thresholds for the excitation of modes which correspond to positive and negative values of equal magnitude. This symmetry breaking in transverse momentum has never been verified in simulations before. The challenges of extending the simulations to 3D where these latter phenomena can be studied numerically will also be discussed.   

Emergent Nonlinear Resonance in KEEN Wave Strength at Low Drive

KEEN-like waves studies [1] in a PIC simulation at low drive agreed with earlier 1-D Vlasov fluid code results [2,3], in that, for a given wavenumber the KEEN waves would, over a wide range of frequencies, give a rather similar response. For at least one frequency in a rather narrow range, keeping the drive going well past the (linearly estimated) trapping period (which usually gives no added benefit), proved to give a significantly larger final amplitude. We discuss our own 1-D Vlasov-fluid study of this nonlinear emergent resonance phenomenon. \newline 1. F. Valentini, T.M. O'Neil, H.E. Dubin, Phys. Plasmas, 13, 052303 (2006) \newline 2. B. Afeyan, K. Won, V. Savchenko, T.W. Johnston, A. Ghizzo, P. Bertrand, 3$^{rd}$ Int. Conf. ``Inertial Fusion Sciences and Applications'' (IFSA) paper M034, Sept. 7-12, Monterey, CA (2003), p.213, eds. B. Hammel, D. Meyerhofer, J. Meyer-ter-Vehn and H. Azechi, Amer. Nucl. Soc. 2004. \newline 3. B. Afeyan, V. Savchenko, K. Won, T.W. Johnston ``New Long-Lived Nonstationary Coherent Structures in Vlasov Plasmas: KEEN Waves'', submitted to Physical Review Letters.   

Vlasov-Maxwell Simulations of Optical Mixing Driven Plasma waves and KEEN Waves in Inhomogeneous Plasmas

A series of simulations using Blue-Blue and Blue-Green Crossing Beams reveal the dynamics of nonlinear electron plasma wave and KEEN wave generation and evolution in inhomogeneous underdense (sub-quarter-critical) plasmas. In particular, we examine the interaction between EPWs at one density with KEEN waves at lower densities. The vortex merger and destruction dynamics will be examined in detail using detailed diagnostics of phase space partitioning and space-time mode structures preserving the coherence of the emerging self consistent fields.   

Effect of Non-Adiabatic Electron Dynamics on the Non-Linear Evolution of Ion Acoustic Waves

The effect of non-adiabatic electrons on the non-linear evolution of Ion Acoustic Waves (IAWs) is studied using a spatially one-dimensional Vlasov code. In a first stage, simulations were carried out to analyze the contribution of resonant particles from both electrons and ions to the non-linear frequency shift of IAWs. For electrons (resp. ions) these resonant particles are located in the bulk (resp. tail) of the distribution and contribute with a positive (resp. negative) shift to the frequency. Besides their dependence on the wave amplitude as well as on the essential plasma parameters, these shifts also vary according to the conditions under which the wave was generated (adiabatic/sudden). At sufficiently low temperature ratios $Z\,T_e / T_i \stackrel{\sim}{<} 10$ the ion and electron contributions can be competitive and thus cancel each other, while for higher ratios of $Z\, T_e / T_i$ the positive electron contribution dominates. Simulation results agree well with theoretical predictions [Morales and O'Neil, PRL {\bf 28}, 417 (1972); Dewar, Phys. Fluids {\bf 15}, 712 (1972)]. The positive frequency shift from non-adiabatic electrons may possibly enable matching conditions for a decay instability of the IAW to be verified. This mechanism is investigated in a second stage.