Collisionless Approach Research Articles

Analytic solution for the electrostatic potential of the solar wind

Context. Some kinetic models of the solar wind, such as the exospheric ones, make certain assumptions about the solar plasma, which for modelling purposes is generally considered collisionless and quasi-neutral. They also assume specific distribution functions for the electron and proton populations from which the fundamental properties of the plasma, including the density, are calculated using the moment integrals. Imposing the quasi-neutrality condition leads to the presence of an ambipolar electrostatic field, which is responsible for the acceleration of the wind. Usually, the calculation of the moment integrals is complicated by the fact that most kinetic models assume different trajectories for the solar wind components, separating the integrals into chunks corresponding to the pitch angles defining the trajectories. Hence, up to now all these integrals and therefore the plasma fundamental quantities have been calculated numerically. Aims. A new model is presented that makes use of similar assumptions to other kinetic collisionless models but does not need to impose the separation of the populations in different trajectories for the calculation of the integrals. As a consequence, an analytic solution for the electrostatic potential of the solar wind valid for all distances is found. Methods. A kinetic collisionless approach was used to characterise the solar wind plasma. A single equation for the electrostatic potential function was found assuming certain distribution functions (Maxwellian or non-thermal such as Kappa), which include an unknown electrostatic potential, calculating the density integral for those distribution functions and making those densities equal for electrons and protons. Results. An analytic solution for the electrostatic potential as a function of radial distance is found (for the first time for all distances) and shown to produce a non-monotonic total potential, which is compatible with other models like the exospheric ones whose electrostatic potential drives the acceleration of the solar wind. This expression can now be used, in a straightforward way, to provide insight into the importance of the electron distribution functions to shape the electrostatic potential of thermal solar-like outflows.

Plasma wave oscillations in a nonequilibrium two-dimensional electron gas: Electric field induced plasmon instability in the terahertz frequency range

We have developed a theory of collective electron oscillations in two-dimensional semiconductor heterostructures subjected to a high electric field. The effect of the stationary electric field has been taken into account on both steady-state and high-frequency electron transport. The analysis has been conducted by solving Boltzmann-Vlasov equations in the collisionless approach for high-frequency electron transport. Two actual types of heterostructures with ungated and gated two-dimensional (2D) electron gas have been considered. We have found that the collective excitation spectra of 2D electron gas are of the multibranch character with high-quality plasmonic modes and a set of thermal modes. Applied electric field induces the following effects: strong nonreciprocal behavior of both oscillation frequency and damping; interaction of plasmonic and thermal modes; instability of excitations propagating along the electron drift (effect of negative Landau damping). The mechanism of this plasma wave instability is different from early discussed Cherenkov, Dyakonov-Shur, and Ryzhii-Satou-Shur mechanisms of instabilities in plasmonic systems. It has been shown that the electrically induced plasmon instability provides amplification of terahertz (THz) radiation in grating-based plasmonic structures. We suggest that presented results can be important for deeper understanding of THz plasma physics and developing of electrically pumping devices for THz optoelectronics.

High performance collisional PIC plasma simulation with modern GPUs

GPU implementation of the collisional Particle-In-Cell plasma model is proposed. The goal of this model is the simulation of Plasma Enhanced Chemical Vapour Deposition (PECVD) reactors with glow discharge plasma and also for simulation of fusion plasma with sufficient role of collisions. Vlasov equation is being solved by the Particle-In-Cell (PIC) method. Collision are simulated with the null collision technique. The important difference from the collisionless approach is that major time is taken by collision evaluation and not by particle push.GPU performance is increased by storing the particles in cells and also by the exclusion of synchronization of threads at the stage of current and density evaluation. Electromagnetic field is given by either the Maxwell equations or be the Poisson equation for electrostatic case. The Maxwell equations are solved by the FDTD method. The Poisson equation is solved by the hybrid method. Performance obtained at the moment is 0.5 TFLOPS for particle push with the Nvidia Tesla V100, and the parallels efficiency is 92% for a cluster with 250 nodes with 2 GPUs each resulting in 500 GPUs.

Transition Between Beam-Plasma and Beam-Dissipative Instability Regimes in the Interaction of Relativistic Large Larmor Orbit Electron Beams and Azimuthal Surface Waves Above the Upper-Hybrid Frequency in Coaxial Plasma Waveguides

Azimuthal surface waves are eigen-electromagnetic waves which propagate in coaxial plasma-vacuum waveguides across an axial stationary magnetic field. Their excitation in the coaxial plasma layer by the flow of electrons which rotate along large Larmor orbits either around or inside the plasma layer has been well studied in the collision-less approach. The influence of weak collisions between the plasma particles on the growth rate of such waves for both cases of the electron beam placement is studied here for the frequency range above the upper-hybrid frequency and compared to the case of the electron cyclotron frequency range. Transition from the regime of beam-plasma instability to that of a beam-dissipative instability is discussed.

Excitation of azimuthal surface waves in the electron cyclotron frequency range by a rotating electron beam in presence of dissipation

Azimuthal surface waves are eigen-electromagnetic oscillations which propagate in cylindrical plasma filled waveguides across an axial stationary magnetic field. Their excitation by a flow of electrons which rotate along large Larmor orbits around the plasma column is well studied mostly in the collisionless approach. The influence of weak collisions between the plasma particles on the growth rate of such waves is studied here. Transfer from the mode of beam-plasma instability that takes place in the case of sufficiently high electron beam particle density and weak collisions to that of a beam dissipative instability that occurs if the beam density is low and the collision frequency is sufficiently high is demonstrated.

Simulation of collisional effects on divertor pumping in JT-60SA

In this work, the exhausted neutral gas flow is modeled for two cases of a simplified JT-60SA sub-divertor geometry and compared via three different approaches, namely (i) a collisionless approach based on the ProVac3D code, (ii) the DSMC approach based on the DIVGAS code that can be run with and without consideration of particle collisions, and (iii) the NEUT2D approach which has been extensively used in the past for the JT-60 design. In a first case study, the transmission probability was calculated by the 3 approaches and very good agreement is found between NEUT2D-ProVac3D whereas discrepancies between DIVGAS and NEUT2D are found and further analyzed. In the second case, the assessment of collisions is done by means of DIVGAS. Simulations showed that the flow is found in the transitional regime with Kn numbers between 0.1 and 0.4. The DIVGAS collisionless case yielded lower values of temperature than the collisional one by factors of 0.5–0.8 in regions near the inlets of the sub-divertor whereas in regions near the pump and the chevron, the temperature difference is marginal. Moreover, a relative percentage difference of 16–40% in pressure values was found between collisionless and collisional approaches.

Application of electrostatic Langmuir probe to atmospheric arc plasmas producing nanostructures

The temporal evolution of a high pressure He arc producing nanotubes was considered and the Langmuir probe technique was applied for plasma parameter measurements. Two modes of arc were observed: cathodic arc where discharge is supported by erosion of cathode material and anodic arc which is supported by ablation of the anode packed with carbon and metallic catalysts in which carbon nanotubes are synthesized. Voltage-current (V-I) characteristics of single probes were measured and unusually low ratio of saturation current on positively biased probe to that on negatively biased of about 1–4 was observed. This effect was explained by increase of measured current at the negatively biased probe above the level of ion saturation current due to secondary electron emission from the probe surface. Since utilization of standard collisionless approach to determine plasma parameters from the measured V-I characteristic is not correct, the electron saturation current was used to estimate the plasma density.

3D modelling of negative ion extraction from a negative ion source

The development of a suitable negative ion source constitutes a crucial step in the construction of the neutral beam injector of ITER. To fulfil the ITER requirements in terms of heating and current drive, the negative ion source should deliver 40 A of D−. The achievement of such a source constitutes a technical and scientific challenge, and it requires a deeper understanding of the underlying physics of the source. The present knowledge of the ion extraction mechanism from the negative ion source is limited. It constitutes a complex problem that involves understanding the behaviour of magnetized plasma sheaths when negative ions and electrons are pulled out from the plasma. Moreover, due to the asymmetry induced by the crossed magnetic configuration used to filter the electrons, any realistic study of this problem must consider the three spatial dimensions. To address this problem in a realistic way, a 3D particles-in-cell electrostatic code specifically designed for this system was developed. The code uses a Cartesian coordinate system and it can deal with complex boundary geometry as it is the case of the extraction apertures (Hemsworth et al 2009 Nucl. Fusion 49 045006). The complex magnetic field that is applied to deflect electrons is also taken into account. This code, called ONIX, was used to investigate the plasma properties and the transport of negative ions and electrons close to a source extraction aperture. Results in the collisionless approach on the formation of the plasma meniscus and the screening of the extraction field by the plasma are presented here, as well as negative ions trajectories. Negative ion extraction efficiency from volume and surfaces is discussed.

Distribution and escape of molecular hydrogen in Titan's thermosphere and exosphere

We present an in‐depth study of the distribution and escape of molecular hydrogen (H2) on Titan, based on the global average H2 distribution at altitudes between 1000 and 6000 km, extracted from a large sample of Cassini/Ion and Neutral Mass Spectrometer (INMS) measurements. Below Titan's exobase, the observed H2 distribution can be described by an isothermal diffusion model, with a most probable flux of (1.37 ± 0.01) × 1010 cm−2 s−1, referred to the surface. This is a factor of ∼3 higher than the Jeans flux of 4.5 × 109 cm−2 s−1, corresponding to a temperature of 152.5 ± 1.7 K, derived from the background N2 distribution. The H2 distribution in Titan's exosphere is modeled with a collisionless approach, with a most probable exobase temperature of 151.2 ± 2.2 K. Kinetic model calculations in the 13‐moment approximation indicate a modest temperature decrement of several kelvin for H2, as a consequence of the local energy balance between heating/cooling through thermal conduction, viscosity, neutral collision, and adiabatic outflow. The variation of the total energy flux defines an exobase level of ∼1600 km, where the perturbation of the Maxwellian velocity distribution function, driven primarily by the heat flow, becomes strong enough to raise the H2 escape flux considerably higher than the Jeans value. Nonthermal processes may not be required to interpret the H2 escape on Titan. In a more general context, we suggest that the widely used Jeans formula may significantly underestimate the actual thermal escape flux and that a gas kinetic model in the 13‐moment approximation provides a better description of thermal escape in planetary atmospheres.

Nonequilibrium dynamics of optical-lattice-loaded Bose-Einstein-condensate atoms: Beyond the Hartree-Fock-Bogoliubov approximation

In this work a two-particle irreducible (2PI) closed-time-path (CTP) effective action is used to describe the nonequilibrium dynamics of a Bose Einstein condensate (BEC) selectively loaded into every third site of a one-dimensional optical lattice. The motivation of this work is the recent experimental realization of this system at National Institute of Standards and Technology (NIST) where the placement of atoms in an optical lattice is controlled by using an intermediate superlattice. Under the 2PI CTP scheme with this initial configuration, three different approximations are considered: a) the Hartree-Fock-Bogoliubov (HFB) approximation, b) the next-to-leading order 1/$\mathcal{N}$ expansion of the 2PI effective action up to second order in the interaction strength and c) a second order perturbative expansion in the interaction strength. We present detailed comparisons between these approximations and determine their range of validity by contrasting them with the exact many body solution for a moderate number of atoms and wells. As a general feature we observe that because the second order 2PI approximations include multi-particle scattering in a systematic way, they are able to capture damping effects exhibited in the exact solution that a mean field collisionless approach fails to produce. While the second order approximations show a clear improvement over the HFB approximation our numerical result shows that they do not work so well at late times, when interaction effects are significant.

Numerical analysis of collisionless particle motion in an observed supercritical shock front

The well‐accepted shock model assumes that the shock front is stationary and one dimensional, in the sense that ion and electron dynamics are determined primarily by their interaction with the quasi‐stationary electric and magnetic fields in the shock front. We study the applicability of this model to an observed high Mach number supercritical shock. For this purpose we numerically analyze ion and electron dynamics in the measured magnetic field and modeled electric field (on the basis of the measurements of electron heating) and check the consistency of the numerically determined particle features with the observed shock profile. We find that the shock must be narrow enough (for given Mach number MA, kinetic‐to‐magnetic pressure ratio β, angle θ between the shock normal and upstream magnetic field, and magnetic compression Bd/Bu) to ensure that ion reflection is not too strong. We also find that the small‐scale structure is an important part of the shock: the shock front would be grossly nonstationary if it were too wide or if small‐scale features were absent. The ion energization due to the reflection and gyration is qualitatively consistent with the ion dynamics in quasi‐stationary electric and magnetic fields. However, smoothing of the downstream ion distribution is insufficient, and deviations from one dimensionality and/or nonstationarity are necessary for the shock to be stable. Electron dynamics are weakly nonadiabatic, and evolution of the collisionless electrons follows the potential and magnetic field. Gap filling cannot be studied within this collisionless approach.

Gas-kinetic schemes for the compressible Euler equations: Positivity-preserving analysis

Numerical schemes based on the collisional BGK model have been developed in recent years. In this paper, we investigate the first-order BGK schemes for the Euler equations. Particular attention is given to finding CFL-like conditions under which the schemes are positivity-preserving (i.e. density and internal energy remain nonnegative). The first-order BGK schemes are linear combinations of collisionless (i.e. kinetic flux-splitting scheme) and collisional approach. We show that the collisionless approach preserves the positivity of density and internal energy under the standard CFL condition. Although the collisionless approach has the positivity-preserving property, it introduces large intrinsic dissipation and heat conductions since the corresponding scheme is based on two half Maxwellians. In order to reduce the viscous error, one obvious method is to use an exact Maxwellian, which leads to the collisional Boltzmann scheme. An CFL-like condition is also found for the collisional approach, which works well for the test problems available in literature. However, by considering a counterexample we find that the collisional approach is not always positivity-preserving. The BGK type schemes are formed by taking the advantages of both approaches, i.e. the less dissipative scheme (collisional) and the more dissipative but positivity-preserving scheme (collisionless).

Modern exospheric theories and their observational relevance

A review and critique of present‐day kinetic theory models of planetary exospheres is presented. Models of ionized exospheres, specifically the solar and the terrestrial polar wind, are also discussed. The objective of the paper is to point out the need for a rigorous kinetic theory treatment of the atmosphere in the altitude region between the thermosphere and the exosphere. This is the region where the atmosphere undergoes a transition from a collision‐dominated to a collisionless situation. The various aspects of the exospheric problem are introduced and developed around this main theme. The exospheric problem and its considerable overlap with several related problems in physics and chemistry are noted. The calculation of the velocity distribution function of exospheric constituents with the spherically symmetric collisionless model is then presented. Various modifications of this standard model with regard to planetary rotation, nonuniform exobasic density and temperature distributions, and time‐dependent effects are subsequently discussed and compared. The extent to which collisionless models suffice to explain observational data of planetary exospheres is assessed. This assessment is given in terms of a comparison of density profiles or reduction factors determined with hydrogen and/or helium cells. A comparison of experimental measurements of the diurnal variation of terrestrial atomic hydrogen densities and theoretical models to explain the asymmetry is presented. The collisionless approach is criticized on theoretical grounds for the neglect of a consideration of the transition region and the resulting artificial boundary between the thermosphere and the exosphere. The aim of collisional models with regard to escape‐induced non‐Maxwellian effects, modifications of the temperature structure, nonthermal escape processes, and satellite particle populations from Monte Carlo simulations and/or kinetic theory models based on a Boltzmann equation is discussed, and the various results are compared. The various attempts to introduce collisional concepts are shown to be incomplete, each considering the problem with different objectives. Throughout, the importance of a more rigorous collisional treatment is stressed, in particular with respect to the description of nonthermal escape processes and satellite particle populations which cannot be considered in a collisionless context. The effects of charge exchange reactions, photoionization, and solar radiation pressure on satellite particles are examined. With regard to nonthermal escape processes, the absence of a detailed kinetic theory of product velocity distributions based on a collisional theory is also noted.