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A growing body of experimental data suggests that non-diffusive radial transport of particles can play a major role in the SOL of tokamaks and other machines. This transport may be associated with the propagation of high density plasma filaments or "blobs" that have been observed in experiments with both fast cameras and probes. Theoretical work has shown that these structures propagate to the wall in the presence of an outwards force F and species- dependent F x B drifts. The transport occurs due to different types of forces in both toroidal and linear machines of greatly varying parameters, so the phenomenon is robust and surprisingly universal. The blob theory is qualitatively consistent with the experimental observations of convective transport, spatial and temporal intermittency, and non-Gaussian statistics in the SOL. Convective transport can be especially important for tokamaks because it reduces the efficiency of the divertor and may be related to the observed density limit on some machines. This talk will discuss the experimental motivation for this work, recent progress in theory and modeling, and some remaining unresolved issues.

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This fall, Physics 4150, Introduction to Plasma Physics, is being taught with many of the homework problems assigned in Mathcad. The assigned problems are similar to exercises posted online at the course web site (debye.Colorado.edu/phys4150), thus the student's work will consist of downloading and modifying the posted Mathcad spreadsheets. For example, an assigned problem to find the potential created by an array of conductors might require only changing the boundary conditions in a spreadsheet that solves Laplace's equation. There are 25 posted exercises which 1) solve Laplace's and Poisson's equation by relaxation (illustrating Debye shielding), 2) plot the trajectories of magnetic field lines from straight wires and loops using Runge-Kutta (illustrating the dipole, x-points, shear, and rotational transform), 3) solve the Lorentz equations of motion for inhomogeneous magnetic fields by Runge-Kutta (illustrating the mirror force and drifts), 4) find the roots of complex dispersion relations using root finders including cases where the waves are growing or damped, 5) illustrate the principal value integral in the plasma dispersion function, 6) perform ray tracing in an inhomogeneous dielectric in the WKB approximation (illustrating ionospheric reflection), 7) illustrate diffusion, mobility and resistivity using equations of motion with Monte Carlo collisions, and 8) illustrate the ponderomotive force by modeling the Paul ion trap.

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Unwanted electron emission from metal walls influences the operation of vacuum waveguides. If the electron density becomes large enough, the electron plasma can reflect the electromagnetic waves that are supposed to be transmitted. We have performed numerical simulations of the generation of electrons in high-power vacuum waveguides. In particular, we studied parameters relevant to the high-power waveguides at the Stanford Linear Accelerator Center. An interesting result of our work is ions and neutrals appear to play an important role in the electron emission.

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Kinetic plasma simulations based on direct integration of the Vlasov equations are much quieter than corresponding simulations using particle-in-cell (PIC) methods. However, the computational cost of Vlasov simulations in higher dimensions is steep because the Vlasov equations must be solved on a grid of at least 2xD phase-space dimensions where D is the number of spatial dimensions. Fortunately, there are regimes where a full kinetic treatment is required only along one "dominant" spatial coordinate (e.g., the direction of a beam or background magnetic field), with the perpendicular dynamics either suppressed by a strong magnetic field or adequately modeled by fluid-like methods. A hierarchy of hybrid simulation schemes for different levels of particle magnetization will be presented. Examples from simulations of current-driven double layers and electron holes in the auroral ionosphere will be used to illustrate the various numerical approaches.

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This talk will describe results of our on-going studies of the temperature and heating rate of trapped and laser-cooled Be+ ions. These studies are mainly motivated by the possibility of producing entangled states of many ions, which could have applications in quantum information processing and possibly lead to an improved microwave frequency standard. In a Penning trap, charged particles are confined by a combination of static electric fields and a uniform magnetic field. Up to ~1 million Be+ ions are trapped in the NIST Penning trap. When laser-cooled down to temperatures below ~10 mK, the trapped ions form a spheroidally shaped crystal with an inter-particle spacing on the order of 20 micron. The temperature of this system can be measured by laser spectroscopy on a single-photon transition in the Be+ ion. We have studied the heating of the ion cloud after that the cooling laser is turned off. We observe a slow increase in the ion temperature from 1 mK to ~10 mK in typically 0.1s followed by a very rapid increase to ~1 K in another 0.1s. Possible heating mechanisms will be discussed and their relative importance assessed. I will argue that the very rapid temperature increase can be attributed to a solid to liquid phase transition.

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VORPAL is an object-oriented multi-dimensional plasma analysis code written in C++. It can handle both relativistic and non-relativistic plasmas using PIC or fluid models. Dynamic load balancing enables it to optimize its performance in parallel by periodically adjusting a simulation's decomposition at runtime. In this talk I will discuss the work that went into implementing a dynamic load balancing solution for VORPAL and how VORPAL's flexible framework made such a task feasible. Performance issues as well as overall results of the design will be addressed.

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The Alfvén wave dominated auroral region has been identified as the region near the open-closed magnetic field line boundary where particle acceleration is dominated by waves rather than by quasi- static potential structures found in the upward (with respect to the Earth) and downward current regions. Various models have been considered to explain the acceleration of electrons by Alfvén waves in the nightside auroral region. I will present the characteristics of the Alfvénic auroral region. A linear 1-D gyrofluid simulation [Jones and Parker, 2003] is applied on a dayside auroral field line. A test particle code is used to simulate two electron populations under the influences of Alfvén waves obtained by the gyrofluid code. The electron distributions obtained from the simulation will be compared with observations from the FAST spacecraft.

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A new numerical algorithm that encompasses both the $\delta f$ particle-in-cell (PIC) method and a continuum similar to Denavit's "hybrid'' method has been analyzed using a new interpolation schemes. The basic algorithm is essentially a variant of the delta-f method. Briefly, the algorithm is the following: 1) load particles (or characteristics) on a uniform lattice in phase space. The loading need not be uniform, but it greatly simplifies the algorithm, 2) advance the characteristics M time steps, using the usual delta-f PIC algorithm which involves a grid interpolation, deposition, then field solve all on a spatial grid only, 3) every M time steps, deposit delta-f on a higher-dimensional phase space grid, then reset the particle phase space coordinates back to their initial value on the phase space lattice. Also, reset the particle value of delta-f to the phase space grid value. As M goes to infinity, one recovers the usual delta-f PIC algorithm with a somewhat peculiar uniform loading of particles. For M=1 the algorithm is similar to the Vlasov method of Cheng and Knorr. Any value of M={1,2,3,...} is permissible. A quadratic weighting interpolation scheme is implemented \cite{HE}for a small $(k_\perp \rho_i)^2$ two-dimensional bounded slab model, where the phase space is (x,y,v_parallel). The ion-temperature-gradient instability is studied assuming adiabatic electrons and gyrokinetic ions. We will present results with both linear and quadratic interpolation. We will calculate the effective phase space diffusion by such a repeated interpolation and compare with simulation results.

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A new electromagnetic kinetic electron simulation model that uses a generalized split-weight scheme and a parallel canonical momentum formulation has been developed in three-dimensional toroidal flux-tube geometry. The long-standing problem in the simulation of kinetic electrons with finite-beta effects, associated with the electron current of the zero-order distribution (Maxwellian in terms of parallel canonical momentum), is solved by evaluating this current using the same marker particles and the same particle shape as that used for the perturbed distribution. The model also includes electron-ion collisional effects and has been linearly benchmarked with continuum codes. It is found that for H-mode parameters, the nonadiabatic effects of kinetic electrons increase linear growth rates of the Ion-Temperature-Gradien-Driven (ITG) modes, mainly due to trapped-electron drive. The ion heat transport is also increased from that obtained with adiabatic electrons. The linear behavior of the zonal flow is not significantly affected by kinetic electrons. The ion heat transport decreases to below the adiabatic electron level when finite plasma beta is included due to finite-beta stabilization of the ITG modes.

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A large part of the expense associated with fusion experiments is due to the uncertainties in the dynamics of the plasma. These dynamics lead to instabilities that can spontaneously erupt and degrade the confinement properties of a plasma and sometimes lead to catastrophic disruptions of the entire plasma itself. These instabilities occur in a broad range of spatial and temporal scales, spanning many orders of magnitude, often resulting from nonlinear interactions. Computational simulations are crucial to understanding these phenomena. This thesis research focuses on the numeric study of kinetic effects on magnetohydrodynamic (MHD) instabilities in fusion plasmas. The significant achievement of this thesis work was the implementation of the $\delta f$ particle-in-cell(PIC) simulation in a general geometry, massively parallel, Lagrange-type finite element based, MHD simulation. This hybrid models captures kinetic effects that are not possible to simulate with a fluid MHD simulation alone. The use of the finite element method(FEM) allow the flexibility of modeling the realistic geometries of fusion devices. However, the irregularity of the simulation grid does not allow for conventional (PIC) coupling to the fluid elements represented by the finite element grid. Particular problems resolved include determining where the particle is in the grid, how to 'gather' the field to the particles, how to 'scatter' the particle effects onto the grid, and implementing in a massively parallel framework compatible with the MHD simulation. The addition of kinetic particle effects captures wave-particle interactions important in the saturation or excitation of various MHD instabilities such as the internal kink mode, sawtooth, and fish bone instabilities. We assume that the kinetic particles are an energetic minority species, i.e. kinetic particle density is small compared to the bulk plasma density but the kinetic particle pressure is comparable to the bulk plasma pressure. The kinetic particles are evolved in the MHD fields using the drift kinetic equations of motion. A pressure tensor is calculated from velocity moments of the kinetic particles. This hot particle pressure tensor is added to the MHD momentum equation forming the hybrid kinetic model. This hybrid kinetic-MHD technique lays the foundations for future work in a kinetic closure to the MHD equations.

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A heavy ion beam probe has been used to measure density and electric potential fluctuations and the equilibrium electric potential in the core region (r/a = 0.3 to 0.6) of the Madison Symmetric Torus reversed field pinch. This is the first measurement of potential and potential fluctuations in a hot reversed field pinch plasma. In standard plasmas, the equilibrium potential is positive and 1 to 2 kV above machine ground with electric fields strengths of 0.7 to 3 kV/m. Plasmas with low flow velocities due to locking have much lower potentials and electric fields. The potential is inversely related to the density and the electric field is consistent with expectations from the ion momentum balance equation. The observed fluctuations consist of 3 components, a potential fluctuation with f < 10 kHz that is believed to be due to m=0 electric field fluctuations at the edge, density and potential fluctuations at f ~ 15 kHz that are coherent with the dominant m=1, n=6 magnetic fluctuations, and broadband density and potential fluctuations between 30 and 100 kHz. The ExB particle transport due to these fluctuations is much smaller than the total particle transport in a standard plasma.

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In the optics of charged particle beams, circular transverse modes can be introduced; they provide an adequate basis for rotation-invariant transformations. A group of these transformations is shown to be identical to a group of the canonical angular momentum preserving mappings.
These mappings and the circular modes are parametrized similar to the Courant-Snyder forms for the conventional uncoupled, or planar, case. The planar-to-circular and reverse transformers (beam adapters) are introduced; their implementation on the basis of skew quadrupole blocks is described. Applications of the planar-to-circular, circular-to-planar and circular-to-circular transformers are discussed. A range of applications includes round beams at the interaction region of circular colliders, flat beams for linear colliders and relativistic electron cooling.

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This talk will begin with a brief introduction to Lie Transform perturbation theory and its use in averaging over small time scales. This is achieved by canonically transforming to slowly oscillating variables. The theory will be applied to a periodic focusing system, that is, a harmonic oscillator with a rapidly oscillating potential. This will be followed by a comparison with numerical results. After this, the theory will be applied to the dynamics of a charged particle in an accelerator with nonlinear focusing. The analysis yields a condition that improves integrability and minimizes chaos in such a system. This will be confirmed by numerical results.

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The dynamics of fusion plasmas lead to instabilities that can sponta- neously erupt and degrade confinement and sometimes lead to catastrophic disruptions of the entire plasma itself. These instabilities occur in a broad range of spatial and temporal scales, spanning many orders of magnitude, often resulting from nonlinear interactions. Computational simulations are crucial to understanding these phenomena.
NIMROD(NonIdeal MHD with Rotation - Open Discussion) is a mas- sively parallel three dimensional magnetohydrodynamic simulation utilizing finite elements (FE) to represent the poloidal plane and a fourier decompo- sition in the toroidal direction. The use of finite elements allows flexibility in the representation of the simulation domain. The ability to model ex- perimental shots with NIMROD provides a platform to test new ideas of plasma behavior. To expand the physics capabilities of NIMROD, kinetic effects have been added to NIMROD by the addition of delta-f PIC(Particle in Cell) module. The addition of kinetic particle effects captures essential wave-particle interactions important in the saturation of various MHD insta- bilities such as the internal kink mode, sawtooth and fishbone instabilities, and toroidal Alfven eigenmodes. Particle simulation capabilities in NIMROD can also be extended to simulate various phenomena such as neutral beam injection, ion cyclotron resonance heating, and anomalous los mechanisms. In addition, this hybrid kinetic-MHD technique lays the foundations for a kinetic closure to the MHD equations.
This talk will briefly introduce NIMROD and delta-f PIC in general, then detail the development of PIC in finite elements and their implementation and some preliminary results.

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Alfvén waves are ubiquitous in space plasma physics, present in field line bending, during magnetic reconnection, and magnetized shock formation. However, due to their typically long wavelength, comparatively few basic laboratory studies have been made of these waves. Experiments must either be long or dense to accommodate several aflvén wavelengths. At New Mexico Tech we use a high-density helicon generated background plasma to study aflvén waves under a steady-state current-free conditions. A summary of early studies of alfvén waves will be presented, as well as our recent results on alfven propagation in plasmas with a varying neutral fraction. favorably.

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Stray electrons are suspected of limiting the performance of many of today's ion accelerators. One source of these electrons is the electrons produced when halo beam ions strike the beam pipe walls. I will discuss computer models developed to help understand this process. In particular, I will discuss this effect as it applies to heavy ion fusion experiments at Lawrence Berkeley National Laboratory. I will show that one can expect as many as 1000 electrons to result from each ion collision and what researchers can do to mitigate the problem.

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