Session NP9: Poster Session V: Magnetic Reconnection II, Fundamental Theory and Modeling II, Flow; MFE Heating & Current Drive; Laser Plasma Interactions and Fast and Shock Ignition

A mechanism for the generation of anomalous cosmic rays: the reconnection of the 3-D sectored heliospheric magnetic field in the heliosheath

The recent observations of the anomalous cosmic ray (ACR) energy spectrum as Voyagers 1 and 2 crossed the heliospheric termination shock have called into question the conventional shock source of these energetic particles. We suggest that the sectored heliospheric magnetic field, which results from the flapping of the heliospheric current sheet, piles up as it approaches the heliopause, narrowing the current sheets that separate the sectors and triggering the onset of collisionless magnetic reconnection. The energetic electron and other data support this scenario. Particle-in-cell simulations have been carried out to explore the 3-D structure of magnetic islands and associated particle acceleration. The magnetic islands develop a finite length in the out-of-plane direction. Nevertheless reconnection releases a large fraction of the energy in the sectored magnetic field. Most of the magnetic energy goes into energetic ions with significant but smaller amounts of energy going into electrons. The signatures of these 3-D magnetic structures are being explored for comparison with the Voyager data. If the reconnection scenario is correct, the observations represent the first in-situ exploration of multi-island particle acceleration.   

Crossed flux tubes 3D magnetic reconnection experiment

The formation and dynamics of writhing, plasma-filled, twisted open magnetic flux tubes is being investigated using laboratory experiments. The behavior of these flux tubes is relevant to solar corona loops, astrophysical jets, spheromak formation, and open field lines in tokamaks and RFP's. MHD forces have been determined to drive fast axial plasma flows into the flux tube from the boundary it intercepts. These flows fill the flux tubes with plasma while simultaneously injecting linked frozen-in azimuthal flux; helicity injection is thus associated with mass injection. An upgraded experiment under construction will have two adjacent arched plasma-filled flux tubes cross over each other. It is anticipated that a localized 3D reconnection will occur at the cross-over. This reconnection should result in half-twists in the post re-connection topology and subsequent Alfven wave propagation to equilibrate the half-twists along the post-reconnection flux tubes. The electrical circuitry requires two initially independent floating capacitor bank power supplies that become series-connected as a result of reconnection.   

Plasma acceleration along arched magnetic flux tubes: observation, quantification, and analysis

Magnetic flux tubes are fundamental structures that occur in a wide range of plasma settings, from the solar atmosphere to the interior of a tokamak. We have used a magnetized plasma gun to create individual, arched flux tubes in the laboratory. These flux tubes are highly reproducible and can be diagnosed via a variety of techniques, thereby facilitating quantitative investigations. The outstanding feature of the dynamics is a dramatic increase in the total length of the flux tube, during which the minor radius of the tube and the plasma density remain relatively constant. The resulting increase in particle number is made possible by bulk flows that accelerate plasma into the tube from both ends; ``color-coded'' dual gas plasmas have shown that the two flows are independent. The characteristic speed is determined by local mass density $\rho$ and electric current $I$. These findings are quantitatively consistent with two interrelated MHD models: the hoop force (which explains the lengthening) and the ``gobble'' model (which explains the flows). \footnote{P. M. Bellan, \textit{Phys. Plasmas} 10 Pt 2, 1999 (2003).}   

Effects of different strapping field profiles on plasma loop expansion

The hoop force causes arched, current-carrying plasma loops to expand unless additional forces are applied. This expansion was slowed and even inhibited by a magnetic field of proper polarity in previous solar coronal loop experiments [1] but there was no attempt to reproduce the slow expansion to fast eruption behavior often exhibited by solar loops. The transition from a slow expansion to a fast eruption is predicted to depend on the strapping field altitude decay profile [2] which is sensitive to the planar distance to the source of the strapping field [3]. The coils are mounted on 3 axis adjustable stands that provide precision placement of the coil relative to the plasma. Preliminary data on the interaction between the plasma and specified strapping field profiles will be presented. \\[4pt] [1] J. F. Hansen and P. M. Bellan, Astrophys. J. Lett. \textbf{563}, L183 (2001)\\[0pt] [2] B. Kleim and T. Torok, Phys. Rev. Lett. \textbf{96}, 255002 (2006)\\[0pt] [3] Y. Wang and J. Zhang, ApJ \textbf{665}, 1428 (2007)   

3-D effects in magnetic reconnection of laser-produced plasma bubbles

Recent experiments have observed magnetic reconnection in high-energy-density, laser-produced plasma bubbles. It is of great interest to extend previous 2-D simulations [1] to understand the full 3-D evolution of the bubbles. This 3-D evolution, studied by PIC simulations, includes the 3-D spherical expansion of the bubbles and 3-D geometry of the interaction, including the formation of isolated magnetic nulls and null-null lines. In cylindrical 3-D geometry, we study the dynamics of long-wavelength kink instabilities and short-wavelength lower-hybrid instabilities in the return currents, over a range of parameters characteristic of the experiments. Observational signatures of 3-D dynamics in the experiments will be discussed.\\[4pt] [1] W. Fox, A. Bhattacharjee, K. Germaschewski, Phys. Rev. Lett. \textbf{106}, 215003 (2011).   

Kinetic Theory of Oblique Collisionless Tearing Instabilities

Recent 3D PIC and linear Vlasov-Maxwell simulations [1] have shown that conventional kinetic tearing mode theory [2] vastly overestimates the growth rate of oblique modes, i.e., those with nonzero $\phi = \textrm{arctan}(k_z/k_y)$ where $k_z$ is the wavenumber in the guide field direction and $k_y$ is the wavenumber perpendicular to this in the plane of the current sheet. Thus, doubts have been cast on the validity of asymptotic boundary-layer analysis in collisionless kinetic theory. We show that this disagreement is a consequence of a strong guide field assumption made in conventional theories. We relax this assumption and obtain a dispersion relation that accounts for oblique angles. Focusing on a Harris equilibrium, Ref. 1 discusses modifications in the ideal MHD region outside the $\mathbf{k} \cdot \mathbf{B}_o = 0$ surface [1]. Here we complete the necessary modifications by correcting the inner layer solution. These show that obliquity has a stabilizing effect in all but the strongest guide field cases. Our theoretical predictions are compared to the previous simulation results. [1] W. Daughton \textit{et al}., Nature Phys. {\bf 7}, 539 (2011). [2] J. Drake and Y. C. Lee, Phys. Fluids {\bf 20}, 1341 (1977).   

Topology and Dynamics of Reconnection in 3D Pair Plasma Without Guide Field

We investigate fast reconnection in 3D pair plasma without a guide field using the Particle Simulation Code (PSC), beginning from a Harris sheet with a neutral line, which is a continuum of nulls and is structurally unstable in 3D. The neutral line is shown to break up into a sequence of discrete nulls of the A- and B-type, which are joined by null-null lines that constitute an AB-web, and provide an underlying topological skeleton for 3D reconnection. The current density distribution in such a system is shown to correspond to recent 3D models of ``spine reconnection.'' The sheet current density is unstable with respect to the kink instability which introduces folding as well as plasmoid instabilities that introduce complex structure formation, while supporting fast time-dependent reconnection.   

Magnetic fluctuations during reconnection with a guide field in plasma merging experiment

Large amplitude magnetic fluctuation with characteristics of long wavelength drift instability was observed using 60 channel pickup coils inside the current sheet during magnetic reconnection in the plasma merging experiment for the fast time. Magnetic fluctuations measurement was carried out by using two radial magnetic probe arrays and a axial probe array. The guide field at the X point $B_X$ of 45\,mT is comparable to the reconnecting magnetic field $B_{//}$. Large amplitude magnetic fluctuation was observed during reconnection inside the current sheet. The frequency spectrum of it has clear peak at 2\,MHz, which is about twice as high as the local ion gyro frequency. The magnetic field variation $\Delta B$ caused by the fluctuation is larger than 10\,\% of the reconnecting magnetic field. Furthermore, the fluctuation appears with increasing the effective resistivity $\eta_{eff} = E_t/j_t$ evaluated at the X point. The typical phase velocity along a guide field is about 100\,km/s, which is close to the relative drift velocity $V_d = j_t / e n_e$. These properties are commonly discussed in the drift kink instability (DKI) modes which appear in the numerical studies. Our results consequently indicate that the fluctuation is responsible for the reconnection rate enhancement and the ion anomalous heating in the plasma merging experiment with a guide field.   

Ion heating characteristics of magnetic reconnection in TS-3 \& TS-4 tokamak and spheromak merging experiments

For the past ten years, we have developed a novel 2-D ion temperature measurement by use of computer tomography and studied the characteristic of ion heating during magnetic reconnection. Its spatial resolution of line-integrated Doppler measurement is 7$\times$5 in r and z directions but will be upgraded to 7$\times$10 by increasing the number of optical fiber [1]. We confirmed the evidence of ion outflow heating in wider range of guide field using co and counter helicity merging spheromaks and (co-helicity) merging tokamaks. In all cases, we observed two high ion temperature Ti regions in the two downstream area of magnetic reconnection and their heating energies depend on the varied guide toroidal field Bt. The maximum ion temperature Ti$\sim$140eV is obtained in the counter helicity merging spheromaks with no guide field Bt, Ti$\sim$100eV in the co-helicity merging spheromaks with Bt$\sim$Bp (reconnection field) and Ti$\sim$50eV in the tokamak merging with Bt$>$Bp. The tokamak merging experiment with varied guide field Bt revealed that the ion temperature increment $\Delta$Ti after reconnection decreases inversely with the guide field Bt but that $\Delta$Ti tends to be constant in high guide field regime Bt$>$3Bp.\\[0pt] [1] H. Tanabe., et al., Rev. Sci. Instrum., submitted (2011)   

Three-dimensional kinetic open boundary simulation of driven reconnection for TS-3 laboratory plasma merging experiment

Using the PArticle Simulation of driven Magnetic reconnection for an Open boundary (PASMO) with parameters similar to the University of Tokyo Spherical Torus (TS-3) experiments a fully kinetic electromagnetic simulation is performed. Upstream boundary conditions in the simulation are modeled after electric fields calculated from measured TS-3 magnetic probe data. Ion temperature measurements from 2-D ion Doppler spectroscopy as well as magnetic probe data are compared with the simulation results. Particle acceleration is investigated through calculation of trajectories based on electromagnetic simulation data and a non-thermal distribution.   

Development of the Visible Light Tomography Diagnostics for UTST Spherical Tokamak Plasmas

The University of Tokyo Spherical Tokamak (UTST) device was designed to form an ultra-high $\beta$ plasma. Since the most dangerous mode for the high $\beta$ ST is the ballooning mode, the visible light computed tomography (CT) has been developed to measure the plasma emission profile of the toroidal cross- section of the ST plasma. We developed a tomographic reconstruction algorithm for an annular toroidal cross-section of plasma (z=0) by using modified Fourier-Bessel expansion method. The visible light emissivity, g(r,?) was expanded into the Fourier series in azimuthal direction and a combination of Bessel functions and Neumann functions in radial direction, for the purpose of satisfying the annular boundary condition. Spatial distribution of HeII(656.0nm) light was reconstructed by using the proposed algorithm in the case of center solenoid coil (CS) and also in the case of poloidal field coils (PF) discharge.   

Toward New Phase of Collisionless Driven Reconnection Studies with Multi-Hierarchy Simulation

For comprehension of magnetic reconnection as a multi-hierarchy phenomenon, we have developed a multi-hierarchy simulation model which solves macroscopic and microscopic physics simultaneously and self-consistently. In our multi-hierarchy model, the simulation domain is divided into macro- and micro-hierarchies. The physics in the macro-hierarchy is calculated by the MHD algorithm, and the dynamics in the micro-hierarchy is expressed by the PIC algorithm. Between two hierarchies, the interface domain is inserted, where physical quantities in the macro- and micro-hierarchies are exchanged. In 2009, using the multi-hierarchy model with periodic condition in the downstream direction, we succeeded in the demonstration of multi-hierarchy simulation of magnetic reconnection. We confirmed that reconnection found in our model exhibit true physics, by comparing it with pure PIC simulation results. Recently we have improved our multi-hierarchy model where open boundary condition is applied in the downstream direction. Reconnection is driven in the same way as the first model. Furthermore, we are creating a model that calculation algorithm is automatically converted from MHD to PIC, vice versa, as reconnection system evolves dynamically.   

Particle Energization in 3D Magnetic Reconnection of Relativistic Pair Plasmas

We present large scale 3D particle-in-cell (PIC) simulations to examine particle energization in magnetic reconnection of relativistic electron-positron (pair) plasmas. The initial configuration is set up as a relativistic Harris equilibrium without a guide field. These simulations are large enough to accommodate a sufficient number of tearing and kink modes. Contrary to the non-relativistic limit, the linear tearing in- stability is faster than the linear kink instability, at least in our specific parameters. We find that the magnetic energy dissipation is first facilitated by the tearing instability and followed by the secondary kink instability. Particles are mostly energized inside the magnetic islands during the tearing stage due to the spatially varying electric fields produced by the outflows from reconnection. Secondary kink instability leads to additional particle acceleration. Accelerated particles are, however, observed to be thermalized quickly. The large amplitude of the vertical magnetic field resulting from the tearing modes by the secondary kink modes further help thermalizing the non-thermal particles generated from the secondary kink instability. Implications of these results for astrophysics are briefly discussed.   

Lower-hybrid instabilities and turbulence associated with reconnection in asymmetric current sheets

The role of microscopic plasma turbulence in enabling magnetic reconnection is a long-standing problem in plasma physics. In this work, we consider reconnection in asymmetric current sheets as encountered for example at the Earth's magnetopause and laboratory experiments, such as MRX. Using 3D PIC simulations with Monte-Carlo treatment of Coulomb collisions, we demonstrate that Lower-Hybrid (LH) turbulence naturally arises in this configuration in both collisionless and weakly collisional plasma. Two sources of LH turbulence are identified. In regimes with moderate ratio of electron-to-ion temperature $T_e \leq T_i$ and low overall $\beta$, electromagnetic LH instability with hybrid wavelength $k (\rho_e \rho_i)^{1/2}\sim 1$ (Daughton, 2003) localized near the X-line can reach large amplitude. This mode produces substantial modifications to the average force balance in the form of fluctuation-induced drag and stress terms and significantly alters the structure of the diffusion region. It persists in weakly collisional regimes typical of MRX. Under parameters typical of the magnetopause, LH turbulence is predominantly localized around the separatrices on the low-$\beta$ side of the current sheet, where it is driven by short-wavelength instability with $k \rho_e\sim 1$ (e.g. Davidson, 1977). Under these conditions, the overall structure of the reconnection region is not appreciably modified compared to 2D simulations.   

Sustained magnetic reconnection requires diffusion

Refer to a plasma model as diffusive if it permits both entropy production and heat flux. Steady two-dimensional reconnection at an X-point is impossible in an energy-conserving model that is not diffusive. We argue that converged simulation of sustained fast magnetic reconnection generally requires a diffusive model. We regard reconnection as sustained if it approaches steady state or is highly sensitive to initial conditions. Examples of sustained reconnection are the GEM problem and steadily driven reconnection; linear tearing is not an example. Examples of nondiffusive models are adiabatic fluid models and models that solve the Vlasov equation. We remark that adiabatic resistive MHD admits steady reconnection by admitting heat flux or by violating energy conservation. Incompressible viscous adiabatic two-fluid models which admit steady reconnection imply that the energy evolution equation is diffusive or nonconservative even if an energy evolution equation is not explicitly evolved.   

Incomplete Reconnection in Sawteeth due to Diamagnetic Effects

Magnetic reconnection is known to play an integral role in the dynamics of sawtooth phenomena in fusion devices. A long-standing puzzle is why reconnection is usually incomplete in sawteeth, meaning it ceases despite the availability of free magnetic energy. We present a model of how the self-consistent evolution of reconnection in tokamak settings can cause incomplete reconnection due to diamagnetic suppression. The crux of the model is that the reconnection inflow self-consistently causes the pressure gradient at the reconnection site to increase due to the ramp in the equilibrium pressure profile. It is known that reconnection ceases if the pressure gradient exceeds a threshold due to diamagnetic effects [1], so the reconnection will shut off if the gradient becomes large enough. This may explain why reconnection is often incomplete but not always. The basic picture is confirmed with proof-of-principle two-fluid simulations. Further, the model makes predictions for the properties of the plasma at the end of a sawtooth crash. We use data from the Mega Ampere Spherical Tokamak to check the predictions, finding good agreement. The present results should be valid both for existing tokamaks and future tokamaks such as ITER, and may be useful for improving transport modeling of sawteeth. \\[4pt] [1] M. Swisdak et al., J. Geophys. Res., 108, 1218 (2003).   

Sawtooth Driven Neoclassical Tearing Modes in HL-2A Plasmas

The m/n=2/1 neoclassical tearing modes (NTMs) are observed together with fully developed m/n=1/1 sawtooth collapses in HL-2A plasmas. A model of sawtooth driven NTMs is proposed to calculate the island growth. In the model, the 2/1 component of the sawtooth due to the toroidal effect is applied as the boundary condition on the 1/1 surface for the NTM. An island equation for the neoclassical tearing mode growth can be then derived. The theoretical result fits well with HL-2A experiment data.   

Diamagnetic Effects on Double Tearing Modes in Hall-MHD and PIC Simulations

Reversed magnetic shear configurations hold promise to stabilize pressure-driven modes in tokamaks and allow for higher pressures and improved confinement, however they give rise to tearing instabilities. We extend recent work on the properties of the double tearing mode (DTM) in collisional as well as collisionless regimes in the presence pressure gradients that drive diamagnetic flows using both Hall MHD and PIC simulations. Diamagnetic drifts act to shift the growing islands relative to each other, competing against the locking mechanism that usually drives fast DTM dynamics. We address the following questions: In the weak coupling limit, does diamagnetic stabilization remain similar to what we have observed previously for the m=1 mode? In the strong coupling limit, can diamagnetic effects suppress the strong DTM dynamics? Our preliminary results indicate significant differences from recent resistive MHD simulations of this problem in the literature.   

Kinetic MHD simulation of large $\Delta^{\prime}$ tearing mode instability

We have developed a second-order accurate semi-implicit $\delta f$ method for kinetic MHD simulation with Lorentz force ion and fluid electron. The model has been implemented in GEM code and benchmarked on Alfv\'en waves, ion sound waves and whistler waves against analytical dispersion relation in a uniform plasma. We have also studied the resistive tearing mode instability by adding a resistive term in the generalized Ohm's law using the Harris sheet equilibrium. For small $\Delta^{\prime}$, the linear growth rate and eigenmode structure are comparable with resistive MHD analysis. The Rutherford stage and saturation are demonstrated, though the simulation exhibits different behaviors than previous MHD simulations. For large $\Delta^{\prime}$, the tearing mode develops multiple islands in the nonlinear regime and the islands start to coalesce later on. The competition between the two processes strongly influences the reconnection rates and eventually leads the reconnection to a steady state. We will identify the role played by particle ions in the process using detailed ion diagnostics.   

Asymmetry and global profile effects on the evolution of magnetic islands

Magnetic islands are important magnetic structures in astrophysics and tokamaks contexts. The magnetic island stability is usually characterized by the tearing index stability parameter $\Delta ^{\prime }$ . When \ $\Delta ^{\prime }$ is positive, magnetic reconnection occurs and tearing modes grow. The \ $\Delta ^{\prime } $ parameter is determined from the solution in the outer region and depends on the boundary conditions. As a result, the \ $\Delta ^{\prime }$ parameter does depend, in essential way, on global properties of the current profile. After the \ $\Delta ^{\prime }$ parameter has been determined, however, the linear and (to a significant extent) nonlinear stability of tearing modes is formulated in as a local theory for any given value of \ $\Delta ^{\prime }$. In this paper we demonstrate that a number of essential properties of nonlinear reconnection, such as saturation of magnetic islands and formation of a Y-point singular layer strongly depends on the global features of the current profile. It is also shown that asymmetry of the external solution generated either by a finite (equilibrium) current gradient or by the asymmetry in boundary conditions affects the linear and nonlinear evolution of magnetic islands. The equation for nonlinear saturation of magnetic island width is derived taking into account asymmetry effects.   

Hyperresistive Plasmoid Instability and Onset of Fast Reconnection

Plasmoid instability in hyperresistive MHD models is studied. A governing parameter is the hyperresistive Lundquist number, defined as $S_{H}\equiv L^{3}V_{A}/\eta_{H}$, where $L$ is the current sheet length, $V_{A}$ is the Alfv\'en speed, and $\eta_{H}$ is the hyperresistivity. The linear instability is found to be super-Alfv\'enic, with a peak growth rate $\gamma\sim S_{H}^{1/6}V_{A}/L$. Nonlinearly the reconnection rate becomes weakly dependent on hyperresistivity. Scaling laws of the number of plasmoids, secondary current sheet length, width, and current density are deduced. Probability distribution of plasmoid magnetic flux $\psi$ is found to be consistent with a power law $\psi^{-2}$. When Hall effect is included, it is found that the plasmoid instability may facilitate Hall reconnection, leading to an even higher reconnection rate. Similar to an earlier resistive Hall MHD study, onset of Hall reconnection does not always expel all plasmoids and result in a single X-point magnetic topology. Our findings suggest that copious plasmoid formation may be a generic feature of magnetic reconnection in large systems, regardless of the mechanism of breaking the frozen-in condition.   

Barriers in the transition to global chaos in collisionless magnetic reconnection

The transitional phase from local to global chaos in the magnetic field of a reconnecting current layer is investigated. Regions where the magnetic field is stochastic exist next to regions where the field is more regular. In regions between stochastic layers and between a stochastic layer and an island structure, the field of the Finite Time Lyapunov Exponent (FTLE) shows a structure with ridges. These ridges, which are special gradient lines that are transverse to the direction of minimum curvature of this field, are approximate Lagrangian Coherent Structures (LCS) that act as barriers for the transport of field lines. The identification of the ridges as barriers is carried out adopting the technique of field line spectroscopy to analyze the radial position of a field line while it winds its way through partial stochastic layers and to compare the frequencies of the field line motion with the corresponding frequencies of the distinguished hyperbolic field lines that are the nonlinear generalizations of linear X-lines.   

GPU Accelerated Reduced MHD Simulations: An Application to Magnetic Island Coalescence in 3D Line-Tied Geometry

We present a comprehensive re-programming of a 3D reduced MHD code for hardware acceleration using graphics processing units (GPUs) with Nvidia CUDA. The code (pseudo-spectral semi-implicit) is tailored for the study of a 3D model of coronal heating [Arxiv:1106.0515]. We discuss our general porting strategy and report code performance and detailed code tracing on GPU accelerated supercomputers (NCSA/Forge, NICS/Keeneland). At $2048^{2}\times256$, the highest resolution tested, the chip-to-chip speedup is $18\times$ comparing Xeon Nehalem QC and Nvidia Fermi. Scaling well up to $256$ GPUs, the code effectively gives a speedup of $46\times$ compared with our original code on a conventional CPU cluster. A test case is presented in which magnetic island coalescence is studied in 3D line-tied geometry, where very large Lundquist numbers are used to induce magnetic flux-tube sloshing. Results are compared with existing 2D simulations and the advantages of the GPU implementation are emphasized.   

Dynamic load-balancing and GPU computing with the particle-in-cell code PSC

We have developed a new version of the Particle Simulation Code (PSC), originally written by H. Ruhl. The new code is designed with state-of-the-art and future massively parallel high-performance computers in mind, and has extensible support for various physics modules, e.g., modeling collisions and QED effects. At its core, the code uses the explicit particle-in-cell method to solve the Vlasov-Maxwell equations in 3D and in reduced dimensions. We will present scaling results on Cray and IBM Bluegene supercomputers up to 100k cores. We developed a novel dynamic load balancing method based on space-filling curves that reduce the imbalance of a sample production run from a factor of larger than 2 to just a few percent. Graphics Processing Units (GPUs) have shown large promise in achieving substantially enhanced performance over conventional processors, but it is hard to find particle-in-cell algorithms that efficiently exploit the fine-grained parallelism provided through nvidia's CUDA programming model. We will present different algorithms and evaluate the performance achieved.   

Positivity-Preserving Space-Time DG-FEM for Kinetic Vlasov Models of Plasma

The Vlasov system describes the evolution of a collisionless plasma, represented through one or more PDFs that interact via electromagnetic forces. One of the main difficulties in numerically solving this system is the severe time-step restriction that arises from parts of the PDF associated with large velocities. The dominant approach in the plasma physics community for removing these time-step restrictions is the so-called particle-in-cell (PIC) method, which discretizes the distribution function into a set of macro-particles, while the electromagnetic field is represented on a mesh. In this work we present an alternative to the PIC methodology using high-order space-time DG-FEM. A novel aspect of this work is that we formulate the method in such a way that the most expensive part of the numerical update (i.e., the solution of a large system of algebraic equation) is linear. Positivity-preserving limiters are developed that ensure that the numerically computed solution remains physical. The proposed method is applied to several test cases.   

A Reduction of the Vlasov--Maxwell System Using Phase-Space Blobs

We develop a new computational approach to solving the Vlasov-Maxwell equation by representing the distribution function by a supper-position of finite-extent phase- space ``blobs.'' Each blob evolves as a warm beamlet\footnote{B.~A. Shadwick, \textit{et al.}, ``Hamiltonian Reductions for Modeling Relativistic Laser-Plasma Interactions,'' \textbf{Commun.\ Nonlinear Sci.\ Numer.\ Sim.} in press (2011).} driven by the collective plasma fields. The underlying approximation treats each blob as a different plasma species and, as such, makes a counting error which we expect to be reflected in the system entropy. This approach results in a non-canonical Hamiltonian model, inheriting various properties of the original system. The primary advance of this technique over traditional Lagrangian particle methods is the near elimination of macro-particle ``noise.'' Since we are evolving elements of phase-space, the distribution function can be readily reconstructed at any instant. We discuss the performance and convergence of this model using a variety of standard examples.   

Vlasov Simulations of Electron Plasma and Ion Acoustic Waves: self-focusing and harmonics

Vlasov simulations of nonlinear electron plasma (EPW) and ion acoustic waves (IAW) are presented in one and two dimensions. In 2D simulations with LOKI (Banks \textit{et al}, \textbf{18}, 052102 (2011)) the waves are created with an external traveling wave potential with a transverse envelope of width $\Delta $y such that thermal electrons transit the wave in a ``sideloss'' time, t$_{sl} \quad \sim \quad \Delta $y/v$_{e}$ where v$_{e }$ is the electron thermal velocity. The quasi-steady distribution of trapped electrons and its self-consistent plasma wave are studied after the external field is turned off. For sufficiently short times and large enough wave amplitudes, the magnitude of the negative frequency shift from trapped electrons is a local function of electrostatic potential. Analysis and simulations are presented of the damping and trapped-electron-induced self-focusing (H. Rose PoP \textbf{12}, 012318 (2005)) of the finite-amplitude EPW. In 1D simulations with SAPRISTI (Brunner and Valeo, PRL \textbf{93}, 145003 (2004)), IAWs are created with an external traveling wave potential with full electron dynamics. For large IAW amplitudes, the contribution from IAW harmonics to the frequency shift is significant and larger than fluid theory predicts.   

Interactive, Extensible PIC Simulations with a Python Interface

Particle-in-Cell (PIC) simulations of plasmas are used for a wide variety of systems, and can range significantly in scale. There are many informative simulations that can be run at interactive speeds, and good tools for interacting with simulations are important for facilitating science. By wrapping simulation code in Python, we gain the use of a full programming language as the simulation interface. This quickly gives us the tools for defining new diagnostics in-flight, enabling more natural investigation of the system. The Python interface also allows very powerful interaction between codes, facilitating iterative approaches for finding target simulation parameters, and working with other simulation codes. The toolset is also developed with parallel simulations in mind, allowing for aggregation of subdomain diagnostics from different nodes.   

CPIC: a curvilinear Particle-In-Cell code for plasma-material interaction studies

We present a recently developed Particle-In-Cell (PIC) code in curvilinear geometry, CPIC (Curvilinear PIC), where the standard PIC algorithm is coupled with a grid generation/adaptation strategy. Through the grid generation strategy (based on Winslow's method), the code can simulate domains of arbitrary complexity, including the interaction of complex objects (with the simulation domain conforming exactly to the objects without any stair-stepping) with a plasma. At present the time-integration is explicit and the code is two-dimensional and electrostatic (only Poisson's equation is solved). It features a hybrid particle mover, where the computational particles are characterized by position in logical space and velocity in physical space. Poisson's equation is solved with preconditioned GMRES. We will present the application of the code to standard test problems such as plasma waves, two--stream instabilities, Landau damping and the charging of a spherical object in a plasma. We will also discuss techniques that can be used to reduce PIC noise, which can be critical when the ratio of the largest to the smallest cell volume becomes large.   

Atmospheric microplasmas: effect of electric and magnetic fields

Small spaces are highly interesting as the complexity of micro-technology systems increases - for instance, for potential applications in spacecraft micropropulsion and active flow control. A self-consistent model of plasma and gas dynamics is applied to microplasmas. Fluid equations of the fully self-consistent model are described with emphasis on the close coupling among the plasma, the fluid and the electric/magnetic field. The microplasmas are studied from an initial cloud and the momentum and energy transfer are investigated for these discharges. Both surface effects (secondary emission) and volume effects (electric or magnetic fields) appear as critical parameters and several characteristic values are parameterized. The close interaction between the fluid and the ionized gas is investigated in microplasmas.   

Cross Section Specific Collision Probability Techniques for DSMC

In direct simulation Monte Carlo (DSMC) methods the probability of collision, or equivalently the collision frequency, as a function of CM closing speed is a central quantity in choosing collision sample pairs. The calibration of DSMC parameters is also tied to this quantity through the linkage of viscosity's temperature variation and the high velocity dependence of the cross section. A common simplification in the selection of collision pairs is to recalibrate this collision frequency parameter to be bounded above by the largest closing speed seen in the DSMC microstate. Such a practice is neither necessary nor without consequence. Here is developed a new method tied to the full range of closing speeds and the adopted model (or even precisely represented) cross section for the binary channel of interest. By scaling out the ensemble average collision frequency, the local value then sets a relative collision probability on the full speed range. The collision frequency integrals for common cross section models are easily evaluated and a numerical inversion then establishes the appropriate collision probability for any value of closing speed. When a conventional method DSMC calculation is interrogated as to the temperature dependence of viscosity, the power law rule that is the basis of the model molecular diameter is not reproduced. The implications for this problem using the new method are reported.   

Non-LTE kinetics modeling of emission from noble gas plasmas

In recent years, international efforts have been made in the development of theoretical models of non-local thermodynamic equilibrium (NLTE) plasma kinetics [1]. Such modeling is of particular relevance to both inertial and magnetic confinement fusion experiments, such as the ongoing $ITER$ project. This work focuses on obtaining emission spectra of neon and krypton over a wide range of electron temperatures and densities. The atomic data are generated with the Los Alamos suite of atomic physics and plasma kinetics codes, developed over many years to calculate atomic structure and atomic scattering quantities. Calculations may be carried out using either a configuration-average model using a mixed UTA approach [2], or a detailed level-to-level fine-structure approach. Previous assessments of the accuracy of these models [3] under a given set of conditions will be of use in this work. \\[4pt] [1] C. J. Fontes {\em et al.}, 2009 {\em High Energy Density Phys.} {\bf 5} 15\\[0pt] [2] S. Mazevet and J. Abdallah, Jr., 2006 JPB {\bf 39} 3419\\[0pt] [3] J. Colgan {\em et al.}, 2006 {\em High Energy Density Phys.} {\bf 2} 90   

Fluid Modeling of the Delayed Nonlinear Raman Response of a Diatomic Gas

Intense laser pulses induce polar alignment of diatomic molecules when propagating through a gas, resulting in nonlinear focusing and frequency shifts. Here the gas is treated as an ensemble of classical rigid rotors that interact with the field through an induced dipole moment. The evolution of the angular distribution of the gas is solved by applying the Finite Volume Method (FVM) to a set of fluid equations derived as moments of the Boltzmann equation. This technique offers considerable computational savings over full quantum mechanical density matrix calculations, while providing good agreement with the initial delayed Raman response of the gas. As a result, the FVM method is ideal for implementation in atmospheric laser pulse propagation simulations.   

Lacuna-based Artificial Boundary Condition And Uncertainty Quantification of the Two-Fluid Plasma Model

Modeling open boundaries is useful for truncating extended or infinite simulation domains to regions of greatest interest. However, artificial wave reflections at the boundaries can result for oblique wave intersections. The lacuna-based artificial boundary condition (ABC) method is applied to numerical simulations of the two-fluid plasma model on unbounded domains to avoid unphysical reflections. The method is temporally nonlocal and can handle arbitrary boundary shapes with no fitting needed nor accuracy loss. The algorithm is based on the presence of lacunae (aft fronts of the waves) in wave-type solutions in odd- dimensional space. The method is applied to Maxwell's equations of the two-fluid model. Placing error bounds on numerical simulations results is important for accurate comparisons, therefore, the multi-level Monte Carlo method is used to quantify the uncertainty of the two-fluid plasma model as applied to the GEM magnetic reconnection problem to study the sensitivity of the problem to uncertainty on the mass ratio, speed of light to Alfven speed ratio and the magnitude of the magnetic field initial perturbation.   

Framework for advanced plasma simulations on many-core architectures and results

A new framework designed for emerging many-core computing architectures is developed. The framework is used for simulation of both multi-fluid plasma models and continuum kinetic models. We provide exemplary physics results, and show performance gains seen using this approach. Many-core architectures will dominate the field of high performance computing in the coming decade. In order to maximize performance and power efficiency on these systems, code design should minimize data movement. The algorithms developed are thus both local and explicit. Fluid and continuum kinetic models on structured grids also benefit from predictable data access patterns as opposed to PIC models. The resulting framework is a hybrid combination of MPI for communication between nodes, threads for task parallelism on each node, and OpenCL for parallel scientific computation on tens or hundreds of cores available on each node - often a GPU machine. The framework fulfills the significant challenges of managing data movement, sub- domain sequencing, and file output such that memory bandwidth bottlenecks can be significantly hidden. Framework users can concentrate on algorithm development specific to their model. Physics results including energetic particle-induced geodesic acoustic mode (EGAM) in tokamaks and two-fluid Whistler wave propagation are demonstrated.   

Multidimensional Plasma Sheath Modeling Using The Three Fluid Plasma Model

There has been renewed interest in the use of plasma actuators for high speed flow control applications. In the plasma actuator, current is driven through the surrounding weakly ionized plasma to impart control moments on the hypersonic vehicle. This expanded study employs the three-fluid (electrons, ions, neutrals) plasma model as it allows the capture of electron inertial effects, as well as energy and momentum transfer between the charged and neutral species. Previous investigations have typically assumed an electrostatic electric field. This work includes the full electrodynamics. Past work was conducted in 1- and 2-D. In this work, the problem is expanded to 3-D with the fluid equations extended from euler to Braginskii.   

Momentum Transport and Associated Scale Lengths in ICF Plasma

Inertial Confinement Fusion (ICF) research suggests that experimental performance lags that predicted in ``clean'' (unmixed) single fluid Lagrange simulations. In this study, viscosity and diffusion in a binary mixture of ion species are considered using a plasma diffusion approximation based on Braginskii plasma transport under various simplifying assumptions. Results are given over a range of ICF conditions and in a specific ICF example by post-processing an ICF Lagrange simulation. Viscosity in the fuel is estimated and viscous diffusive scale lengths are found to be large compared to the fuel size suggesting viscosity may be an important dissipation mechanism at small scales in turbulent or unstable mixing. Plasma species mass flux and diffusion approximations include effects of the local electric field, thermal gradients and mixture averaged pressure gradients (barodiffusion). Plasma species mass flux estimates applied to the fuel-capsule interface are found to contribute a small but significant amount of ``mix'' leading up to ICF burn, and reduce the ``clean'' fuel volume by 30{\%} in this example. Transport of high Z impurities, used in the capsule or fuel for experimental diagnostics, are considered. Plasma transport is likely to be an important mechanism in explaining some experimental observations.   

Validation of SPHC and CRASH codes in modeling of linear and non-linear Richtmyer-Meshkov instabilities

Richtmyer-Meshkov instability (RMI) plays an important role in variety of phenomena in nature and technology and is of special interest in the fields inertial confinement and magneto-inertial fusion. The instability develops when a shock refracts an interface between two fluids with different values of the acoustic impedance, and RMI dynamics is defined primarily by the flow Mach number and the Atwood number for the two fluids. This work was done under the Plasma Liner Experiment (PLX) program, with intentions of verifying whether SPHC and CRASH codes are capable of successful modeling of different modes of RMI that are expected to be seen during the plasma liner implosion. We used SPHC and CRASH codes to mutually evaluate the codes and compared results against the analytical RMI theory. The numerical and theoretical results are in good qualitative and quantitative agreement with one another. Results indicate that at large scales the nonlinear dynamics of RMI is a multi-scale process; at small scale the flow field is heterogeneous and is characterized by appearance of local microscopic structures; the coupling between the scales has a complicated character.   

Overview of the ZaP Flow Z-pinch Experiment

The ZaP Flow Z-pinch experiment is a basic plasma physics experiment that uses sheared axial flows to maintain the gross stability of a Z-pinch plasma. Z-pinches generated are approximately 1 cm in radius, greater than 100 cm long and exhibit stability for many Alfven transit times. Measurements of the axial flow velocity profile indicate low magnetic mode fluctuations are coincident with a sheared profile. The flow profile is uniform near the axis of the pinch with the shear localized near the edges. Investigation of pinch stability in the absence of a close-fitting conducting wall suggests that a wall is not necessary when flow shear is present. Multiple diagnostics indicate evidence of a coherent pinch structure with a length greater than 100 cm that persists for many flow-through times. The effects of adiabatic compression on the pinch are investigated with two electrode configuration. The larger inner electrode is predicted to increase temperature. A two-point Thomson scattering system measures electron temperature and relative electron density at two radial locations. These measurements indicate increased temperature for the larger inner electrode. Ion temperature measurements from Doppler broadening and force balance calculations agree with these measurements.   

Plasma flows in MPD thrusters

A fundamental description of the plasma acceleration process in magnetoplasmadynamic (MPD) thrusters is presented. The properties of plasma flows in self-field MPD thrusters are investigated by adopting a stationary, axisymmetric, resistive magnetohydrodynamic plasma model. First, the acceleration process in a cylindrical MPD channel is analyzed by neglecting the gasdynamic pressure term. A class of solutions is presented, which allows for a simple analytical treatment of the flow. The physical and mathematical nature of the flow is thus described in terms of two characteristic parameters: a dimensionless channel length, scaled with the plasma resistive length, and a dimensionless parameter which depends on the applied voltage. Then, the effect of gasdynamic pressure is investigated. The presented approach gives an effective description of the plasma acceleration process and defines a framework for the parametric analysis of plasma flows in MPD thrusters.   

Mechanism of Counter Current Flow with Lower-Hybrid-Driven Current

Strong counter current plasma flow has been observed in the Alcator C-Mod with Lower Hybrid Current Drive (LHCD). An investigation of the momentum source of the flow indicates that an improvement of electron momentum confinement is the possible reason of the counter-current spinning up. Simulations of counter-current flow generation are carried out by applying a simplified momentum transport model with a two-fluid equation system. Numerical results agree well with the experimental data of the Alcator C-Mod.   

Turbulence Suppression in a coherent structure of localized current and vorticity

Motivated by the quasi-single helicity state of reversed field pinches, we examine turbulence suppression by a localized vortex structure of electric current and flow vorticity within the framework of reduced MHD. Assuming that the vortex structure evolves on a slower time scale than an Alfven time scale of turbulent fluctuations, a boundary layer between turbulent fluctuations and the coherent structure forms through the balance of the turbulent decorrelation rate and the shearing rates. The dependence of the boundary width on shear and turbulence is obtained applying a variant of eddy-damped quasinormal Markovian (EDQNM) closure to the turbulent fluctuation and applying asymptotic analysis for strong shear. The coherent structure of localized current and flow vorticity can suppress ambient turbulence through magnetic field shear or flow shear. Also, both shear effects may combine to suppress the turbulence. The suppression mechanism can be classified into magnetic shear dominant, flow shear dominate, or intermediate. The details will be presented. The life time of the coherent structure is presented in each case. Simple numerical calculation will be presented as a test case.   

3D modeling of blobs with the BOUT++ code

Blobs are filamentary structures found in the edge region of tokamaks during L-mode discharges and can contribute to more than 50{\%} of the plasma particle transport near the last closed flux surface. Most of the theory and simulation of blobs is done in the 2D limit by invoking different closure schemes of the 3D dynamics along the field line. However, 3D dynamics can be very important and alter the blobs speed and lifetime, which in turn alters the particle and energy transport of the blobs. For example, a finite resistivity along the field line can lead to standing drift waves along the field line and a finite density gradient along the field line can lead to a potential difference along the field line that wants to spin the blob. These 3D effects and more are investigated here analytically and numerically using the 3D fluid BOUT++ code.   

Neoclassical Toroidal Viscosity Calculations in Tokamaks using a $\delta f$ Monte Carlo Simulation and Their Verifications

Effect of magnetic perturbation on plasma rotation is an important issue in tokamaks, since recent studies have shown that perturbation as small as $\delta B/B_0\sim 10^{-4}$ can induce significant rotation damping. A new simulation to calculate neoclassical toroidal viscosity (NTV) in tokamaks with weak non-axisymmetric perturbation has been developed by adopting the $\delta f$ Monte Carlo method [1]. Previous benchmark has proven that in $\mathbf{E}\times\mathbf{B}\rightarrow 0$ limit the simulation result agrees well with the combined analytic formula by Park [2] in wide range of collision frequency [3]. In the presentation, further benchmark results of NTV calculation will be reported for the cases with finite $\mathbf{E}\times \mathbf{B}$ rotation and toroidal flow. Non-local (finite-orbit-width) effects on NTV, which may appear only in the $\delta f$ simulation, will also be investigated.\\[4pt] [1] S. Satake et al., Plasma Phys. Controlled Fusion {\bf 53}, 054018 (2011).\\[0pt] [2] J.-K. Park et al., Phys. Plasmas {\bf 16}, 056115 (2009).\\[0pt] [3] S. Satake et al., accepted to Phys. Rev. Lett.   

Generation of Azimuthal Plasma Rotation due to Ion Stream Line Detachment in a Diverging Magnetic Field Region

Flow structure of ions in a diverging magnetic field has been experimentally studied in a steady-state electron cyclotron resonance plasma. We have measured the ion flow velocity using a directional Langmuir probe calibrated by the laser induced fluorescence (LIF) spectroscopy. A weakly diverging magnetic field configuration was adopted in the experiment, where the ions are accelerated from subsonic to near sonic speeds by the ambipolar electric field along the magnetic field line. It was found that the ion stream line detachment takes place in a diverging magnetic field region, when the non-adiabaticity parameter of ions becomes order of unity. In the detachment region, the generation of plasma rotation due to the {\boldmath $E\times B$} drift has also been found. The radial electric field is generated by the difference of motions between the magnetized electrons and the unmagnetized ions. The generation of azimuthal rotation implies that the electromagnetic angular momentum is important as well as the mechanical angular momentum in the detachment region, where the ion stream line is different from the magnetic field line.   

Spontaneous Excitation of Intermittent Electron Currents in an ECR Discharge Plasma

Laboratory plasmas are intrinsically non-equilibrium open system in which energy and particles are being injected and exhausted continuously; such systems exhibit various intermittent behaviors. Recently, the spontaneous excitation of 1-cycle magnetic pulses has been observed in an electron cyclotron resonance (ECR) discharge plasma produced in the HYPER-I device at the National Institute for Fusion Science. Simultaneous measurement using two magnetic probes and a directional Langmuir probe revealed that the magnetic pulses were excited by intermittent electron currents, or high-energy electron fluxes, along the magnetic field. The energy distribution of those electrons was examined by a retarding field analyzer. We also developed a wire-grid probe which consists of 16 electrically floated electrodes to measure the two-dimensional profile of the high-energy electrons. Since the occurrence of high-energy electron fluxes appeared to be random in time and space, we applied several statistical analyses to the intermittent events. The waiting time analysis demonstrated an exponential-like distribution, which implies the stochastic nature of the events.   

The effect of a supersonic plasma jet expansion on a magnetized, ambient plasma measured using laser-induced fluorescence

The supersonic expansion of a laser-produced carbon plasma through an ambient argon plasma ($n\sim2\cdot10^{12}cm^{-3},c_{s}=4\cdot10^{5}cm/s$) is studied in the Large Plasma Device at UCLA. A laser-induced fluorescence diagnostic characterized the interface of the plasma species' populations as the carbon plasma expands ($\tau_{exp}\sim.5\mu s$) along the background magnetic field. A planar beam of a YAG-pumped, tunable dye laser sampled the distribution function of the Ar-II ions using the Doppler broadened transition at 611.5 nm. A CCD camera with a fast ($\geq$3 ns) shutter provided a spatially and temporally resolved image of the fluorescence. Time lapsed imaging revealed a front of argon ion excitation moving at a speed comparable to the carbon parallel expansion velocity ($v_{exp}\sim1\cdot10^{7}cm/s$) while the distribution function from the transition spectra showed a significant fraction of argon ions accelerated to an ion sound speed mach number of 2-3. The laser-induced fluorescence measurements are supplemented by magnetic and Langmuir probe measurements.   

A paradigm for the stability of the plasma sheath

we present an investigation of the linear stability of the sheath of a (non-electron emitting) wall at floating potential in the framework of a fluid plasma model where the continuity and momentum equations of the electrons and ions are coupled through Poisson's equation. Initially, we neglect the presence of a magnetic field and the wall is negatively charged. In the limit where the equilibrium ion flow is artificially suppressed, we show that the system can be unstable to the Rayleigh-Taylor (RT) instability, driven by the favourable combination of the ion density gradient and electric field in the sheath equilibrium. However, the sonic ion flow strongly stabilizes the RT modes due to convective stabilization, ultimately leading to a stable sheath. Thus, we cast the paradigm of sheath stability as a balance between two competing effects: the RT instability and the flow stabilization. While the sheath of a negatively charged wall at floating potential is stable, we discuss how this balance can be altered (for instance by negatively biasing the wall) so that the sheath can become unstable. We will also present our latest results on the effect of an equilibrium magnetic field, obtained by PIC simulations, on the sheath stability.   

Stable plasma flow to absorbing boundary in a magnetized two ion species plasma

Study has been carried out to analyze the effect of magnetic field on the behavior of plasma flow to a perfectly absorbing plasma boundary in a magnetized two ion-species plasma. Recent experiments and theoretical studies [D. Lee, L. Oksuz and N. Hershkovitz, Phys. Rev. Lett. 99, 155004 (2007), C. S. Yip, N. Hershkowitz and G. Severn, Phys. Rev. Lett. 104, 225003 (2010)] have indicated that in unmagnetized cases, the two ion velocities approach a common ion sound speed of the system near the sheath-presheath boundary and satisfy the generalized form of Bohm-Criterion. This behavior is influenced further by the presence of a magnetic field in the cases where the presheath mechanisms scale with the ion-Larmour radius. Our analysis indicates additional regions in the parameter-space of magnetized plasma where the boundary flow is unstable. The effect appears as a consequence of modification of the usual ion-acoustic dispersion relation resulting from the partial magnetization of the ion species.   

Stopping of Ions in a Plasma Irradiated by an Intense laser Field

The inelastic interaction between heavy ions and electron target plasma in the presence of an intense radiation field (RF)is investigated. The stopping power of the test ion averaged over a period of the RF is calculated assuming that RF frequency $>$ plasma frequency. In order to highlight the effect of the RF we compare analytical and numerical results obtained for nonzero RF with those for vanishing RF. It is thus observed that RF may strongly reduce the mean energy loss of the slow ions while increasing it at high projectile velocity. More specifically, RF acceleration of the projectile ion is expected at high velocity and in the RF high- intensity limit, when quiver velocity of plasma electrons exceeds the ion projectile velocity [1].\\[4pt] [1] H.B. Nersisyan and C. Deutsch, Laser Part.Beams (to appear 2011)   

Dispersion of electrostatic and electromagnetic waves in a relativistically drifting plasma

Multi-dimensional electron beam-plasma instabilities in the relativistic regime [1] are of interest in a number of scenarios, such as fast ignition for inertial confinement fusion and generation of cosmic gamma ray. A closely related problem arises for drifting plasmas with relativistic electron and ion velocities typically found in laser ion acceleration [2] and also in numerical simulations with the boosted frame technique [3] for plasma wakefield acceleration. We study the dispersion of the electrostatic and electromagnetic waves in such plasma using a linear analysis in the cold-fluid limit and a kinetic approach. Possible instabilities are analyzed and compared with those found in an electron beam-plasma system. The potential implications for the boosted frame simulation technique will also be discussed. \\[4pt][1] A. Bret et al., Physics Of Plasmas 17, 120501 (2010). \newline [2] L. Yin et al., Physics Of Plasmas 14, 056706 (2007). \newline [3] J.-L. Vay, Physical Review Letters 98, 130405 (2007).   

Theory and numerical modeling of radiation from sub-Larmor-scale magnetic turbulence

Spontaneous rapid growth of strong magnetic fields is ubiquitous in high-energy density environments ranging from astrophysical sources and relativistic shocks, to reconnection, to laser-plasma interaction laboratory experiments, where they are produced by kinetic streaming instabilities of the Weibel type. Relativistic electrons propagating through these sub-Larmor-scale magnetic fields radiate in the jitter regime, in which the anisotropy of the magnetic fields and the particle distribution have a strong effect on the produced radiation. We present the general theory of jitter radiation, which includes (i) anisotropic magnetic fields and electron velocity distributions, (ii) the effects of trapped electrons and (iii) the large deflection angle regime thus establishing a cross-over between the classical jitter and synchrotron regimes. Our results are in remarkable agreement with dedicated particle-in-cell simulations of the classical Weibel instability. Particularly interesting is the onset of the field growth, when the transient hard synchrotron-violating spectra are common, which can serve as a distinct observational signature of the violent field growth in astro sources and lab experiments. It is also interesting that a system with small-scale magnetic turbulence fields tends to evolve toward the small-angle jitter regime. This work is supported by grants DE-FG02-07ER54940, AST-0708213, NNX-08AL39G.   

Persistence of the Polarization in a Fusion Process

We propose an experiment to test the persistence of the polarization in a fusion process,using a TW laser hitting a prepolarized HD target [1].The polarized protons and deuterons heated in the plasma induced by the laser have a significany probability to fuse producing a 3He nucleus and a Gamma ray or a neutron in the final state. The angular distribution of the radiated Gamma rays and changes in corresponding total cross-section are related to the polarization persistence, but the resulting signal appears rather weak. Neutrons are hadronically produced with a larger cross-section and, are much more easily detected. A significant reduction of the cross-section by parallel deuterons polarization as well as a structured angular distribution of emitted neutrons is fairly predicted by theory arguments. It is thus expected that the pertaining signal on the neutron counting rate could be experimentally observed. Magnetic field,relaxation times and possibilities of local investigations will also be discussed.\\[4pt] [1] J.P. Didelez and C. Deutsch, J. Physics: Conference Series 295, 012169 (2011) and laser Part. Beams 29, 169 (2011)   

Radio-frequency sheath boundary condition for fast wave propagation

Analyzing the formation and consequences of rf-sheaths in ICRF-heated fusion devices is an important issue in rf physics. Quantitative calculation of the sheath properties can be included in rf codes by means of a sheath boundary condition (BC) [D. D'Ippolito et al., Phys. Plasmas 13, 102508 (2006); J.R. Myra et al., Phys. Plasmas 1, 2890 (1994).]. However, this requires resolving both the long fast wave (FW) and short slow wave (SW) space scales in the same simulation, which is computationally challenging, even on a parallel computer [H. Kohno, PhD thesis, 2011]. Here, we describe and test a modified approach which is valid when the SW is evanescent near the wall. The SW is incorporated into the sheath BC analytically, so that the simulation only has to solve the FW equations numerically with the lower resolution appropriate to the ion scale length. The derivation of the new BC will be described and its use will be illustrated in a sample problem.   

Numerical analysis of radio-frequency sheath-plasma interactions in the ion cyclotron range of frequencies

In this study a numerical code that solves self-consistent RF sheath-plasma interactions in the SOL for ICRF heating is developed based on a nonlinear finite element technique and is applied to various problems represented by simplified models for the poloidal plane of a tokamak. The present code solves for plasma waves based on the cold plasma model subject to a sheath boundary condition. Using the developed finite element code, some new properties of the RF sheath-plasma interactions are discovered. For example, it is found in the 1D domain that multiple roots can be present due to the resonance of the propagating slow wave and its nonlinear interaction with the sheath. An approach that deals with the singularity in the sheath boundary condition will also be presented.   

Differences Between Quasi-linear and Exact Ion Cyclotron Resonant Diffusion

These studies investigate the validity of ICRF quasilinear(QL) diffusion theory by comparison of QL coefficients from the AORSA full-wave code [1] with ``exact'' Lorentz equation orbit-based coefficients calculated with the DC code using AORSA full-wave fields, for a C-Mod minority-H ICRF heating scenario. We also compare time-dependent distribution functions and power deposition obtained with the coupled CQL3D Fokker-Planck code [2], using the two RF diffusion sets. The resulting synthetic diagnostic NPA energy spectra are compared with experiment. Initial results indicate that ``exact'' RF coefficient-based NPA spectra give improved agreement with experiment [3]. This work investigates the dominant causes of the QL/``exact'' RF diffusion discrepancy.\\[4pt] [1] E.F. Jaeger et al, Nucl. Fusion 46, (2006) S397-S408.\\[0pt] [2] R.W. Harvey and M.G. McCoy, http://www.compxco.com/cql3d.html.\\[0pt] [3] A. Bader et al, Proc. of 13th RF Power in Plasmas Conference, Newport, RI (2011).   

Development of Finite Orbit Width features in the CQL3D code

The bounce-averaged Collision-Quasilinear Fokker-Planck equation solver, CQL3D [1], is being upgraded to include the Finite-Orbit-Width (FOW) effects. For the RF Quasilinear operator, the finite width guiding center orbits are traced for each particle in the distribution. For the collisional operator, a fast lookup table is used to determine the radial coordinate for the particles interacting with given particle along its orbit. The lookup table is based on mapping of the Constants-Of-Motion (COM) space onto the coordinates of orbits' crossing with the midplane. The same lookup table is used to form a particle source and for the Neutral Particle Analyzer synthetic diagnostic. The results are compared with the first-order FOW corrections recently added to the CQL3D [2]. \\[4pt] [1] R.W. Harvey and M. McCoy, ``The CQL3D Fokker Planck Code,'' www.compxco.com \\[0pt] [2] R.W. Harvey, Yu. V. Petrov, E.F. Jaeger, W.W. Heidbrink, G. Taylor, C.K. Phillips, B.P. LeBlanc, Proc. of the 38$^{th}$ EPS Conf. on Plasma Phys., Strasbourg, P4.017, (2011).   

Full-wave ICRF simulations with non-Maxwellian particle distributions

RF induced departure of particle distribution functions from local Maxwellians affects, in general, the amount of single pass absorption, the absorption profile and the distribution of absorbed energy amongst species. The capability to incorporate general distribution functions in the TORIC full-wave finite Larmor radius field solver has been rewritten and optimized so that the additional computational burden (compared to the Maxwellian case) is modest ($<$ 30{\%}). Progress toward fully self-consistent simulations to be obtained by iterating between TORIC field solutions and CQL3D Fokker Planck solutions for the bounce-averaged distribution will be described. Self-consistency is achieved in these simulations by re-evaluating the plasma conductivity using the non-thermal particle distribution from the most recent calculation by the Fokker Planck solver. Likewise, the ICRF wave fields from the most recent field solve are used to evaluate the RF diffusion coefficient that is used to advance the non-Maxwellian particle distribution. This effort complements previous research with the AORSA+CQL3D package, but is specialized to the FLR regime.   

Integrated Plasma Simulation of Lower Hybrid Current Drive Modification of Sawtooth

It has been shown in Alcator C-Mod that the onset time for sawteeth can be delayed significantly (up to 0.5 s) relative to ohmically heated plasmas, through the injection of off-axis LH current drive power [1]. We are simulating these experiments using the Integrated Plasma Simulator (IPS) [2], through which driven current density profiles are computed using a ray tracing code (GENRAY) and Fokker Planck code (CQL3D) [3]. These modules are executed repeatedly as the background plasma is evolved using the TSC transport code with the Porcelli sawtooth model [4]. Predictions of the driven LH current profiles will be compared with simpler ``reduced'' models for LHCD such as the LSC code which is implemented in TSC. \\[4pt] [1] C. E. Kessel \textit{et al}, Bull. of the Am. Phys. Soc. \textbf{53}, Poster PP6.00074 (2008). \\[0pt] [2] D. Batchelor \textit{et al}, Journal of Physics: Conf. Series \textbf{125}, 012039 (2008). \\[0pt] [3] R. W. Harvey and M. G. McCoy, Proc. of the IAEA Tech. Comm. Meeting on Simulation and Modeling of Therm. Plasmas, Montreal, Canada (1992). \\[0pt] [4] S. C. Jardin \textit{et al}, J. Comp. Phys. \textbf{66}, 481 (1986).   

On the importance of physical optics effects for lower hybrid waves in linear and non-linear regimes

Lower hybrid waves in fusion plasmas have perpendicular wavelengths of $\approx$ 1mm. Historically, the propogation and power deposition of these waves has been modeled by coupled geometric optics (ray tracing) and Fokker-Planck codes. Recently [Wright, J. et al {\em Phys. Plasmas\/} {\bf 16} 072502 (2009)] the ability to use physical optics (full wave) in this regime became available. A comparison of the two methods at low and high power demonstrates when reflections, diffraction and interference affect the rf depostion profile in the plasma. At lower input power for which quasilinear effects are not important, ray tracing and full wave results are in close agreement for both low and high phase velocity waves. At higher power when the distribution function is evolved by quasilinear diffusion, significant differences in the power deposition profiles appear when the launched wave phase velocity is high (low $n_\|$.) These differences can be explained by intereference effects in the quasilinear diffusion operator which is a quadratic function of the wave electric field.   

Full-wave simulations of HHFW heating in NSTX with non-Maxwellian distributions

In order to improve the analysis and simulation of combined high harmonic fast wave (HHFW) and neutral beam injection (NBI) heated discharges in NSTX, a generalization of the HHFW version of TORIC to include non-Maxwellian ions has been implemented to include species with arbitrary velocity distribution functions. This generalization is important to investigate finite ion orbit width (FOW) effects in conjunction with the FOW version of CQL3D that is under development. It is also needed in the TRANSP code for time-dependent simulations of these combined heating experiments. Test cases in which the modified code reproduces previous simulations with thermal ions are presented along with some calculations of the power deposition profile in a plasma with a given non-Maxwellian ions. In addition, the simulations are compared with results from the AORSA code, which has already been extended to include non-Maxwellian ions.   

Anti-alias filter in AORSA for modeling ICRF heating of DT plasmas in ITER

The spectral wave solver AORSA [1] has been used extensively to model full-field, ICRF heating scenarios for DT plasmas in ITER. In these scenarios, the tritium (T) second harmonic cyclotron resonance is positioned near the magnetic axis, where fast magnetosonic waves are efficiently absorbed by tritium ions. In some cases, a fundamental deuterium (D) cyclotron layer can also be located within the plasma, but close to the high field boundary. In this case, the existence of multiple ion cyclotron resonances presents a serious challenge for numerical simulation because short-wavelength, mode-converted waves can be excited close to the plasma edge at the ion-ion hybrid layer. Although the left hand circularly polarized component of the wave field is partially shielded from the fundamental D resonance, some power penetrates, and a small fraction (typically $<$ 10{\%}) can be absorbed by the D ions. We find that an anti-aliasing filter is required in AORSA to calculate this fraction correctly while including up-shift and down-shift in the parallel wave spectrum. \\[4pt] [1] E.F. Jaeger, L.A. Berry, E.F. D'Azevedo, \textit{et al}., Phys. Plasmas \textbf{8}, 1573 (2001).   

Simulation of RF Antenna Loading with 3-D Time-Domain Model Including Edge Plasma

We use three-dimensional geometry of ITER and NSTX RF launchers in time-domain finite-difference simulations, done with the VORPAL software [1], to look at both vacuum and edge plasma loaded conditions. These simulations provide antenna loading measurements, including S-parameters, as measured in the coaxial feed lines. We import EQdisk data for the equilibrium plasma, and various models and measurement data to provide edge plasma profiles, including profiles with asymmetry in poloidal and toroidal directions. We are able to treat plasma that is in contact with the launchers, and even diffuse plasma within the antenna boxes. We also compute sheath potential for all surfaces, and report on progress in terms of making this model as self-consistent as possible. The simulation volumes requires office-cluster scale and super-computing scale platforms, and we also report on computational tradeoffs in terms of simulation volume, run-time, and cpu use. \\[4pt] [1] Nieter, C. and Cary, J. R., JCP 196 (2004) 448-473.   

Electric Fields near RF Heating and Current Drive Antennas in Tore Supra Measured with Dynamic Stark Effect Spectroscopy*

Computational models of the interaction between RF waves and the scrape-off layer plasma near ion cyclotron resonant heating (ICRH) and lower hybrid current drive launch antennas are continuously improving. These models mainly predict the RF electric fields produced in the SOL and, therefore, the best measurement for verification of these models would be a direct measurement of these electric fields. Both types of launch antennas are used on Tore Supra and are designed for high power (up to 4MW/antenna) and long pulse ($>>$25s) operation. Direct, non-intrusive measurement of the RF electric fields in the vicinity of these structures is achieved by fitting spectral profiles of deuterium Balmer-alpha and Balmer-beta to a model that includes the dynamic, external-field Stark effect, as well as Zeeman splitting and Doppler broadening mechanisms. The measurements are compared to the mentioned, near-field region, RF antenna models. *Work supported in part by the US DOE under Contract No. DE-AC05-00OR22725 with UT-Battelle, LLC.   

Experimental Measurements of the Dynamic Electric Field Topology Associated with Magnetized RF Sheaths

The dynamic Stark effect is a phenomenon in which photon(s) associated with an oscillating electric field are absorbed or emitted with the photon associated with an electronic transition. This multiphoton process leads to the formation of satellites in the spectrum at integer multiples of the frequency associated with the dynamic electric field. Utilizing the dynamic Stark effect the electric field parameters can be determined from the time-averaged and phase resolved emission spectra. Currently two methods are available to calculate the emission spectrum associated with an atomic system in the presence of a dynamic electric field: the quasi-static method and the Floquet method. The methodology and applicability of the quasi-static and Floquet methods will be discussed. The RF sheath electric field parameters are determined, utilizing a generalized dynamic Stark effect model and a novel line shape analysis package, from the time-averaged and phase resolved optical emission spectra. Results will be presented for working gases of hydrogen and helium.   

Experimental Study of Radio Frequency Sheaths Created by Fast Wave Antennae

There is a great deal of interest in radio frequency (RF) sheaths as the result of ion cyclotron resonant frequency heating (ICRF). During high power operation in fusion devices, large RF sheaths on the order of several kV can form on the RF antenna or at the machine wall. These large sheaths are detrimental because of impurity generation, local heating, arcing, etc. A series of experiments at the Large Plasma Device (LAPD) at UCLA is underway to study the generation of RF sheaths on conductors both in the near field and in the far field of the fast wave antenna. A fast wave antenna has been constructed for LAPD and has been shown to launch fast waves. The potential in the RF sheath near a metallic conductor will be probed with Langmuir probes and emissive probes. These probes can be positioned with an accuracy of ten micron perpendicular to the metallic plate, and can thus probe the sheath and pre-sheath over a distance of several cm. The design and first tests of the probe system will be presented as well as antenna coupling studies for different plasma conditions.   

Mitigation of parallel RF potentials using TOPICA code

The design of an Ion Cyclotron (IC) launcher is not only driven by its coupling properties, but also by its capability of maintaining low parallel electric fields, in order first to provide good power transfer to plasma and then to reduce the impurities production. However, due to the impossibility to verify the antenna performances before the starting of the operations, advanced numerical simulation tools are the only alternative to carry out reliable design. With this in mind, it should be clear that the adoption of a code, such as TOPICA [1], able to precisely take into account a realistic antenna geometry and an accurate plasma description, is extremely important to achieve these goals. Because of the recently introduced features that allow to compute the electric field and RF potential distribution everywhere inside the antenna enclosure and in the plasma column, the TOPICA code appears to be the best candidate in helping to understand which elements may have a not negligible impact on the antenna design. The present work reports a detailed analysis of antenna concepts and their further optimization in order to mitigate RF potentials; the evaluation of the effect of different plasma loadings is included as well. \\[4pt] [1] D. Milanesio et al., Nucl. Fusion \textbf{49}, 115019 (2009).   

ECCD-induced tearing mode stabilization in coupled IPS/NIMROD/GENRAY HPC simulations

We present developments toward an integrated, predictive model for determining optimal ECCD-based NTM stabilization strategies in ITER. We demonstrate the capability of the SWIM Project's Integrated Plasma Simulator (IPS) framework to choreograph multiple executions of, and data exchanges between, physics codes modeling various spatiotemporal scales of this coupled RF/MHD problem on several thousand HPC processors. As NIMROD evolves fluid equations to model bulk plasma behavior, self-consistent propagation/deposition of RF power in the ensuing plasma profiles is calculated by GENRAY. A third code (QLCALC) then interfaces with computational geometry packages to construct the RF-induced quasilinear diffusion tensor from NIMROD/GENRAY data, and the moments of this tensor (entering as additional terms in NIMROD's fluid equations due to the disparity in RF/MHD spatiotemporal scales) influence the dynamics of current, momentum, and energy evolution. Initial results are shown to correctly capture the physics of magnetic island stabilization [Jenkins {\it et al.}, PoP {\bf 17} 012502 (2010)]; we also discuss the development of a numerical plasma control system for active feedback stabilization of tearing modes. Funded by USDoE SciDAC.   

Scattering of radio frequency waves by edge density blobs and fluctuations in tokamak plasmas

The density blobs and fluctuations present in the edge region of magnetic fusion devices can scatter radio frequency (RF) waves through refraction and diffraction. Using the geometric optics approximation for the waves, a Fokker-Planck equation for the refractive scattering of rays by a random distribution of blobs has been derived [1]. It is found that the scattering can diffuse the rays in space and in wave-vector space. The diffusion in space can make the rays miss their intended target region, while the diffusion in wave-vector space can broaden the wave spectrum and modify the wave damping profile. In ITER-type plasmas, it is found that spatial diffusion is important for electron cyclotron (EC) waves. For LH waves, diffusion in wave vector space is important which leads to a broadening of the current profile. The diffractive scattering of waves can lead to ``shadowing'' effects and coupling of the primary RF wave to surface waves and other plasma waves. Diffractive scattering, as opposed to refractive scattering, requires a full-wave treatment. The effect of diffractive scattering on RF waves will be discussed. \\[4pt] [1] K. Hizanidis, A.K. Ram, Y. Kominis, and C. Tsironis, {\it Phys. Plasmas} {\bf 17}, 022505 (2010).   

Quasilinear kinetic formulation of wave-particle interactions in RF heating and current drive

In fusion plasmas, coherent RF waves are routinely used for heating the plasma and for controlling the current profile. RF waves alter the particle distribution function away from an equilibrium Maxwell-Boltzmann distribution through wave-particle interactions. Meanwhile, collisions try to restore the distribution function to its equilibrium state. In high-temperature plasmas, the modification due to RF waves occurs over time scales much shorter than collisional times. In this long mean-free path limit, particles interacting with RF waves do not undergo Brownian or Markovian diffusion. There persist long time correlations which invalidate Markovian assumption inherent in the usual quasilinear models. We have recently developed a quasilinear theory for particles interacting with coherent RF waves in the long mean-free path limit [1]. The distribution function is evolved concurrently with the particle motion and takes into account the complexity of the dynamical phase space in the presence of RF waves. In stark contrast to the usual quasilinear theories, the wave-particle interaction operator in the evolution equation is time dependent resulting in markedly different results. This will be illustrated by comparing averaged quantities like current and temperature. Supported by DoE, EFDA, and Assoc. EURATOM-Helenic Republic. \\[4pt] [1] Y. Kominis, A.K. Ram and K. Hizanidis, {\it Phys. Rev. Lett.} {\bf 104}, 235001 (2010).   

Ion heating by high frequency RF waves

In ionospheric plasmas, high frequency lower hybrid waves are observed to heat ions through nonlinear wave-particle interactions [1]. Using a similar approach, we consider the nonlinear heating of ions in magnetized fusion plasmas by high frequency waves propagating across the magnetic field. The nonlinear interaction is a result of two waves whose beat frequency is equal to the cyclotron frequency of the ions in the spatial region where the two waves overlap. The energy transfer from the waves to the ions occurs through a second order (in wave amplitude) resonance between the beat frequency and the ion cyclotron frequency. The low energy ions can be coherently accelerated into a dynamically chaotic phase space where the ions can gain substantial energy. The ratio of the group velocity to the phase velocity of the waves plays a crucial role in the energy transfer. The optimal energy transfer occurs when the ratio is near unity. Along with the theoretical nonlinear analysis, we will present numerical results illustrating the heating of ions by quasi-electrostatic and electromagnetic waves. Possible application of ion heating by electron cyclotron waves will be discussed. \\[4pt] [1] A.K. Ram, A. Bers, and D. B\'enisti, {\it J. Geophys. Res.} {\bf 103}, 9431 (1998).   

Enhancement of Fusion Rate by Superthermal Tritium Ions

We propose a new concept of a nuclear fusion reactor. It is based on the enhancement of the DT fusion rate in tokamak plasmas by a superthermal population of Tritium ions heated by ICRH. It was already shown that break-even conditions might be reached [C. Castaldo and A. Cardinali, Phys. Plasmas 17, 072513 (2010)]. Here we show that Q$\approx $20, suitable for nuclear fusion power station, can be achieved in a compact tokamak configuration (major radius R=160cm, minor radius a=55cm, elongation k=1.9, triangularity $\delta $=0.4, q95=3.5), operating with I$_{P}$=8MA plasma current, B$_{T}$=11.3T toroidal field, line averaged plasma density n=5X10$^{20}$m$^{-3}$, and 40{\%} D, 35{\%} H, 25{\%} T concentrations of the Hydrogen isotopes. The burning plasma is obtained by the injection of 15 MW ICRF power, coupled by six antennas, with radiating areas of 0.25m$^2$, at the operating frequency f=125 MHz and toroidal wave number n$_{//}$=4. The heating scenario has been analyzed by the code TORIC, and approximated analytical equilibria are considered. As a result the total fusion power expected for the proposed scenario is about 350MW, with Q$\approx $20, assuming that at least 70{\%} of the fusion power carried by the $\alpha $ particles is absorbed by the electrons in the plasma core so that the expected central plasma temperature is about 10keV.   

EBW Current Drive and Heating for Fusion/Fission Hybrids

From the RF requirements for spherical tokamak and the need to reduce antenna exposure to neutron bombardment, EBW are an important source for both heating and current drive (CD). ICRF, LH, HHFW antennas are subject to significant neutron damage (as are NBI) because of their very large size and necessary proximity to the plasma. Recently Mahajan et. al. have studied other important uses of fusion neutrons - in particular their use in the efficient breeding of fission reactor fuel as well as in the ``rapid'' destruction of nuclear waste using their Compact High Power Density Fast Neutron Source (CFNS). For overdense plasmas the standard electromagnetic O- and X- mode experience cutoffs. EBW can propagate and be absorbed in such plasmas but its characteristics are strongly dependent on the plasma parameters with important variations in the parallel wave number. If the required temperatures in CFNS are around 35 KeV, then one will may need to revisit the electrostatic approximation and incorporate relativistic effects for EBW rays.   

Full torus kinetic simulation of radio frequency wave in fusion plasmas

We are looking into a new kinetic simulation model to study the radio frequency heating and current drive of plasma using gyrokinetic toroidal code GTC. In this model electrons are treated as drift kinetic (DK) particles and ions are considered as fully kinetic (FK) particles. This scheme is particularly suitable for plasma heating and current drive with wave frequencies lower than the electron cyclotron frequency, ranging from fast wave and ion cyclotron wave to lower hybrid wave. This model also can handle physics with realistic electron-to-ion mass ratio and nonlinear dynamics in the full torus simulation.   

Guided radar for arc detection: new results

The GUIded raDAR technonolgy has been recently proposed for the detection and localization of electric arcs in the transmission lines feeding antennas for plasma heating and current drive. The first experiments with real arcs were conducted on the MXP test-bed installed at IPP, Garching: results showed the capability of the GUIDAR system to detect both high voltage and low voltage arcs. For those experiments, the low frequency (25 MHz) GUIDAR signal was up-shifted to around 400MHz, injected in and extracted from the transmission line by mean of two directional couplers and then down-shifted to its original frequency before the elaboration performed on the DSP board. Another possibility is to use a septate coupler in place of the directional couplers, together with an up-shift/down-shift circuit, tuned accordingly to the behavior of the septate coupler, and a circulator for the transmission and extraction of the signal. A new test campaign, based on the described setup, is planned to start in September 2011 on DIII-D in collaboration with ORNL. The results, compared to the ones obtained at IPP, will allow to define which method (directional couplers or septate) is more efficient and to better understand which are the issues related to the localization of the arcs.   

Exploration of the ion-ion hybrid resonator

Fusion plasmas must operate with two dominant ion species: Tritium and Deuterium. In magnetized plasmas with two ion species there exists a unique frequency, the ion-ion hybrid frequency, which has a significant impact on the propagation of Alfven waves. For compressional modes propagating across the magnetic field, the ion-ion hybrid frequency acts as a resonance, which can be used for plasma heating. In contrast, the shear Alfven wave experiences a cutoff at locations where the wave frequency equals the ion-ion hybrid frequency. Due to the periodic variation in the strength of the magnetic field along a field--line in a tokamak, two conjugate ion-ion hybrid points give rise to an inherent shear Alfven wave resonator. Modes trapped within such a resonator could have consequences for plasma heating, proposed alpha channeling schemes, and instabilities. In addition, the modes could have useful diagnostic signatures. Recent experiments in the linear device LAPD at UCLA have demonstrated the existence of such a resonator. Motivated by these results and also by related magnetospheric studies, the properties of a similar resonator in a fusion environment are explored. Theoretical results relevant to the modeling of the resonator in LAPD and in ITER-like plasmas are presented.   

CRH Physics and Burn Control for the IGNITOR Experiment

The ICRH heating in the IGNITOR experiment, among other applications, is expected to stabilize the power of the thermonuclear burning by automatic regulation of the RF coupled power. In the case where internal plasma modes may not be effective in saturating the thermonuclear instability at acceptable levels without external action, a scenario is considered where IGNITOR is led to operate in a slightly sub-critical regime by adding a small fraction of He3 to the nominal 50-50 Deuterium-Tritium mixture. The difference between power lost and alpha heating is compensated by additional ICRH heating, which should be able to increase the global plasma temperature via collisions between He3 minority and the background D-T ions. The non-linear thermal balance equation is analytically and numerically investigated for equilibrium and stability, which includes this kind of external control mechanism. The ICRH system for IGNITOR is designed to operate over a broad frequency range (80-120MHz), which is consistent with the use of magnetic fields in the range 9-13 T. The maximum delivered power ranges from 8MW (at 80MHz) to 6 MW (at 120MHz) distributed over 4 ports, and the analysis of power deposition profile is obtained by using a 2D full wave code (TORIC), which includes a Fokker-Planck solver for distribution function of the heated species.   

Plasma current ramp-up by waves in the lower hybrid frequency range on TST-2

Noninductive plasma current ($I_{\rm p}$) ramp-up by RF power is being studied on TST-2. A tokamak configuration with $I_{\rm p}\simeq 1\rm\,kA$ is formed spontaneously by injecting RF power (2.45\,GHz, 200\,MHz or 21\,MHz). Subsequent $I_{\rm p}$ ramp-up is achieved by gradual increases of RF power and vertical field. As $I_{\rm p}$ is ramped up, the fraction of RF driven current becomes larger, and a clear dependence on wave directionality becomes observable. Up to 12\,kA of $I_{\rm p}$ has been achieved by launching a traveling wave in the co current drive direction. X-ray measurements indicate gradual increases of electron temperature and superthermal electron population. An attempt is being made to obtain information on superthermal electrons from directional Langmuir probe measurements.   

Inline model for energy transfer between crossing laser beams in HYDRA

Energy transfer between laser beams crossing in National Ignition Facility (NIF) hohlraums has an important effect on the symmetry of a capsule implosion. Previous calculations using a linear model\footnote{P. Michel et. al, Phys. Plasmas 17, 056305 (2010).} applied through post-processing HYDRA simulations allowed fast assessment of the effect and provided a useful correspondence to experiments. That technique does not couple the effects of energy transfer between beams, or the associated momentum deposition, back to the plasma in a fully self-consistent manner. We have implemented the model in HYDRA through the 3D laser ray tracing package. We have also implemented empirical models for stimulated Raman scattering and stimulated Brillouin scattering. Together these allow for the energy flow and coupling to the plasma to be handled in a self-consistent manner. The inline models also enable a faster turnaround time to simulate an experiment. To achieve consistency the ray tracing is iterated, recomputing the beam resolved intensity in every cell for each iteration. We examine the importance of self-consistent treatment of energy and momentum deposition for a NIF ignition target.   

Angular distribution of SRS backscatter in NIF ignition experiments

Modeling the SRS backscatter from NIF hohlraums provides a path to a better understanding of the under-dense plasma conditions created within, which have yet to be measured directly. The spatial location of SRS amplification regions influences the amount of refraction that the scattered light undergoes, and thus its angular distribution exiting the hohlraum. Here we describe how we use pF3D [R. L. Berger et al., Phys. Plasmas 5, 4337 (1998); C. H. Still et al., Phys. Plasmas 7, 2023 (2000)], SLIP [P. Michel et al., Phys. Plasmas 17, 056305 (2010)] and a simple ray-tracing application to model the near-field (angular) distribution of SRS backscatter in NIF ignition experiments. We compare these results to the measurements made by the improved time-dependent NBI (Near-Backscatter Imager) and the FABS (Full-Aperture Backscatter) diagnostics [J. D. Moody et al., Rev. Sci. Instrum. 81, 10D921 (2010)].   

Scaling and mitigating stimulated scattering and two plasmon decay in ignition-scale hohlraums

Experiments [1] have now well established that stimulated Raman and Brillouin scattering can occur at significant levels in ignition-scale hohlraums. Calculations [2] further show that the two plasmon decay instability (and related high frequency instabilities near the quarter-critical density) can be a significant source of hot electron preheat. Overlapped beam effects such as cross beam energy transfer [3] play an important role in enhancing these instability levels. Some models for the scaling with laser energy are presented for the stimulated scattering and the laser energy at risk to the two plasmon decay instability. Ways to improve the calculation of cross beam energy transfer so as to avoid the use of ad hoc nonlinear limiters are discussed, as well as some ways to reduce the stimulated scattering. \\[4pt] [1] R. Town \textit{et.al}., Phys. Plasmas \textbf{18}, 056302 (2011) and references therein.\\[0pt] [2] W.L. Kruer \textit{et. al}., Journal of Physics Conference Series 244, 022020 (2010); E. Williams (private communication, 2011)\\[0pt] [3] P. Michel \textit{et. al}., Phys. Plasmas \textbf{17}, 056305 (2010) and references therein   

Linear plasma response, electrostatic fluctuations and Thomson scattering

Our nonlocal and nonstationary transport theory provides a method of solution of the initial value problem for the full set of linearized Fokker-Planck kinetic equations with Landau collision operators. The closure relations reduce the problem of finding particle distribution functions to the solution of the close set of fluid equations. This has been recently realized for the electron-ion plasma in the entire range of plasma collisionality. No particular choice of the initial distribution function is necessary to derive the longitudinal plasma susceptibility from the full set of kinetic equations. We will discuss new complete results for in electron-ion plasmas. The full description of the longitudinal plasma response is used in the derivation of damping and dispersion relations for electrostatic fluctuations such as Langmuir waves, ion-acoustic and entropy modes. Particle collision effects are rigorously accounted for. The Onsager's regression of fluctuations method is applied to derive dynamical form factor S(k,w) and Thomson scattering (TS) cross-section from the set of fluid equations. We will discuss application of the nonlocal hydrodynamics to the derivation of S(k,w). In particular, we will examine the importance of an entropy mode peak as the direct measure of ion temperature in TS experiments.   

Far Superior Control of LPI Is Achieved Using STUD Pulses than RPP, SSD, ISI or Pseudo-STUD Pulses

In a series of simulations using a modified and improved version of the code Harmony, we have compared the Brillouin backscattering reflectivity and ion acoustic wave generation in a STUD pulse\footnote{Afeyan, B., http://meetings.aps.org/link/BAPS.2009.DPP.TO5.7} (Spike Trains of Uneven Duration and Delay), vs more primitive beam smoothing techniques. The less effective techniques considered are RPP, SSD with realistic and exceedingly high bandwidths, ISI and pseudo-STUD pulses. In the latter, there is rapid temporal variation of the laser profile but always for the same RPP pattern in space. In STUD pulses, each laser spike samples a different RPP pattern. Orders of magnitude reduction in IAW generation and nonlinear reflection is observed in the case of STUD pulses compared to all other competitors. The effects of strong coupling, pump depletion and flow gradients are included.   

PIC Simulations of Stimulated Raman Scattering for NIF Scale Lengths and Density Profiles

Stimulated Raman scattering (SRS) is a threat to the successful operation of the National Ignition Facility (NIF). Particle-in-cell (PIC) simulations for NIF-relevant plasma conditions have shown SRS to be bursty in space and time, with localized plasma wave packets and bursts of light on the sub- picosecond time scale. However, these simulations have only simulated speckle- size plasmas. Here we present 1D and 2D PIC simulation results for plasmas 1.5 mm in length, $T_e$ = 2.5-3.0 keV, $I_{laser} = 4-8 \times 10^{14}$ W/cm$^2$, and NIF-relevant density profiles over $n_e/n_{cr}$ = 0.09-0.15. Most SRS bursts are again spatially localized within 200 microns and generate sub-picosecond bursts of light whose periodicity is as shown in our previous work. For linear density profiles with scale lengths $\sim$ 3 mm, SRS initially grows at densities of $n_e/n_{cr} \approx$ 0.13-0.14, corresponding to $k\lambda_D \sim 0.30$, while for other density profiles, SRS grows at densities below $n_e/n_{cr}$ = 0.11 if the slope in density is sufficiently shallow. The location of SRS growth changes very little as laser intensity increases, although additional bursts start occurring at lower densities. Rescatter is also observed under some conditions. We discuss the range of scattered light wavelengths, the reflectivity levels, and the electron spectra. *Supported under Grants DE-FG52-09NA29552 and NSF-Phy-0904039; simulations were performed on the UCLA Hoffman2 Cluster.   

Characterization of Electron Temperature and Density Profiles of Plasmas Produced by Nike KrF Laser for Laser Plasma Instability (LPI) Research

Previous experiments\footnote{J. Oh, et al, GO5.4, APS DPP (2010)} with Nike KrF laser ($\lambda=248nm$, $\Delta \nu \sim 1$THz) observed LPI signatures near quarter critical density ($n_c/4$) in CH plasmas, however, detailed measurement of the temperature ($T_e$) and density ($n_e$) profiles was missing. The current Nike LPI campaign will perform experimental determination of the plasma profiles. A side-on grid imaging refractometer (GIR)\footnote{R. S. Craxton, et al, Phys. Fluids B 5, 4419 (1993)} is the main diagnostic to resolve $T_e$ and $n_e$ in space taking 2D snapshots of probe laser ($\lambda=266 nm$, $\Delta t=8psec$) beamlets ($50\mu m$ spacing) refracted by the plasma at laser peak time. Ray tracing of the beamlets through hydrodynamically simulated (FASTRAD3D) plasma profiles estimates the refractometer may access densities up to $\sim$$0.2n_c$. With the measured $T_e$ and $n_e$ profiles in the plasma corona, we will discuss analysis of light data radiated from the plasmas in spectral ranges relevant to two plasmon decay and convective Raman instabilities. Validity of the ($T_e, n_e$) data will also be discussed for the thermal transport study.   

Bandwidth Dependence of Laser Plasma Instabilities Driven by the Nike KrF Laser

The Nike krypton-fluoride (KrF) laser at the Naval Research Laboratory operates in the deep UV (248 nm) and employs beam smoothing by induced spatial incoherence (ISI). In the first ISI studies at longer wavelengths (1054 nm and 527 nm) [Obenschain, PRL \textbf{62}, 768(1989);Mostovych, PRL, \textbf{59}, 1193(1987);Peyser, Phys. Fluids B \textbf{3}, 1479(1991)], stimulated Raman scattering, stimulated Brillouin scattering, and the two plasmon decay instability were reduced when wide bandwidth ISI ($\delta \nu $/$\nu \sim $0.03-0.19{\%}) pulses irradiated targets at moderate to high intensities (10$^{14}$-10$^{15 }$W/cm$^{2})$. Recent Nike work showed that the threshold for quarter critical instabilities increased with the expected wavelength scaling, without accounting for the large bandwidth ($\delta \nu \sim $1-3 THz). New experiments will compare laser plasma instabilities (LPI) driven by narrower bandwidth pulses to those observed with the standard operation. The bandwidth of KrF lasers can be reduced by adding narrow filters (etalons or gratings) in the initial stages of the laser. This talk will discuss the method used to narrow the output spectrum of Nike, the laser performance for this new operating mode, and target observations of LPI in planar CH targets.   

Predictions and Observations of Two-Plasmon Decay on the NIKE Laser System

NIKE is a Krf laser system at the Naval Research Laboratory used to explore hydrodynamic stability, equation of state, and other physics problems arising in IFE research. The short wavelength and large bandwidth of the NIKE laser is predicted to raise the threshold of parametric instabilities such as two-plasmon decay (TPD). We report on simulations performed using the FAST3d radiation hydrocode to design TPD experiments that have allowed us to explore the validity of simple threshold formulas and demonstrate the advantages of the KrF wavelength in suppressing LPI. We consider proposed high-gain shock ignition designs and show, through analytic estimates and simulations, that we can explore the relevant scalelength-temperature regime, providing an experimental method to study the LPI threat to these targets at a small fraction of their designed input energies.   

Focusing of Intense Subpicosecond Laser Pulses in Wedge Targets

Two dimensional particle-in-cell simulations characterizing the focusing of ultraintense lasers in the range $10^{18} \le I \le 10^{20}W/cm^2$ in idealized wedge targets over $\sim2$ picoseconds are presented. We describe key dynamical features and trends as laser intensity and cone angle are systematically varied, such as optimal order-of-magnitude laser focusing in the narrow 17 target at early times. Also observed in this geometry is a clear trend where the region of peak laser intensity regresses away from the target tip at intensity-dependent rates that saturate at $d z_{peak}/dt\approx 17 \ \mu m/ps$. Particle heating in the narrow and intermediate width targets is characterized by the presence of a dominant hot electron filament aligned with the target tip, while the wide 45 target exhibits two equally dominant filaments off to the sides of the tip with electron acceleration through the tip effectively suppressed.   

Water bag model for kinetic Raman scattering in a nonuniform plasma

Resonant wave interactions play a major role in plasmas and other nonlinear media. Resonantly driven waves may exhibit autoresonance, i.e. a continuous nonlinear phase-locking despite variation of system parameters [1]. Recently, we have presented a kinetic autoresonant plasma wave paradigm, where a driven BGK mode was excited in a uniform plasma by slow variation of the driving wave frequency [2]. Similarly, autoresonant BGK modes can be excited in nonuniform plasmas, driven by a constant frequency wave resulting from beating between two laser beams. We will suggest a water-bag model of a nonuniform plasma and formulate a Lagrangian theory of autoresonant three-wave interactions involving two laser waves and a BGK mode. The evolution of such a driven BGK mode will be illustrated in Liouville-type numerical simulations.\\[4pt] [1] L. Friedland, Scholarpedia 4, 5473 (2009).\\[0pt] [2] P. Khain and L. Friedland, Phys. Plasmas 17, 102308 (2010).   

Comparison of Thomas-Fermi and Impact Ionization models for ultra intense laser-mater interactions

Having a good model of ionization is important to study the hot electron transport in ultra-intense laser-solid interactions. One of the commonly applied models to calculate ionization in a plasma is the Thomas- Fermi (TF) model. This model is derived from equations of state which in turn assumes the plasma is in an equilibrium state. However, for the timescales of interest for the study of laser-matter interactions, laser created plasmas are highly transients and thus are not in an equilibrium state. The predicted ionization levels by the TF model are based on incorrect assumptions about the plasma conditions. In an effort to improve the accuracy of predicted ionization levels, an impact ionization model is applied to particle-in-cell simulations. This model calculates ionization levels from electron-ion collisional cross-sections and should be better suited to predict ionization levels for non-equilibrium plasmas. A comparison between the TF and Impact model is made for different plasma parameters. Preliminary results indicate the discrepancies between the models to increase as the atomic number (Z) of the target increases. Additionally, the laser intensity is varied to explore how each models reacts in different hot electron energy regimes.   

Mechanism of pre-formed plasma electrons heating in relativistic laser-solid interactions

Recent experiments have shown that fast electron generation is significantly modified due to long pre-formed plasma in front of a target. In particular, electrons with significantly greater than laser ponderomotive energy are observed in presence of pre-formed plasma. In our recent work [1], we have demonstrated the influence of large electrostatic potential well, produced self consistently inside pre-formed plasma on electron heating. The synergetic effects of potential well and laser radiation are found to be responsible for the generation of high energy tail of the electron energy distribution. In present work, we have studied in detail this heating mechanism by analyzing, both analytically and numerically, the stochastic motion of an electron in presence of electrostatic field and laser radiation. Results of electron dynamics and stochastic heating in presence of such fields will be presented in this paper. \\[4pt] [1] B. S. Paradkar \textit{et al.}, Phys. Rev. E \textbf{83} 046401(2011)   

Effects of radiation damping in extreme ultra-intense laser-plasma interaction

Effects of the radiation damping in the interaction of extremely intense laser ($>$ $10^{22}$ W/cm$^2$) with overdense plasma are studied via a relativistic collisional particle-in-cell simulation, PICLS1D. We had derived the Landau-Lifshitz equation, which is the first order term of the Lorentz-Dirac equation, and also derived the second order term as the first time and implemented in the code. The code had been tested in a single particle motion at the extreme intensity laser. It was found that the first order damping term is reasonable up to the intensity $10^{22}$ W/cm$^2$, but the second oder term becomes not negligible and comparable to the first order term beyond $10^{23}$ W/cm$^2$. The radiation damping model was introduced to a one- dimensional particle-in-cell code (PIC), and tested in the laser - plasma interaction at extreme intensity. The strong damping of hot electrons in high energy tail was demonstrated in PIC simulations. Hot electrons generated by such extreme-intense laser lights on the plasma get the relativistic energy with gamma factor $>$ 100, and lose energy strongly by emitting radiation. The second order term becomes comparable to the first order term when the laser intensity $>$ $10^{23}$ W/cm$^2$.   

Neutron production from ultrashort pulse lasers in linear and circular polarization

Neutron production driven by ultrashort pulse lasers using linear and circular polarization has been investigated. Three representative reactions, $d-d$, $d-$\textit{Li} and$ p-$\textit{Li} have been selected, for which the neutron yield has been calculated and compared. The properties of the proton and deuteron beams (conversion efficiency, maximum energy and energy distribution) have been analyzed and the neutron yield calculated as a function of foil thickness. The advantages and disadvantages of using protons and deuterons have been analyzed. A direct comparison of the neutron yield for linear and circular polarization revealed that the laser polarization strongly affects the neutron production. Liner polarization is more favorable for neutron production, but for ultrathin foils (20 nm) in the Radiation Pressure Acceleration regime circular polarization yields results that are comparable to that in linear polarization.   

Fusion plasmas produced by femtosecond laser irradiation of clusters in a megagauss magnetic field

Interactions of intense femtosecond lasers with atomic clusters can create plasmas with high density (10$^{19}$ cm$^{-3})$ and high average ion energies (10 keV) and significant numbers (10$^{7})$ of DD fusion neutrons can be produced. We have built and are testing a 2 MA driver to create a 200 T field that can be used on the Texas Petawatt laser to create a magnetized hot, dense deuterium plasma with a high neutron yield. A cooled gas jet will be used to produce deuterium clusters with radius $\sim $ 10 nm. The magnetic field is produced by a 10 capacitor (100 kV) low inductance bank that discharges through a 1 cm diameter coil in vacuum. First experiments will be done on the 2 J, 120 fs GHOST laser; later experiments are scheduled on the 180 J, 160 fs Texas Petawatt. Details and status of components will be presented.   

Channeling of relativistic laser pulses in underdense plasmas and electron acceleration

We present results of 3D PIC simulations and the corresponding theoretical analysis of relativistic self-focusing, laser pulse channeling, surface wave generation and electron acceleration. For laser pulse powers above the threshold for channeling, we have observed the stability of the laser pulse propagation as a single mode in an electron free channel. These results apply to sub-picosecond laser pulses, and a very good agreement has been observed between the stationary analytical theory predictions and our PIC simulations. The sharp front of the laser pulse excites surface wakes in the channels. These surface waves play a fundamental role in electron acceleration. The nonlinear longitudinal fields of the surface waves first trap and accelerate the electrons located on the channel walls. These fast particles can be further accelerated by the laser field through a betatron-like mechanism involving the transverse fields of the surface wave. This two- stage process is necessary to explain the large number of high energy electrons observed in the simulations. This acceleration mechanism ultimately results in the channel destruction.   

Low frequency electromagnetic emission from an interaction between carbon nanotubes and two frequency lasers

Single-walled carbon nanotube is one of exotic material as a target for laser-plasma interaction. Carbon nanotubes are vertically grown on a substrate and they look like nano-scale woods. One of our previous simulation results shows that a nano scale cylindrical cluster largely absorbs laser energy when the laser intensity exceeds a certain critical value. This is because the strongly heated electrons coherently oscillate in a deep electrostatic potential formed by expanded fast electrons and rest ions. Since this electrostatic potential is symmetric due to the symmetry of a cylinder, the single mode laser irradiation only excites odd harmonics. When we intend to excite even harmonics or subharmonics, an another frequency laser must be simultaneously irradiated to the target in addition to the original laser. We will show 0 frequency mode excitation caused by nonlinear coupling between two frequency lasers, $\omega$ and $2\omega$, using our collisional-ionization PIC code. Enhancement of the low frequency radiation from periodically aligned carbon nanotubes will also be discussed.\\[4pt] [1] T. Taguchi, et al. Optics Express 18, 3, (2010), 2380.   

Radiation cooling dominated regimes in the interaction of ultra intense lasers with electron beams and on ion acceleration

Under extreme acceleration, charged particles can radiate strongly and the corresponding radiation damping can become important. Using a single particle dynamics code and Osiris 2.0 framework, we have identified different qualitative regimes for electron interaction with counter- and co- propagating ultra-intense laser fields. For conditions where the radiation cooling is important, qualitative differences arise as compared with the scenarios where radiation cooling is absent; this is reflected not only in the particle phase space trajectories, but also on the net velocity imparted to the counter-propagating electrons and the possibility of cooling particle beams. Possibilities to explore signatures for radiation cooling in future experiments (e.g. ELI) will be discussed. We have also explored how the radiation cooling affects the ion energy spectrum for laser-induced ion acceleration. In 1D simulations, we observe that the radiation cooling has stronger impact, the proton spectrum is narrower and has a slightly lower mean energy, while in 2D runs with a finite laser spot-size, the difference in the proton spectrum is not as strong.   

Absorption of High Intensity Lasers at Solid Density

Understanding the interaction of very intense lasers ($I \ge 5 \times 10^{19} W/cm^2$) with dense plasmas is critical to the fast ignition (FI) approach to confined fusion, as well as other processes such as radiation pressure acceleration (RPA). To investigate this regime we use the particle-in-cell (PIC) code OSIRIS, looking at such lasers interacting directly with solid density targets ($n \gg n_c$). We find that electrons are accelerated in a way distinct from the commonly proposed absorption mechanisms, i.e. Brunel or JxB. Specifically, we see a standing wave structure being setup at the target surface, and electrons accelerated directly by the transverse electric field of this wave in the vacuum region. Furthermore the magnetic field of this structure reflects all electrons except those with sufficient transverse momentum in phase with this wave, meaning that absorption is very low until the target surface heats to keV temperatures, and also for circular laser polarization. Particle tracking in OSIRIS and a test particle simulation confirm that this model explains well the acceleration we see in simulations.   

Generation of energetic electrons in preplasma via parametric instability

Underdense preplasma is a common feature in experiments with laser-irradiated solid-density targets. The preplasma created by the prepulse can extend many wavelengths along the direction of laser beam propagation. Hot electrons produced in the target are essential for fast proton production. We find that there is a density threshold for electron heating in the preplasma. This is determined by the onset of parametric instability for ultra- relativistic electrons moving within the laser beam. Such electrons are confined in the transverse direction by the ion electric field. Their oscillations in this field become parametrically unstable because the electron $\gamma$-factor that determines the oscillation frequency changes itself at double the laser frequency. The effect is illustrated in a 2D setup for an s-polarized Gaussian laser beam. In this case the instability develops in the plane perpendicular to the laser electric field.   

High Order harmonic generation from laser pulses interacting with solid density plasma at intensities in excess of 10$^{21}$ W/cm$^2$

Using the HERCULES laser system operating at powers greater than 150 TW, experiments were performed at the Center for Ultrafast Optical Science at the University of Michigan to examine the generation of high order harmonics at very high intensity from interactions with solid density plasmas. Harmonics greater than the 60$^{th}$ order were measured and the effect of incident laser polarization was investigated. The angular divergence of the emitted harmonics was also measured and it was found that the harmonic frequencies shifted depending on the observation angle. It is possible that such shifts may be caused by the motion of the critical surface during the interaction. Particle in Cell simulations were performed to model these experiments and will also be discussed.   

Enhanced Bremsstrahlung Emission in Intense Laser-Cluster Interactions

What dynamics ensues when a sub-picosecond, 248 nm, pulse of laser light interacts with a xenon cluster of 10-10$^{4}$ atoms at intensities $>$10$^{19}$ W/cm$^{2}$? Measurements in such experiments are difficult to make. However, in them [1], two features stood out. One, a 2 mm long, 1-3 $\mu $m diameter channel of self-focused laser light was formed, and two, amplification of $\approx $2.8 {\AA} x-radiation along the channel was observed. A model that would generate the population inversions needed to produce the observed amplifications was recently constructed [2]. It assumed that inner-shell n=2 holes were being generated through inner-shell photoionizations that came about through bremsstrahlung emissions that were being greatly enhanced in the presence of intense laser fields ($>$10$^{19}$ W/cm$^{2})$. In this talk, we present results from quantum electrodynamics calculations [3] that support the production of such enhancements.\\[4pt] [1] Borisov A. B., \textit{et. al.}, J. Phys. B, \textbf{41},105602 (2008). [2] Petrova Tz. B., \textit{et. al.}, J. Phys. B, \textbf{43}, 025601 (2010); \textbf{44}, 125601 (2011). [3] Lebed A. A. and Roshchupkin S. P., Phys. Rev. A, \textbf{81}, 033413 (2010).   

X-Ray Driven Planar Target

Lasing at $\sim $ 4.45 keV has been observed in a series of experiments\footnote{Borisov A. B. \textit{et. al.}, J. Phys B, \textbf{41}, 105602, (2008).} in which an intense ultrashort KrF laser pulse was incident on a collection of small Xe clusters. Extensive modeling and simulation corroborate these findings.\footnote{Petrova Tz., \textit{et. al.}, J. Phys B, \textbf{43}, 025602, (2010); \textbf{44}, 125601 (2011).} In this talk we investigate the interaction of an intense 4.45 keV x-ray pulse with a gold target. A robust non-LTE model is assembled to investigate the ionization physics and population dynamics of the gold target. We will focus on the absorption physics of the incident coherent x-ray pulse interacting with the gold target in order to evaluate the ionization states and excited state populations reached during the interaction. Both the early time and the late time phenomenology will be studied to determine the radiation characteristics and behavior of the x-ray emission from the gold target.   

Emission Spectra of Low-Z Atoms for Lasing Without Inversion in Helium-Like Atoms

Emission lines relevant to lasing without inversion (LWI) studies were observed. LWI in low-Z helium-like atoms presents a technique for achieving gain in the vacuum ultraviolet (VUV) and soft X-ray regimes. For helium-like atoms, the 2$^{3}$S -- 2$^{3}$P transition is used as the pumping transition, and the 2$^{3}$P -- 1$^{1}$S is used as the lasing transition. In helium-like boron (B IV) and carbon (C V), the pumping transition wavelengths are 282.2 and 227.8 nm, respectively, and the lasing transition wavelengths are 6.1 nm and 4.1 nm, respectively. Laser ablated boron and carbon plasmas were created, and their emission spectra were studied in the visible and VUV regimes. In the visible regime, emission spectra show the presence of helium-like boron through the 2$^{nd}$ order of the 282.2nm, 2$^{3}$S -- 2$^{3}$P transition line (at 564.4 nm). Emission spectra in the VUV and soft X-ray regimes will be presented and discussed. Future experiments include measurements of experimental properties of these plasmas for the purpose of LWI in the VUV and soft X-ray regimes.   

Geometrical Constraints on Plasma Couplers for Raman Compression

One of the key issues in achieving the next generation of laser intensities through resonant Raman compression in plasma is the plasma geometry. Since the plasma mediates a resonant interaction of counterpropagating lasers, only the plasma density at resonance achieves the compression effect. On the other hand, the lasers must pass through tenuous plasma as well, which, if extensive, can produce deleterious effects. Here we consider compression in a plasma slab, composed of a homogeneous middle section and two symmetrically placed inhomogeneous end sections, such that the electron density in each end section decreases to zero. We show that at high plasma densities and high pump intensity (close to the wave-breaking threshold) the gain of the seed pulse is limited by its dispersion. However, chirping both the seed and the pump pulse enables compression with a self-contracting seed, at least partially overcoming the dispersion effect.   

Backward Raman amplification of laser pulses in mildly undercritical plasmas

Next generations of ultrapowerful laser pulses of exawatt and zetawatt powers are feasible now within reasonably compact facilities using the backward Raman amplification (BRA) in plasmas. The output powers hundreds times higher than the input were already observed experimentally in gas-jets plasmas. For higher power BRA, plasmas of larger cross-section and better homogeneity are needed. Such plasmas could be produced by ionization of low-density solids. However, even the lowest density solids, having densities 1-3 mg/cc, are still dense enough for the most energetic laser pulses, like NIF laser pulses having 0.351 micron wavelength, so that the seed pulse frequency cannot much exceed plasma frequency (unless significant expansion of plasmas is allowed which would make resonant BRA more challenging). In such mildly undercritical plasmas, BRA might differ from that in strongly undercritical plasmas, in particular, due to the stronger dispersion of the group velocity of laser pulses and due to the greater sensitivity of laser pulses to plasma inhomogeneities. This work examines these effects and determines the optimal duration and focal distance of the input seed laser pulse which allow to achieve the maximal output fluence and intensity. Supported through the NNSA SSAA Program through DOE Research Grant No. DE274-FG52-08NA28553.   

Saturation of stimulated Raman scattering in short-pulse laser amplification

Recent theoretical and experimental work has focused on using stimulated Raman scattering (SRS) in plasmas as a means of laser pulse amplification and compression [1] as an alternative to the CPA technique. Initial experiments have demonstrated the amplification and compression of laser pulses in plasma to an unfocused intensity of $\sim $10$^{16}$ W/cm$^{2 }$[2]. However, the amplification saturated and was accompanied by deleterious spatial and temporal incoherence, and the reasons for this incoherence are not well understood. In this presentation, we will show results from recent particle-in-cell simulations using the LSP code and discuss several factors leading to the gain saturation and the importance of electron trapping. An understanding of the saturation process can lead to models for use in 3-wave calculations and subsequent experimental designs that avoid competing instabilities. We will discuss these results in the context of plasma channels with electron temperatures of $\sim $0.75 eV, electron densities of $\sim $10$^{19}$ cm$^{-3}$, and channel lengths $>$ 1 mm. [1] G. Shvets, N. J. Fisch, A. Pukhov, and J. Meyer-ter-Vehn, \textit{Phys. Rev. Lett.} \textbf{81} 4879 (1998). [2] J. Ren, W.-F. Cheng, S.-L Li, and S. Suckewer, \textit{Nat. Phys.} \textbf{3} 732 (2007).   

Status of Directly-Driven Shock Ignition Target Designs

We report on the status of directly driven shock ignition targets designed for mega-joule scale laser drivers. We have examined the impacts of laser-plasma-instability (LPI) induced intensity limitations and hydrodynamic instability on the gain and robustness of these targets. Increasing the target's initial aspect ratio will limit the drive intensity prior to the ignitor pulse, but this can have a detrimental impact on the target hydrodynamic stability. Target robustness can be increased by strengthening the shock wave launched by the ignitor pulse. This igniting shock pressure will in turn depend upon the inevitable and as yet unpredictable laser-plasma instabilities generated during the high intensities ($I > 10^{16} W/cm^2$) required to generate the ignitor shock. We present simulation results of target performance in 1D and 2D that demonstrate the importance of the tradeoffs between LPI risk during compression and robustness due to hydrodynamic instability.   

Shock ignition electron transport simulations with the hybrid particle in cell code OSIRIS

In order evaluate and optimize shock ignition target designs, hot electron generation and transport must be well understood and incorporated into simulation codes. The temperature of electrons generated at the shock will determine whether non-local electron transport is important in shock ignition. Non-local transport can affect the stability and symmetry of the target. This is particularly important in assessing the feasibility of polar drive for shock ignition designs. To investigate electron transport in the context of the interaction of intense short-pulse lasers with plasmas, the density of which can range from less than critical to more than solid, we use hybrid-PIC version of OSIRIS. The PIC code accurately simulates the laser plasma interaction while the fluid model is used to model electron transport at high density. These simulations are performed in one and two dimensions.   

Hot Electrons in Shock Ignition

With Shock Ignition [1] a series semi-adiabatic pulses compress pellet fuel to high densities but relatively low temperatures, while an intense final $\sim $0.1 ns scale $\sim $5 x 10$^{15}$ W/cm$^{2}$ pulse is subsequently used to heat the fuel to burn conditions. Hot, 35-50 keV electrons can be generated by this final spike. We will discuss the coupling of such hot electrons to the fuel with the ePLAS implicit/hybrid simulation code. This model calculates self-consistent \textit{E{\&}B-}Fields by the Implicit Moment Method [2], and drags and scatters the hot electrons against the background plasma at Spitzer rates. It tracks laser light to the critical density where it launches hot electrons at a prescribed temperature. We will discuss the hot electron transport in the compressed fuel, and possible shock generation and fuel heating as a function of the hot electron emission conditions.\\[4pt] [1] R. Betti et al., PRL \textbf{98,} 155001 (2007)\\[0pt] [2] R. J. Mason, J. Comp. Phys. \textbf{71,} 429 (1987).   

Polar Direct Drive Shock Ignition Design on LMJ

A low aspect ratio target family is designed in order to demonstrate the potential of ignition conditions of hydrogen isotopes on the LMJ by Shock Ignition without major modification of the facility i.e. for low laser induced damage on optics in the range of laser energy of 400-600 kJ. The shock ignition scheme is divided in two steps: first the compression of the fuel at low velocities and secondly the launch of strong shock allows to ignite the central hot spot. The presented work reports on the use of LMJ indirect drive laser hardware to compress the fuel at low implosion velocity in using a possible polar direct drive irradiation of the target. The ignition condition are produced from the launch of a bipolar strong converging shock by dedicated LMJ beams. A 1D robustness study is also performed with CHIC code for different target sizes and spike power and timing. The figure of merit is the bandwidth of the shock ignition window. We present a solution for a LMJ PDD laser illumination for the target compression and for the spike. We show first 2D CHIC simulations using this new PDD configuration. This strategy for implementation of PDD shock ignition on LMJ participate of a first proof of principle of shock ignition scheme in the frame of HiPER future reactor design.   

Interpretation of planar shock ignition experiments at LULI

The capacity to launch a strong shock wave in a compressed target in presence of large pre-plasma has been investigated in a planar geometry, at 2$\omega $. Experiments were performed at the LULI facility. The target is a three-material target: CH on the laser side, Titanium and Quartz on the opposite side. Two beams are involved. A low-intensity beam launches a first shock and compresses the target. Then, an intensity spike launches a strong chock in the pre-shocked plasma. Shock chronometry and velocity in quartz are measured with a VISAR on the rear side of the target. Three events are observed in both experiments and calculations. We observed a good agreement on chronometry which, nevertheless, departs with time.   

Proton Beam Fast Ignition Fusion: Nonlinear Generation of B$_{\theta}$-Fields by Knock-on Electrons

The knock-on electrons, generated by the fast proton beam\footnote{M. Roth et al, Phys. Rev. Lett. 86, 436 (2001); M. Tabak et al, Phys. Plasmas 1 (5), 1626 (1994); H. L. Buchanan, F. W. Chambers, E. P. Lee, S. S. Yu, R. J. Briggs, and M. N. Rosenbluth, LLNL , UCRL Report 82586, 1979.} in interaction with the free and bound electrons in a precompressed DT fusion pellet, outrun the proton beam, generating the B$_{\theta}$-fields ahead of the beam, which may lead to the defocusing of the beam, if B$_{\theta } \quad <$ 0. The B$_{\theta }$-fields are generated due to the magnetic instability, $\partial $\textbf{B}$_{\theta }$/$\partial $t $\sim $ (c/$\sigma )$\textbf{$\nabla $} x \textbf{j}$_{ne}$, where j$_{ne}$ is the knock-on electron current density,$\sigma$ is the background plasma conductivity, and c the speed of light. \footnote{ V. Alexander Stefan, \textit{Laser Thermonuclear Fusion}: Res. Review, (1984-2008), on Generation of Suprathermal Particles, Laser Radiation Harmonics, and Quasistationary B-Fields. (Stefan University Graduate Courses: ISSN:1543-558X), (S-U-Press, 2008).} The instability growth rate compensates for relatively low knock-on generation efficiency by a proton beam. The saturation level,(electron trapping mechanism), of the B-field ahead of the beam, is of the order of 10 MG and is reached on the time scale of 10ps.   

Energetic proton emission from cone-wire targets interacting with short pulse high intensity laser

Cone-guided Fast Ignition (FI) relies on successful coupling of laser energy to the dense compressed core through relativistic fast electrons produced at the cone tip. These electrons are extracted for study using Cu wires attached to the cone tip; time integrated fluorescence gives electron temperature and number. However, it does not give detailed dynamics of fast electrons. A recent experiment, carried out at the OMEGA-EP laser shows generation of 18 MeV protons from the Cu wire in radial direction, which facilitate useful information about electron dynamics. The physics of fast electron dynamics, radial field generation and subsequent acceleration of protons has been modeled using hybrid/PIC code LSP. Experimental results along with numerical simulations will be discussed at the meeting.   

Hot Electron Generation from Laser-Cone Target Interactions in Fast Ignition

We present recent 2D PIC simulations for the cone-in-shell integrated fast ignition experiments on the Omega laser facility [W. Theobald et al., Phys. Plasmas, May 2011]. The initial plasma density profile in the PIC simulations is taken from hydrodynamic simulations, including the pre-plasma inside the gold cone generated by the prepulse. The main pulse of Omega-EP has a peak intensity of 10$^{19}$W/cm$^2$, duration of 10 ps and total energy of 1 kJ. Hot electron generation from laser-pre-plasma interactions and electron transport in under-100nc plasmas are studied. An artificial drag is applied to hot electrons above 30kev in the $>$100 nc region to facilitate the establishment of an return current and allow the simulations to run close to 10ps. The simulation results show a large average divergence angle of 57 degree and high absorption rate of $\sim $50{\%} for the hot electrons generated.   

Coupling Fast Electrons to Compressed Fuel for Fast Ignition

We discuss three schemes that can improve the coupling of short pulse laser generated hot electrons to the fuel. First, we extend the ideas of A. Robinson, et.al., where azimuthal B fields are grown where there are gradients in resistivity. We utilize higher-Z materials where the material temperature can be kept low and resistivity gradients high by a combination of ionization energy costs and radiative losses. The resulting 100 MG fields are sufficient to trap relativistic electrons in cones or pipes. Second, we compress a B$_{z}$ as part of the capsule implosion. We discuss the constraints that avoiding magnetic field mirroring places on the magnetic field gradients and the hydrodynamic system required to assemble the fuel and field. Third, we investigate short pulse laser driven shock ignition. Here, the compressed fuel stagnates against and deforms a high-Z cone tip. The cone tip is sufficiently thick that the shock does not break out the back side and short-pulse laser produced electrons are trapped within it. This high-Z material is then driven with the short pulse laser. The cone tip then sends a strong convergent shock into the fuel, igniting it.   

Characterization of The Laser-Induced Fast Electron Scattering

Imaging the electron-stimulated K$_{\alpha }$ fluorescence is a canonical way to measure the divergence of fast electrons.\footnote{R. B. Stephens \textit{et al.}, Phys. Rev. E 69, 066414} However, the scattering effect often enlarges the measured X-ray spot diameter. We are attempting to determine the role of fast electron scattering in X-ray imaging by performing the Monte-Carlo (MCNP) simulations. An injection source based on the prescription of Debayle et al.\footnote{A. Debayle \textit{et al.}, Phys. Rev. E 82, 036405} is employed to launch the electrons into the target. The subsequent density of both X-ray production and electron energy deposition versus transverse distance is calculated at various depths. The electron spatial distribution can show substantial differences with and without scattering, leading us to infer that other analyses that do not include fast electron scattering could be misleading. The amount of angular divergence induced by scattering of electrons from different sources is estimated according to MCNP results.   

Ion Beams from Short Pulse Laser Irradiation for Fast Ignition

The ePLAS implicit/hybrid code is being used to model fast ion generation for ignition in targets irradiated by short pulse lasers. The code calculates \textit{E{\&}B-}Fields by the implicit moment method\footnote{R. J. Mason, JCP \textbf{71,} 429 (1987) and R. J. Mason, PRL \textbf{96,} 035001 (2006).} and couples electrons to ions at corrected Spitzer rates with variable Z from the Sesame Tables. The moderate to low Z ions are modeled as either PIC particles or a fluid. Typical laser illumination is from 5 x 10$^{19}$ to 3 x 10$^{20}$W/cm$^{2}$ in 1-10 Picosecond pulses, 7 -- 40 $\mu $m in diameter. We will discuss results for a variety of illumination schemes and tuning options to focus and collect the ions, including the use of multiple shells and beams.   

Study of dependence of fast electron transport on target material using the 10ps, 1.5kJ Omega EP laser

Igniting a Fast Ignition (FI) target requires generation of hot electrons inside a cone tip that travel to the compressed fuel through the tip. Its material must withstand the shell implosion. The effect of different materials on electron transport was previously studied at the Titan laser (150J 0.7ps); emission from a buried fluor characterized the laser-generated electrons transmission through Al, Mo, or Au [1]. Recent experiments using the OMEGA EP (300J, 1ps) showed similar effects on transport---going from Al to Au halved the detected electrons and decreased their divergence. We have extended these experiments to 10ps, 1.5kJ pulses to study pulse length effects. Experiments are modeled using both collisional and hybrid PIC codes. Detailed results will be presented. \\[4pt] [1] S. Chawla et al., ``Z-effects on Fast Electron Transport in Fast Ignition ICF,'' this conference.   

A reactor-scale point design of cone-guided implosion for Fast Ignition

The formation of high-areal-density core plasma in cone-guided non-spherical implosion is required for Fast Ignition. Although many experiments have been conducted successfully at ILE and LLE using existing lasers facilities, difficulties are inherent in designing larger scale size implosion for reactors, where energy of implosion lasers will be about a MJ. One of the significant problems is high pressure at hot-spot region, if implosion is scaled up simply in similarity rule. This high pressure leads fatal break at the tip of the cone which should be located near the center of the implosion. In this work, optimization of low isentrope and high areal density implosion [1] is attempted using 2-D radiation hydrodynamic code.\\[4pt] [1] R. Betti et al. Phys. Plasmas, 12, 110702 (2005)\\[0pt] [2] H. Nagatomo, et. al, Phys. Plasmas, 14 056303 (2007).   

A Study of Electron Divergence in Fast Ignition using the Hybrid-PIC Simulation Code OSIRIS

Understanding and Controlling Electron Divergence is Critical for the success of Fast Ignition. We show recent results of 2D PIC with OSIRIS modeling of electron divergence relevant to fast ignition. As a baseline we use slab targets with periodic transverse boundary conditions. These conditions have been used to study electron divergence in fast ignition. We compare divergence in large-scale isolated fast ignition targets to the divergence observed in slab targets. A promising method of controlling electron divergence is to induce a resistivity gradient in the target so collimating magnetic fields are induced by the return current. We will present preliminary studies of the effect of resistivity gradients on electron divergence.   

Effects of dual lasers on hot electron source in fast ignition

Sufficient energy coupling between ignition laser and implosion core is critical for the feasibility of the fast ignition fusion scheme. The laser energy is deposited at the critical density, producing hot electrons which must traverse the gap to the core which can be more than 100 $\mu$m away. In this study, 2D particle-in-cell simulations are used to examine the effects of dual, superposed ignition lasers on hot electron generation and divergence by varying their relative frequencies and incident angles. Initial results show that dual, converging lasers at oblique incident angles and identical frequencies can substantially improve hot electron generation and energy coupling over a single laser of equal total input energy for intensities above 10$^{19}$ W/cm$^{2}$, and lasers with differing frequencies and normal incidence can do likewise for intensities below 10$^{19}$ W/cm$^{2}$.   

Status of Fast Ignition Program at LLNL

The fast ignition (FI) approach to inertial confinement fusion offers the potential for achieving the high target gains required for Inertial Fusion Energy (IFE). This paper reports progress at LLNL on the development of a point design for an indirect-drive re-entrant-cone FI target. Integrated hohlraum and capsule designs are described that optimize the peak density, $\rho $R and spatial uniformity of the fuel assembly around the cone tip. The interaction of the short-pulse ignitor beam in the cone is simulated with the PSC explicit particle-in-cell (PIC) code, and the subsequent transport of the electrons and core heating calculated with the Zuma hybrid transport code coupled to the Hydra radiation-hydrodynamics code. Progress will be described in the integrated modeling approach to fast ignition target design through the self-consistent treatment of the hohlraum radiation drive, capsule implosion, fast electron generation and transport, and core heating. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.   

Stopping Power in Dense Plasmas: Models, Simulations and Experiments

Our goal is to conclusively determine the minimal model for stopping power in dense plasmas via a three-pronged theoretical, simulation, and experimental program. Stopping power in dense plasma is important for ion beam heating of targets (e.g., fast ignition) and alpha particle energy deposition in inertial confinement fusion targets. We wish to minimize our uncertainties in the stopping power by comparing a wide range of theoretical approaches to both detailed molecular dynamics (MD) simulations and experiments. The largest uncertainties occur for slow-to-moderate velocity projectiles, dense plasmas, and highly charged projectiles. We have performed MD simulations of a classical, one component plasma to reveal where there are weaknesses in our kinetic theories of stopping power, over a wide range of plasma conditions. We have also performed stopping experiments of protons in heated warm dense carbon for validation of such models, including MD calculations, of realistic plasmas for which bound contributions are important.