Collisional Simulations Research Articles

Spokes and charged particle transport in HiPIMS magnetrons

Two separate scientific communities are shown to have studied one common phenomenon, azimuthally rotating dense plasma structures, also called spokes, in pulsed-power E × B discharges, starting from quite different approaches. The first body of work is motivated by fundamental plasma science and concerns a phenomenon called the critical ionization velocity, CIV, while the other body of work is motivated by the applied plasma science of high power impulse magnetron sputtering (HiPIMS). Here we make use of this situation by applying experimental observations, and theoretical analysis, from the CIV literature to HiPIMS discharges. For a practical example, we take data from observed spokes in HiPIMS discharges and focus on their role in charged particle transport, and in electron energization. We also touch upon the closely related questions of how they channel the cross-B discharge current, how they maintain their internal potential structure and how they influence the energy spectrum of the ions? New particle-in-cell Monte Carlo collisional simulations that shed light on the azimuthal drift and expansion of the spokes are also presented.

Electron kinetics in dc argon microplasmas

We carried out one-dimensional particle-in-cell and Monte Carlo collisional simulations of argon dc microplasmas. It is found that argon dc microplasmas have quite different electron kinetics from those of conventional low-pressure argon dc plasmas or helium dc microplasmas. The electron energy probability functions (EEPFs) of the argon dc microplasma are bi-Maxwellian for pressures exceeding 100 Torr, whereas it shows a convex-shaped profile for 10 Torr. The different EEPFs at high pressures come from the fact that, as the pressure is increased, elastic and inelastic electron–neutral collisions increase, because the cathode fall length decreases more slowly than the electron–neutral collisional mean free paths.

Synergy between ion temperature gradient turbulence and neoclassical processes in global gyrokinetic particle-in-cell simulations

Based on the CYCLONE case, simulations of collisional electrostatic ion temperature gradient (ITG) microturbulence carried out with the global gyrokinetic particle-in-cell (PIC) code ORB5 are presented. Considering adiabatic electrons, an increase in ion heat transport over the collisionless turbulent case due to ion-ion collisions is found to exceed the neoclassical contribution. This synergetic effect is due to interaction of collisions, turbulence, and zonal flows. When going from a collisionless to a collisional ITG turbulence simulation, a moderate reduction of the average zonal flow level is observed. The collisional zonal flow level turns out to be roughly independent of the finite collisionality considered. The Dimits shift softening by collisions [Z. Lin et al., Phys. Rev. Lett. 83, 3645 (1999)] is further characterized, and the shearing rate saturation mechanism is emphasized. Turbulence simulations start from a neoclassical equilibrium [T. Vernay et al., Phys. Plasmas 17, 122301 (2010)] and are carried out over significant turbulence times and several collision times thanks to a coarse-graining procedure, ensuring a sufficient signal/noise ratio even at late times in the simulation. The relevance of the Lorentz approximation for ion-ion collisions, compared to a linearized Landau self-collision operator, is finally addressed in the frame of both neoclassical and turbulence studies.

Kinetic simulations of a deuterium-tritium Z pinch with >1016 neutron yield

Fully kinetic, collisional, and electromagnetic simulations of the time evolution of an imploding and burning Z pinch plasma have been performed. Using the implicit particle-in-cell (PIC) code, multidimensional (1D and 3D) simulations of deuterium and deuterium-tritium Z pinches provide insight into the mechanisms of neutron production. The PIC code allows non-Maxwellian particle distributions, simulates finite mean-free-path effects, performs self-consistent calculations of anomalous resistivity, and permits charge separation. At low pinch current, neutron production is dominated by high energy ions driven by instabilities. The instabilities produce a power-law ion-energy distribution function in the distribution tail. At higher currents with deuterium-tritium fuel, the vast majority of the neutrons is thermonuclear in origin and neutron yield follows an I4 neutron yield scaling with current. High-current, multidimension simulations (up to 40 MA with > 1016 neutron yield) suggest that the fraction of thermonuclear neutrons increases with current and the strong dependence of neutron yield with current will continue at still higher currents. Scenarios for fusion breakeven and possible ignition in the 40–80 MA regime are discussed.

Anomalous self-generated electrostatic fields in nanosecond laser-plasma interaction

Electrostatic (E) fields associated with the interaction of a well-controlled, high-power, nanosecond laser pulse with an underdense plasma are diagnosed by proton radiography. Using a current three-dimensional wave propagation code equipped with nonlinear and nonlocal hydrodynamics, we can model the measured E-fields that are driven by the laser ponderomotive force in the region where the laser undergoes filamentation. However, strong fields of up to 110 MV/m measured in the first millimeter of propagation cannot be reproduced in the simulations. This could point to the presence of unexpected strong thermal electron pressure gradients possibly linked to ion acoustic turbulence, thus emphasizing the need for the development of full kinetic collisional simulations in order to properly model laser-plasma interaction in these strongly nonlinear conditions.

Cellular model for sand dunes with saltation, avalanche and strong erosion: collisional simulation of barchans

AbstractBarchans are crescent‐shaped dunes that form under unidirectional wind in areas of limited sand supply. The recent development of flume experiments and computer simulations has renewed interest in the interaction dynamics of two or more barchans. From the flume experiment, four distinguishable types of collision patterns between two barchans have been observed: coalescence, ejection, split and reorganization. We have proposed a simple cellular model for numerical simulations of dune dynamics, in which saltation and avalanche are elementary processes. In the present paper, we first describe the model in detail. The model reproduces three types of collision patterns: coalescence, ejection, and reorganization. The largest reason for a split pattern not to occur is the lack of an effect of the flow separation at the brink line of dunes and the recirculation bubble that it produces. We then model the effect of the recirculation bubble by assuming that strong erosion occurs at the reattachment point of the separation flow. The strong‐erosion model successfully reproduces all the collision patterns. Thus, three elementary processes – saltation, avalanche and strong‐erosion – are sufficient for a phenomenological description of the interaction dynamics of aqueous barchans. It is also shown that the type of collision is determined by competition between the filling‐up of the interdune between two barchans and the change in height of each dune. Copyright © 2010 John Wiley & Sons, Ltd.

Neoclassical equilibria as starting point for global gyrokinetic microturbulence simulations

The implementation of linearized operators describing inter- and like-species collisions in the global gyrokinetic particle-in-cell code ORB5 [S. Jolliet, Comput. Phys. Commun. 177, 409 (2007)] is presented. A neoclassical axisymmetric equilibrium with self-consistent electric field can be obtained with no assumption made on the radial width of the particle trajectories. The formulation thus makes it possible to study collisional transport in regions where the neoclassical approximation breaks down such as near the magnetic axis. The numerical model is validated against both analytical results as well as other simulation codes. The effects of the poloidally asymmetric Fourier modes of the electric field are discussed, and the contribution of collisional kinetic electrons is studied. In view of subsequent gyrokinetic simulations of turbulence started from a neoclassical equilibrium, the problem of numerical noise inherent to the particle-in-cell approach is addressed. A novel algorithm for collisional gyrokinetic simulation switching between a local and a canonical Maxwellian background for, respectively, carrying out the collisional and collisionless dynamics is proposed, and its beneficial effects together with a coarse graining procedure [Y. Chen and S. E. Parker, Phys. Plasmas 14, 082301 (2007)] on noise and weight spreading reduction are discussed.

Global collisional gyrokinetic simulations of ITG microturbulence starting from a neoclassical equilibrium

Linearized operators describing inter-species and like-species collisions have been discretized and implemented in the gyrokinetic Particle-In-Cell (PIC) code ORB5 [S. Jolliet, Comp. Phys. Comm. 177, 409 (2007)] based on the delta-f approach. Simulation results for neoclassical transport are compared with both analytical predictions as well as results from other codes. This new version of ORB5 including collisional dynamics thus makes it possible to carry out simulations of microturbulence starting from a global neoclassical equilibrium including self-consistent electric fields. First results of ITG microturbulence simulations carried out in this way are presented. The issue of numerical noise, inherent to the PIC approach and further accentuated by the implementation of collisions in the delta-f scheme, is addressed. It is shown how a noise reduction scheme based on a coarse graining procedure [Y. Chen and S. E. Parker, Phys. Plasmas 14, 082301 (2007)] ensures the physical relevance of such simulations. Furthermore, a novel delta-f algorithm is presented, which switches between a canonical and a local Maxwellian background for carrying out the collisonless and collisional dynamics respectively, and its advantages are discussed.

Kinetic simulation of thermonuclear-neutron production by a 107-A deuterium Z pinch

Fully kinetic simulations have demonstrated that at sufficiently high currents, half of the neutrons produced by a deuterium Z-pinch are thermonuclear in origin. At 150-kA pinch current, O. A. Anderson et al. [Phys. Rev. 110, 1375 (1958)] clearly shows that essentially all of the neutrons produced by a deuterium pinch are not thermonuclear, but are initiated by an instability that creates beam-target neutrons. Since this paper, many subsequent authors have supported this result while others have claimed that pinch neutrons are, on the contrary, thermonuclear. To resolve this issue, fully kinetic, collisional, and electromagnetic simulations of the complete time evolution of a deuterium pinch have been performed. The simulations were performed with the implicit particle-in-cell code LSP, as described in D. R. Welch et al. [Phys. Rev. Lett. 103, 255002 (2009)]. At 106 -A pinch currents, most of the neutrons are, indeed, beam-target in origin. At 15-MA current, half of the neutrons are thermonuclear and half are beam-target driven by instabilities that produce a power law fall off in the ion energy distribution function at large energy. Simulation results suggest that from 7- to 15-MA current, the fraction of thermonuclear neutrons is not sensitive to current and that the strong dependence of neutron yield on current will continue at currents greater than 15 MA.

Fully Kinetic Particle-in-Cell Simulations of a Deuterium Gas PuffzPinch

We present the first fully kinetic, collisional, and electromagnetic simulations of the complete time evolution of a deuterium gas puff z pinch. Recent experiments with 15-MA current pinches have suggested that the dominant neutron-production mechanism is thermonuclear. We observe distinct differences between the kinetic and magnetohydrodynamic simulations in the pinch evolution with the kinetic simulations producing both thermonuclear and beam-target neutrons. The kinetic approach demonstrated in this Letter represents a viable alternative for performing future plasma physics calculations.

Response to “Comment on ‘Scaling of asymmetric magnetic reconnection: General theory and collisional simulations’ ” [Phys. Plasmas 16, 034701 (2009)

The comment by Semenov et al. has called into question our derivation of the outflow velocity in asymmetric magnetic reconnection. We present three reasons that the analysis presented in the comment is incorrect. Most importantly, the authors of the comment have incorrectly applied results from one-dimensional shock theory to the problem of conservation through a two-dimensional dissipation region. For completeness, we compare their predictions to numerical simulation results, finding that their theory does not describe the data. We conclude the analysis in the comment is without merit.

Comment on “Scaling of asymmetric magnetic reconnection: General theory and collisional simulations” [Phys. Plasmas 14, 102114 (2007)

Recently, Cassak and Shay [Phys. Plasmas 14, 102114 (2007)] proposed a new scaling for asymmetric reconnection referred to as Sweet–Parker-type scaling. We set into question the derivation of those scaling laws.

The origin of the energy-dose window in separation-by-implanted-oxygen materials processing

The energy-dose (ED) window (so called Izumi window) for the formation of a perfect planar and homogeneous buried oxide layer in silicon using ion implantation is controlled by the interaction of excess radiation defects and the local oxygen concentration. The ED window is defined by an appropriate correlation between the distribution of implantation-induced excess defects and the position of the finally formed oxide layer. A quantitative relation is established on the basis of collisional computer simulations. The findings are discussed in terms of oxide precipitation under the influence of defects.

Enhanced energy localization and heating in high contrast ultra-intense laser produced plasmas via novel conical micro-target design

We report new experiments showing enhanced laser-target coupling and energy localization using nano-fabricated micro-conical Cu targets performed at the 100 TW CPA laser at LULI. A comparison was made between 1ω (λ = 1.057 μm, I = 1019 W/cm2) and 2ω (λ = 0.53 μm, I = 4-8 × 1018 W/cm2) irradiation to determine the effect of ASE induced preformed plasma filling the cone, using as principal diagnostics 2D Cu Kα imaging (transverse and rear-side), and high-resolution conical crystal spectroscopy of the Cu Kα bands. The 2ω irradiation exhibits laser absorption up to 50 μm deeper into the cone tip (versus at 1 ω), with a commensurately smaller Kα emission zone. Spectroscopy indicates a higher average charge state for the Cu emission at 2ω, with some shots exhibiting up to at least O-like emission. We deduce that micro-cone targets have similar performance in terms of material heating as a 50 μm diameter reduced mass target, despite a 900-fold larger mass. The observed enhancement in energy localization and heating in the cone geometry is supported by 2D collisional PIC simulations which indicate the presence of self-generated resistive magnetic field structures (≥ 10 MG) which confine the energetic electrons to the tip region

Modeling of plasma-target interaction during reactive magnetron sputtering of TiN

The nitrogen incorporation at the target during reactive magnetron sputtering of TiN is described by a simple stationary global model of the magnetron plasma, in combination with an analytical two-layer stationary surface model or dynamic collisional computer simulation (TRIDYN) of the surface processes. Results are shown for different nitrogen gas additions in Ar∕N2 and Xe∕N2 gas mixtures at a total pressure of 0.3Pa and a magnetron current of 0.3A. The nitrogen incorporation predicted by the analytical model is significantly less than obtained from computer simulation. The computer simulation yields nitrogen depth profiles which extend to about 2.5nm, exhibiting a quasirectangular shape in case of stoichiometric saturation with an integrated nitrogen areal density of ∼1.25×1016N∕cm2. The stationary-state nitrogen incorporation results from the balance of surface adsorption in connection with recoil implantation, direct ion implantation, and resputtering. The most relevant species are nitrogen gas molecules for adsorption, molecular nitrogen ions for implantation, and inert gas ions for recoil implantation and sputtering. The model results are in good agreement with experiment provided that nonzero sticking of nitrogen gas molecules is assumed on the unsaturated surface. The analytical surface model is preferable, which favors the picture of a continuous transition to bulk and surface saturation rather than discrete local saturation which is inherent in TRIDYN. Also the relative nitrogen incorporation for Xe∕N2 versus Ar∕N2 gas mixtures is well described.

Scaling of asymmetric magnetic reconnection: General theory and collisional simulations

A Sweet-Parker-type scaling analysis for asymmetric antiparallel reconnection (in which the reconnecting magnetic field strengths and plasma densities are different on opposite sides of the dissipation region) is performed. Scaling laws for the reconnection rate, outflow speed, the density of the outflow, and the structure of the dissipation region are derived from first principles. These results are independent of the dissipation mechanism. It is shown that a generic feature of asymmetric reconnection is that the X-line and stagnation point are not colocated, leading to a bulk flow of plasma across the X-line. The scaling laws are verified using two-dimensional resistive magnetohydrodynamics numerical simulations for the special case of asymmetric magnetic fields with symmetric density. Observational signatures and applications to reconnection in the magnetosphere are discussed.

MeV proton generation and efficiency from an intense laser irradiated foil

The proton energy distribution generated from the interaction of an intense ( Iλ 2 ≈ 10 20 W/cm 2 μm 2) short-pulse (100 fs) laser with a thin foil is investigated using energy resolved measurements and 2D collisional PIC-hybrid simulations. The measured absolute proton spectrum is well matched by a 1.7 MeV exponential function for energies <11 MeV. The proton conversion efficiency from hot electrons ≈6%. Simulations predict a strong radial dependence on the maximum proton energy and on the radial extent of 12 Å hydrocarbon depletion region. C and O ions in the hydrocarbon layer gain significant energies, limiting the efficiency to the protons. The efficiency scaling for ion mixtures is derived using a simple model, and is shown to strongly depend on the cooling rate of the hot electrons. Simulations using hydrogen-rich, layered targets predict much higher efficiencies.

Collisional Relaxation of Superthermal Electrons Generated by Relativistic Laser Pulses in Dense Plasma

Energy relaxation of the hot electron population generated by relativistic laser pulses in overdense plasma is analyzed for densities ranging from below to 1000 times solid density. It is predicted that longitudinal beam-plasma instabilities, which dominate energy transfer between hot electrons and plasma at lower densities, are suppressed by collisions beyond solid density. The respective roles of collisional energy transfer modes, i.e., direct collisions, diffusion, and resistive return current heating, are identified with respect to plasma density. The transition between the kinetic and the collisional regimes and scalings of collisional process are demonstrated by a fully integrated one-dimensional collisional particle simulation.

Collisional particle simulation of ion acoustic instability

The nonlinear evolution of ion acoustic fluctuations in the presence of a uniform electron drift which exceeds the sound speed and electron–ion collisions is investigated using a collisional particle simulation model for parameters relevant to laser-heated plasmas. The results indicate that for the one-dimensional case, strong electron–ion collisionality can lead to a significantly higher saturation level of the fluctuations, which is comparable to the saturation level in the two-dimensional collisionless regime. This relatively high turbulence level can act to enhance heat flux inhibition and strongly influence the absorption and transport properties of laser-produced plasmas.

Multiscale Monte Carlo Simulation of Circular DC Magnetron Sputtering: Influence of Magnetron Design on Target Erosion and Film Deposition

We present an experimental and computational study of the effect of magnetron design on the target erosion profile, wafer-level deposition uniformity, and feature-scale deposition topography in a circular DC magnetron sputtering system. We have conducted a multiscale Monte Carlo simulation consisting of a particle-in-cell Monte Carlo collision plasma simulation for target sputter erosion, a collisional transport simulation for film deposition, and a feature-scale deposition topography simulation. The entire simulation results for each step are verified in comparison with the experimental results for various process conditions. A new semiempirical calibration method, for converting an estimated ion current density distribution into a target erosion profile, is proposed with regard to the gas rarefaction effect due to sputtering wind. In conclusion, the whole performance indices of a circular DC magnetron sputtering system are substantially influenced by magnetron design, and the effectiveness of our multiscale Monte Carlo simulation methodology is validated.