Physics of plasmas, nonlinear dynamics, and electromagnetics
257
Scopus Publications
Scopus Publications
Pressure dependence of magnetron sputtering: 2D-RZ particle-in-cell and 1D fluid modeling Joseph G. Theis, Gregory R. Werner, Thomas G. Jenkins, Daniel Main, John R. Cary Physics of Plasmas, 2026 We reproduce the consistently-seen experimental voltage vs pressure (V–p) dependence of DC magnetron sputtering with two-dimensional-RZ particle-in-cell (PIC) simulation. Informed by PIC simulation, we develop a steady-state, 1D-axial fluid model of the sheath and presheath that also reproduces this V–p dependence. The V–p dependence is the relationship between the steady-state voltage needed to maintain a constant discharge current and the neutral gas pressure. V–p dependence is fundamental to device performance, but has not previously been reproduced with simulation or satisfactorily explained. We find that the decrease in voltage with increasing pressure is not due to electron recapture at the cathode. Rather, the constant current dictates a constant global ionization rate, so the voltage decrease compensates for the increase in neutral gas density by lowering the energy of the plasma electrons, which decreases their ionization probability. The PIC simulations also reveal that the presheath and bulk plasma are unaffected by the electron reflection coefficient at the cathode; the only effect of increasing reflection is a reduction in the sheath voltage and width. In addition to the potential structure, we explore how pressure affects the plasma density, particle drifts, and particle energy distributions.
Modeling the role of secondary electron emission in direct current magnetron sputtering using explicit energy-conserving particle-in-cell methods Daniel Main, Thomas G. Jenkins, Joseph G. Theis, Gregory R. Werner, John R. Cary, et al. Physics of Plasmas, 2026 We present results from particle-in-cell (PIC) simulations of direct current magnetron sputtering (dcMS) in a 2D cylindrically symmetric geometry. The PIC model assumes an electrostatic approximation and includes the Monte Carlo collision method to model collisions between electrons and the neutral gas. A newly implemented explicit energy-conserving PIC algorithm (EC-PIC) is also exercised by the model, and results are compared with the standard momentum-conserving PIC (MC-PIC) method. We use these simulation tools to examine how changes in ion-induced secondary electron yield (SEY) and the external circuit impact the steady-state current, voltage, and plasma density of dcMS discharges. We show that in general, higher ion-induced SEY and lower external resistance values lead to larger currents, smaller voltages, and larger plasma densities. Simulation results presented in this paper related to the ion-induced SEY demonstrate similar trends that have been observed in previous experimental work and theory. Finally, we demonstrate that EC-PIC maintains numerical stability up to cell sizes as large as ten times the electron Debye length. While we have not performed a comprehensive stability study of MC-PIC, this paper demonstrates improved stability over the standard practice often assumed in MC-PIC. We therefore demonstrate that EC-PIC allows for modeling a wide range of plasma currents and densities using modest computational resources compared with PIC models that require resolution of the electron Debye length.
Grid instability growth rates for explicit, electrostatic momentum- and energy-conserving particle-in-cell algorithms Luke C. Adams, Gregory R. Werner, John R. Cary Physics of Plasmas, 2025 When the Debye length is not resolved in a simulation using the most common particle-in-cell (PIC) algorithm, the plasma will unphysically heat until the Debye length becomes resolved via a phenomenon known as grid heating. This paper presents detailed numerical measurements of grid heating for several explicit PIC algorithms, including the first systematic (covering the Debye length resolution and drift-velocity parameter space) study of grid-heating growth rates for the most common electrostatic momentum-conserving PIC algorithm. Additionally, we derive and test a cubic-spline-based PIC algorithm that ensures that the interpolated electric field has a continuous first derivative but find that a differentiable electric field has minimal impact on grid-heating stability. We also considered energy-conserving PIC algorithms with linear and quadratic interpolation functions. In all cases, we find that unphysical heating can occur for some combinations of Debye under-resolution and plasma drift. We demonstrate analytically and numerically that grid heating cannot be eliminated by using a higher-order field solve and give an analytical expression for the cold-beam stability limits of some energy-conserving algorithms.
Nonlocal effects on thermal transport in hydrodynamic simulations of unmagnetized MagLIF-relevant gaspipes on NIF R. Y. Lau, D. J. Strozzi, M. Sherlock, M. Weis, A. S. Joglekar, et al. Physics of Plasmas, 2025 We present simulations of heat flow relevant to gaspipe experiments on the National Ignition Facility to investigate kinetic effects on transport phenomena. D2 and neopentane (C5H12) filled targets are used to study the laser preheat stage of a MagLIF scheme where an axial magnetic field is sometimes applied to the target. Simulations were done with the radiation-MHD code HYDRA with a collision-dominated fluid model and the SNB nonlocal electron thermal conduction model. Using the SNB model to evolve the electron temperature increased the heat front propagation of neopentane gas targets compared to a local model by limiting radial heat flow. This increases electron temperature near the axis, which decreases laser absorption. We find that the effect of heat flow models on temperature profiles and laser propagation is modest. Beyond the SNB model, we utilize HYDRA to initialize plasma conditions for the Vlasov–Fokker–Planck K2 code. We run K2 until a quasi-steady state is reached and examine the impact of kinetic effects on heat transport. Although axial heat flow is well predicted by fluid models, the fluid model consistently overpredicts radial heat flow up to 150% in regions with the largest temperature gradient of D2 filled gaspipes. On the other hand, the SNB nonlocal electron conduction model is found to be adequate for capturing kinetic heat flow in gaspipes.
Kinetic simulations of low-temperature plasmas used for plasma processing: ICP and feature-scale models Daniel Main, Thomas G. Jenkins, Eve Lanham, Scott E. Kruger, John R. Cary Proceedings of SPIE the International Society for Optical Engineering, 2025 Low-temperature kinetic plasma simulations using Particle-in-Cell (PIC) and Monte Carlo methods (DSMC/MCC) for the chemistry can provide many advantages over fluid simulations, including detailed information about the Ion Energy Distribution Function (IEDF) and Ion Angular Distribution Function (IADF) that are critical for plasma processing. In this presentation, two different types of simulations illustrating the advantages of kinetic modeling are demonstrated. The first is a macroscopic-scale simulation of an Inductively Coupled Plasma (ICP). We demonstrate how implicit methods can make these challenging simulations feasible, and how process parameters such as neutral gas density and bias frequency affect the IEDF and IADF at the wafer surface. We also demonstrate a method of providing constant power to the plasma which decreases run-times to reach steady state and examine the steady-state ion fluxes and IEDFs/IADFs incident on the wafer as a function of bias frequency and waveform shape. Secondly, we discuss efforts to develop microscopic feature-scale simulation capabilities, e.g. for through-silicon vias or other high-aspect-ratio etch features wherein the trajectories of etching species may be affected by charge accumulation on feature sidewalls. Here, our recent efforts have focused on the development of self-consistent flux boundary conditions from macroscopic (sheath)-scale simulations that can be used as inputs for such feature-scale simulations.
Empirically extending 1D Child-Langmuir theory to a finite temperature beam Jesse M. Snelling, Gregory R. Werner, John R. Cary Physics of Plasmas, 2024 Numerical solutions to the 1D steady-state Vlasov–Poisson system are used to develop a straightforward empirical formula for the electric current density transmitted through a vacuum diode (voltage gap) as a function of gap distance, gap voltage, the injected current density, and the average velocity and temperature of injected particles, as well as their charge and mass. This formula generalizes the 1D cold beam Child–Langmuir law (which predicts the maximum transmitted current for mono-energetic particles in a planar diode as a function of gap voltage and distance) to the case where particles are injected with a finite velocity spread. Though this case is of practical importance, no analytical solution is known. Found by a best fit to results from particle-in-cell simulations, the empirical formula characterizes the current transmitted across the diode for an injected velocity distribution of a drifting Maxwellian. It is not meant to yield a precise answer, but approximately characterizes the effect of space charge on transmitted current density over a large input space. The formula allows quick quantitative estimation of the effect of space charge in diode-like devices, such as gate-anode gaps in nanoscale vacuum channel transistors.
Temporal evolution of the light emitted by a thin, laser-ionized plasma source Valentina Lee, Robert Ariniello, Christopher Doss, Kathryn Wolfinger, Peter Stoltz, et al. Physics of Plasmas, 2024 We present an experimental and simulation-based investigation of the temporal evolution of light emission from a thin, laser-ionized helium plasma source. We demonstrate an analytic model to calculate the approximate scaling of the time-integrated, on-axis light emission with the initial plasma density and temperature, supported by the experiment, which enhances the understanding of plasma light measurement for plasma wakefield accelerator (PWFA) plasma sources. Our model simulates the plasma density and temperature using a split-step Fourier code and a particle-in-cell code. A fluid simulation is then used to model the plasma and neutral density, and the electron temperature as a function of time and position. We then show the numerical results of the space-and-time-resolved light emission and that collisional excitation is the dominant source of light emission. We validate our model by measuring the light emitted by a laser-ionized plasma using a novel statistical method capable of resolving the nanosecond-scale temporal dynamics of the plasma light using a cost-effective camera with microsecond-scale timing jitter. This method is ideal for deployment in the high radiation environment of a particle accelerator that precludes the use of expensive nanosecond-gated cameras. Our results show that our models can effectively simulate the dynamics of a thin, laser-ionized plasma source. In addition, this work provides a detailed understanding of the plasma light measurement, which is one of the few diagnostic signals available for the direct measurement of PWFA plasma sources.
Attosecond-Angstrom free-electron-laser towards the cold beam limit A. F. Habib, G. G. Manahan, P. Scherkl, T. Heinemann, A. Sutherland, et al. Nature Communications, 2023 Electron beam quality is paramount for X-ray pulse production in free-electron-lasers (FELs). State-of-the-art linear accelerators (linacs) can deliver multi-GeV electron beams with sufficient quality for hard X-ray-FELs, albeit requiring km-scale setups, whereas plasma-based accelerators can produce multi-GeV electron beams on metre-scale distances, and begin to reach beam qualities sufficient for EUV FELs. Here we show, that electron beams from plasma photocathodes many orders of magnitude brighter than state-of-the-art can be generated in plasma wakefield accelerators (PWFAs), and then extracted, captured, transported and injected into undulators without significant quality loss. These ultrabright, sub-femtosecond electron beams can drive hard X-FELs near the cold beam limit to generate coherent X-ray pulses of attosecond-Angstrom class, reaching saturation after only 10 metres of undulator. This plasma-X-FEL opens pathways for advanced photon science capabilities, such as unperturbed observation of electronic motion inside atoms at their natural time and length scale, and towards higher photon energies.
Plasma Photocathodes Ahmad Fahim Habib, Thomas Heinemann, Grace G. Manahan, Daniel Ullmann, Paul Scherkl, et al. Annalen Der Physik, 2023 Plasma wakefield accelerators offer accelerating and focusing electric fields three to four orders of magnitude larger than state‐of‐the‐art radiofrequency cavity‐based accelerators. Plasma photocathodes can release ultracold electron populations within such plasma waves and thus open a path toward tunable production of well‐defined, compact electron beams with normalized emittance and brightness many orders of magnitude better than state‐of‐the‐art. Such beams will have far‐reaching impact for applications such as light sources, but also open up new vistas on high energy and high field physics. This paper reviews the innovation of plasma photocathodes, and reports on the experimental progress, challenges, and future prospects of the approach. Details of the proof‐of‐concept demonstration of a plasma photocathode in 90° geometry at SLAC FACET within the E‐210: Trojan Horse program are described. Using this experience, alongside theoretical and simulation‐supported advances, an outlook is given on future realizations of plasma photocathodes such as the upcoming E‐310: Trojan Horse‐II program at FACET‐II with prospects toward excellent witness beam parameter quality, tunability, and stability. Future installations of plasma photocathodes also at compact, hybrid plasma wakefield accelerators, will then boost capacities and open up novel capabilities for experiments at the forefront of interaction of high brightness electron and photon beams.
