Maxwellian Velocity Distribution Research Articles

Trend to Equilibrium for Run and Tumble Equations with Non-uniform Tumbling Kernels

We study the long-time behaviour of a run and tumble model which is a kinetic-transport equation describing bacterial movement under the effect of a chemical stimulus. The experiments suggest that the non-uniform tumbling kernels are physically relevant ones as opposed to the uniform tumbling kernel which is widely considered in the literature to reduce the complexity of the mathematical analysis. We consider two cases: (i) the tumbling kernel depends on the angle between pre- and post-tumbling velocities, (ii) the velocity space is unbounded and the post-tumbling velocities follow the Maxwellian velocity distribution. We prove that the probability density distribution of bacteria converges to an equilibrium distribution with explicit (exponential for (i) and algebraic for (ii)) convergence rates, for any probability measure initial data. To the best of our knowledge, our results are the first results concerning the long-time behaviour of run and tumble equations with non-uniform tumbling kernels.

IDENTIFICATION OF THE INTERACTION OF LITHIUM HEXAFLUOROPHOSPHATE SALT AND ETHYLENE CARBONATE (EC) SOLVENT IN LITHIUM ION BATTERY REDOX EVENTS USING CLASSICAL MOLECULAR DYNAMICS (MD) SIMULATION

The aim of the research is to find the maximum velocity possessed by the molecules (Maxwell velocity distribution) of the solvation event of lithium hexafluorophosphate salt interacting with ethylene carbonate (EC) solvent. We examined the electrolyte simulation of the reaction between lithium ions and hexafluorophosphate with ethylene carbonate (EC) solvent while the potential involved is the Lennard Jones potential. We use the epsilon (ε) and sigma (σ) parameters of Lennard Jones. These parameters are the independent variables used as a reference in determining the response variable which is the velocity of the molecules. Due to the large number of molecules involving the parameters and response variables per molecule mentioned above, we use a microcanonical assembly system (N, V, E) where the number of particles (N), system volume (V) and energy (E) are constant. The energy kT and the distance between molecules σ of 1 are inputted to the program in order to facilitate the computer in the simulation process. Solvation events where litium hexafluorophosphate salt and solvent ethylene carbonate interact then in the final positions of particles (equilibrium) the result is almost symmetry randomly in all planes. The velocity used is the most frequent velocity ( ) and is related to the kinetic energy.

Ion cyclotron emission in Maxwellian plasmas

Destabilization of ion cyclotron waves—waves with frequencies close to ion cyclotron harmonics—in inhomogeneous plasmas with Maxwell velocity distribution is considered. A new mechanism of destabilization of these waves is found, whereas the known interaction between cyclotron waves and drift waves is shown to be hardly able to lead to instabilities in realistic tokamak plasmas. Our finding is that the resonance wave–particle interaction in the presence of temperature gradient can change the diamagnetic drift frequency in such a way that the destabilizing influence of the diamagnetic drift exceeds Landau damping. This occurs when the energy of resonance particles is sufficiently high, which is always the case due to the infinite tail of the Maxwell distribution. Particles with higher energies provide a larger ratio of drive to damping, but the number of resonance particles and, thus, instability growth rates are exponentially small when particle energy is very high. Therefore, only moderately suprathermal particles can lead to observable instabilities. A condition for instabilities driven by these particles is obtained. Destabilization of electrostatic cyclotron waves and ordinary cyclotron waves is studied.

Solar Energetic Particle Charge States and Abundances with Nonthermal Electrons

An important aspect of solar energetic particle (SEP) events is their source populations. Elemental abundance enhancements of impulsive SEP events, originating in presumed coronal reconnection episodes, can be fitted to steep power laws of A/Q, where A and Q are the atomic mass and ionic charge. Since thermal electron energies are enhanced and nonthermal electron distributions arise in the reconnection process, we might expect that ionic charge states Q would be increased through ionization interactions with those electron populations during the acceleration process. The temperature estimated from the SEPs corresponds to the charge state during the acceleration process, while the actual charge state measured in situ may be modified as the SEPs pass through the corona. We examine whether the temperature estimation from the A/Q would differ with various κ values in a κ function representing high-energy tail deviating from a Maxwellian velocity distribution. We find that the differences in the A/Q between a Maxwellian and an extreme κ distribution are about 10%–30%. We fit power-law enhancement of element abundances as a function of their A/Q with various κ values. Then, we find that the derived source region temperature is not significantly affected by whether or not the electron velocity distribution deviates from a Maxwellian, i.e., thermal, distribution. Assuming that electrons are heated in the acceleration region, the agreement of the SEP charge state during acceleration with typical active region temperatures suggests that SEPs are accelerated and leave the acceleration region in a shorter time than the ionization timescale.

Gas Kinetic Scheme Coupled with High-Speed Modifications for Hypersonic Transition Flow Simulations.

The issue of hypersonic boundary layer transition prediction is a critical aerodynamic concern that must be addressed during the aerodynamic design process of high-speed vehicles. In this context, we propose an advanced mesoscopic method that couples the gas kinetic scheme (GKS) with the Langtry-Menter transition model, including its three high-speed modification methods, tailored for accurate predictions of high-speed transition flows. The new method incorporates the turbulent kinetic energy term into the Maxwellian velocity distribution function, and it couples the effects of high-speed modifications on turbulent kinetic energy within the computational framework of the GKS solver. This integration elevates both the transition model and its high-speed enhancements to the mesoscopic level, enhancing the method's predictive capability. The GKS-coupled mesoscopic method is validated through a series of test cases, including supersonic flat plate simulation, multiple hypersonic cone cases, the Hypersonic International Flight Research Experimentation (HIFiRE)-1 flight test, and the HIFiRE-5 case. The computational results obtained from these cases exhibit favorable agreement with experimental data. In comparison with the conventional Godunov method, the new approach encompasses a broader range of physical mechanisms, yielding computational results that closely align with the true physical phenomena and marking a notable elevation in computational fidelity and accuracy. This innovative method potentially satisfies the compelling demand for developing a precise and rapid method for predicting hypersonic boundary layer transition, which can be readily used in engineering applications.

Condensation and evaporation of boson stars

Axion-like particles, including the QCD axion, are well-motivated dark matter candidates. Numerical simulations have revealed coherent soliton configurations, also known as boson stars, in the centers of axion halos. We study evolution of axion solitons immersed into a gas of axion waves with Maxwellian velocity distribution. Combining analytical approach with controlled numerical simulations we find that heavy solitons grow by condensation of axions from the gas, while light solitons evaporate. We deduce the parametric dependence of the soliton growth/evaporation rate and show that it is proportional to the rate of the kinetic relaxation in the gas. The proportionality coefficient is controlled by the product of the soliton radius and the typical gas momentum or, equivalently, the ratio of the gas and soliton virial temperatures. We discuss the asymptotics of the rate when this parameter is large or small.

Kinetic Modeling of Ionospheric Outflows in Pressure Cooker Environments

AbstractPlasma escape from the high‐latitude ionosphere (ion outflow) serves as a significant source of heavy plasma to the magnetospheric plasma sheet and ring current regions. Outflows alter mass density and reconnection rates, hence global responses of the magnetosphere. A new fully kinetic and semi‐kinetic model, KAOS (Kinetic model of Auroral ion OutflowS), is constructed from first principles which traces large numbers of individual O+ ion macro‐particles along curved magnetic field lines, using a guiding‐center approximation, in order to facilitate calculation of ion distribution functions and moments. Particle forces include mirror and parallel electric field forces, a self‐consistent ambipolar electric field, and a parameterized source of ion cyclotron resonance wave heating, thought to be central to the transverse energization of ions. The model is initiated with a steady‐state ion density altitude profile and Maxwellian velocity distribution and particle trajectories are advanced via a direct simulation Monte Carlo scheme. This outlines the implementation of the kinetic outflow model, demonstrates the model's ability to achieve near‐hydrostatic equilibrium necessary for simulation spin‐up, and investigates L‐shell dependent wave heating and pressure cookers scenarios. This paper illustrates the model initialization process and numerical investigations of L‐shell dependent outflows and pressure cooker environments and serves to advance our understanding of the drivers and particle dynamics in the auroral ionosphere.

Generalized Harris Sheet Equilibrium in Regularized Kappa Distributed Plasmas

Harris sheet models with antiparallel magnetic field are the equilibrium solutions to the steady Vlasov–Maxwell equations, which have been widely adopted for the study of plasma instabilities and magnetic reconnection in thin current sheets. The original Harris equilibrium model assumes the Maxwellian velocity distribution, which necessarily gives rise to the isothermal current sheets. Many observations have shown that the suprathermal populations are indispensable features of particle distribution profiles, which may well be fitted by the Kappa distribution (KD) functions with the free parameter κ. The Harris equilibrium based on the standard Kappa distribution (SKD), however, may become unphysical for . Alternatively, the regularized KD (RKD) with two adjustable parameters, κ and α 2, has been proposed to replace the SKD in various studies. The RKD may recover the SKD for α 2 = 0, and Maxwellian model for α 2 = 0 and κ → ∞ . This paper presents the first results of adopting the nonthermal RKDs in the Harris equilibrium models. It is shown that the new RKD–Harris equilibrium is applicable for all κ values, and exhibits a stronger magnetic field associated with higher temperature in the asymptotic region. The proposed formulations for the generalized Harris sheet equilibrium may be applied to multiple component plasmas (e.g., electrons, protons) with different RKDs and temperatures.

On the impact of runaway stars on dwarf galaxies with resolved interstellar medium

ABSTRACT ‘Runaway stars’ might play a role in driving galactic outflows and enriching the circumgalactic medium with metals. To study this effect, we carry out high-resolution dwarf galaxy simulations that include velocity ‘kicks’ to massive stars above eigth solar masses. We consider two scenarios, one that adopts a power law velocity distribution for kick velocities, resulting in more stars with high-velocity kicks, and a more moderate scenario with a Maxwellian velocity distribution. We explicitly resolve the multiphase interstellar medium (ISM) and include non-equilibrium cooling and chemistry. We sample individual massive stars from an IMF and follow their radiation input and SN feedback (core-collapse) channel at the end of their lifetime. In the simulations with runaway stars, we add additional (natal) velocity kicks that mimic two- and three-body interactions that cannot be fully resolved in our simulations. We find that including runaway or ‘walkaway’ star scenarios impacts mass, metal, momentum, and energy outflows as well as the corresponding loading factors. The effect on the mass loading factor is small, but we find an increase in the metal loading by a factor of 1.5 to 2. The momentum loading increases by a factor of 1.5–2. The energy loading increases by roughly a factor of 5 when runaway stars are included. Additionally, we find that the overall level of star formation is increased in the models that include runaway stars. We conclude that the inclusion of runaway stars could have an impact on the global star formation and subsequent outflow properties of dwarf galaxies.

The linear response of stellar systems does not diverge at marginal stability

ABSTRACT The linear response of a stellar system’s gravitational potential to a perturbing mass comprises two distinct contributions. Most famously, the system will respond by forming a polarization ‘wake’ around the perturber. At the same time, the perturber may also excite one or more ‘Landau modes’, i.e. coherent oscillations of the entire stellar system which are either stable or unstable depending on the system parameters. The amplitude of the first (wake) contribution is known to diverge as a system approaches marginal stability. In this paper, we consider the linear response of a homogeneous stellar system to a point mass moving on a straight line orbit. We prove analytically that the divergence of the wake response is in fact cancelled by a corresponding divergence in the Landau mode response, rendering the total response finite. We demonstrate this cancellation explicitly for a box of stars with Maxwellian velocity distribution. Our results imply that polarization wakes may be much less efficient drivers of secular evolution than previously thought. More generally, any prior calculation that accounted for wakes but ignored modes – such as those based on the Balescu-Lenard equation – may need to be revised.

Particle-photon radiative interactions and thermalization.

We analyze the statistical properties of radiative transitions for a molecular system possessing discrete, equally spaced, energy levels, interacting with thermal radiation at constant temperature. A radiative fluctuation-dissipation theorem is derived and the particle velocity distribution analyzed. It is shown analytically that, neglecting molecular collisions, the velocity distribution function cannot be Gaussian, as the equilibrium value for the kurtosis κ is different from κ=3. A Maxwellian velocity distribution can be recovered in the limit of small radiative friction.

Bracketing the direct detection exclusion plot for a WIMP of spin one half in non-relativistic effective theory

Assuming a standard Maxwellian velocity distribution for the WIMPs in the halo of our Galaxy we use the null results of an exhaustive set of 9 direct detection experiments to calculate the maximal variation of the exclusion plot for each Wilson coefficient of the most general Galilean–invariant effective Hamiltonian for a WIMP of spin one half due to interferences. We consider 56 Wilson coefficients cip,n and αin,p for WIMP–proton and WIMP–neutron contact interactions Oip,n and the corresponding long range interaction Oip,n/q2, parameterized by a massless propagator 1/q2. For each coupling we provide a different exclusion plot when the following set of operators is allowed to interfere: proton–neutron, i.e. cip–cin or αip–αin; contact–contact or long range–long range, i.e. cip,n–cjp,n or αip,n–αjp,n; contact– long range, i.e. cip,n–αjp,n. For each of the 56 Wilson coefficients cip,n and αjp,n and for the largest number of interfering operators the exclusion plot variation can reach 3 orders of magnitude and reduces to a factor as small as a few for the Wilson coefficients of the effective interactions where the WIMP couples to the nuclear spin, thanks to the combination of experiments using proton-odd and neutron-odd targets. Some of the conservative bounds require an extremely high level of cancellation, putting into question the reliability of the result. We analyze this issue in a systematic way, showing that it affects some of the couplings driven by the operators O1, O3, O11, O12 and O15, especially when interferences among contact and long range interactions are considered.

Particle-in-Cell Modeling of Omega Experiments on Ablation of Plasmas

The large electric fields due to charge separation generated by a laser pulse propagating in a plasma can accelerate the electrons to very high energies. The hydrodynamics models that are based on the local thermodynamic equilibrium assuming a Maxwellian distribution of velocities cannot describe the evolution of groups of hot electrons of different energy ranges and kinetic particle-in-cell (PIC) simulations are required. The SMILEI PIC code is used to investigate the generation of hot electrons in plasmas produced by laser pulses in the Omega extended performance (EP) experiments. In 2-D PIC simulation using SMILEI code, a Gaussian-shaped laser pulse of 100-ps duration with the intensity of 10 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{15}$</tex-math> </inline-formula> W/cm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{2}$</tex-math> </inline-formula> and a wavelength of 351 nm impinges onto a plasma with the electron density and temperature profiles. The electromagnetic field, electron, and total energies of a plasma as a function of time are evaluated. The evolution of number density, electromagnetic fields, and energy spectra of electrons is studied. The time evolution of hot electrons in a plasma is investigated. These PIC results provide insights into the contribution and importance of the kinetic effects in the expansion dynamics of ablated plasmas, thereby helping to analyze and explain the Omega experimental data and computational fluid dynamics results.

Inversion of Upstream Solar Wind Parameters from ENA Observations at Mars

An algorithm has been developed to invert the solar wind parameters from the hydrogen energetic neutral atom (H-ENA) measured in near-Mars space. Supposing the H-ENA is produced by change exchange collision between protons that originated in the solar wind and neutrals in the exosphere, an H-ENA model is established based on the magnetohydrodynamic (MHD) simulation of the solar wind interaction with Mars, to study the H-ENA characteristics. It is revealed that the solar wind H-ENAs are high-speed, low-temperature beams, just like the solar wind, while the magnetosheath H-ENAs are slower and hotter, with broader energy distribution. Assuming Maxwellian velocity distribution, the solar wind H-ENA flux is best fitted by a Gaussian function, from which the solar wind velocity, density, and temperature can be retrieved. Further investigation, based on the ENA flux simulated by the H-ENA model, reveals that the accuracy of inversed solar wind parameters is related to the angular and energy resolutions of the ENA detector. Finally, the algorithm is verified using the H-ENA observations from the Tianwen-1 mission. The upstream solar wind velocity when inversed is close to that of the in situ plasma measurement. Our result suggests the solar wind parameters inversed from H-ENA observation could be an important supplement to the dataset supporting studies on the Martian space environment, where long-term continuous monitoring of the upstream SW condition is lacking.

Three-dimensional coupling of electron cyclotron drift instability and ion–ion two stream instability

Electron cyclotron drift instability (ECDI) and ion–ion two stream instability (IITSI) are both kinetic instabilities that can be present in low-temperature, partially magnetized plasmas. The coupling of instabilities in a three-dimensional configuration leads to the existence of more than one unstable roots to the kinetic dispersion relation. In this paper, a generalized method has been developed for numerically evaluating solutions to the three-dimensional dispersion relation for coupled ECDI and IITSI, assuming cold singly and doubly charged ions and a Maxwellian velocity distribution function for the electrons. The present study demonstrates the coupling between ECDI and IITSI that affects the most unstable mode as a function of the wavenumbers in three dimensions and various plasma properties, including the applied electric field, magnetic field, electron temperature, ion velocities, and plasma density. One of the most notable results is that, while the most unstable mode with the largest growth rate is in the direction of the E×B drift in the two-dimensional cases, the most unstable mode for the three-dimensional configuration occurs in the oblique direction between the applied electric field and the E×B drift. This agrees with experimental observations in cross field plasma sources using coherent Thomson scattering.

Wave–particle interaction in contact with a chaotic thermostat

This numerical investigation explores the properties of the wave–particle interaction in a situation in which the particle is simultaneously in contact with a chaotic thermostat [G. J. Morales, Phys. Rev. E 99, 062218 (2019)]. The role of the thermostat is to establish a Maxwellian velocity distribution function through deterministic chaotic orbits. The particle response is quantified by calculating the complex mobility, μk, ω, from the numerically obtained orbits for a wave of constant amplitude, with wave number k and frequency ω. It is found that in the limit of weak coupling to the thermostat, the behavior is that predicted by the plasma dispersion function, which implies collisionless Landau damping. As the coupling to the thermostat is increased (equivalent to increasing collisionality), the behavior follows the generalized collisional plasma dispersion function [Fried et al., Phys. Fluids 9, 292 (1966)]. For strong coupling, the response agrees with the Braginskii mobility. The nonlinear mobility associated with intermittent particle trapping is obtained for the various collisional regimes.

The local dark matter distribution in self-interacting dark matter halos

We study the effects of dark matter self-interactions on the local dark matter distribution in selected Milky Way-like galaxies in the EAGLE hydrodynamical simulations. The simulations were run with two different self-interacting dark matter models, a constant and velocity-dependent self-interaction cross-section. We find that the local dark matter velocity distribution of the Milky Way-like halos in the simulations with dark matter self-interactions and baryons are generally similar to those extracted from cold collisionless dark matter simulations with baryons. In both cases, the local dark matter speed distributions agree well with their best fit Maxwellian distributions. Including baryons in the simulations with or without dark matter self-interactions increases the local dark matter density and shifts the dark matter speed distributions to higher speeds. To study the implications for direct detection, we compute the dark matter halo integrals obtained directly from the simulations and compare them to those obtained from the best fit Maxwellian velocity distribution. We find that a Maxwellian distribution provides a good fit to the halo integrals of most halos, without any significant difference between the results of different dark matter self-interaction models.

Early Microjet Experimentation with Liquid Water in Vacuum.

ConspectusIn this brief look at the history of liquid microjets, I recollect some personal reminiscences on initial challenges for introduction of this method, as well as unexpected problems and exemplary results using this new tool for liquid evaporation and photoelectron spectroscopy studies.Many efficient and direct, atomic level diagnostic instruments in use at solid state surfaces and in gas-phase atom or cluster studies require high vacuum. They have therefore not been applied to investigations of aqueous solutions because liquid water both strongly evaporates and rapidly freezes in vacuum. Only fairly recently, over the past three decades, have liquid microjets been considered as practicable targets for research on liquid-water interfaces in vacuum. The working principle is analogous to the functioning of a free molecular beam source, where molecules enter through a small aperture into a vacuum without being disturbed by subsequent collisions in their original Maxwellian velocity distribution. Similarly, above a microjet surface in vacuum, water vapor molecules do not interact with each other, or with different probe particles, as long as the liquid jet diameter is small in relation to the mean free path of the liquids' vapor at equilibrium conditions. For pure liquid water, this constraint is Djet < λvap < 10 μm for 6.1 mbar vapor pressure at the triple point of water. A high streaming velocity of the liquid jet, >50 m/s, delays freezing and exposes a steadily renewed fresh vacuum surface for experiments.For experimental verification of the microjet free surface concept, H2O vapor velocities were measured in a molecular beam time-of-flight experiment. These studies showed Maxwellian velocity distributions with the expected local water-jet temperatures for 5 and 10 μm jets, whereas larger liquid jet diameters of 50 μm exhibit narrowed vapor velocity profiles. This narrowing is the known signature of incipient, collision dominated, supersonic hydrodynamic expansions in nozzle beam sources. As a completely unexpected new result in evaporation studies of carboxylic acid solutions, freely evaporating acetic acid dimers showed apparent non-equilibrium liquid surface source temperatures several hundred kelvin above the simultaneously measured monomer temperatures, a phenomenon shown to be correlated with surface tension.Continuing with improvements, the vacuum water microjets were implemented inside a photoelectron spectroscopy apparatus that was modified for handling large amounts of water vapor. After initial complications with liquid jet charging phenomena, the first partial liquid-water photoelectron spectra were recorded using 21 eV photons from a He I discharge lamp. In the next step, the equipment was taken to a synchrotron radiation beamline at BESSY II, resulting in substantial improvements of signal intensity and in photon tunability for narrow band monochromatic soft X-rays up to 1 keV. Two early examples of these continuing experiments are considered, briefly, for aqueous alkali halide salt solutions and for the pH-value dependent protonation of an NH2/NH3+ group in an amino acid directly in a photoelectron spectrum of a solution.In conclusion, liquid microjets have opened up a completely new approach to studies of arbitrary liquids with chemical and biological relevance.

Incoherent Scattering of a Bessel Vortex Electromagnetic Beam From a Nonmagnetized Plasma

Starting from the description of plane wave angular spectrum superposition of a Bessel vortex beam, with the aid of Thomson scattering theory of a Bessel vortex electromagnetic beam (BVEB) by a low-velocity election, the incoherent scattering power spectra of a BVEB by a non-magnetized plasma is investigated in this paper. The incoherent scattering power spectrum for a BVEB incidence is defined for the backscattered case, and the expression of the scattered power spectral density function is derived. The proposed method is verified in the physical sense by comparing the profiles of distribution parameter of scattered power and the magnitude of average Poynting vector of the incident beam. The effects of the beam parameters (topological charge and half-cone angle) on the scattered power spectral density function are analyzed for the plasmas with Maxwellian velocity distribution. Furtherly, the expression of the scattered power spectral density function is extended to the case of macroscopic moving plasmas. Taking plasma vortices as an example, the results indicate that the direction of the frequency shift of the scattered power spectral density function due to the rotational Doppler effect of the vortex beam is related to angular velocity of the plasma vortex. Additionally, as the topological charge increases, the magnitude of the frequency shifts also increases. Our proposed method provides a theoretical basis for exploring the feasibility of using vortex beams with single or multi orbital angular momentum (OAM) modes in the identifying and inverting parameters of plasma irregularities in ionospheric plasma or laboratory plasma environments.

Kinetic modeling of solitary wave dynamics in a neutralizing ion beam

In this work, we characterize the formation and evolution of electrostatic solitary waves (ESWs) in the space-charge neutralization of ion beams using particle-in-cell simulations. These waves become excited when the electrons emitted from an external filament source initiate a two-stream instability in the beam. We show that such electrostatic waves become excited in both two-dimensional (2D) and three-dimensional (3D) beams with different shapes and sizes. Through a 1D Bernstein–Greene–Kruskal (BGK) analysis of the 2D beam, we find that the non-Maxwellian nature of the beam electrons gives rise to large-sized ESWs that are not predicted by BGK theory since it assumes a Maxwellian electron velocity distribution in the beam. Finally, we show that a 1D BGK theory is inadequate to describe ESWs in 3D beams because of complex electron trajectories.