[en] The Plasma Theory and Simulation Group (PTSG) is collaborating with LLNL in order to model the edge region of a tokamak plasma and its interaction with the diverter plate. In the overall framework of the project, MHD will be used to model the bulk plasma. Near the edge, the MHD model will interface with the gyrokinetic code UEDGE developed at LLNL. Since the UEDGE model approximations may not be accurate within a few cyclotron radii of the diverter plate, the UEDGE code will interface with a collisional PIC-hybrid code developed by the PTSG under this project. The PTSG PIC code will include a self-consistent potential with kinetic or fixed hydrogen ions. The sputtering profile of the plate, under development at LLNL, will be used as input to the PIC code in order to correctly model the kinetic behavior of sputtered carbon. These carbon products will interact with hydrogen according to known chemistry cross-sections. While some kinetic electrons may be used to model the fast tail of the distribution function (if necessary), the bulk of the electron population will be modeled as being in thermal equilibrium using the Boltzmann relation, resulting in a significant improvement in code speed. Coulomb collisions may also be considered. The Boltzmann model has been implemented with various features in three of the PTSG codes: XPDP1 and OOPD1 (both 1d-3v), and OOPIC (2d-3v), according to the methodology of Cartwright [1]. When the model is fully implemented, it will include fluid interaction with the boundaries, energy conservation through the temperature term, and take into account collisions with the Boltzmann species. A more rigorous convergence analysis has been developed than is outlined in [1]; boundary effects are included explicitly in a formulation valid in arbitrary coordinate systems. In OOPD1, the Boltzmann model is included in an object-oriented manner as part of a general fluid model framework. The basic Boltzmann solver has been implemented and shown to give self-consistent results. The details and results were described in detail in a talk presented at LLNL (updated slides attached). Currently, the output of the three codes is being compared for a test case of a current-driven DC discharge. Computational speed-up and accuracy will be compared between PIC and the Boltzmann-PIC hybrid. A framework for general binary and three-body collisions is being developed for OOPD1. Given known cross-sections or reaction rates, this will function as a chemistry model for the code. The framework may then be imported into OOPIC

[en] Particle simulation of plasmas, employed since the 1960s, provides a self-consistent, fully kinetic representation of general plasmas. Early incarnations looked for fundamental plasma effects in one-dimensional systems with ∼10²-10³ particles in periodic electrostatic systems on computers with ≤100 kB memory. Recent advances model boundary conditions, such as external circuits to wave launchers, collisions and effects of particle-surface impact, all in fully relativistic three-dimensional electromagnetic systems using ∼10⁶-10¹⁰ particles on massively parallel computers. While particle codes still enjoy prominance in a number of basic physics areas, they are now often used for engineering devices as well

[en] In high-power microwave systems, the transition of window breakdown from single surface vacuum multipactor discharge to rf plasma with increasing gas pressure is investigated using particle-in-cell simulations. An intermediate pressure regime where multipactor discharge and rf plasma coexist was found. The pressure range where the multipactor can be maintained is summarized in the plot of the secondary electron emission yield as a function of the gas pressure. As the gas pressure increases, electron-neutral collisions prevail against secondary electron emissions and the electron energy probability function changes from the bi-Maxwellian at low pressures to Druyvesteyn at high pressures as a result of the change in electron heating and cooling processes. The discharge formation time in argon, neon, and xenon is shown for different gas pressures. Different scaling laws in the discharge formation time are presented at low and high pressures, respectively

[en] Modeling the interaction of relativistic electromagnetic plasmas with a background gas is described. The timescales range over many orders of magnitude, from the electromagnetic Courant condition (∼10^-12 sec) to electron-neutral collision times (∼10^-7 sec) to ion transit times (∼10^-5 sec). For this work, the traditional Monte Carlo algorithm [1] is described for relativistic electrons. Subcycling is employed to improve efficiency, and smoothing is employed to reduce particle noise. Applications include plasma-focused electron guns, gas-filled microwave tubes, surface wave discharges driven at microwave frequencies, and electron-cyclotron resonance discharges. The method is implemented in the OOPIC code [2]

[en] The solution for space-charge-limited (SCL) currents in electron vacuum diodes with monoenergetic initial velocity is extended to the relativistic regime. Two types of solutions are found: Type I corresponds to zero steady state surface electric field (field emission with high enhancement factor), and Type II corresponds to a finite steady state surface electric field (other emission mechanisms). Our solution compares well to the classical space-charge-limited currents with initial energy and relativistic space-charge limited currents without initial energy in the appropriate limits. The scaling law between the true SCL and the applied voltage is discussed and the two solution types are verified by particle-in-cell simulation.

[en] The Fowler-Nordheim law gives the current density extracted from a surface under strong fields, by treating the emission of electrons from a metal-vacuum interface in the presence of an electric field normal to the surface as a quantum mechanical tunneling process. Child's law predicts the maximum transmitted current density by considering the space charge effect. When the electric field becomes high enough, the emitted current density will be limited by Child's law. This work analyzes the transition of the transmitted current density from the Fowler-Nordheim law to Child's law space charge limit using a one-dimensional particle-in-cell code. Also studied is the response of the emission model to strong electric fields near the transition point. We find the transition without geometrical effort is smooth and much slower than reported previously [J. P. Barbour, W. W. Dolan, J. K. Trolan, E. E. Martin, and W. P. Dyke, Phys. Rev. 92, 45 (1953)]. We analyze the effects of geometric field enhancement and work function on the transition. Using our previous model for effective field enhancement [Y. Feng and J. P. Verboncoeur, Phys. Plasmas 12, 103301 (2005)], we find the geometric effect dominates, and enhancement β>10 can accelerate the approach to the space charge limit at practical electric field. A damped oscillation near the local plasma frequency is observed in the transient system response

[en] The scaling laws for the initiation time of radio frequency (rf) window breakdown are constructed for three gases: Ar, Xe, and Ne. They apply to the vacuum, to the multipactor-triggered regime, and to the collisional rf plasma regime, and they are corroborated by computer simulations of these three gases over a wide range of pressures. This work elucidates the key factors that are needed for the prediction of rf window breakdown in complex gases, such as air, at various pressures

[en] The formation of a double layer (DL) in a two-dimensional (2D) electronegative plasma with a source (heating) section connected to a larger downstream section is described. A 2D particle-in-cell (PIC) code is used to exhibit the DL, which appears near the transition between the source and downstream chambers, over a range of pressures and electronegativities. Diagnostics of the PIC code allow the calculation of various plasma parameters, not easily measured in experiments, to be compared with an analytic theory. The theory consists of a collisionless one-dimensional model of a DL connected to 2D source and downstream global models. The conditions of positive and negative ion balance upstream and downstream, and the downstream energy balance determine the DL potential, electron temperatures, and other plasma parameters. A rescaled oxygen reaction set is used both for the simulation and for the analytic comparison. The PIC simulations exhibit a Maxwellian electron distribution in the source region at temperature T_h, and a bi-Maxwellian distribution downstream, with a low energy population at temperature T_c< T_h and with a hotter tail also having temperature T_h. At the upstream DL edge, an accelerated electron component is observed. Using these results in the model, a DL is found in reasonable agreement with that obtained in the simulation.

[en] When particles are injected according to the Fowler-Nordheim (FN) field emission equation, the transmitted current density will transition to the space charge limited (SCL) current density, with increasing applied diode voltage. The actual transmitted current density is the so-called SCL-FN current density. In this work, Barbour's analytic solution for the SCL-FN current density is modified with consideration of injection velocity and also geometric effects, by solving the advanced FN equation with the effective field enhancement factor, the energy conservation equation with an initial velocity term, and Poisson's equation simultaneously. The solution is also extended to the relativistic regime where similar transition process is found. This solution has been verified using particle-in-cell simulation with varying diode voltage, electron injection velocity, and field enhancement factor

[en] The ion energy distribution (IED) at a surface is an important parameter for processing in multiple radio frequency driven capacitive discharges. An analytical model is developed for the IED in a low pressure discharge based on a linear transfer function that relates the time-varying sheath voltage to the time-varying ion energy response at the surface. This model is in good agreement with particle-in-cell simulations over a wide range of single, dual, and triple frequency driven capacitive discharge excitations