Coulomb Collisions Research Articles

Implications of Kappa Suprathermal Halo of the Solar Wind Electrons

The electron velocity distributions measured in-situ in space plasmas reveal two central populations, a low-energy and highly dense (quasi-)thermal core, and a more diffuse but hotter suprathermal halo. Even if the core contributes much more to the total number density than the suprathermal particles, the energetic electrons play an important role in the higher moments. Using a dataset of more than 120,000 solar wind observations of electron distributions, measured in the ecliptic between 0.35 and 3.3 AU, we investigate here the main characteristics of the halo population and its potential influence on the core, and macroscopic properties of electrons, i.e., number density (n), bulk velocity (u), temperature (T) and temperature anisotropy (T⊥/Τ//). The analysis indicates that the parameters exhibit interdependence trends characterized by correlations between certain of these parameters and the kappa exponent (κ) corresponding to the power law of the halo population tail. The links between low kappa and low number densities (of both the core and halo populations) confirm that Coulomb collisions can be quite ineffective even at low radial distances if the density of the plasma is sufficiently low. Moreover, halo populations with lower values of κ are also associated to higher temperature anisotropies, and to higher bulk velocity. An interdependence between core and halo populations is also suggested by an apparent (inverse) correlation between their density and temperature ratios. We further show relations between the parameters fitting the sum of a Maxwellian core and a Kappa halo, and those of a global (single) Kappa fit that incorporates both the core and halo components. Such a global Kappa is used in an exospheric model of the solar wind, to predict the influence of suprathermal electrons on the characteristics of the solar wind. These results should stimulate future detailed analysis of these relationships and correlations, which may contribute to a realistic modeling of the solar wind and the formation and evolution of suprathermal populations.

Direct observations of anomalous resistivity and diffusion in collisionless plasma

Coulomb collisions provide plasma resistivity and diffusion but in many low-density astrophysical plasmas such collisions between particles are extremely rare. Scattering of particles by electromagnetic waves can lower the plasma conductivity. Such anomalous resistivity due to wave-particle interactions could be crucial to many processes, including magnetic reconnection. It has been suggested that waves provide both diffusion and resistivity, which can support the reconnection electric field, but this requires direct observation to confirm. Here, we directly quantify anomalous resistivity, viscosity, and cross-field electron diffusion associated with lower hybrid waves using measurements from the four Magnetospheric Multiscale (MMS) spacecraft. We show that anomalous resistivity is approximately balanced by anomalous viscosity, and thus the waves do not contribute to the reconnection electric field. However, the waves do produce an anomalous electron drift and diffusion across the current layer associated with magnetic reconnection. This leads to relaxation of density gradients at timescales of order the ion cyclotron period, and hence modifies the reconnection process.

Local gyrokinetic collisional theory of the ion-temperature gradient mode

We present a study of the linear properties of the ion-temperature gradient (ITG) modes with collisions modelled for the first time by the linearized gyrokinetic (GK) Coulomb collision operator (Freiet al.,J. Plasma Phys., vol. 87, issue 5, 2021, 905870501) in the local limit. The study is based on a Hermite–Laguerre polynomial expansion of the perturbed ion distribution function applied to the linearized GK Boltzmann equation, yielding a hierarchy of coupled equations for the expansion coefficients, referred to as gyromoments. We explore the collisionless and high-collisional limits of the gyromoment hierarchy analytically. Parameter scans revealing the dependence of the ITG growth rate on the collisionality modelled using the GK Coulomb operator are reported, showing strong damping at small scales as the collisionality increases and, therefore, the need for a steeper gradient for the ITG onset at high collisionality to overcome the finite Larmor radius (FLR) collisional stabilization. The predictions on the ITG growth rate by the GK Coulomb operator are compared with other collision operator models, such as the Sugama, the Dougherty, as well as the momentum-conserving pitch-angle scattering and the Hirshman–Sigmar–Clarke collision operators derived for the first time in terms of gyromoments. The importance of FLR terms in the collision operators is pointed out by the appearance of a short wavelength ITG branch when collisional FLR terms are neglected, this branch being completely suppressed by FLR collisional effects. Energy diffusion is shown to be important at high collisionality and at small scale lengths. Among the GK collision operators considered in this work, the GK Sugama collision operator yields, in general, the smallest deviation compared with the GK Coulomb collision operator, while the largest deviations are found with the GK Dougherty operator. Convergence studies of the gyromoment method are reported and show that the drifts associated with the gradient and curvature of the magnetic field increase the required number of gyromoments at low collisionality. Nevertheless, the low number of gyromoments necessary for convergence at high collisionality constitutes an attractive numerical and analytical feature of the gyromoment approach to study the plasma dynamics in the boundary of fusion devices.

Solar Flare Heating with Turbulent Suppression of Thermal Conduction

During solar flares, plasma is typically heated to very high temperatures, and the resulting redistribution of energy via thermal conduction is a primary mechanism transporting energy throughout the flaring solar atmosphere. The thermal flux is usually modeled using Spitzer’s theory, which is based on local Coulomb collisions between the electrons carrying the thermal flux and those in the background. However, often during flares, temperature gradients become sufficiently steep that the collisional mean free path exceeds the temperature-gradient scale size, so that thermal conduction becomes inherently nonlocal. Further, turbulent angular scattering, which is detectable in nonthermal widths of atomic emission lines, can also act to increase the collision frequency and thus suppress the heat flux. Recent work by Emslie & Bian extended Spitzer’s theory of thermal conduction to account for both nonlocality and turbulent suppression. We have implemented their theoretical expression for the heat flux (which is a convolution of the Spitzer flux with a kernel function) into the RADYN flare-modeling code and performed a parameter study to understand how the resulting changes in thermal conduction affect the flare dynamics and hence the radiation produced. We find that models with reduced heat fluxes predict slower bulk flows, less intense line emission, and longer cooling times. By comparing the features of atomic emission lines predicted by the models with Doppler velocities and nonthermal line widths deduced from a particular flare observation, we find that models with suppression factors between 0.3 and 0.5 relative to the Spitzer value best reproduce the observed Doppler velocities across emission lines forming over a wide range of temperatures. Interestingly, the model that best matches the observed nonthermal line widths has a kappa-type velocity distribution function.

Collisional magnetized shock waves: One-dimensional full particle-in-cell simulations.

Although collisional electrostatic shock waves have been investigated extensively via theory, simulations, and experiments, there are comparatively few studies about collisional magnetized shock waves. We investigate collisional magnetized shocks by performing one-dimensional full particle-in-cell simulations that incorporate ion-ion, electron-electron, and ion-electron Coulomb collisions, for perpendicular and quasiparallel shock waves. The effect of Coulomb collisions is to drive a shock wave into a more laminar state. For a perpendicular shock, the magnetic overshoot becomes small because the electron pressure perpendicular to the magnetic field is isotropized and decreases due to electron-electron collisions. For the quasiparallel case, we find that ion-electron collisions severely suppress the standing whistler wave, which is present in the form of large amplitude waves in a collisionless shock wave.

Effects of collisional ion orbit loss on neoclassical tokamak radial electric fields

Ion orbit loss is considered important for generating the radially inward electric field E r in a tokamak edge plasma. In particular, this effect is emphasized in diverted tokamaks with a magnetic X point. In neoclassical equilibria, Coulomb collisions can scatter ions onto loss orbits and generate a radially outward current, which in steady state is balanced by the radially inward current from viscosity. To quantitatively measure this loss-orbit current in an edge pedestal, an ion-orbit-flux diagnostic has been implemented in the axisymmetric version of the gyrokinetic particle-in-cell code XGC. As the first application of this diagnostic, a neoclassical DIII-D H-mode plasma is studied using gyrokinetic ions and adiabatic electrons. The validity of the diagnostic is demonstrated by studying the collisional relaxation of E r in the core. After this demonstration, the loss-orbit current is numerically measured in the edge pedestal in quasisteady state. In this plasma, it is found that the radial electric force on ions from E r approximately balances the ion radial pressure gradient in the edge pedestal, with the radial force from the plasma flow term being a minor component. The effect of orbit loss on E r is found to be only mild.

Space charge compensation of positive ion beams used in magnetic fusion applications

A model is presented for space charge neutralisation of positive ion beams. The model is used for the particular case of the beams used for magnetic based fusion applications. The beams consist, after a gas neutraliser, of ions and atoms at different energies. Account is taken of the contribution of all beam components to ionization of the background gas. Consideration is also given to not only beam heating of the plasma generated by the beam, due to Coulomb collisions, but also to Coulomb heating by fast electrons produced in ionization by all beam particles and stripping of the neutral components. Two approximations are considered for the motion of the secondary ions out of the beam potential; a drift approximation and a freefall approximation. All the beam plasma parameters can be calculated. The model is applied to a typical extracted beam of deuterium ions of 120 kV, 60 A. It is found that these beams are very highly compensated and that beam plasma heating by the electrons produced is generally greater than that due to the beam ions.

Impact of azimuthal forcing on the Brillouin limit in a collisional two-species Ohkawa filter

This paper investigates the physics of plasma separation in a two species rotating collisional Ohkawa filter, when the source of rotation is an orbital angular momentum carrying wave. The electric field is treated self-consistently with ion and electron radial motion. The injection of angular momentum causes radial currents leading to charge penetration and electric field build up. The electric field varies until an equilibrium with the friction forces is reached. Both collisions with neutrals and Coulomb collisions are considered. In the case where the electric field is driven by the resonant wave, there is no collisional breakdown of the Brillouin limit [Rax et al., Phys. Plasmas 22, 092101 (2015)]; on the contrary, the maximum achievable electric field decreases when the collision frequency is increased. When two species are present, one that undergoes the wave forcing while the second does not interact with the wave, we find the following: the first species is confined, while the second species can be expelled or confined depending on the charge to mass ratio and the collisionalities. Assuming equal charge numbers, if the second species is the heavy one, it is always expelled, which is a standard result. When the second species is the light one, it can also be expelled in the common case where neutral collisions dominate over Coulomb collisions, which constitutes a new result.

On Modeling ICME Cross-Sections as Static MHD Columns

Solar coronal mass ejections are well known to expand as they propagate through the heliosphere. Despite this, their cross-sections are usually modeled as static plasma columns within the magnetohydrodynamics (MHD) framework. We test the validity of this approach using in-situ plasma data from 151 magnetic clouds (MCs) observed by the WIND spacecraft and 45 observed by the Helios spacecrafts. We find that the most probable cross-section expansion speeds for the WIND events are only $\approx 0.06$ times the Alfv\'en speed inside the MCs while the most probable cross-section expansion speeds for the Helios events is $\approx 0.03$. MC cross-sections can thus be considered to be nearly static over an Alfv\'en crossing timescale. Using estimates of electrical conductivity arising from Coulomb collisions, we find that the Lundquist number inside MCs is high ($\approx 10^{13}$), suggesting that the MHD description is well justified. The Joule heating rates using our conductivity estimates are several orders of magnitude lower than the requirement for plasma heating inside MCs near the Earth. While the (low) heating rates we compute are consistent with the MHD description, the discrepancy with the heating requirement points to possible departures from MHD and the need for a better understanding of plasma heating in MCs.

Numerical analysis of isotope effect in NIFS negative ion source

Result of hydrogen (H) and deuterium (D) experiments done by NIFS research and development negative ion source (RNIS) demonstrated that the co-extracted electron current with the negative ions and the electron density in the driver region in the D experiment have been around three times higher than that in the H experiment. To investigate mechanism of this difference, electron transport simulation using 3D kinetic particle tracking model KEIO-MARC code has been modified and applied to analysis of the isotope effect in the NIFS negative ion source. Simulation result suggests that impacts of isotope effects of sheath potential drop, coulomb collisions, and some reactions of ground state molecules and ions on the electron density is not large to explain the experimental result of the increase in the electron density in the plasma.

Sudden collapse of a pressure profile generated by off-axis heating in a linear magnetized plasma

The features of an unexpected, large event that arises spontaneously during a basic heat transport experiment are presented. It consists of the sudden collapse of the radial plasma pressure profile, akin to disruption events observed in toroidal magnetic confinement devices. The experiment is performed on the Large Plasma Device at the University of California, Los Angeles (UCLA). It uses a LaB6 thermionic emitter of annular shape to induce off-axis heating of a cold, afterglow plasma, in a linear magnetic geometry. The temporal evolution consists of three regimes. During an early, quiescent period, classical heat transport along and across the magnetic field arises from Coulomb collisions. After significant pressure gradients develop, drift-Alfvén waves become unstable. Upon reaching large amplitude, they trigger avalanche events that flatten the outer part of the heated region, which, in turn, quenches the instability. Due to the sustained heating, the pressure profile rebuilds and the process repeats, leading to a relatively long, second regime that displays multiple avalanches, but suddenly, the annular pressure profile is observed to collapse. After this collapse, the system enters a third regime with large fluctuations. Before the collapse, a rapid, runaway heating environment arises whose time evolution exhibits a self-similar dependence on the applied voltage. The time evolution, morphology, and scaling of the collapse event are presented, and an examination is made of the underlying mechanisms.

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

AbstractA reduction of the two‐time formalism [V. I. Erofeev, Journal of Plasma Physics 85, 905850104 (2019)] to a highly informative scenario of redistribution of plasma particles in momentum due to Coulomb collisions is reported. The standard case of an ideal classical ionized homogeneous plasma is considered. It is found that the leading‐order approximation of the scenario is consistent with the well‐known Lenard–Balescu Equation [A. Lenard, Ann. Phys. 10, 390–400 (1960); R. Balescu, Phys. Fluids 3, 52–63 (1960)]. A correction to the collision integral of this equation is developed to account for the time variation of plasma parameters. This correction is shown to differ from its analogs related to the existing generalizations of the Lenard–Balescu kinetic equation [Yu.L. Klimontovich, Kinetic theory of nonideal gases and nonideal plasmas (Pergamon Press, Oxford [1982]); V.V. Belyi, Yu.A. Kukharenko, J. Wallenborn, Journal of plasma physics 59, 657–669 (1998)].

Enhancement of the Nonresonant Streaming Instability by Particle Collisions.

Streaming cosmic rays can power the exponential growth of a seed magnetic field by exciting a nonresonant instability that feeds on their bulk kinetic energy. By generating the necessary turbulent magnetic field, it is thought to play a key role in the confinement and acceleration of cosmic rays at shocks. In this Letter we present hybrid-particle-in-cell simulations of the nonresonant mode including MonteCarlo collisions, and investigate the interplay between the pressure anisotropies produced by the instability and particle collisions in the background plasma. Simulations of poorly ionized plasmas confirm the rapid damping of the instability by proton-neutral collisions predicted by linear fluid theory calculations. In contrast we find that Coulomb collisions in fully ionized plasmas do not oppose the growth of the magnetic field, but under certain conditions suppress the pressure anisotropies and actually enhance the magnetic field amplification.

Effect of electrostatic forces on the dispersion of like-charged solid particles transported by homogeneous isotropic turbulence

The effect of electrostatic forces on the dispersion of small like-charged inertial particles transported by a homogeneous isotropic turbulent flow is analysed by means of direct numerical simulations coupled with the Lagrangian tracking of charged particles. The results show that particle dispersion decreases for increasing charge. Since turbulent particle dispersion is related to the intensity of particle agitation and to the Lagrangian particle integral time scale, we analyse the effects of electrostatic forces on these two quantities. Particle agitation decreases for increasing particle charge. In fact, particle kinetic energy is not directly modified by electrostatic forces, which are conservative, it is rather the particle entrainment by fluid turbulence that is modified. To support this claim, one shows that the fluid–particle velocity covariance is destructed by electrostatic forces, a destruction can be predicted by drawing an analogy between inter-particle collisions and Coulomb collisions. As expected, electrostatic forces decorrelate particle velocities leading to a decrease of the Lagrangian particle integral time scale. Finally, one shows that the analogy with inter-particle collisions allows us to predict the reduction of particle dispersion.

Modeling of beam ions loss and slowing down with Coulomb collisions in EAST

This paper uses the implicit Monte–Carlo full-orbit-following parallel program ISSDE to calculate the prompt loss and slowing down process of neutral beam injection (NBI)-generated fast ions due to Coulomb collisions in the equilibrium configuration of Experimental Advanced Superconducting Tokamak (EAST). This program is based on the weak equivalence of the Fokker–Planck equation under Rosenbluth MacDonald Judd (RMJ) potential and Stratonovich stochastic differential equation (SDE). The prompt loss with the LCFS boundary and the first wall (FW) boundary of the two co-current neutral injection beams are studied. Simulation results indicate that the loss behavior of fast ions using the FW boundary is very different from that of the LCFS boundary, especially for fast ions with a large gyration radius. According to our calculations, about 5.11% of fast ions generated by perpendicular injection drift out of the LCFS and then return inside the LCFS to be captured by the magnetic field. The prompt loss ratio of fast ions and the ratio of orbital types depend on the initial distribution of fast ions in the Pζ –Λ space. Under the effect of Coulomb collisions, the pitch-angle scattering and stochastic diffusion happens, which will cause more fast ion loss. For short time scales, among the particles lost due to collisions, the fraction of banana ions reaches 92.31% in the perpendicular beam and 58.65% in the tangential beam when the fraction of banana ions in the tangential beam is 3.4% of the total ions, which means that the effect of Coulomb collisions on banana fast ions is more significant. For long time scales, the additional fast ion loss caused by Coulomb collisions of tangential and perpendicular beams accounted for 16.21% and 25.05% of the total particles, respectively. We have also investigated the slowing down process of NBI fast ions.

Edge tokamak transport in regimes with high collisionality

AbstractIn the strongly detached regimes, especially in future tokamak reactors, plasma in the divertor and in some special regions like vicinity of highly radiating X‐point is strongly collisional. Ion gyrofrequency becomes less than Coulomb collision frequency and might be of the order of ion‐neutral collision frequency. For such parameters, parallel and perpendicular ion diffusion and mobility caused by ion‐neutral collision becomes important and can to large extent determine density profiles and currents distribution in the divertor. In the present article, plasma profiles in the vicinity of divertor plates were analysed. It is demonstrated that density profiles are determined by combination of parallel and perpendicular ambipolar diffusion. Results of analytic calculations are compared with Particle‐In‐Cell Monte‐Carlo Collisions (PIC MCC) simulations of magnetized plasma and collisional transport of magnetized ions from quasi‐neutral region to the material surface. Analytic expressions are compared with the results of particle in cell simulations done for different angles between magnetic field and material surface and different plasma parameters. Impact of velocity of neutral particles on ion fluxes and currents is also investigated. Consequences for divertor plasma typical for ITER and other future tokamak‐reactors are discussed.

Space charge compensation of positive ion beams used in magnetic fusion applications

Abstract A model is presented for space charge neutralisation of positive ion beams. The model is used for the particular case of the beams used for magnetic based fusion applications. The beams consist, after a gas neutraliser, of ions and atoms at different energies. Account is taken of the contribution of all beam components to ionization of the background gas. Consideration is also given to not only beam heating of the plasma generated by the beam, due to Coulomb collisions, but also to Coulomb heating by fast electrons produced in ionization by all beam particles and stripping of the neutral components. Two approximations are considered for the motion of the secondary ions out of the beam potential; a drift approximation and a freefall approximation. All the beam plasma parameters can be calculated. The model is applied to a typical extracted beam of deuterium ions of 120kV,60A. It is found that these beams are very highly compensated and that beam plasma heating by the electrons produced is generally greater than that due to the beam ions.

On numerical energy conservation for an implicit particle-in-cell method coupled with a binary Monte-Carlo algorithm for Coulomb collisions

Conventional particle-in-cell (PIC) methods suffer from enhanced numerical heating (explicit PIC) or cooling (semi-implicit PIC) when coupled with a binary Monte-Carlo algorithm for Coulomb collisions. In this work, a fully-implicit θ-PIC scheme (with adjustable time-biasing parameter 1/2≤θ≤1) is considered. The discrete change in energy of a closed system after a time step for this scheme scales with (1/2−θ)Cθ, where Cθ is a positive definite quantity that depends on the frequency spectrum of the energy in the fields. Collisions lead to additional energy in the field fluctuations associated with high-frequency light waves produced by a numerical Bremsstrahlung process, which can result in a large increase in the numerical cooling rate for θ>1/2. However, for θ=1/2, energy is exactly conserved. The energy in the field fluctuations on long time scales agrees with that calculated using the equipartition theorem for a classical system in thermodynamic equilibrium.

Ionization waves (striations) in a low-current plasma column revisited with kinetic and fluid models

A one-dimensional particle-in-cell Monte Carlo collisions method has been used to model the development and propagation of ionization waves in neon and argon positive columns. Low-current conditions are considered, that is, conditions where stepwise ionization or Coulomb collisions are negligible (linear ionization rate). This self-consistent model describes the development of self-excited moving striations, reproduces many of the well-known experimental characteristics (wavelength, spatial resonances, potential drop over one striation, and electron “bunching” effect) of the ionization waves called p, r, and s waves in the literature, and sheds light on their physical properties and on the mechanisms responsible for their existence. These are the first fully kinetic self-consistent simulations over a large range of conditions reproducing the development of p, r, and s ionization waves. Although the spatial resonances and the detailed properties of the striations in the nonlinear regime are of kinetic nature, the conditions of existence of the instability can be obtained and understood from a linear stability analysis of a three-moment set of quasi-neutral fluid equations where the electron transport coefficients are expressed as a function of electron temperature and are obtained from solutions of a 0D Boltzmann equation. An essential aspect of the instability leading to the development of these striations is the non-Maxwellian nature of the electron energy distribution function in the uniform electric field prior to the instability onset, resulting in an electron diffusion coefficient in space much larger than the energy diffusion coefficient.

Effects of Coulomb collisions on lower hybrid drift waves inside a laboratory reconnection current sheet

We have developed a local, linear theoretical model for lower hybrid drift waves that can be used for plasmas in the weakly collisional regime. Two cases with typical plasma and field parameters for the current sheet of the magnetic reconnection experiment have been studied. For a case with a low electron beta (βe=0.25, high guide field case), the quasi-electrostatic lower hybrid drift wave is unstable, while the electromagnetic lower hybrid drift wave has a positive growth rate for a high-βe case (βe=8.9, low guide field case). For both cases, including the effects of Coulomb collisions reduces the growth rate but collisional impacts on the dispersion and growth rate are limited (≲20%).