- Seminars at CIPS

For the last several years Advanced Energy has worked in the development of plasma and ion sources. These development efforts encompass activities ranging from basic research to product and application development. During the first part of this talk we will present, as an example of basic research, the study of transient phenomena in planar magnetron discharges. It will be shown that high-speed imaging reveals interesting details of the dynamics of arcs occurring on these discharges, and can be used to estimate the drift speed of electrons on cross-field configurations. The second part of the talk will describe some of our products and the commercial applications they are used in.

Charged dust grains orbiting Saturn are subject to the simultaneous influence of several different forces, including planetary gravitational and electromagnetic forces, plasma drag, and solar radiation pressure. In addition, sputtering producted by the erosive magnetospheric plasma leads to a significant diminution of submicron grain radii in a matter of decades. As it shrinks, a grain becomes more responsive to the electromagnetic forces, while the topology of the confining effective potential undergoes qualitative changes. At the same time the motion becomes more chaotic and therefore increasingly ergodic. The synergism of topology and ergodicity can lead to significant particle loss to the planet or to interplanetary space, while more regular orbits can remain trapped by local invariants. In addition, the symmetry-breaking effects of radiation pressure can enhance chaos, while planetary oblateness J2 can contribute to orbital ergodicity. The results are applied to the CDA experiment on the Cassini Spacecraft now orbiting Saturn.

The well developed linear theory of ion-cyclotron range of frequencies (ICRF) wave interactions with plasma has enjoyed considerable success in describing antenna coupling and wave propagation, and provides a well-known framework for calculating power absorption, current drive, etc. in fusion experiments. In some situations, less well studied nonlinear effects are of interest, such as rf driven flows, ponderomotive forces, rf sheaths, and related interactions with the edge plasma. A tutorial-style overview of these effects will be presented, concentrating on basic rf-plasma-interaction physics. For fast waves, the parallel electric field near launching structures is known to drive rf-sheaths which can give rise to convective cells, interaction with plasma "blobs", impurity production, and edge power dissipation. In addition to sheaths, ion Bernstein waves in the edge plasma are subject to strong ponderomotive effects and parametric decay. In the core plasma, slow waves can sometimes induce nonlinear effects. Mechanisms by which these waves can influence the radial electric field and its shear are summarized, and related to the general (reactive-ponderomotive and dissipative) force on a plasma from rf waves. It is argued that there are significant opportunities now for new predictive capabilities by advances in integrated simulation of these mechanisms.

*In collaboration with D.A. D'Ippolito, D.A. Russell [Lodestar], L.A. Berry, E.F. Jaeger, and M.D. Carter [ORNL]

** Work supported by U.S. DOE grant DE-FG02-97ER54392 and the RF-SciDAC project.

It is quite possible that nuclear fusion will be the only source that can provide the prodigious power demands that the world will face in the future. The difficulty however for most nuclear fusion concepts is the complexity and large mass associated with the confinement systems. The challenge that the fusion community is faced with today is a consequence of this scaling. The high cost of tokamak research (and thus reactors) is primarily due to the large reactor sizes required for fusion gain with low ( steady state plasmas (( being the ratio of the plasma to magnetic energy density). At the other end of the spectrum, for most pulsed devices, the mass and complexity of the fast energy delivery systems (lasers, liners, beams etc.) become the problem. It is the contention here that a simpler path to fusion, that avoids many of these major difficulties, can be achieved by creating fusion conditions in a different regime at small scale (rp ~ a few cm). A new experimental program has begun that will take advantage of developments in the very compact, high energy density regime of fusion employing a plasmoid commonly referred to as a Field Reversed Configuration (FRC). The FRC is a closed field configuration where the confining magnetic field is provided by plasma toroidal currents alone. Of all fusion reactor embodiments, only the FRC has the linear geometry, low confining field, and intrinsic high plasma ( required for magnetic fusion at high energy density. Most importantly, the FRC has already demonstrated the confinement scaling with size and density required for fusion at high density. A fusion reactor based on the formation, acceleration, and compression of the FRC will be presented.

Phase contrast imaging diagnostic (PCI) is an internal reference beam interferometric technique which has been used successfully in high temperature tokamak plasma experiments to image the line integrated plasma density fluctuations. The diagnostic exploits the insertion into the beam path of a 1/8 deep grooved "phase plate" which then allows measurement of wavelengths and correlation lengths of fluctuations propagating perpendicular to the laser beam (near forward scatter). In the Alcator C-Mod and DIII-D tokamak PCI experiments a CO2 laser beam is used to probe both low frequency (f?1 MHz) instabilities and high power launched RF waves (80 MHz) in the ion cyclotron range of frequencies. The modes studied in the past in Alcator C-Mod include the so-called "quasi-coherent mode" (an edge ballooning fluctuation localized to the edge pedestal), semi-coherent TAE -like modes, including Alfven wave cascades, low frequency turbulence, and high power launched ICRF waves. The ICRF waves are detected by a heterodyne technique assist using optical modulation of the laser beam. The ICRF wave propagation studies have revealed an important aspect of mode conversion phenomena in multi-ion species plasmas, namely that in the typical case of sheared magnetic fields in tokamaks, mode conversion into kinetic ion cyclotron waves (the shear wave branch) may dominate over that into electrostatic ion Bernstein waves. This has important implication for using these waves to drive currents or generate shear flow in tokamak plasmas. In DIII-D, PCI diagnostic has been used to study low frequency turbulence during L to H mode transition, ELMS, and coherent edge modes during the Quiescent H-mode. Signatures of zonal flows have also been observed in past experiments. While most of the past studies were limited to wavelengths equal or longer than the ion gyro-radius (kri ? 1, f ? 1MHz ), new upgrades to the electronics will allow detection of wavelengths and frequencies in the electron gyro-radius regimes (kre ? 1, f ? 10MHz). This new capability will allow us to study the electron temperature gradient modes and the trapped electron mode, both being candidates for determining electron transport in magnetically confined plasmas. While spatial localization of long wavelength modes along the PCI laser beam is often lacking, in the short wavelength regimes in a sheared magnetic field localization can be achieved by using a rotating masking plate in conjunction with the phase plate. I will describe some of the results and the upgrades being implemented now on both C-Mod and DIII-D.

Acknowledgements:

This work is being supported by the US DOE, OFES Novel Diagnostics Initiative.

Key contributions to the PCI diagnostic by J. Dorris and C. Rost (at DIII-D), N. Basse, L. Lin, and E. Edlund (at C-Mod) are acknowledged. In addition, key contributions to the C-Mod ICRF physics by P. Bonoli, Y. Lin, J. Wright, and S. Wukitch are noted. Past contributions by S. Coda, A. Mazurenko and E. Nelson-Melby are also noted here.

Plasmelt Glass Technologies LLC (Plasmelt) is developing and testing a full-scale, modular, high intensity, plasma melter capable of producing 500-1500 lb/h (230-680 kg/h) of high-quality glass. The melter uses a remotely-coupled arc that operates at power levels up to 1.4 mW at atmospheric pressures. This presentation will discuss the theory behind the remotely coupled plasmas and the current and future industrial applications of this technology.

The Field Reversed Configuration (FRC) is a compact toroidal equilibrium that appears to relax to a state with large pressure gradients. Related fundamental plasma physics questions extend beyond MHD models, and are relevant to geophysical and astrophysical phenomena. The very successful Taylor paradigm for relaxation to a zero pressure, force free state does not apply. The FRC has large b, and can confine large plasma pressure for a given magnetic field. FRC's are interesting because they have vanishing rotational transform, magnetic shear, and helicity. The equilibrium is thought to be dominated by cross-field diamagnetic current and strong flows. Stability lifetimes greatly exceed Alfv?n times and defy MHD predictions. Magnetic reconnection and anomalously large resistivity drives essential ohmic dissipative heating. At Los Alamos National Laboratory, we have formed high density, high b FRC's for use as a target for Magnetized Target Fusion (MTF). MTF may be a low cost path to fusion, in a regime that is very different from, and intermediate between, magnetic and inertial fusion energy. It requires compression of a magnetized target plasma and consequent heating to fusion relevant conditions inside a converging flux conserver. We will describe FRC's, some of the physics issues, our applications to MTF, and recent data.

The multi-ion species flow onto the plasma boundary has recently begun to attract interest since multi-ion species are often present in practical systems. The ion flow created in the presheath of a weakly ionized He-Ar plasma is studied experimentally. A Modified-Mobility-Limited-Flow (MMLF) model was used to predict ion drift velocities of each species and found to be in agreement with previous LIF measurements [1] for Ar ions 2.0cm from the boundary. The phase velocity of ion acoustic wave was measured by launching a continuous sinusoidal wave, detecting the wave from electron saturation current with a Langmuir probe. The relationship between Ar+ and He+ drift velocities was established by the wave dispersion relation. He+ drift velocities were determined for given Ar+ drift velocities. Ion-ion electrostatic two stream instabilities were observed in the presheath for different positions, partial and total pressures to determine if this instability alters ion drift velocities near the sheath-presheath boundary. The instabilities predicted by fluid and kinetic dispersion relations are compared to the data.

The production of electrons from collisions between charged particles and targets (either solid or gas) is important to problems such as beam transport of heavy ion beams, current avalanche in low voltage diodes, and transmission breakdown in high power waveguides. Collaborators at Tech-X, Lawrence Berkely and Lawrence Livermore Labs are developing a set of easy-to-use computational modules to help model electron production in these systems. In this talk, I'll demonstrate how to use these modules and how I've applied them to study the problems above.

The classical finite-difference time-domain (FDTD) approach to the numerical solution of the time-dependent Maxwell's equations is based on the second order, in space and time, Yee algorithm. However, for an increasing number of applications this algorithm has insufficient accuracy. We replace it by a compact implicit 4th order accuracy scheme that uses the same stencil, but doesn't have drawbacks of the Yee algorithm. A major difficulty with high order methods is the treatment of the dielectric coefficient which is discontinuous across the interface. So we also study the asymptotic and numerical behavior of the solution of the Maxwell equations and the wave equation with discontinuous coefficients in one dimension in both time and frequency space. We present a method for the treatment of the discontinuity that preserves a high order of accuracy for the numerical scheme.

Recent advances in the direct kinetic simulation of fusion plasma turbulence now lay the groundwork and provide an enormous impetus for kinetic closure (using kinetic simulation) of MHD computational models. The topic is lively and is still very much an open research area. This is because efficient and practical nonlinear MHD and kinetic methods require subtle underlying orderings, equations and numerical methods (gyrokinetics, gyro-Landau fluid, semi-implicit, finite-element, particle-in-cell, drift-ordering, etc.) all of which must properly meld together into one grand simulation. Even on a particular and well-defined MHD problem, (e.g. internal kink instability, edge- localized modes, tearing modes) knowing whether it is better to use kinetic closure of MHD or solve the problem directly using kinetics is very much unanswered at this point. In this talk we will discuss the possible ways to close MHD equations using kinetics, as well as more direct MHD-like kinetic models. This talk will highlight some recent successes in kinetic-MHD, including modeling of energetic particle effects in fusion plasmas. We will also discuss recent kinetic and kinetic-MHD models of tearing mode behavior.

Magnetic self-organization via Taylor relaxation in a driven plasma underlies the guiding principle of laboratory helicity injection experiments that form spheromaks and the reversed field pinch, and provide non-inductive current drive in a spherical torus. It is also thought to explain the large scale astrophysical magnetic field, for example, in a radio-lobe powered by the accretion disk of a black hole. The critical concept in Taylor relaxation is a linear resonance effect that provides flux amplification. We will first explain the nature of this resonance and its fate when plasma departs from Taylor state. The second part of the talk approaches the same problem by following the dynamics that lead to relaxation. In particular, the so-called instability cascade route to relaxation will be illustrated. Laboratory and astrophysical examples will be drawn upon to appreciate the physical consequences of our analysis.

We analyze single ion motion in a model field-reversed configuration. A two-dimensional effective potential is derived and shown to possess a potential trough as well as isolated critical points. Sufficient conditions for Lyapunov stability are derived for these equilibria and shown to allow large populations of energetically trapped orbits, which can be regular or chaotic. Among these the classical guiding center orbits gyrating about closed field lines form a small minority. Indeed, for moderate field elongation the great majority of trapped orbits appear to be chaotic, with significant populations of regular orbits librating about stable periodic orbits. For larger conserved angular momentum the potential trough disappears and ions are energetically trapped in a larger convex potential well. The dynamics in this regime is very sensitive to elongation, with large resonances and chaotic regions for particular integer values of the inverse elongation. These theoretical results are well confirmed by numerical orbits, Poincare' sections, and Lyapunov exponents. The abundance of periodic orbits and paucity of guiding center orbits suggests that the frequency of the imposed rotating magnetic field in RMP experiments should be chosen close to the libration frequencies of the dominant periodic orbits rather than the cyclotron frequency.

There are two holy grails regarding the production of charged-particle beams: high brightness and high average current. Both are within reach using the latest accelerator technology. However, conventional design codes based on controlling global moments of the beam provide grossly insufficient intelligence as to the whereabouts of these grails. Consequently, the Beam Physics and Astrophysics Group at Northern Illinois University has been delving into the fundamental physics of space charge. Major topics of investigation have included: chaotic orbits in both time-independent and time-dependent beams, phase mixing and rapid collisionless relaxation, the validity of the Vlasov-Poisson limit, halo formation, and the importance of noise. In short, the lesson learned is that details do matter: the phenomenology of space charge is intricate and involves multiscale dynamics. This talk will present illustrative examples and point to future directions for beam simulation codes.

Modeling a magnetized plasma using single-fluid MHD is inadequate to describe many phenomena. The next simplest model describes the plasma as two fluids, ions and electrons. While this two-fluid model still omits most important kinetic physics, an efficient and accurate numerical treatment of a two-fluid plasma forms the basis for many additional kinetic extensions. Additionally, some examples are given, including the field-reversed configuration and Harris sheet reconnection, where two-fluid calculations would be (or have already been) extremely useful. Next, the problem of efficient numerical solution using time-implicit methods is discussed and contrasted to the single-fluid situation. A uniform, two-fluid plasma supports only real frequency waves, and we seek difference approximations which preserve this feature. The required time differencing is developed and implemented in the NIMROD code, a fusion community-wide finite element code previously applied to single fluid modeling of tokamak and other toroidal plasmas. Results of dispersion tests are discussed and future applications discussed.

The evolution of collisionless and semi-collisional tearing mode instabilities is studied using an electromagnetic gyrokinetic $\delta f$ particle-in-cell simulation model. Drift-kinetic electrons are used. Linear eigenmode analysis is presented for the case of fixed ions and there is excellent agreement with simulation. A double peaked eigenmode structure is seen indicative of a positive $\Delta^\prime$. Nonlinear evolution of a magnetic island is studied and the results compare well with existing theory in terms of saturation level and electron bounce oscillations. Electron-ion collisions are included to study the semi-collisional regime. The algebraic growth stage is observed and compares favorably with theory. Nonlinear saturation following the Rutherford regime is observed.

I will present results from DC breakdown experiments designed to imitate (to some extent) breakdown in superconducting microwave resonators. "Before" and "after" pictures demonstrate the dangers of contaminant particles, and post-breakdown surface analyses show the damage caused by the arc around the field emitter, including the extent of ion bombardment. A simple model can explain the initiation of breakdown at a field emitter around which a monolayer of neutral atoms suddenly desorbs; computer simulations using OOPIC show in more detail how breakdown might be thus triggered, and confirm the model`s predictions of a critical current and gas density necessary for breakdown. Although the source of the gas remains unexplained in most cases, I will present a possible explanation for helium processing of superconducting microwave cavities.

For a radio-frequency sheath, it has been found that the rf sheath dynamics is characterized by the ratio of the rf frequency and the ion transit frequency crossing the sheath. Based on a one-dimensional fluid model, the sheath dynamics in different frequency regimes have been studied by solving the continuity and momentum equations for electrons and ions and Poisson's equation. In this model, the presheath dynamics is taken into account. If the rf frequency is smaller than the ion transit frequency crossing the presheath, the ions in the presheath respond instantaneously to the rf field. Consequently, the ion current entering the sheath is time-varying which affects the sheath dynamics significantly. To investigate the ion kinetic effects, the one-dimensional Vlasov equation for ions is solved by using the cubic interpolated propagation scheme (CIP) while the drift-diffusion model is assumed for electrons. It is found that the ion energy distributions (IEDs) of the kinetic model depend on the ionization term. If the ion production rate is significant in the sheath, multiple peaks of the IED will be formed.

I will discuss the formulation and the properties of the moment implicit particle in cell (PIC) method developed at Los Alamos National Laboratory.

The talk will be divided into three parts.

First, I will discus the challenges of multiple scale problems in plasma physics. Plasmas host a variety of processes, often some are of more interest than others. Often the processes of interest are on long space and time scales. The implicit approach is an excellent way to handle this situation. It focuses on the long scales of interest, with proportionate resolution, without needing to resolve smaller scales accurately. The method implicitly averages over the smaller and faster scales. I will discuss the general properties of the implicit method.

Second, I will discuss how the implicit moment method is designed and turned into a computer code. I will summarize the actual formulation we currently use in our CELESTE3D code. I will spend a little more time discussing the most recent advances in this area: the formulation of the Maxwell's equations and the boundary conditions for them.

Lastly, I will discuss some benchmark calculations meant to illustrate the performance of CELESTE3D.