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Hybrid particle-spectral method for kinetic plasma simulations
A hybrid model for numerical solutions of the Vlasov–Poisson equations is presented, which blends spectral and particle approaches. The model splits the distribution function for plasma species into both spectral and particle representations in the velocity space to combine the advantages of each approach. The spectral representation leverages asymmetrically weighted Hermite basis, whereas the particle representation leverages the particle-in-cell method. Configuration phase space is decomposed with the Fourier method, which is well suited for periodic problems. We derive conservation equations for mass, momentum, and energy for the proposed combined method. It is shown that the coupling error between the two methods is absent in the semi-discrete setting (not taking into account time discretization). Finally, numerical test cases are presented simulating a weak electron beam interaction with plasma, leading to beam–plasma instability. The initially localized electron beam evolved into a highly non-equilibrium distribution function in the velocity space. A small growth rate and the resonance nature of instability make it difficult to obtain accurate solutions for purely particle methods due to noise, which falls as ~1/$\sqrt{N_p}$ with a number of particles. At the same time, purely spectral methods may require a large number of modes to capture the highly nonequilibrium state of the evolved beam. We show that the hybrid method is well suited for such problems: it reproduces the linear stage as well as nonlinear dynamics with sufficient accuracy using a highly non-equilibrium distribution function.
Low-Temperature Plasma Assisted Kinetics Study of Ethanol
Non-equilibrium plasma assisted kinetics of ethanol at 0.5 atm over a temperature range of 523-1203 K were studied at stoichiometric conditions by using a plasma flow reactor (PFR). The effects of plasma chemistry on fuel and its influence on neutral chemistry is decoupled with both experimental and modelling efforts. Enhanced reactivity was observed experimentally in both plasma-assisted oxidation and pyrolysis cases with fuel consumption beginning at temperatures as low as 523 K. Absolute fuel consumption was observed at temperatures nearly 200 K earlier than pure thermal reactions highlighting the effectiveness of non-equilibrium plasma to promote reactivity. Furthermore, modelling results illustrated the effect of electron impact reactions towards accelerating fuel consumption and promoting low temperature chemistry by generating excited state N2 and reactive O and OH radicals.
Phase-space Energization of Ions in Oblique Shocks
Abstract Examining energization of kinetic plasmas in phase space is a growing topic of interest, owing to the wealth of data in phase space compared to traditional bulk energization diagnostics. Via the field-particle correlation (FPC) technique and using multiple means of numerically integrating the plasma kinetic equation, we have studied the energization of ions in phase space within oblique collisionless shocks. The perspective afforded to us with this analysis in phase space allows us to characterize distinct populations of energized ions. In particular, we focus on ions that reflect multiple times off the shock front through shock-drift acceleration, and how to distinguish these different reflected populations in phase space using the FPC technique. We further extend our analysis to simulations of three-dimensional shocks undergoing more complicated dynamics, such as shock ripple, to demonstrate the ability to recover the phase-space signatures of this energization process in a more general system. This work thus extends previous applications of the FPC technique to more realistic collisionless shock environments, providing stronger evidence of the technique’s utility for simulation, laboratory, and spacecraft analysis.
A kinetic model of friction in strongly coupled strongly magnetized plasmas
Plasmas that are strongly magnetized in the sense that the gyrofrequency exceeds the plasma frequency exhibit novel transport properties that are not well understood. As a representative example, we compute the friction force acting on a massive test charge moving through a strongly coupled and strongly magnetized one-component plasma using a generalized Boltzmann kinetic theory. Recent works studying the weakly coupled regime have shown that strong magnetization leads to a transverse component of the friction force that is perpendicular to both the Lorentz force and velocity of the test charge, in addition to the stopping power component aligned antiparallel to the velocity. Recent molecular dynamics simulations have also shown that strong Coulomb coupling in addition to strong magnetization gives rise to a third component of the friction force in the direction of the Lorentz force. Here, we show that the generalized Boltzmann kinetic theory captures these effects and generally agrees well with the molecular dynamics simulations over a broad range of Coulomb coupling and magnetization strength regimes. The theory is also used to show that the “gyro” component of the friction in the direction of the Lorentz force arises due to asymmetries associated with gyromotion during short-range collisions. Computing the average motion of the test charge through the background plasma, the transverse force is found to strongly influence the trajectory by changing the gyroradius and the gyrofriction force is found to slightly change the gyrofrequency of the test charge resulting in a phase shift.
Low-Temperature Plasma Assisted Kinetics Study of Ethanol
Abstract: Non- equilibrium plasma assisted kinetics of ethanol at 0.5 atm over a temperature range of 523-1203 K were studied at stoichiometric conditions by using a plasma flow reactor (PFR). The effects of plasma chemistry on fuel and its influence on neutral chemistry is decoupled with both experimental and modelling efforts. Enhanced reactivity was observed experimentally in both plasma-assisted oxidation and pyrolysis cases with fuel consumption beginning at temperatures as low as 523 K. Absolute fuel consumption was observed at temperatures nearly 200 K earlier than pure thermal reactions highlighting the effectiveness of non-equilibrium plasma to promote reactivity. Modelling results illustrated the effect of electron impact reactions towards accelerating fuel consumption and promoting low temperature chemistry by generating excited state N2 and reactive O and OH radicals.
Self-organization of photoionized plasmas via kinetic instabilities
Abstract Self-organization in an unmagnetized collisionless plasma (in this paper) refers to formation of transient coherent structures such as collective oscillations (electrostatic waves) or magnetic fields resulting from so-called kinetic effects in the plasma. This topical review provides a comprehensive analysis of the self-organization of strong-field photoionized, non-equilibrium plasmas through kinetic instabilities. The authors propose and demonstrate a novel experimental platform that enables the formation of dense plasmas with known highly anisotropic and non-thermal electron velocity distribution functions on a timescale on the order of an inverse electron plasma frequency. We then show that such plasmas are highly susceptible to a hierarchy of kinetic instabilities, including two-stream, current filamentation and Weibel, that convert a fraction of the electron kinetic energy into electric and/or magnetic energy stored in self-organized structures. The electrostatic waves so produced are measured using a collective light (Thomson) scattering technique with femtosecond resolution as the kinetic instabilities aided by collisions eventually thermalize the plasma electrons. In addition, we describe a novel experimental technique that has made it possible to map the temporal evolution of the wavenumber spectrum of the thermal Weibel instability with picosecond resolution, which leads to the formation of quasi-static coherent magnetic fields with different topologies in photoionized plasmas. Finally, the paper summarizes the important results and discusses future directions on this topic.
Unsupervised discovery of nonlinear plasma physics using differentiable kinetic simulations
Plasma supports collective modes and particle–wave interactions that lead to complex behaviour in, for example, inertial fusion energy applications. While plasma can sometimes be modelled as a charged fluid, a kinetic description is often crucial for studying nonlinear effects in the higher-dimensional momentum–position phase space that describes the full complexity of the plasma dynamics. We create a differentiable solver for the three-dimensional partial-differential equation describing the plasma kinetics and introduce a domain-specific objective function. Using this framework, we perform gradient-based optimization of neural networks that provide forcing function parameters to the differentiable solver given a set of initial conditions. We apply this to an inertial-fusion-relevant configuration and find that the optimization process exploits a novel physical effect.
Plasma-Coupled Flow Reactor Studies of Low-Temperature Plasma Assisted Kinetics of Methanol Blended with CO2
Ignition technologies based on low-temperature plasmas (LTP) have the potential to operate next generation engines at elevated pressures and increased dilution limits promoting higher efficiencies. From a practical standpoint, research on LTP igniters has shown to enhance combustion and ignition, improve flame stability, and extend the dilution limits of combustion. All of the aforementioned gains are complemented with higher ignition efficiencies. However, the biggest challenge with incorporating this technology into engines is the knowledge gap of how exactly plasma chemistry effects can enhance the basic combustion phenomena. This coupled with the lack of validated kinetic mechanisms for plasma-combustion chemistry is the biggest obstruction to recognize efficient ignition, especially for application relevant fuels and biofuels. In order to comprehensively evaluate the effects of LTP on an oxygenated fuel specific system, this present study examines the kinetics of methanol plasma-assisted pyrolysis and oxidation using a custom-built plasma flow reactor (PFR). Experimental regimes are also further extended to understand the effects of adding CO2 to the mixture and its consequence on reaction kinetics. The PFR is installed with a dielectric-barrier discharge (DBD) configuration to induce LTP into the fuel mixture. Non-equilibrium plasmas are generated by high-voltage pulses (nearing 20 KV) administered by a plasma pulser at high-pulse repetition rates (up to 10 kHz). In order to better understand and isolate plasma chemistry and its effect on neutral chemistry, the experiments were carried out by heavily diluting reactive mixtures in nitrogen at near isothermal conditions. This suppresses the effect of exothermic reactions on chemistry allowing stable intermediates and products to be detected and quantified using ex-situ GC/MS diagnostic methods. Experiments were carried out at 0.5 atm pressure and over a wide range of temperatures from 523 K to 1203 K. Experimental results depicted the enhancement in intermediates production as well as overall lower temperatures required for complete fuel consumption in the plasma specific cases as opposed to their pure thermal counterpart. Formation of oxygenated and nitrile compounds specific to plasma assisted pyrolysis cases illustrated the efficacy of LTP to introduce new reaction pathways accelerating fuel decomposition. Increase in reactivity at lower temperatures is sought to be an effect induced by plasma chemistry postulating the acceleration in intermediates production. The onset of thermal ignition in plasma assisted oxidation is seen 200 K earlier than thermal oxidation highlighting efficient fuel conversion to final byproducts. Enhanced collisional processes afforded by LTP is seen to perturb reaction pathways between oxygenated fuel radicals and N-atoms to alter overall chemical reactivity. New insights into kinetics are gained from this study highlighting governing plasma assisted combustion (PAC) pathways for oxygenated fuel reaction chemistry. The results from this study can be used to develop future mechanisms specific to plasma chemistry which can bridge the mechanistic knowledge gap for LTP ignition so that future engines can adopt LTPs in their design for efficient combustion.
Nonlinear coupling of whistler waves to oblique electrostatic turbulence enabled by cold plasma
Kinetic simulations and theory demonstrate that whistler waves can excite oblique, short-wavelength fluctuations through secondary drift instabilities if a population of sufficiently cold plasma is present. The excited modes lead to heating of the cold populations and damping of the primary whistler waves. The instability threshold depends on the density and temperature of the cold population and can be relatively small if the temperature of the cold population is sufficiently low. Furthermore, this mechanism may thus play a significant role in controlling amplitude of whistlers in the regions of the Earth's magnetosphere where cold background plasma of sufficient density is present.
Electron-scale current sheets and energy dissipation in 3D kinetic-scale plasma turbulence with low electron beta
ABSTRACT Three-dimensional kinetic-scale turbulence is studied numerically in the regime where electrons are strongly magnetized (the ratio of plasma species pressure to magnetic pressure is βe = 0.1 for electrons and βi = 1 for ions). Such a regime is relevant in the vicinity of the solar corona, the Earth’s magnetosheath, and other astrophysical systems. The simulations, performed using the fluid-kinetic spectral plasma solver (sps) code, demonstrate that the turbulent cascade in such regimes can reach scales smaller than the electron inertial scale, and results in the formation of electron-scale current sheets (ESCS). Statistical analysis of the geometrical properties of the detected ESCS is performed using an algorithm based on the medial axis transform. A typical half-thickness of the current sheets is found to be on the order of electron inertial length or below, while their half-length falls between the electron and ion inertial length. The pressure–strain interaction, used as a measure of energy dissipation, exhibits high intermittency, with the majority of the total energy exchange occurring in current structures occupying approximately 20 per cent of the total volume. Some of the current sheets corresponding to the largest pressure–strain interaction are found to be associated with Alfvénic electron jets and magnetic configurations typical of reconnection. These reconnection candidates represent about 1 per cent of all the current sheets identified.
Topanga: A kinetic ion plasma code for large-scale ionospheric simulations on magnetohydrodynamic timescales
Topanga is a kinetic ion code developed for simulating large-scale plasma phenomena in the Earth's ionosphere on magnetohydrodynamic timescales. It is a domain-decomposed parallel code that runs on high-performance computing platforms. Features of Topanga include spherical geometry for simplified boundary conditions and computational efficiency; a hybrid plasma model with inertia-less fluid electrons, kinetic ions, and an electric field specified via an Ohm's law; a Maxwell-FDTD (finite difference time domain) plasma model which retains the displacement current in Maxwell's equations and models electron currents in the ionosphere with a tensor conductivity; sponge-layer boundary conditions for absorption of electromagnetic and plasma waves incident on the domain boundaries; and a novel mixed-implicit algorithm for evolving the EM fields inside the Maxwell-FDTD region that is stable over many orders of magnitude in the electron–ion collision frequency. We verify the numerical methods used in Topanga on a pair of test problems. The first test involves modeling a three-dimensional collisionless shock using the hybrid set of equations. The second test involves modeling a spherical TEM mode in vacuum using the Maxwell-FDTD set of equations. Finally, we demonstrate how using the combined set of hybrid and Maxwell-FDTD equations to model the Starfish Prime high-altitude nuclear test recovers a “missing” EM signal on the ground that is not present when using only the hybrid set of equations. The magnitude of this signal in the simulation containing the Maxwell-FDTD region agrees well with the E3a portion of the magnetohydrodynamic electromagnetic pulse from Starfish Prime.
Role of Parallel Solenoidal Electric Field on Energy Conversion in 2.5D Decaying Turbulence with a Guide Magnetic Field
We perform 2.5D particle-in-cell simulations of decaying turbulence in the presence of a guide (out-of-plane) background magnetic field. The fluctuating magnetic field initially consists of Fourier modes at low wavenumbers (long wavelengths). With time, the electromagnetic energy is converted to plasma kinetic energy (bulk flow+thermal energy) at the rate per unit volume of J· E for current density J and electric field E. Such decaying turbulence is well known to evolve toward a state with strongly intermittent plasma current. Here we decompose the electric field into components that are irrotational, E ir , and solenoidal (divergence-free), E so . E ir is associated with charge separation, and J · E ir is a rate of energy transfer between ions and electrons with little net change in plasma kinetic energy. Therefore, the net rate of conversion of electromagnetic energy to plasma kinetic energy is strongly dominated by J · E so , and for a strong guide magnetic field, this mainly involves the component E so,∥ parallel to the total magnetic field B. We examine various indicators of the spatial distribution of the energy transfer rate J ∥ · E so,∥ , which relates to magnetic reconnection, the best of which are (1) the ratio of the out-of-plane electric field to the in-plane magnetic field, (2) the out-of-plane component of the nonideal electric field, and (3) the magnitude of the estimate of current helicity.
LLNL FESP Theory Highlights: October 2024
I. Novikau, I. Y. Dodin, E. A. Startsev, I. Joseph, Quantum algorithms for simulating dissipative linear and nonlinear dynamics of plasmas. Invited talk at the 66th Annual Meeting of the APS Division of Plasma Physics, Atlanta, Georgia. Novikau I., Dodin I.Y., Startsev E.A., Encoding of linear kinetic plasma problems in quantum circuits via data compression, Journal of Plasma Physics. 2024;90(4):805900401, doi:10.1017/S0022377824000795. We propose an algorithm for encoding linear kinetic plasma problems in quantum circuits. The focus is on modelling electrostatic linear waves in a one-dimensional Maxwellian electron plasma. The waves are described by the linearized Vlasov–Ampère system with a spatially localized external current that drives plasma oscillations. This system is formulated as a boundary-value problem and cast in the form of a linear vector equation to be solved by using the quantum signal processing algorithm. The latter requires encoding of a matrix in a quantum circuit as a sub-block of a unitary matrix. We propose how to encode in a circuit in a compressed form and discuss how the resulting circuit scales with the problem size and the desired precision.
Laboratory Study of Collisionless Magnetic Reconnection
A concise review is given on the past two decades’ results from laboratory experiments on collisionless magnetic reconnection in direct relation with space measurements, especially by the Magnetospheric Multiscale (MMS) mission. Highlights include spatial structures of electromagnetic fields in ion and electron diffusion regions as a function of upstream symmetry and guide field strength, energy conversion and partitioning from magnetic field to ions and electrons including particle acceleration, electrostatic and electromagnetic kinetic plasma waves with various wavelengths, and plasmoid-mediated multiscale reconnection. Combined with the progress in theoretical, numerical, and observational studies, the physics foundation of fast reconnection in collisionless plasmas has been largely established, at least within the parameter ranges and spatial scales that were studied. Immediate and long-term future opportunities based on multiscale experiments and space missions supported by exascale computation are discussed, including dissipation by kinetic plasma waves, particle heating and acceleration, and multiscale physics across fluid and kinetic scales.
Modeling and verification of dynamic field ionization for laser-target interactions
Integrating field ionization models into kinetic plasma simulations is required for a variety of applications, especially when field strengths vary from low to high regimes, such as in laser-target interactions. The introduction of new physics models into kinetic codes requires a rigorous verification of their accuracy through well-defined verification problems. In this work, the field ionization model that has been included in the kinetic plasma code VPIC is presented, along with the detailed approach adopted for its integration. This model includes a comprehensive range of field ionization mechanisms: multiphoton ionization, tunneling ionization, and barrier suppression ionization. New verification problems employed to evaluate the ionization model's fidelity are outlined, and the simulation parameters that affect the accuracy of simulation results are explored. Additionally, this work addresses the impact of field ionization on computational performance.
Second-Phase Hepatitis C Plasma Viral Kinetics Directly Reflects Reduced Intrahepatic Burden of Hepatitis C Virus
Mathematical models explain how antivirals control viral infections. Hepatitis C virus (HCV) treatment results in at least 2 phases of decline in viremia. Here, the first phase reflects clearance of rapidly produced virions. The second phase is hypothesized to derive from loss of infected cells but has been challenging to prove. Using single-cell methods, we quantified the number of hepatitis C virus (HCV)-infected hepatocytes in liver biopsies taken before and within 7 days of initiating direct-acting antivirals (DAAs) in a double-blinded randomized controlled trial testing 2 (sofosbuvir-velpatasvir) versus 3 (sofosbuvir-velpatasvir-voxilaprevir) DAAs. We employed thousands of intrahepatic measurements in 10 persons with chronic genotype 1a HCV infection: median proportion of infected hepatocytes declined from 11.3% (range, 1.3%–59%) to 0.6% (range, <0.3%–5.8%), a loss of 75%–95% infected hepatocytes. Plasma viremia correlated with numbers of HCV-infected hepatocytes (r = 0.77; P < .0001). Second-phase plasma dynamics and changes in infected hepatocytes were indistinct (P = .16), demonstrating that second-phase viral dynamics derive from loss of infected cells. DAAs led to a decline in intracellular HCV RNA and interferon-stimulated gene expression (P < .05 for both). We proved that second-phase viral dynamics reflect decay of intrahepatic burden of HCV, partly due to clearance of HCV RNA from hepatocytes.