Coulomb Collisions Research Articles

Global Electron Thermodynamics in Radiatively Inefficient Accretion Flows

In the collisionless plasmas of radiatively inefficient accretion flows, heating and acceleration of ions and electrons are not well understood. Recent studies in the gyrokinetic limit revealed the importance of incorporating both the compressive and Alfvénic cascades when calculating the partition of dissipated energy between the plasma species. In this paper, we use a covariant analytic model of the accretion flow to explore the impact of compressive and Alfvénic heating, Coulomb collisions, compressional heating, and radiative cooling on the radial temperature profiles of ions and electrons. We show that, independent of the partition of heat between the plasma species, even a small fraction of turbulent energy dissipated to the electrons makes their temperature scale with a virial profile and the ion-to-electron temperature ratio smaller than in the case of pure Coulomb heating. In contrast, the presence of compressive cascades makes this ratio larger because compressive turbulent energy is channeled primarily into the ions. We calculate the ion-to-electron temperature in the inner accretion flow for a broad range of plasma properties, mass accretion rates, and black hole spins and show that it ranges between 5 ≲ T i /T e ≲ 40. We provide a physically motivated expression for this ratio that can be used to calculate observables from simulations of black hole accretion flows for a wide range of conditions.

Particle simulation on the ion acceleration in vacuum arc discharge

The supersonic ion jet generated in vacuum arc plasma has numerous applications, but the ion acceleration mechanism is incompletely understood. In this paper, a one-dimensional spherical vacuum arc discharge model is established, and the ion acceleration from vacuum breakdown to steady arc stage is investigated using particle-in-cell direct simulation Monte Carlo method. The results show that a potential hump exists and locates about far away from the cathode, but the potential drop provides a small contribution to the ion acceleration. A potential valley forms near the plasma–vacuum boundary and propagates towards the anode as the plasma expands during the vacuum breakdown stage. The ion mounting this valley experiences continuous acceleration by the dynamic electric field of the potential valley. As the plasma reaches the anode, a steady arc stage is gradually build-up, and the potential valley disappears. Consequently, the maximum mean ion velocity decreases. The source dominating the ion acceleration in this stage is turned into the electron–ion Coulomb collision.

Suprathermal Electron Transport and Electron Beam Formation in the Solar Corona

Electron beams that are commonly observed in the corona were discovered to be associated with solar flares. These “coronal” electron beams are found ≥300 Mm above the acceleration region and have velocities ranging from 0.1c up to 0.6c. However, the mechanism for producing these beams remains unclear. In this paper, we use kinetic transport theory to investigate how isotropic suprathermal energetic electrons escaping from the acceleration region of flares are transported upwardly along the magnetic field lines of flares to develop coronal electron beams. We find that magnetic focusing can suppress the diffusion of Coulomb collisions and background turbulence and sharply collimate the suprathermal electron distribution into beams with the observed velocity within the observed distance. A higher bulk velocity is produced if energetic electrons have harder energy spectra or travel along a more rapidly expanding coronal magnetic field. By modeling the observed velocity and location distributions of coronal electron beams, we predict that the temperature of acceleration regions ranges from 5 × 106 to 2 × 107 K. Our model also indicates that the acceleration region may have a boundary where the temperature abruptly decreases so that the electron beam velocity can become more than triple (even up to 10 times) the background thermal velocity and produce the coronal type III radio bursts.

On the spatial distribution of electron energy loss due to gyro-cooling in hot star magnetospheres

ABSTRACT Hot magnetic stars often exhibit incoherent circularly polarized radio emission thought to arise from gyro-synchrotron emission by energetic electrons trapped in the circumstellar magnetosphere. Theoretical scalings for electron acceleration by magnetic reconnection driven by centrifugal breakout match well the empirical scalings for observed radio luminosity with both the magnetic field strength and the stellar rotation rate. This paper now examines how energetic electrons introduced near the top of closed magnetic loops are subsequently cooled by the energy loss associated with their gyro-synchrotron radio emission. For sample assumed distributions for energetic electron deposition about the loop apex, we derive the spatial distribution of the radiated energy from such ‘gyro-cooling’. For sub-relativistic electrons, we show explicitly that this is independent of the input energy, but also find that even extensions to the relativistic regime still yield a quite similar spatial distribution. However, cooling by Coulomb collisions with even a modest ambient density of thermal electrons can effectively quench the emission from sub-relativistic electrons, indicating that the observed radio emission likely stems from relativistic electrons that are less affected by such collisional cooling. The overall results form an initial basis for computing radio emission spectra in future models that account for such cooling and multimode excitation about the fundamental gyro-frequency. Though motivated in the context of hot stars, the basic results here could also be applied to gyro-emission in any dipole magnetospheres, including those of ultra-cool dwarfs and even (exo)-planets.

Influence of the beam-beam collisions on the energetic particle distribution in large helical device

The influence of Coulomb collisions between energetic particles in a neutral beam injection (NBI)-heated plasma is numerically investigated utilizing the improved collision operator for the orbit-following type of Monte Carlo codes. This nonlinear collision operator enables the collisional effect by non-Maxwellian plasmas including energetic particles to be taken into account. We have implemented it into GNET, one of the orbit-following Monte Carlo codes solving drift kinetic equation in the 5D phase-space, and performed simulations for tangentially injected NBI cases (beam energy: 180 keV), taking account of beam–beam Coulomb collisions. It is found that the beam–beam collisions cause energetic particle orbits to transition from passing to trapped and enhance the collisional transport, which results in the deterioration of the energetic particle confinement.

Moment-based approach to the flux-tube linear gyrokinetic model

This work reports on the development and numerical implementation of the linear electromagnetic gyrokinetic (GK) model in a tokamak flux-tube geometry using a moment approach based on the expansion of the perturbed distribution function on a velocity-space Hermite–Laguerre polynomials basis. A hierarchy of equations of the expansion coefficients, referred to as the gyro-moments (GMs), is derived. We verify the numerical implementation of the GM hierarchy in the collisionless limit by performing a comparison with the continuum GK code GENE, recovering the linear properties of the ion temperature gradient, trapped electron, kinetic ballooning and microtearing modes, as well as the collisionless damping of zonal flows. An analysis of the distribution functions and ballooning eigenmode structures is performed. The present investigation reveals the ability of the GM approach to describe fine velocity-space-scale structures appearing near the trapped and passing boundary and kinetic effects associated with parallel and perpendicular particle drifts. In addition, the effects of collisions are studied using advanced collision operators, including the GK Coulomb collision operator. The main findings are that the number of GMs necessary for convergence decreases with plasma collisionality and is lower for pressure gradient-driven modes, such as in H-mode pedestal regions, compared with instabilities driven by trapped particles and magnetic gradient drifts often found in the core. The accuracy of approximations often used to model collisions (relative to the GK Coulomb operator) is studied in the case of trapped electron modes, showing differences between collision operator models that increase with collisionality and electron temperature gradient, consistent with the results of Pan et al. (Phys. Rev. E, vol. 103, 2021, L051202). Such differences are not observed in other edge microinstabilities, such as microtearing modes. The importance of a proper collision operator model is also confirmed by analysing the collisional damping of geodesic acoustic modes and zonal flows.

Spin-exchange carrier multiplication in manganese-doped colloidal quantum dots.

Carrier multiplication is a process whereby a kinetic energy of a carrier relaxes via generation of additional electron-hole pairs (excitons). This effect has been extensively studied in the context of advanced photoconversion as it could boost the yield of generated excitons. Carrier multiplication is driven by carrier-carrier interactions that lead to excitation of a valence-band electron to the conduction band. Normally, the rate of phonon-assisted relaxation exceeds that of Coulombic collisions, which limits the carrier multiplication yield. Here we show that this limitation can be overcome by exploiting not 'direct' but 'spin-exchange' Coulomb interactions in manganese-doped core/shell PbSe/CdSe quantum dots. In these structures, carrier multiplication occurs via two spin-exchange steps. First, an exciton generated in the CdSe shell is rapidly transferred to a Mn dopant. Then, the excited Mn ion undergoes spin-flip relaxation via a spin-conserving pathway, which creates two excitons in the PbSe core. Due to the extremely fast, subpicosecond timescales of spin-exchange interactions, the Mn-doped quantum dots exhibit an up-to-threefold enhancement of the multiexciton yield versus the undoped samples, which points towards the considerable potential of spin-exchange carrier multiplication in advanced photoconversion.

The influence of plasma evolution on a kinetic scenario of collisional relaxation of a magnetized plasma

For a magnetized plasma, a reduction of the two-time formalism (Erofeev 2019 J. Plasma Phys. 85 905850104, Erofeev 2022 Contrib. Plasma Phys. 62 e202100140) to a highly informative scenario of redistribution of charged particles in momentum due to Coulomb collisions is reported. The consideration focuses on the standard case of an ideal classical ionized homogeneous plasma. It is found that the leading-order approximation of the scenario is consistent with the well-known generalizations of the Lenard–Balescu equation (Lenard 1960 Ann. Phys. 10 390–400, Balescu 1960 Phys. Fluids 3 52–63) that take into account the leading magnetic field effect (Rostoker 1960 Phys. Fluids 3 922–7, Hassan and Watson 1977 Plasma Phys. 19 237–47). A correction to the collision integral of this equation is developed that is due to time variations of plasma parameters.

RF plugging of multi-mirror machines

One of the main challenges of fusion reactors based on magnetic mirrors is the axial particle loss through the loss cones. In multi-mirror (MM) systems, the particle loss is addressed by adding mirror cells on each end of the central fusion cell. Coulomb collisions in the MM sections serve as the retrapping mechanism for the escaping particles. Unfortunately, the confinement time in this system only scales linearly with the number of cells in the MM sections and requires an unreasonably large number of cells to satisfy the Lawson criterion. Here, it is suggested to reduce the outflow by applying a traveling radio frequency (RF) electric field that mainly targets the particles in the outgoing loss cone. The Doppler shift compensates for the detuning of the RF frequency from the ion cyclotron resonance mainly for the escaping particles resulting in a selectivity effect. The transition rates between the different phase space populations are quantified via single-particle calculations and then incorporated into a semi-kinetic rate equations model for the MM system, including the RF effect. It is found that for optimized parameters, the confinement time can scale exponentially with the number of MM cells, orders of magnitude better than a similar MM system of the same length but without the RF plugging, and can satisfy the Lawson criterion for a reasonable system size.

Faraday effect in collisional magnetized plasmas

Faraday rotation is a valuable diagnostic tool for investigating laboratory and astrophysical plasmas, but it has almost exclusively been treated in the collisionless limit (despite the non-negligible role of Coulomb collisions in many laboratory plasmas). Here, we show that Faraday rotation can occur in collisional plasmas and that the usual effect is curiously altered by collisions. Namely, an initially linearly polarized light wave—propagating parallel to a uniform magnetic field—becomes elliptically polarized in the collisional plasma, and collisional absorption of the wave also occurs. Moreover, the ellipticity and rotation angle are quantifiably sensitive to the fidelity of the collisional transport coefficients. As we will demonstrate with particle-in-cell EPOCH simulations, these effects offer a stringent diagnostic tool for benchmarking multi-scale plasma simulation codes.

Gas kinetic schemes for solving the magnetohydrodynamic equations with pressure anisotropy

In many astrophysical plasmas, the Coulomb collision is insufficient to maintain an isotropic temperature, and the system is driven to the anisotropic regime. In this case, magnetohydrodynamic (MHD) models with anisotropic pressure are needed to describe such a plasma system. To solve the anisotropic MHD equation numerically, we develop a robust Gas-Kinetic flux scheme for non-linear MHD flows. Using anisotropic velocity distribution functions, the numerical flux functions are derived for updating the macroscopic plasma variables. The schemes are suitable for finite-volume solvers which utilize a conservative form of the mass, momentum and total energy equations, and can be easily applied to multi-fluid problems and extended to more generalized double polytropic plasma systems. Test results show that the numerical scheme is very robust and performs well for both linear wave and non-linear MHD problems.

Əyləc sürtünmə cütlərində ifratkeçiricilik effekti Ə.X. Canəhmədov, D.A. Volçenko, M.Ya. Cavadov, N.N. Fidrovskaya, N.A. Volçenko, D.Yu. Juravlev, V.N. Lunin

The article addresses the following issues: general principles of the state of superconductivity in brake friction pairs; isotropic and Josephson effects; paired electron and its role in superconductivity; vibrations of the crystal lattice and vortices in the metal friction element; the discussion of the results. The exciting factor for particles of various kinds in metal friction elements is pulsed normal forces in the mating of friction pairs. Conduction electrons in a metal at a low ambient temperature and its thermally stabilized state are capable of forming pairs that unite particles with equal, oppositely directed impulses. For this to happen, there must be an attraction between the electrons. Behavior and connections of pairs of electrons and the interaction of their energy levels with the nodes of the crystal lattice of a metal friction element. The presence of positive ions in the crystal lattice ensures that a moving electron attracts nearby ions, they shift towards it and create a local excess of positive charge. A locally polarized region attracts another electron, which moves towards the first one. Elastic vibrations of the crystal lattice are the movement of phonons-quanta of sound waves. In this case, electrons are attracted, emitting and absorbing phonons. Between electrons and vibrations of the crystal lattice occurring directly by the attraction of the lattice of electrons prevailing over the Coulomb collision. The emergence of mechanical and magnetic vortices, when the transport current fields exceed the minimum limit of its intensity, magnetic vortices are born near the surface and migrate deep into the metal friction element. Keywords: braking device, friction pairs, metal friction element, superconductivity, electric, magnetic field.

Collisional particle-in-cell investigations of electromagnetic pulses in hypervelocity impact plasmas

A collisional, 2D discontinuous Galerkin particle-in-cell (DG-PIC) code is developed to analyze electromagnetic pulses (EMPs) generated from hypervelocity impact plasmas. The discontinuous Galerkin scheme is used to solve the 2D transverse electric Maxwell’s equations while the particle-in-cell scheme is used to model charged species dynamics. Two models for Coulomb collisions are tested: a small-angle “particle-moment” model and a general Langevin equation model. Both collisionless and collisional simulations are able to reliably reproduce EMP generation due to charge separation within the bulk and the resulting electrostatic oscillations that occur. Both collision models cause a decrease in the frequency of the EMPs that are formed; however, this decrease is not significant enough to explain the discrepancy between experiments and simulations in previous literature. Despite this, Coulomb collisions can be significant in the physics of the plasma behind EMP generation for hypervelocity impacts, particularly in increased heating within the plasma. Overall, although Coulomb collisions are highly influential in the temperature of the plasma, they are not important in the EMP generated and its threat to spacecraft.

Anterograde Collisional Analysis of Solar Wind Ions

Owing to its low density and high temperature, the solar wind frequently exhibits strong departures from local thermodynamic equilibrium, which include distinct temperatures for its constituent ions. Prior studies have found that the ratio of the temperatures of the two most abundant ions—protons (ionized hydrogen) and α-particles (ionized helium)—is strongly correlated with the Coulomb collisional age. These previous studies, though, have been largely limited to using observations from single missions. In contrast, this present study utilizes contemporaneous, in situ observations from two different spacecraft at two different distances from the Sun: the Parker Solar Probe (PSP; r = 0.1–0.3 au) and Wind (r = 1.0 au). Collisional analysis, which incorporates the equations of collisional relaxation and large-scale expansion, was applied to each PSP datum to predict the state of the plasma farther from the Sun at r = 1.0 au. The distribution of these predicted α–proton relative temperatures agrees well with that of values observed by Wind. These results strongly suggest that, outside of the corona, relative ion temperatures are principally affected by Coulomb collisions and that the preferential heating of α-particles is largely limited to the corona.

Time-resolved Coulomb collision of single electrons.

A series of recent experiments have shown that collision of ballistic electrons in semiconductors can be used to probe the indistinguishability of single-electron wavepackets. Perhaps surprisingly, their Coulomb interaction has not been seen due to screening. Here we show Coulomb-dominated collision of high-energy single electrons in counter-propagating ballistic edge states, probed by measuring partition statistics while adjusting the collision timing. Although some experimental data suggest antibunching behaviour, we show that this is not due to quantum statistics but to strong repulsive Coulomb interactions. This prevents the wavepacket overlap needed for fermionic exchange statistics but suggests new ways to utilize Coulomb interactions: microscopically isolated and time-resolved interactions between ballistic electrons can enable the use of the Coulomb interaction for high-speed sensing or gate operations on flying electron qubits.

The Role of Electrons and Helium Atoms in Global Modeling of the Heliosphere

We present a new three-dimensional, MHD-plasma/kinetic-neutrals model of the solar wind (SW) interaction with the local interstellar medium (LISM), which self-consistently includes neutral hydrogen and helium atoms. This new model also treats electrons as a separate fluid and includes the effect of Coulomb collisions. While the properties of electrons in the distant SW and in the LISM are mostly unknown due to the lack of in situ observations, a common assumption for any global, single-ion model is to assume that electrons have the temperature of the ion mixture, which includes pickup ions. In the new model, electrons in the SW are colder, which results in a better agreement with New Horizons observations in the supersonic SW. In the LISM, however, ions and electrons are almost in thermal equilibrium. As for the plasma mixture, the major differences between the models are in the inner heliosheath, where the new model predicts a charge-exchange-driven cooling and a decrease of the heliosheath thickness. The filtration of interstellar neutral atoms at the heliospheric interface is discussed. The new model predicts an increase in the H density by ∼2% at 1 au. However, the fraction of pristine H atoms decreases by ∼12%, while the density of atoms born in the outer and inner heliosheath increases by 5% and ∼35%, respectively. While at 1 au the density of He atoms remains unchanged, the contribution from the “warm breeze” increases by ∼3%.

Resolving the mystery of electron perpendicular temperature spike in the plasma sheath

A large family of plasmas has collisional mean-free-path much longer than the non-neutral sheath width, which scales with the plasma Debye length. The plasmas, particularly the electrons, assume strong temperature anisotropy in the sheath. The temperature in the sheath flow direction (Te∥) is lower and drops toward the wall as a result of the decompressional cooling by the accelerating sheath flow. The electron temperature in the transverse direction of the flow field (Te⊥) not only is higher but also spikes up in the sheath. This abnormal behavior of Te⊥ spike is found to be the result of a negative gradient of the parallel heat flux of transverse degrees of freedom (qes) in the sheath. The non-zero heat flux qes is induced by pitch-angle scattering of electrons via either their interaction with self-excited electromagnetic waves in a nearly collisionless plasma or Coulomb collision in a collisional plasma, or both in the intermediate regime of plasma collisionality.

Neural network model of neutral beam injection in the EAST tokamak to enable fast transport simulations

The neutral beam injection (NBI) system in EAST produces energetic neutral particles, which collide with electrons and ions in tokamak plasmas and heat the plasmas through Coulomb collisions. Moreover, it drives a non-inductive source of current, due to the charge-exchange collision between neutral particles and ions, and injects toroidal torque, which generates a toroidal rotation of the plasma. The effect caused by the NBI system, such as plasma heating, current drive, total neutron rate, momentum transfer, and shine-through, are modeled by a comprehensive module called NUBEAM. However, NUBEAM is computationally intensive since it relies on Monte Carlo methods. In this work, a neural network model has been developed as a surrogate model for NUBEAM in EAST. The database for neural-network model training, validation and testing is generated by running TRANSP for experimental discharges from recent EAST campaigns (after the latest NBI upgrade) while using the NUBEAM module. Simulation results illustrate that the trained neural network has the capability of replicating the predictions made by NUBEAM while demanding a significantly shorter execution time. These results indicate that surrogate models like the one proposed in this work could enable fast transport simulations for EAST after integrating them into a control-oriented predictive code such as COTSIM.

The Origin of Persistently Nonthermal Solar Wind Electrons: the Steady Electron Runaway Model's Demonstration of Dreicer Bifurcation using Measured and Ion–Electron Coulomb Drag

The Steady Electron Runaway Model (SERM) develops the hypothesis that the solar wind’s observed ubiquitous nonthermal electron velocity distribution functions (eVDFs) are caused by Dreicer's velocity space bifurcation in the strong dimensionless required by quasi-neutrality. SERM’s predicted partitions for the pressure and density are contrasted with appropriately adapted eVDF properties from the Wind 3DP experiment (1995–1998), based on in situ observations of . The observed number fraction of electrons in runaway, δ 3DP, follows a thousandfold decline of Dreicer’s predicted fraction, δ, across the observed tenfold reduction of , satisfying δ 3DP ≃ δ 0.89. SERM’s predictions are shown to reproduce the observed variations with of the electron partial pressure and excess kurtosis, . and are positively correlated across 4 yr, as expected by the SERM–Dreicer origin of the suprathermals. SERM quantitatively explains the observed 50 yr anticorrelation between δ 3DP and the partition slope temperature ratios. This documentation quantitatively establishes Coulomb runaway physics as the missing determinant of the ubiquitous nonthermal solar wind eVDF. Astrophysical plasmas, like stellar winds, are unavoidably inhomogeneous, requiring to enforce quasi-neutrality. Between the stars is expected to be sufficiently large that measurable runaway density fractions (0.1%–30%) will occur, producing widespread leptokurtic eVDFs. Using inhomogeneous two-fluid information, SERM predicts spatially dependent leptokurtic eVDF profiles consonant with Coulomb collisions and the fluid’s E ∥(r). SERM can also comment on its eVDFs’ consistency with Maxwellians presumed in the Spitzer–Härm closure. The solar wind profile shows the implied strong radial gradient of the plasma eVDF’s transformation from near thermal to strongly leptokurtic across 1.5–6 R ⊙.

Parallel transport modeling of linear divertor simulators with fundamental ion cyclotron heating *

The Material Plasma Exposure eXperiment (MPEX) is a steady state linear device with the goal to perform plasma material interaction studies at future fusion reactor relevant conditions. A prototype of MPEX referred as ‘Proto-MPEX’ is designed to carry out research and development related to source, heating and transport concepts on the planned full MPEX device. The auxiliary heating schemes in MPEX are based on cyclotron resonance heating with radio frequency (RF) waves. Ion cyclotron heating (ICH) and electron cyclotron heating in MPEX are used to independently heat the ions and electrons and provide fusion divertor conditions ranging from sheath-limited to fully detached divertor regimes at a material target. A hybrid particle-in-cell code- PICOS++ is developed and applied to understand the plasma parallel transport during ICH in MPEX/Proto-MPEX to the target. With this tool, evolution of the distribution function of MPEX/Proto-MPEX ions is modeled in the presence of (a) Coulomb collisions, (b) volumetric particle sources and (c) quasi-linear RF-based ICH. The code is benchmarked against experimental data from Proto-MPEX and simulation data from B2.5 EIRENE. The experimental observation of ‘density-drop’ near the target in Proto-MPEX and MPEX during ICH is demonstrated and explained via physics-based arguments using PICOS++ modeling. In fact, the density drops at the target during ICH in Proto-MPEX/MPEX to conserve the flux and to compensate for the increased flow during ICH. Furthermore, sensitivity scans of various plasma parameters with respect to ICH power are performed for MPEX to investigate its role on plasma transport and particle and energy fluxes at the target.