Coulomb Collisions Research Articles

Theory and simulation of the electrothermal instability in pulsed power electrode plasmas

Linear theory of the electrothermal instability is rederived and applied to conditions expected in pulsed power electrode surface plasmas comprised of either hydrogen or carbon. The analysis includes losses due to Coulomb collisions, inelastic processes derived from a collisional radiative model, and thermal conduction. The predicted growth rates are relevant for pulse durations typical of pulsed power devices. Linear theory reveals that the growth rate peaks at a characteristic wavenumber kmax, which is dependent on electron current density Je, number density ne, and temperature Te. Analysis of nonlinear simulations finds that saturation occurs as a result of Coulomb collisions, which limit the electron temperature to go no lower than the ion temperature such that Te≳Ti. When the instability is driven by a perturbation with broadband sinusoidal content, the peak in the energy spectrum nonlinearly shifts away from kmax toward smaller wavenumbers (or longer wavelengths) during saturation. The ETI is shown to be capable of driving plasma filaments with perturbed current densities and electron temperatures that exceed the initial, steady-state values.

Time evolutions of information entropies in a one-dimensional Vlasov–Poisson system

A one-dimensional Vlasov–Poisson system is considered to elucidate how the information entropies of the probability distribution functions of the electron position and velocity variables evolve in the Landau damping process. Considering the initial condition given by the Maxwellian velocity distribution with the spatial density perturbation in the form of the cosine function of the position, we derive linear and quasilinear analytical solutions that accurately describe both early and late time behaviors of the distribution function and the electric field. The validity of these solutions is confirmed by comparison with numerical simulations based on contour dynamics. Using the quasilinear analytical solution, the time evolutions of the velocity distribution function and its kurtosis indicating deviation from the Gaussian distribution are evaluated with the accuracy of the squared perturbation amplitude. We also determine the time evolutions of the information entropies of the electron position and velocity variables and their mutual information. We further consider Coulomb collisions that relax the state in the late-time limit in the collisionless process to the thermal equilibrium state. In this collisional relaxation process, the mutual information of the position and velocity variables decreases to zero, while the total information entropy of the phase-space distribution function increases by the decrease in the mutual information and demonstrates the validity of Boltzmann's H-theorem.

Verification of the kinetic electron role in the microinstabilities in a negative triangularity model equilibrium

Effect of kinetic electrons on negative triangularity plasmas has been investigated and compared against the corresponding positive triangularity plasmas, using the global gyrokinetic code X-point Gyrokinetic Code with scale-separated delta-f option without Coulomb collisions. Our model magnetic equilibria have strong positive and negative triangularities and weak magnetic shear. However, unusually large ρi/a and low density plasmas are chosen to maximize the nonlocal effect to investigate the finite ρi effect and to be clearly away from kinetic ballooning modes. Similar conclusions to previous flux tube and global simulations have been obtained in this highly nonlocal model plasma: it is essential to include kinetic electrons in the micro-instability study of negative triangularity plasmas. Most physics findings agree with existing reports, with some disagreement. We offer a new “effective trapping fraction” concept that can add to the explanation of the growth rate difference between NT and PT plasmas, pointing to the significant variation in trapped particle fractions that have turning points in the mode growth regions.

A Coulomb collision model based on collision cross section and its effects on kinetic characteristics of atmospheric thermal microplasmas

A Coulomb collision model based on collision cross section and its effects on kinetic characteristics of atmospheric thermal microplasmas

Ion velocity separation mechanism during vacuum spark stage

Abstract Supersonic ion jets produced in vacuum arc discharges have a wide range of applications, where precise control of ion kinetic energy is crucial. However, a comprehensive understanding of the ion acceleration mechanism remains elusive, particularly regarding whether there is ion velocity separation in the vacuum spark stage. In this paper, a 1D spherical implicit particle-in-cell (PIC) with Monte Carlo collision (MCC) model is employed to investigate the ion velocity separation in multi-charged vacuum arc plasma with varying electrode bias voltages and plasma ion densities. The results show that ion kinetic energy can reach hundreds of electron volts due to continuous acceleration by the formed potential valley, which leads to ion velocity separation at low electrode bias voltage or low plasma density. An increasing electrode bias voltage flattens the potential valley, reducing the electric field acceleration. While increasing the plasma density deepens the valley and intensifies Coulomb collisions, resulting in nearly-equal velocities across ions in different charge states. These findings can theoretically explain the discrepancies observed in previous experiments regarding the dependence of the ion velocity on its charge state during the vacuum spark stage.

Alpha–Proton Differential Flow of a Coronal Mass Ejection at 15 Solar Radii

Alpha–proton differential flow (V α p ) of coronal mass ejections (CMEs) and solar wind from the Sun to 1 au and beyond could influence the instantaneous correspondence of absolute abundances of alpha particles (He2+/H+) between the solar corona and interplanetary space as the abundance of a coronal source can vary with time. Previous studies based on Ulysses and Helios showed that V α p is negligible within CMEs from 5 to 0.3 au, similar to slow solar wind (<400 km s−1). However, recent new observations using Parker Solar Probe (PSP) revealed that the V α p of slow wind increases to ∼60 km s−1 inside 0.1 au. It is important to answer whether the V α p of CMEs exhibits similar behavior near the Sun. In this Letter, we report the V α p of a CME measured by PSP at ∼15 R ⊙ for the first time, which demonstrates that the V α p of CMEs is obvious and complex inside 0.1 au while keeping lower than the local Alfvén speed. A very interesting point is that the same one CME duration can be divided into A and B intervals clearly with Coulomb number below and beyond 0.5, respectively. The means of V α p and alpha-to-proton temperature ratios of interval A (B) is 96.52 (21.96) km s−1 and 7.65 (2.23), respectively. This directly illustrates that Coulomb collisions play an important role in reducing the nonequilibrium features of CMEs. Our study indicates that the absolute elemental abundances of CMEs also might vary during their propagation.

Establishing criteria for the transition from kinetic to fluid modeling in hollow cathode analysis

Hollow cathodes for plasma switch applications are investigated via 2D3V particle-in-cell simulations of the channel and plume region. The kinetic nature of the plasma within the channel is dependent on the thermalization rate of electrons, emitted from the insert. When Coulomb collisions occur at a much greater rate than ionization or excitation collisions, the electron energy distribution function rapidly relaxes to a Maxwellian and the plasma within the channel can be described accurately via a fluid model. In contrast, if inelastic processes are much faster than Coulomb collisions, then the electron energy distribution function in the channel exhibits a notable high-energy tail, and a kinetic treatment is required. This criterion is applied to hollow cathodes from the literature, revealing that a fluid approach is suitable for most electric propulsion applications, whereas a kinetic treatment can be more critical to accurate modeling of plasma switches.

Electron-proton relaxation in hot-dense plasmas with a screened quantum statistical potential.

Modeling the nonequilibrium process between ions and electrons is of great importance in laboratory fusion ignition, laser-plasma interaction, and astrophysics. For hot and dense plasmas, theoretical descriptions of Coulomb collisions remain complicated due to quantum effect at short distances and screening effect at long distances. In this paper, we propose an analytical screened quantum statistical potential that takes into account both the short-range quantum diffraction effect and the long-range screening effect. By implementing the newly developed potential into the binary scattering framework, the electron-proton temperature relaxation in hot-dense hydrogen plasmas is investigated. In both the classical and quantum limits, analytical expressions for the Coulomb logarithm have been obtained, which are generally embedded in an asymptotic matching formula. Quantitative comparisons with molecular dynamics simulations and recent OMEGA experiments demonstrate that the present modeling is well suited to describe the temperature relaxation process between electrons and ions in hot-dense plasmas.

Interplay between the non-resonant streaming instability and self-generated pressure anisotropies

ABSTRACT The non-thermal particles escaping from collision-less shocks into the surrounding medium can trigger a non-resonant streaming instability that converts parts of their drift kinetic energy into large amplitude magnetic field perturbations, and promote the confinement and acceleration of high energy cosmic rays. We present simulations of the instability using an hybrid-Particle-in-Cell approach including Monte Carlo collisions, and demonstrate that the development of the non-resonant mode is associated with important ion pressure anisotropies in the background plasma. Depending on the initial conditions, the anisotropies may act on the instability by lowering its growth and trigger secondary micro-instabilities. Introducing collisions with neutrals yield a strong reduction of the magnetic field amplification as predicted by linear fluid theory. In contrast, Coulomb collisions in fully ionized plasmas are found to mitigate the self-generated pressure anisotropies and promote the growth of the magnetic field.

A machine-learning augmented mixed method for simulating α particle transport in inertial confinement fusion

The plasma heating by the α particle transport is a main self-heating source in inertial confinement fusion (ICF) that determines the capsule implosion performance. Due to the high energy of α particle and the high temperature in the ICF capsule hot spot, significant non-equilibrium effect exists and the continuum mechanics breaks down. For the numerical simulation of implosion and charged particle transport, the Boltzmann equation needs to be solved to capture the kinetic effects. However, the 7-dimensional Boltzmann equation, the highly frequent Coulomb collision, and the multi-folded integral stopping power formulation greatly limits the computational efficiency and challenges the computational power. To overcome the high computational cost of high-frequent Coulomb collisions, we propose a mixed collision model according to which the collisions are categorized into low-frequent large-angle collisions and high frequent small-angle grazing collisions. The large-angle collision process is precisely solved based on the Coulomb cross-section. For the highly frequent small-angle grazing, a statistic model is constructed with second-order accuracy in time. The mixed collision model reduces the computational cost of scattering calculation by two orders of magnitude. For the multi-folded integral stopping power formulation, a neural network is used to improve computational efficiency. Based on the proposed algorithm, we develop one-dimensional to three-dimensional module code to directly solve the α particle transport Boltzmann equation. The α transport module code is integrated into the multi-physics LARED-S program. The MC version ICF software is verified by a simulation study of the N210207 and N191110 experiment.

Study of Particle Acceleration Using Fine Structures and Oscillations in Microwaves from the Electron Cyclotron Maser

The accelerated electrons during solar flares produce radio bursts and nonthermal X-ray signatures. The quasi-periodic pulsations (QPPs) and fine structures in spatial–spectral–temporal space in radio bursts depend on the emission mechanism and the local conditions, such as magnetic fields, electron density, and pitch-angle distribution. Radio burst observations with high-frequency time resolution imaging provide excellent diagnostics. In converging magnetic field geometries, the radio bursts can be produced via the electron cyclotron maser (ECM). Recently, using observations made by the Karl G. Jansky Very Large Array (VLA) at 1–2 GHz, Yu et al. reported a discovery of long-lasting auroral-like radio bursts persistent over a sunspot and interpreted them as ECM-generated emission. Here we investigate the detailed second and subsecond temporal variability of this continuous ECM source. We study the association of 5 s period QPPs with a concurrent GOES C1.5-class flare, utilizing VLA’s imaging spectroscopy capability with an extremely high temporal resolution (50 ms). We use the density and magnetic field extrapolation model to constrain the ECM emission to the second harmonic O-mode. Using the delay of QPPs from X-ray emission times, combined with X-ray spectroscopy and magnetic extrapolation, we constrain the energies and pitch angles of the ECM-emitting electrons to ≈4–8 keV and >26°. Our analysis shows that the loss-cone diffusion continuously fuels the ECM via Coulomb collisions and magnetic turbulence between a length scale of 5 and 100 Mm. We conclude that the QPP occurs via the Lotka–Volterra system, where the electrons from solar flares saturate the continuously operating ECM and cause temporary oscillations.

Study on the properties of deuterium ions in a composite cathode vacuum arc discharge

A vacuum arc discharge with a metal-deuteride cathode can generate a supersonic deuterium ion jet, which finds important applications in vacuum arc ion sources. In this study, a 1D3V spherical particle-in-cell direct simulation Monte Carlo cathode spot model with a titanium-deuteride cathode is developed to investigate the ionization and acceleration of deuterium ions from vacuum breakdown to the steady-arc stage. The effects of cathode deuteration concentration on the deuterium ion fraction and kinetic energy are also analyzed. The results show that the released deuterium atoms start to be ionized at around tens of nanometers from the cathode and then become fully ionized at about 0.4μm as the cathode potential drop gradually builds up. The proportion of deuterium ions in the plasma is slightly higher than the proportion of deuterium atoms in the cathode material. Velocity separation of deuterium and titanium ions occurs due to the acceleration of the electric field during the vacuum breakdown stage; however, the predominant ion–ion Coulomb collisions wipe out this separation in the steady-arc stage. Shifting the deuterium atom concentration in the cathode under a constant arc burning voltage produces an approximately equal current density, and increases the velocities of all ion species. A higher ion kinetic energy is gained by reducing the ohmic heating dissipation, facilitated by the lower plasma resistivity under the increased deuterium ion density.

Electron acceleration and transport in the 2023-03-06 solar flare

We investigated in detail the M5.8 class solar flare that occurred on 2023-03-06. This flare was one of the first strong flares observed by the Siberian Radioheliograph in the microwave range and the Advanced Space-based Solar Observatory in the X-ray range. The flare consisted of two separate flaring events (a “thermal” and a “cooler” ones), and was associated with (and probably triggered by) a filament eruption. During the first part of the flare, the microwave emission was produced in an arcade of relatively short and low flaring loops. During the second part of the flare, the microwave emission was produced by energetic electrons trapped near the top of a large-scale flaring loop; the evolution of the trapped electrons was mostly affected by the Coulomb collisions. Using the available observations and the GX Simulator tool, we created a 3D model of the flare, and estimated the parameters of the energetic electrons in it.

Energy exchange between electrons and ions in ion temperature gradient turbulence

Microturbulence in magnetic confined plasmas contributes to energy exchange between particles of different species as well as the particle and heat fluxes. Although the effect of turbulent energy exchange has not been considered significant in previous studies, it is anticipated to have a greater impact than collisional energy exchange in low collisional plasmas such as those in future fusion reactors. In this study, gyrokinetic simulations are performed to evaluate the energy exchange due to ion temperature gradient (ITG) turbulence in a tokamak configuration. The energy exchange due to the ITG turbulence mainly consists of the cooling of ions in the ∇B-curvature drift motion and the heating of electrons streaming along a field line. It is found that the ITG turbulence transfers energy from ions to electrons regardless of whether the ions or electrons are hotter, which is in marked contrast to the energy transfer by Coulomb collisions. This implies that the ITG turbulence should be suppressed from the viewpoint of sustaining the high ion temperature required for fusion reactions since it prevents energy transfer from alpha-heated electrons to ions as well as enhancing ion heat transport toward the outside of the reactor. Furthermore, linear and nonlinear simulation analyses confirm the feasibility of quasilinear modeling for predicting the turbulent energy exchange in addition to the particle and heat fluxes.

Divergence of the energy-losing rate of charged particles in plasmas

In modeling the charged alpha particle transport in hot-spot plasmas of inertial confinement fusion, the energy-losing rate is a major concern in the Monte Carlo simulations of alpha particle transport of a radiative-hydrodynamic code. However, the traditionally used energy stopping-power only describes the averaged energy-losing rate of the incident charged particles, whereas the variance of the energy exchange with the background particles is generally ignored. In this paper, the variance of charged particle collisions is studied by both analytical derivation and Monte Carlo simulations. An expression of the divergence of the charged particle energy-losing rate is given for the first time, which can be directly used for practical estimations. It indicates that when the areal density of the target particles along the incident particle path length is low, the divergence of the lost energy would be much larger than the average value, and the traditionally used energy stopping-power would be no longer sufficient to describe the charged particle Coulomb collisions. It helps to obtain a more comprehensive understanding about the charged particle transport in plasmas.

Toward Cosmological Simulations of the Magnetized Intracluster Medium with Resolved Coulomb Collision Scale

We present the first results of one extremely high-resolution, nonradiative magnetohydrodynamical cosmological zoom-in simulation of a massive cluster with a virial mass of M vir = 2.0 × 1015 solar masses. We adopt a mass resolution of 4 × 105 M ⊙ with a maximum spatial resolution of around 250 pc in the central regions of the cluster. We follow the detailed amplification process in a resolved small-scale turbulent dynamo in the intracluster medium (ICM) with strong exponential growth until redshift 4, after which the field grows weakly in the adiabatic compression limit until redshift 2. The energy in the field is slightly reduced as the system approaches redshift zero in agreement with adiabatic decompression. The field structure is highly turbulent in the center and shows field reversals on a length scale of a few tens of kiloparsecs and an anticorrelation between the radial and angular field components in the central region that is ordered by small-scale turbulent dynamo action. The large-scale field on megaparsec scales is almost isotropic, indicating that the structure formation process in massive galaxy cluster formation suppresses any memory of both the initial field configuration and the amplified morphology via the turbulent dynamo. We demonstrate that extremely high-resolution simulations of the magnetized ICM are within reach that can simultaneously resolve the small-scale magnetic field structure, which is of major importance for the injection of and transport of cosmic rays in the ICM. This work is a major cornerstone for follow-up studies with an on-the-fly treatment of cosmic rays to model in detail electron-synchrotron and gamma-ray emissions.

A collision operator for describing dissipation in noncanonical phase space

The phase space of a noncanonical Hamiltonian system is partially inaccessible due to dynamical constraints (Casimir invariants) arising from the kernel of the Poisson tensor. When an ensemble of noncanonical Hamiltonian systems is allowed to interact, dissipative processes eventually break the phase space constraints, resulting in a thermodynamic equilibrium described by a Maxwell–Boltzmann distribution. However, the time scale required to reach Maxwell–Boltzmann statistics is often much longer than the time scale over which a given system achieves a state of thermal equilibrium. Examples include diffusion in rigid mechanical systems, as well as collisionless relaxation in magnetized plasmas and stellar systems, where the interval between binary Coulomb or gravitational collisions can be longer than the time scale over which stable structures are self-organized. Here, we focus on self-organizing phenomena over spacetime scales such that particle interactions respect the noncanonical Hamiltonian structure, but yet act to create a state of thermodynamic equilibrium. We derive a collision operator for general noncanonical Hamiltonian systems, applicable to fast, localized interactions. This collision operator depends on the interaction exchanged by colliding particles and on the Poisson tensor encoding the noncanonical phase space structure, is consistent with entropy growth and conservation of particle number and energy, preserves the interior Casimir invariants, reduces to the Landau collision operator in the limit of grazing binary Coulomb collisions in canonical phase space, and exhibits a metriplectic structure. We further show how thermodynamic equilibria depart from Maxwell–Boltzmann statistics due to the noncanonical phase space structure, and how self-organization and collisionless relaxation in magnetized plasmas and stellar systems can be described through the derived collision operator.

Characterization of a filamentary discharge ignited in a gliding arc plasmatron operated in nitrogen flow

A gliding arc plasmatron (GAP) is a promising warm plasma source for the use in gas conversion applications but lacks an understanding of the plasma dynamics. In this paper, the gliding arc plasma conditions of a GAP operated with nitrogen flow (10 slm) are characterized using optical emission spectroscopy (OES) and numerical simulation. A simultaneously two-wavelength OES method and Abel inversion of the measured images with a spatial resolution of 19.6 μm are applied. The collisional radiative model used in this study includes Coulomb collisions of electrons. An iterative method of plasma parameter determination is applied. The determined values of the electric field up to 49 Td and electron density up to 2.5∙1015 cm−3 fit well to the plasma parameters received with different diagnostics methods in comparable plasma sources. Additionally, the electric current, which is calculated using the determined reduced electric field and electron density, is compared with the measured one.

Probing Turbulent Scattering Effects on Suprathermal Electrons in the Solar Wind: Modeling, Observations, and Implications

This study explores the impact of a turbulent scattering mechanism, akin to those influencing solar and galactic cosmic rays propagating in the interplanetary medium, on the population of suprathermal electrons in the solar wind. We employ a Fokker–Planck equation to model the radial evolution of electron pitch angle distributions under the action of magnetic focusing, which moves the electrons away from isotropy, and of a diffusion process that tends to bring them back to it. We compare the steady-state solutions of this Fokker–Planck equation with data obtained from the Solar Orbiter and Parker Solar Probe missions and find a remarkable agreement, varying the turbulent mean free path as the sole free parameter in our model. The obtained mean free paths are of the order of the astronomical unit, and display weak dependence on electron energy within the 100 eV–1 keV range. This value is notably lower than Coulomb collision estimates but aligns well with observed mean free paths of low-rigidity solar energetic particle events. The strong agreement between our model and observations leads us to conclude that the hypothesis of turbulent scattering at work on electrons at all heliospheric distances is justified. We discuss several implications, notably the existence of a low Knudsen number region at large distances from the Sun, which offers a natural explanation for the presence of an isotropic “halo” component at all distances from the Sun—electrons being isotropized in this distant region before traveling back into the inner part of the interplanetary medium.

Acceleration mechanisms of energetic ion debris in laser-driven tin plasma EUV sources

Laser-driven tin plasmas are driving new-generation nanolithography as sources of extreme ultraviolet (EUV) radiation centered at 13.5 nm. A major challenge facing industrial EUV source development is predicting energetic ion debris produced during the plasma expansion that may damage the sensitive EUV channeling multilayer optics. Gaining a detailed understanding of the plasma dynamics and ion acceleration mechanisms in these sources could provide critical insights for designing debris mitigation strategies in future high-power EUV sources. We develop a fully kinetic model of tin-EUV sources using one-dimensional particle-in-cell simulations to study ion debris acceleration, which will be valuable for cross-validation of radiation-hydrodynamic simulations. An inverse-bremsstrahlung heating operator is used to model the interaction of a tin target with an Nd:YAG laser, and thermal conduction is included through a Monte Carlo Coulomb collision operator. While the large-scale evolution is in reasonable agreement with analogous hydrodynamic simulations, the significant timescale for collisional equilibration between electrons and ions allows for the development of prominent two-temperature features. A collimated flow of energetic ions is produced with a spectrum that is significantly enhanced at high energies compared to fluid simulations. The dominant acceleration mechanism is found to be a large-scale electric field supported mainly by the electron pressure gradient, which is enhanced in the kinetic simulations due to the increased electron temperature. We discuss the implications of these results for future modeling of tin-EUV sources and the development of debris mitigation schemes.