Collisionless Kinetic Model Research Articles

Plasma sheath in the presence of surface-emitted negative ions

The need for negative hydrogen ion sources for heating in future fusion devices demands a full investigation of its production and interaction with plasma. To understand the interaction of emitted negative ions with plasma sheath, a one-dimensional collisionless kinetic model of a negative ion emitting electrode/grid in a low-density isotropic plasma is developed for conventional and the inverse sheath. The plasma electron and emitted negative ions are assumed to be half Maxwellian along with cold positive plasma ions for the conventional sheath and half Maxwellian for the inverse sheath. The influence of surface-produced negative ions, from floating and current-carrying electrode/grid, with varying temperatures on sheath structures, is analyzed for subcritical, critical, and supercritical emissions. The formation of potential well and inverse sheath is observed at high and very high emitted negative ion temperatures, respectively. The critical emission is observed at specific values of emitted negative ion temperature and number density, below which the solution does not exists. In critical and supercritical emission, the emitted negative ion number density remains low compared with plasma positive ions, but it is high in inverse sheath. The inverse sheath solutions for floating and current-carrying negative ion-emitting electrode/grid are also discussed, and a rough estimation between the experiment and this theory shows the existence of inverse sheath in currently existing negative ion sources, but for full understanding, we need further investigations.

Kinetic investigation of the planar multipole resonance probe under arbitrary pressure

A new plasma diagnostic tool called planar multipole resonance probe (pMRP) has been proposed in the past decade. It has a minimally invasive structure and allows simultaneous measurement of electron density, temperature, and collision frequency. Previous work has investigated the behavior of the pRMP by the Drude model, which misses kinetic effects, and the collisionless kinetic model, which misses collisional damping. To further study the pMRP at arbitrary pressure, a collisional kinetic model is proposed in this paper. The electron dynamics is described by the kinetic equation, which considers the electron-neutral elastic collision. Under the electrostatic approximation, the kinetic equation is coupled to the Poisson equation. The real part of the general complex admittance is calculated to describe the spectral response of the probe–plasma system. The calculated spectra of the idealized pMRP demonstrate that this collisional kinetic model can capture both collisionless kinetic damping and collisional damping. This model overcomes the limitations of the Drude model and the collisionless kinetic model and allows discussion of the validity of simpler models.

Kinetic investigation of the planar multipole resonance probe in the low-pressure plasma

Active Plasma Resonance Spectroscopy (APRS) is a well-established plasma diagnostic method: a radio frequency signal is coupled into the plasma via a probe or antenna, excites it to oscillate, and the response is evaluated through a mathematical model. The majority of APRS probes are invasive and perturb the plasma by their physical presence. The planar multipole resonance probe (pMRP) solves this problem: it can be integrated into the chamber wall and minimize the perturbation. Previous work has studied the pMRP in the frame of the Drude model, but it misses important kinetic effects like collision-less damping. In this work, a collision-less kinetic model is developed to further investigate the behavior of the pMRP. This model consists of the Vlasov equation, which is coupled with the Poisson equation under electrostatic approximation. The spectral response of the probe–plasma system is found by calculating the complex admittance. This model covers the kinetic effects and overcomes the limitations of the Drude model.

The Structure of Titan’s N2 and CH4 Coronae

Abstract In this study, we analyze the structures of Titan’s N2 and CH4 coronae using a large data set acquired by the Ion Neutral Mass Spectrometer (INMS) instrument on board Cassini. The N2 and CH4 densities measured from the exobase up to 2000 km imply a mean exobase temperature of 146 K and 143 K, respectively, which is lower than the mean upper atmospheric temperature by 4 and 7 K. This indicates that on average, Titan possesses a subthermal rather than suprathermal corona. A careful examination reveals that the variability in corona structure is not very likely to be solar driven. Within the framework of the collisionless kinetic model, we investigate how the CH4 energy distribution near the exobase could be constrained if strong CH4 escape occurs on Titan. Several functional forms for the CH4 energy distribution are attempted, assuming two representative CH4 escape rates of s−1 and s−1. We find that the double Maxwellian and power-law distributions can reproduce the shape of the CH4 corona structure as well as the imposed CH4 escape rate. In both cases, the escape rate is contributed by a suprathermal CH4 population on the high-energy tail, with a number fraction below 5% and a characteristic energy of 0.1–0.6 eV per suprathermal CH4 molecule. The coexistence of the subthermal CH4 corona revealed by the INMS data and substantial CH4 escape suggested by some previous works could be reconciled by a significant departure in the exobase CH4 energy distribution from ideal Maxwellian that enhances escape and causes a noticeable redistribution of the corona structure.

Kinetic model for an auroral double layer that spans many gravitational scale heights

The electrostatic potential profile and the particle densities of a simplified auroral double layer are found using a relaxation method to solve Poisson's equation in one dimension. The electron and ion distribution functions for the ionosphere and magnetosphere are specified at the boundaries, and the particle densities are found from a collisionless kinetic model. The ion distribution function includes the gravitational potential energy; hence, the unperturbed ionospheric plasma has a density gradient. The plasma potential at the upper boundary is given a large negative value to accelerate electrons downward. The solutions for a wide range of dimensionless parameters show that the double layer forms just above a critical altitude that occurs approximately where the ionospheric density has fallen to the magnetospheric density. Below this altitude, the ionospheric ions are gravitationally confined and have the expected scale height for quasineutral plasma in gravity.

Magnetohydrodynamic stability comparison theorems revisited

Magnetohydrodynamic (MHD) stability comparison theorems are presented for several different plasma models, each one corresponding to a different level of collisionality: a collisional fluid model (ideal MHD), a collisionless kinetic model (kinetic MHD), and two intermediate collisionality hybrid models (Vlasov-fluid and kinetic MHD-fluid). Of particular interest is the re-examination of the often quoted statement that ideal MHD makes the most conservative predictions with respect to stability boundaries for ideal modes. Some of the models have already been investigated in the literature and we clarify and generalize these results. Other models are essentially new and for them we derive new comparison theorems. Three main conclusions can be drawn: (1) it is crucial to distinguish between ergodic and closed field line systems; (2) in the case of ergodic systems, ideal MHD does indeed make conservative predictions compared to the other models; (3) in closed line systems undergoing perturbations that maintain the closed line symmetry this is no longer true. Specifically, when the ions are collisionless and their gyroradius is finite, as in the Vlasov-fluid model, there is no compressibility stabilization. The Vlasov-fluid model is more unstable than ideal MHD. The reason for this is related to the wave-particle resonance associated with the perpendicular precession drift motion of the particles (i.e., the E×B drift and magnetic drifts), combined with the absence of any truly toroidally trapped particles. The overall conclusion is that to determine macroscopic stability boundaries for ideal modes for any magnetic geometry using a simple conservative approach, one should analyze the ideal MHD energy principle for incompressible displacements.

Latitudinal structure of outer Io plasma torus

We present a model of the latitudinal structure of the Io plasma torus (IPT), which is able to explain Ulysses results and to reconcile several in situ data sets. Basically, the observed temperature inversion and the polytropic law are due to “velocity filtration” of particles having non‐Maxwellian velocity distributions. This mechanism acts as a high‐pass filter for particle energies if the particles are confined in an attractive monotonic potential well. These conditions are met in the IPT, where the attractive potential is due to the centrifugal force that confines plasma ions since the plasma is corotating with Jupiter, whereas electrons are confined by an ambipolar electric field preserving electric neutrality, and the electron velocity distribution is known to have a suprathermal tail. The suprathermal electron population has a velocity distribution that decreases with increasing energy as a power law, as is frequently observed in space plasmas, and the velocity distribution can be conveniently modeled with a “kappa” function [Meyer‐Vernet et al., 1995]. Adopting such a kappa distribution for the electrons and for all ion species detected in the torus and including temperature anisotropy, we construct a collisionless kinetic model based on the so‐called “bi‐kappa distributions” to calculate the latitudinal structure. Following Bagenal [1994], we adopt the nearly equatorial data set from Voyager 1 to represent empirically the radial structure. The model reconciles the Voyager 1 and 2 and Ulysses observations and demonstrates that these data sets possess similar latitudinal and radial variations of the IPT densities and temperatures. This model also generates a radial ion temperature profile past ∼7.5 Jovian radii, which is compatible with a quasiadiabatic radial temperature decrease at the torus equator.

Kinetic theory of ion collection by probing objects in flowing strongly magnetized plasmas.

A new one-dimensional collisionless kinetic model is developed for the flow of ions to probing structures in drifting plasmas. The cross-field flow into the presheath is modeled by accounting consistently for particle exchange between the collection flux tube and the outer plasma. Numerical solutions of the self-consistent plasma-sheath equations are obtained with arbitrary external ion temperature and parallel plasma flow velocity. Results are presented of the spatial dependence of the ion distribution function as well as its moments (density, particle flux, temperature, and power flux). The ion current to the probe is obtained and the ratio of the upstream to downstream currents is found to be well represented by the form R=exp(${\mathrm{Ku}}_{d}$), where K\ensuremath{\sim}1.7 and ${u}_{d}$ is the drift velocity in units of \ensuremath{\surd}(${T}_{e}$/${m}_{i}$) . The results are in good agreement with comparable recent fluid calculations but show substantial deviations from other models which ignore particle exchange out of the presheath. No evidence is found of the formation of shocks in the downstream wake, contrary to the implications of some fluid theories.

A kinetic model for divertors and pumped limiters

In divertors and pumped limiters, plasma flows along magnetic field lines from the scrape-off layer to a material wall where it is neutralized. The neutrals refluxing from the wall will undergo ionization and charge exchange, producing cold ions. This problem has been examined by using a largely analytical, collisionless kinetic model which includes the effects of charge exchange. Cases with uniform magnetic field and with magnetic fields possessing a constriction (as in a bundle divertor) are treated. The cold ions increase the electric potential over that which otherwise would exist. Solutions are found with a peak in the potential near the plate, with cold ions flowing down the potential gradient either toward the scrape-off zone or towards the wall, depending on where they are produced. This is in agreement with the predictions of fluid theories and numerical kinetic calculations. The net effect is to reduce the heat flux in hot ions to the divertor plate, desirable for reducing sputtering loss. This analytical approach can be used to produce computationally efficient routines to determine particle and energy losses from the scrape-off layer which are suitable for inclusion in transport codes.