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DOE OSTI2025

Ohm’s Law, the Reconnection Rate, and Energy Conversion in Collisionless Magnetic Reconnection

Magnetic reconnection is a ubiquitous plasma process that transforms magnetic energy into particle energy during eruptive events throughout the universe. Reconnection not only converts energy during solar flares and geomagnetic substorms that drive space weather near Earth, but it may also play critical roles in the high energy emissions from the magnetospheres of neutron stars and black holes. In this review article, we focus on collisionless plasmas that are most relevant to reconnection in many space and astrophysical plasmas. Guided by first-principles kinetic simulations and spaceborne in-situ observations, we highlight the most recent progress in understanding this fundamental plasma process. We start by discussing the non-ideal electric field in the generalized Ohm’s law that breaks the frozen-in flux condition in ideal magnetohydrodynamics and allows magnetic reconnection to occur. We point out that this same reconnection electric field also plays an important role in sustaining the current and pressure in the current sheet and then discuss the determination of its magnitude (i.e., the reconnection rate), based on force balance and energy conservation. This approach to determining the reconnection rate is applied to kinetic current sheets with a wide variety of magnetic geometries, parameters, and background conditions. We also briefly review the key diagnostics and modeling of energy conversion around the reconnection diffusion region, seeking insights from recently developed theories. Finally, future prospects and open questions are discussed.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Bohm Criterion of Plasma Sheaths away from Asymptotic Limits

The plasma exit flow speed at the sheath entrance is constrained by the Bohm criterion. The so-called Bohm speed regulates the plasma particle and power exhaust fluxes to the wall, and it is commonly deployed as a boundary condition to exclude the sheath region in quasineutral plasma modeling. In this work, the Bohm criterion analysis is performed in the intermediate plasma regime away from the previously known limiting cases of adiabatic laws and the asymptotic limit of infinitesimal Debye length in a finite-size system, using the transport equations of an anisotropic plasma. The resulting Bohm speed has explicit dependence on local plasma heat flux, temperature isotropization, and thermal force. Comparison with kinetic simulations demonstrates its accuracy over the plasma-sheath transition region in which quasineutrality is weakly perturbed and the Bohm criterion applies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Neutralization of ion beam by electron injection: Accumulation of cold electrons

Ion beam charge neutralization by electron injection is a complex kinetic process. Recent experiments show that the resulting self-potential of the ion beam after neutralization by plasma is much lower than the temperature of plasma electrons [Stepanov et al., Phys. Plasmas 23, 043113 (2016)], indicating that kinetic effects are important and may affect the neutralization of the ion beam. We performed a numerical study of the charge neutralization process of an ion beam making use of a two-dimensional electrostatic particle-in-cell code. The results show that the process of charge neutralization by electron injection is composed of two stages. During the first stage, the self-potential of the beam is higher than the temperature of injected electrons (T e /e) and all injected electrons are captured by the ion beam. During the second stage, hot electrons escape from the ion beam and the beam self-potential (φ) decreases because cold electrons slowly accumulate resulting in the beam self-potential φ to become much lower than Te/e in agreement with previous experimental observations at Princeton Advanced Teststand. We also determined that the resulting φ scales as φ~√T e , in agreement with previous experimental observations from Gabovich's group. In addition, the results show that the transverse position of the electron source has a great impact on ion beam neutralization. A slight shift of the electron source as relevant to the ion thrusters leads to a large increase in the beam self-potential because of an increase in potential energy of injected electrons.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Explicit structure-preserving geometric particle-in-cell algorithm in curvilinear orthogonal coordinate systems and its applications to whole-device 6D kinetic simulations of tokamak physics

Explicit structure-preserving geometric particle-in-cell (PIC) algorithm in curvilinear orthogonal coordinate systems is developed. The work reported represents a further development of the structure-preserving geometric PIC algorithm achieving the goal of practical applications in magnetic fusion research. The algorithm is constructed by discretizing the field theory for the system of charged particles and electromagnetic field using Whitney forms, discrete exterior calculus, and explicit non-canonical symplectic integration. In addition to the truncated infinitely dimensional symplectic structure, the algorithm preserves exactly many important physical symmetries and conservation laws, such as local energy conservation, gauge symmetry and the corresponding local charge conservation. As a result, the algorithm possesses the long-term accuracy and fidelity required for first-principles-based simulations of the multiscale tokamak physics. The algorithm has been implemented in the SymPIC code, which is designed for high-efficiency massively-parallel PIC simulations in modern clusters. The code has been applied to carry out whole-device 6D kinetic simulation studies of tokamak physics. A self-consistent kinetic steady state for fusion plasma in the tokamak geometry is numerically found with a predominately diagonal and anisotropic pressure tensor. The state also admits a steady-state sub-sonic ion flow in the range of 10 km s -1 , agreeing with experimental observations and analytical calculations Kinetic ballooning instability in the self-consistent kinetic steady state is simulated. It is shown that high-n ballooning modes have larger growth rates than low-n global modes, and in the nonlinear phase the modes saturate approximately in 5 ion transit times at the 2% level by the E × B flow generated by the instability. These results are consistent with early and recent electromagnetic gyrokinetic simulations.

43 PARTICLE ACCELERATORS↗

DOE OSTI2021

Production and Persistence of Extreme Two-temperature Plasmas in Radiative Relativistic Turbulence

Turbulence is a predominant process for energizing electrons and ions in collisionless astrophysical plasmas, and thus is responsible for shaping their radiative signatures (luminosity, spectra, and variability). To better understand the kinetic properties of a collisionless radiative plasma subject to externally driven turbulence, we investigate particle-in-cell simulations of relativistic plasma turbulence with external inverse Compton cooling acting on the electrons. We find that ions continuously heat up while electrons gradually cool down (due to the net effect of radiation), and hence the ion-to-electron temperature ratio T i /T e grows in time. Furthermore, we show that Ti/Te is limited only by the size and duration of the simulations (reaching ${T}_{i}/{T}_{e}\sim {10}^{3}$), indicating that there are no efficient collisionless mechanisms of electron–ion thermal coupling. This result has implications for models of radiatively inefficient accretion flows, such as observed in the Galactic center and in M87, for which so-called two-temperature plasmas with ${T}_{i}/{T}_{e}\gg 1$ have been invoked to explain their low luminosity. Additionally, we find that electrons acquire a quasi-thermal distribution (dictated by the competition of turbulent particle energization and radiative cooling), while ions undergo efficient nonthermal acceleration (acquiring a harder distribution than in equivalent nonradiative simulations). There is a modest nonthermal population of high-energy electrons that are beamed intermittently in space, time, and direction; these beamed electrons may explain rapid flares in certain high-energy astrophysical systems (e.g., in the Galactic center). These numerical results demonstrate that extreme two-temperature plasmas can be produced and maintained by relativistic radiative turbulence.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

An investigation of shock formation vs shock mitigation of colliding plasma jets

Here, this work studies the interaction between colliding plasma jets to understand regimes in which jet merging results in shock formation vs regimes in which the shock formation is mitigated due to the collisionless interpenetration of the jets. A kinetic model is required for this study because fluid models will always produce a shock upon the collision of plasma jets. The continuum-kinetic, Vlasov–Maxwell–Dougherty model with one velocity dimension is used to accurately capture shock heating, along with a novel coupling with a moment equation to evolve perpendicular temperature for computational efficiency. As a result, this relatively inexpensive simulation can be used for detailed scans of the parameter space toward predictions of shocked vs shock-mitigated regimes, which is of interest for several fusion concepts such as plasma-jet-driven magneto-inertial fusion, high-energy-density plasmas, astrophysical phenomena, and other laboratory plasmas. The initial results obtained using this approach are in agreement with the preliminary outcomes of the plasma liner experiment.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Higher Harmonics in Multipactor Induced Plasma Ionization Breakdown near a Dielectric Surface

In this Letter, the novel physics of higher harmonic (HH) generation of the normal electric field near a dielectric surface is reported in multipactor induced plasma ionization breakdown, as determined by kinetic particle-in-cell simulations. The observed HH frequency is around ten times the fundamental rf driving frequency, but lower than the electron plasma frequency. A theory is constructed which indicates that stream plasma interaction-induced instability is the mechanism of HH generation in the collisional regime. The HH frequency and its corresponding growth rate of the HH oscillation amplitude from the theory are in good agreement with kinetic particle-in-cell simulations.

60 APPLIED LIFE SCIENCES↗

NASA NTRS2003

Magnetized Plasma Expansion and its Interaction with a Plasma Stream

Expansion of magnetized plasma in the magnetic field of a solenoid is studied by means of simulations using a 3-dimensional hybrid code. The plasma expands against a high- density and slow plasma stream (PS). The expansion causes inflation of the magnetic field; near the solenoid the magnetic field variation with increasing distance (r) remains as B(alpha)r(sup -3), but at farther distances B(alpha)r(sup -p), where the exponent p is found in the range 0.5 approx. less than p approx. less than 1.2 forming a plateau in the magnetic field distribution B(r). At the start of injection of plasma from the ends of the solenoid, the PS interacts with the solenoid magnetic field and creates a bow shock at a distance where the Larmor radius (r(sub il)) of the PS ions in the solenoid magnetic field nearly equals the scale length (L) of B(r), that is, r(sub il) approx. L = (B(sup -1)dB L /dr)(sup -1). As the injected plasma accumulates in the solenoid magnetic field, it expands inflating the magnetic field and the bow shock moves outward. The speed of the expansion front and the shock progressively decreases and eventually a stand-off occurs when the PS dynamic pressure is eventually balanced by the magnetic and kinetic pressures of the expanding plasma and the inflating magnetic field. The inflating field shows wave-like behavior, with considerable structures in the field and current distributions.

Singh, Nagendra↗

DOE OSTI2021

The scaling of kinetic and transport behaviors in the solution-phase chemistry of a plasma–liquid interface

The reactions at a plasma–liquid interface often involve species such as the solvated electron or the hydroxyl radical, which initiate the reduction or oxidation of solution-phase reactants (so-called scavengers) or are consumed by their own second-order recombination. Here, the mathematical scaling of the reaction–diffusion equations at the interface is used to obtain a characteristic time that can be used to determine the transition from highly efficient scavenger reduction or oxidation to lower efficiencies due to transport limitations. The characteristic time (tc) is validated using numerical solutions of the reaction–diffusion equations. When the scavenger kinetics are faster than second-order recombination, this characteristic transition time scales proportionally with the scavenger diffusivity (Ds) and the square of the scavenger bulk concentration (SB) and inversely proportional to the electron flux (J) squared; that is, t c = D s S B 2 F 2 /J 2 , where F is Faraday’s constant. However, when the scavenger kinetics are comparable or slower than second-order recombination, this scaling does not hold. Extending this analysis to three-dimensional systems shows that the profile of the electron flux on the surface affects the spatial location where reactions are most effective. Finally, the assessment of the implications of these behaviors for the reactor design highlights how effectively controlling the electron flux and solution transport may be necessary to improve the efficiency of scavenger reactions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1987

The interaction of quasiperpendicular shock waves in a collisionless plasma

The interaction between collisionless shocks is examined from a kinetic viewpoint using computer simulations of shock collisions spanning the range of ambient plasma and shock parameters typical of the interplanetary medium. It is found that the interaction between two subcritical, perpendicular shocks is largely fluidlike with no evidence for accelerated particles. The electromagnetic fields associated with each shock, but not the plasmas, pass through each other during the collision. This interaction is due to self-consistently generated electric fields which adjust to the value needed to bring to rest the two incoming streams. The interaction between two supercritical perpendicular collisionless shocks is similar to the subcritical case, in that the electromagnetic fields associated with each shock are transmitted whereas particles are not. However, the interaction is also highly dynamic with substantial acceleration of ions. Increasing the Mach number gives rise to an increasing number of energetic particles.

Cargill, P. J.↗

DOE OSTI2024

Low-pressure inductively coupled plasmas in hydrogen: impact of gas heating on the spatial distribution of atomic hydrogen and vibrationally excited states

Non-equilibrium inductively coupled plasmas (ICPs) operating in hydrogen are of significant interest for applications including large-area materials processing. Increasing control of spatial gas heating, which drives the formation of neutral species density gradients and the rate of gas-temperature-dependent reactions, is critical. In this study, we use 2D fluid-kinetic simulations with the Hybrid Plasma Equipment Model to investigate the spatially resolved production of atomic hydrogen in a low-pressure planar ICP operating in pure hydrogen (10–20 Pa or 0.075–0.15 Torr, 300 W). The reaction set incorporates self-consistent calculation of the spatially resolved gas temperature and 14 vibrationally excited states. We find that the formation of neutral-gas density gradients, which result from spatially non-uniform electrical power deposition at constant pressure, can drive significant variations in the vibrational distribution function and density of atomic hydrogen when gas heating is spatially resolved. This highlights the significance of spatial gas heating on the production of reactive species in relatively high-power-density plasma processing sources.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2002

Momentum Flux Measuring Instrument for Neutral and Charged Particle Flows

An instrument to measure the momentum flux (total pressure) of plasma and neutral particle jets onto a surface has been developed. While this instrument was developed for magnetized plasmas, the concept works for non-magnetized plasmas as well. We have measured forces as small as 10(exp -4) Newtons on a surface immersed in the plasma where small forces are due to ionic and neutral particles with kinetic energies on the order of a few eV impacting the surface. This instrument, a force sensor, uses a target plate (surface) that is immersed in the plasma and connected to one end of an alumina rod while the opposite end of the alumina rod is mechanically connected to a titanium beam on which four strain gauges are mounted. The force on the target generates torque causing strain in the beam. The resulting strain measurements can be correlated to a force on the target plate. The alumina rod electrically and thermally isolates the target plate from the strain gauge beam and allows the strain gauges to be located out of the plasma flow while also serving as a moment arm of several inches to increase the strain in the beam at the strain gauge location. These force measurements correspond directly to momentum flux and may be used with known plasma conditions to place boundaries on the kinetic energies of the plasma and neutral particles. The force measurements may also be used to infer thrust produced by a plasma propulsive device. Stainless steel, titanium, molybdenum, and aluminum flat target plates have been used. Momentum flux measurements of H2, D2, He, and Ar plasmas produced in a magnetized plasma device have been performed.

Chavers, Greg↗

DOE OSTI2024

Relativistic Alfvén Turbulence at Kinetic Scales

Abstract In a strongly magnetized, magnetically dominated relativistic plasma, Alfvénic turbulence can extend to scales much smaller than the particle inertial scales. It leads to an energy cascade somewhat analogous to inertial- or kinetic-Alfvén turbulent cascades existing in nonrelativistic space and astrophysical plasmas. Based on phenomenological modeling and particle-in-cell numerical simulations, we propose that the energy spectrum of such relativistic kinetic-scale Alfvénic turbulence is close to k −3 or slightly steeper than that due to intermittency corrections or Landau damping. We note the analogy of this spectrum with the Kraichnan spectrum corresponding to the enstrophy cascade in 2D incompressible fluid turbulence. Such turbulence strongly energizes particles in the direction parallel to the background magnetic field, leading to nearly one-dimensional particle momentum distributions. We find that these distributions have universal log-normal statistics.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

How transient effects can change the inferred plasma temperatures when using K-shell sulfur line ratios in a time dependent iron sulfide plasma

This paper describes how the steady state atomic kinetics approximation can underestimate the electron temperature determined from K-shell lines in ps-time-scale transient plasmas. In particular, we model the temperature determination of solid FeS targets used in opacity experiments at the Orion laser facility from the ratio of sulfur He-α to Ly-α lines. Such experiments use short-pulse lasers to heat a thin microdot of FeS buried in a plastic target to temperatures of more than 1 keV and densities of approximately 1–2 g/cm 3 . Using atomic kinetics calculations based on a temperature history from a radiation hydrodynamic simulation of the target evolution, the peak temperature inferred from the sulfur line ratios is 1.29 keV at 3.1 ps as compared with the input peak temperature of 1.41 keV at 2.0 ps. There is a time lag of 1.2 ps at the peak, and an overall 0.5 ps time lag in the temporal history of the temperature as the plasma cools over the next 10 ps.

Rilloraza, Francisco↗

NASA NTRS1982

The probability distributions of S/+/ gyrospeeds in the Io torus

The first detailed thermal speed probability distribution for a Jovian plasma ion is presented. The distribution of heavy ion thermal speeds appears to be highly significant for an evaluation of the processes by which the particle and energy budgets of the Io plasma torus are maintained. Attention is given to the measurement, reduction, and analysis procedures which yield the reported probability distribution. A kinetic energy inventory of the Jovian plasma heavy ion component can be obtained from high-resolution, high-precision spectrophotometry of emission lines. The current S(+) study finds that detection of the line wings results in a mean energy (approximately 60 eV) which is higher by a factor of approximately 10 than is implied by the line core. This illustrates that a dispersive measurement may provide only a lower limit to the kinetic energy content.

Brown, R. A.↗

NASA NTRS1973

Energy distribution in parallel plate plasma accelerators

A parallel plate accelerator operated in the quasi-steady regime of argon mass flow discharges permits, on account of its geometry, the appraisal of the initial ratio of energy disposition into the kinetic and thermal modes of the plasma while retaining the essential features of coaxial high power self-field MPD accelerators. The energy disposition ratio, calculated as the ratio of kinetic energy to enthalpy in the exhaust flow, shows reasonable agreement with the ratio of the induced emf in the accelerator to resistive voltage drop. Both these ratios indicate that the discharge imparts more energy to the flow by resistive heating than by direct body force acceleration. This is turn suggests that other acceleration mechanisms must be responsible for the high performance of conventional MPD arcs.

Dicapua, M. S.↗

DOE OSTI2021

Nonlinear kinetic simulation study of the ion–ion streaming instability in single- and multi-ion species plasmas

The nonlinear evolution of the ion–ion streaming instability (IISI) is studied using numerical techniques novel to this problem that afford direct insight into the evolution of the particle distributions of each species. Here, during the linear phase of the instability, we demonstrate quantitative agreement with linear kinetic theory. Subsequently, the electrostatic field generated by the IISI causes ring-like velocity distributions of ions to form that are both heated and slowed to varying degrees relative to their initial flows. Due to variation in the trapping conditions for ion species of differing charge-to-mass ratio, when flows of multiple species interact, the nonlinear evolution of each species can be starkly different: we show a case where a lighter ion species is completely stopped by a heavier ion species via the IISI alone (i.e., without collisions) and, for the first time, demonstrate how the IISI can introduce a relative flow between ion species that initially have the same flow velocities, thereby separating them.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Numerical modeling of plasma assisted deflagration to detonation transition in a microscale channel

Here, this work numerically studies the plasma assisted deflagration to detonation transition (DDT) of H 2 /O 2 mixtures in a microscale channel with detailed chemistry and transport. The results show that the DDT onset time is non-monotonically dependent on the discharge pulse number. The DDT is accelerated with small pulse numbers, whereas retarded with large ones. Two different DDT regimes, respectively at a small and large plasma discharge number, via acoustic choking of the burned gas and plasma-enhanced reactivity gradient without acoustic choking, are observed. Without plasma discharge, pronounced pressure and temperature gradients in front of the flame are generated by acoustic compression after the choking of the burned gas, triggering DDT via autoignition. With small plasma pulse numbers, the plasma-generated species enhance the ignition kinetics and lead to an increased reactivity in the boundary layer. After the choking of the burned gas, the plasma-enhanced reactivity advances the sequence of autoignition near the wall, strengthens ignition-shock wave coupling, and accelerates DDT. However, with a large discharge pulse number, a direct autoignition initiating DDT can occur without the acoustic choking of the burned gas due to the strongly accelerated reactivity and elevated temperature. In this case, DDT onset is retarded because the elevated temperature increases sonic velocity and the increased reactivity accelerates fuel oxidation in front of the flame, decelerating the formation of a leading shock and subsequent pressure buildup ahead of the flame. The present modeling reveals that no matter with or without plasma discharge, DDT is initiated by autoignition in thermal, pressure, and reactivity gradient fields via the Zel'dovich gradient mechanism. The acoustic choking of the burned gas may not be the necessary condition of DDT with strong plasma-enhanced reactivity gradient. This work provides an answer to the experimentally observed non-monotonic DDT onset time by plasma, which provides guidance to control DDT in advanced detonation engines and fire safety of hydrogen-fueled catalytic reactors in microchannels by non-equilibrium plasma discharge.

33 ADVANCED PROPULSION SYSTEMS↗