Unperturbed Plasma Research Articles

One-dimensional multi-fluid model of the plasma wall transition

A one-dimensional multi-fluid model of the plasma wall transition is presented. The plasma is composed of singly charged positive ions, electrons and negative ions. Positive ions are assumed to obey the continuity, momentum transfer and energy transport equation, while the electrons and negative ions are treated by the continuity and momentum transfer equation. For the positive ions the closure is done by assuming that heat flux in the plasma is zero, while both negative species are treated as isothermal, with the pressure gradient term being proportional to the density gradient. The potential drop in the pre-sheath can be determined either by the electrons or the negative ions – depending on their densities in the unperturbed plasma. It is shown how the boundary density of both particle species can be in some cases determined very precisely.

Characteristics of atmospheric pressure Ar-plasma around a spherical particle: Numerical study

The characteristics of atmospheric pressure Ar-plasma such as the spatial distributions of number densities, fluxes, and temperatures of electrons and heavy plasma particles, as well as the spatial distribution of electric potential around an individual spherical particle, were studied numerically on the basis of the hydrodynamic (diffusion) equations for plasma components. The governing equations were formulated for plasma that is not in thermal and ionization equilibrium. The boundary conditions near the particle were set on the edge of the space charge layer (sheath) adjacent to the particle surface. The nonlinear problem was solved taking into account the temperature dependencies of transport and kinetic coefficients. The heat flux introduced by the plasma into the particle was calculated and compared with the results of the simple heat conduction model. The range 10 − 5 – 10 − 4 m of particle radius and the range 6–18 kK of unperturbed plasma temperature were considered.

Testing the conservative character of particle simulations: I. Canonical and noncanonical guiding center model in Boozer coordinates

The guiding center (GC) Lagrangian in Boozer coordinates for toroidally confined plasmas can be cast into canonical form by eliminating terms containing the covariant component BΨP of the magnetic field vector with respect to the poloidal flux function ΨP. In an unperturbed plasma, BΨP can be eliminated via exact coordinate transformations, but, in general, one relies on approximations, assuming that the effect of BΨP is small. Here, we are interested in the question whether Hamiltonian conservation laws are still satisfied when BΨP is retained in the presence of fluctuations. Considering fast ions in the presence of a shear Alfvén wave field with fixed amplitude, fixed frequency, and a single toroidal mode number n, we show that simulations using the code ORBIT with and without BΨP yield practically the same resonant and nonresonant GC orbits. The numerical results are consistent with theoretical analyses (presented in the appendix), which show that the unabridged GC Lagrangian with BΨP retained yields equations of motion that possess two key properties of Hamiltonian flows: (i) phase space conservation and (ii) energy conservation. As counter-examples, we also show cases where energy conservation (ii) or both conservation laws (i) and (ii) are broken by omitting certain small terms. When testing the conservative character of the simulation code, it is found to be beneficial to apply perturbations that do not resemble normal (eigen) modes of the plasma. The deviations are enhanced and, thus, more easily spotted when one inspects wave-particle interactions using nonnormal modes.

Grid-based Vlasov simulation of collisionless plasma expansion

Grid-based Vlasov simulations are carried out to re-evaluate the one-dimensional collisionless plasma expansion into vacuum. The grid-based method eliminates the inherent statistical noise in particle-based methods and allows us to extend the solution beyond the self-similar expansion region and resolve small electron timescale wave perturbations. It is shown that the expansion generates both an ion-acoustic rarefaction wave mode and an electron Langmuir wave mode that propagate into the unperturbed plasma upstream. The assumption used in the classical expansion solution that the electrons are an isothermal fluid is accurate within a quasi-neutral, self-similar expansion region but fails in both the upstream and downstream of that region due to electron timescale perturbations.

Obtaining the unperturbed plasma potential in low-density, low-temperature plasmas

A method is proposed to effectively obtain plasma parameters in low-density, low-temperature plasmas that are easily perturbed by Langmuir probes. The methodology is based on the perimeter sheath expansion method because it provides a simple, but effective interpretation of the Langmuir probe characteristics and, in particular, of the non-saturating trend of the ion saturation due to the expansion of the probe sheath. However, the perimeter sheath expansion method is proposed here in a modified version with a dual purpose: to permit the verification of the Child–Langmuir dependence of the sheath thickness from the potential and, most importantly, to properly assess the plasma potential. When probe perturbation is significant the proposed method provides an effective correction term for the plasma potential. The resulting sheath voltage is consistent in all analysed cases and in close agreement with the expected value for cylindrical probes in Ar. The method is applied to Ar plasmas here, but because no specific assumption was made on the atomic species, it may be applicable to other situations of interest.

Numerical investigation of ion collection by a planar probe in stationary and parallel flowing plasmas

3D hybrid particle-in-cell simulations were performed to investigate the ion current collection behavior by a thin double-sided circular planar probe in both stationary and parallel flowing plasmas with cold ions and Boltzmann electrons. Results for stationary plasma cases showed that the assumption of a constant ion density ratio at the sheath boundary to that of unperturbed plasma is inaccurate for planar probes for probe radii from 10 to 30 Debye length and probe biases from −5 to −30 times the electron temperature. The flowing plasma results showed that ion current strongly depends on the parallel flowing velocity, contrary to earlier models. The collected ion current decreases with increasing parallel velocity, reaching a minimum at around ion sound speed, then slowly recovers and even exceeds the value of the stationary case at high flow speed. The deviation of ion current due to parallel flow from stationary case could be −35% to +20% for flowing plasmas with flow speed comparable to ion sound speed. Therefore, it is important to consider the flow impact on ion collection when using planar probes in such circumstances, e.g. electric propulsion plume measurements. The mechanism for this behavior is qualitatively investigated and discussed.

Dispersion relation of modulational instability for one-dimensional standing solitary waves in hot ultrarelativistic electron–positron plasmas

In this paper, the non-linear dispersion relation of the system for interactions between high intensity laser and hot relativistic electron–positron plasma is derived. We restrict the problem to the standing solitons in ultrarelativistic plasmas and apply the quasineutrality condition. The modulational instability growth rate for different values of plasma temperatures, velocities and wave numbers are illustrated numerically. It is shown that, by increasing the unperturbed plasma enthalpy, the modulational instability growth rate decreases for all the values of plasma fluid velocities. It is also found that the growth rate shows an increasing trend with plasma fluid velocity. Furthermore, the impact of wave amplitude on the modulational instability growth rate is investigated explicitly. The growth rate increases with wave number as well as wave amplitude.

On the ion distributions at the separatrices during symmetric magnetic reconnection

A particle-in-cell simulation of symmetric reconnection with zero guide field is carried out to understand the dynamics of ions along the separatrices. Through the investigation of ion velocity distributions at different moments and locations along the separatrices, a typical distribution is found: two counter-streaming populations in the perpendicular direction, with another two populations accelerated into distinct energy levels in the parallel direction. Backward tracing of ions reveals that the counter-streaming cores are mostly composed of ions initially located at the same side of the separatrix, while the other two accelerated populations in the parallel direction are composed of ions crossing through the neutral sheet. Through analysis of energy conversion of these populations, it is found that the ion energization along the separatrix is attributable primarily to the Hall electric field, while that in the region between the two separatrices is caused primarily by the induced reconnection electric field. For the counter-streaming population, the low-energy ions that cross the separatrix twice are affected by both Hall and reconnection electric fields, while the high-energy ions that directly enter the separatrix from the unperturbed plasma are energized mainly by the Hall electric field. For the two energized populations in the parallel direction, the ions with lower-energy are accelerated mainly by the in-plane electric field and the Hall electric field on the opposite side of the separatrix, whereas the ions with higher-energy not only experience the same energization process but also are constantly accelerated by the reconnection electric field.

Some Similarities and Differences Between the Observed Alfvénic Fluctuations in the Fast Solar Wind and Navier–Stokes Turbulence

Abstract: Using two long data sets analyzed on equal footing, the properties of Alfvenic fluctuations in the fast (coronal-hole-origin) solar wind and Navier-stokes turbulence are compared. A 26.4-s-long interval of hot-wire measurements in the ONERA wind tunnel is used and a 71-hr-long interval of unperturbed coronal-hole plasma measured by the WIND spacecraft at 1 AU is used. Similarities and differences between a Navier-Stokes fluid and the collisionless magnetized solar-wind plasma are discussed, as are differences between the physical natures of the advecting evolving turbulent fluctuations and the propagating non-evolving Alfvenic fluctuations. The details of the power spectral densities of the turbulence and the Alfvenic fluctuations are compared. Statistics of first and second time derivatives are examined for the wind-tunnel and solar-wind time series and the statistics are compared with the statistics of time derivatives of phase-randomized time series. Using running medians, the statistics of flat spots in the time series of Alfvenic fluctuations is examined, which is evidence of a cellular structure to the magnetic field and velocity field. A call for a campaign of expanded coordinated future work is made.

Standing autoresonant plasma waves

The formation and control of strongly nonlinear standing plasma waves (SPWs) from a trivial equilibrium by a chirped frequency drive are discussed. If the drive amplitude exceeds a threshold, after passage through the linear resonance in this system, the excited wave preserves the phase locking with the drive, yielding a controlled growth of the wave amplitude. We illustrate these autoresonant waves via Vlasov–Poisson simulations, showing the formation of sharply peaked excitations with local electron density maxima significantly exceeding the unperturbed plasma density. The Whitham averaged variational approach applied to a simplified water bag model yields the weakly nonlinear evolution of the autoresonant SPWs and the autoresonance threshold. If the chirped driving frequency approaches some constant level, the driven SPW saturates at a target amplitude, avoiding the kinetic wave breaking.

On violent instability of a plasma-vacuum interface for an incompressible plasma flow and a nonzero displacement current in vacuum

In the classical statement of the plasma-vacuum interface problem in ideal magnetohydrodynamics (MHD) one neglects the displacement current in the vacuum region that gives the div-curl system of pre-Maxwell dynamics for the vacuum magnetic field. For understanding the influence of the vacuum electric field on the evolution of a plasma-vacuum interface we do not neglect the displacement current and consider the full Maxwell equations in vacuum. For the case of an incompressible plasma flow, by constructing an Hadamard-type ill-posedness example for the constant coefficients linearized problem we find a necessary and sufficient condition for the violent instability of a planar plasma-vacuum interface. In particular, we prove that as soon as the unperturbed plasma and vacuum magnetic fields are collinear, any nonzero unperturbed vacuum electric field makes the planar interface violently unstable. This shows the necessity of the corresponding non-collinearity condition for well-posedness and a crucial role of the vacuum electric field in the evolution of a plasma-vacuum interface.

Structure of the Wall Sheath in a Gas-Discharge Plasma for an Arbitrary Orientation of a Flat Probe Relative to the Electric Field in the Plasma

We investigate the structure of the wall sheath of a gas discharge near a flat surface at a negative potential for high mean electron energy. It is shown that in the conditions where the mean energy of ions in the plasma is much lower than the mean electron energy, the parameters of the wall sheath weakly depend on the mutual orientation of the normal to the surface and the electric field in the plasma for an arbitrary ratio of the Debye radius to the ion mean free path relative to the resonant charge exchange process. It is found that for inert gases (He, Ar) for ratio E/P of the electric field to pressure exceeding 10 V/(cm Torr) in the plasma, the disregard of ionization in the perturbed wall sheath can lead to substantial errors in the calculation of its parameters. It is shown that the ionization leads to an increase in the electric field in the wall sheath and, as a consequence, to an increase in the mean velocity of ions at the boundary between the quasi-neutral presheath and the part of the perturbed wall sheath in which quasi-neutrality is substantially violated. The parameters of the wall sheath where quasi-neutrality is significantly violated depend on the ionization rate much less strongly than the corresponding parameters of the quasi-neutral presheath. We have determined the relation for concentration of charged particles in the unperturbed plasma from the ion saturation current considering the actual ion energy distribution function in the plasma as well as ionization in the presheath and the part of the perturbed wall sheath in which quasi-neutrality is violated significantly.

Kinetic Theory of the Wall Sheath for Arbitrary Conditions in a Gas-Discharge Plasma

The self-consistent problem of the structure of a perturbed wall sheath in a dc gas-discharge plasma near a flat surface under negative potential relative to the plasma has been solved for an arbitrary relation between the Debye radius and the ion mean free path. The solution has been obtained without artificial separation of this layer into the quasi-neutral “presheath” and the wall sheath in which quasi-neutrality is violated substantially. The actual ion distribution function in the unperturbed plasma, the dependence of the charge-exchange cross section on the ion energy, and the nonzero electric field in the unperturbed plasma have been considered. It is shown that when the average electron energy is conserved the structure of the perturbed wall sheath weakly depends on the form of the electron distribution function. It has been established that the mean energy of ions in the unperturbed plasma substantially affects the structure of the quasi-neutral presheath as well as the structure of a part of the wall sheath in which quasi-neutrality is not observed even under the assumption that the mean electron energy is much higher than the mean energy of ions. The calculations of ion flow parameters and the structure of the perturbed wall sheath are in conformity with experimental data obtained by other authors, which could not be adequately interpreted earlier.

Excitation and control of large amplitude standing ion acoustic waves

We study the formation of large-amplitude standing ion acoustic waves (SIAWs) by nonlinear phase-locking (autoresonance) with a weak, chirped frequency standing ponderomotive drive. These waves comprise a nonlinear two-phase solution, with each phase locked to one of the two traveling waves comprising the drive. The autoresonance in the system is guaranteed provided that the driving amplitude exceeds a threshold. The phenomenon is illustrated via water bag simulations within a nonlinear ion fluid model and analyzed using Whitham's averaged variational principle. The local ion and electron densities in the autoresonant SIAWs may significantly exceed the initial unperturbed plasma density and are only limited by kinetic wave-breaking.

Кинетическая теория пристеночного слоя при произвольных условиях в газоразрядной плазме

For an arbitrary relation of the Debye length to the ion free path, based on the kinetic approach, it was solved the self consistent problem of the structure of the perturbed wall sheath in a DC plasma gas discharge, near a flat surface at a negative potential in relation to the plasma. The solution was obtained without an artificial separation of the perturbed wall sheath into a quasineutral "presheath" and a wall sheath where quasineutrality is substantially violated. They were taken into account the real ion distribution function in the unperturbed plasma, the dependence of the charge exchange cross section on the ion energy, and the nonzero electric field in the unperturbed plasma. It was found that, if the mean electron energy is preserved, the structure of the perturbed wall sheath weakly depends on the form of the electron distribution function. It was shown that, even under the assumption that the mean electron energy is much higher than the mean ion energy, is the mean ion energy in the unperturbed plasma the one that has a significant effect both on the structure of the quasineutral "presheath" and on the structure of a part of the wall sheath, where there is no quasineutrality. The calculations of the parameters of the ion flux and the structure of the perturbed wall sheath are in agreement with other authors’ experimental results that didn’t have previously an adequate interpretation.

Структура призондового слоя в газоразрядной плазме при произвольной ориентации плоского зонда относительно электрического поля в плазме

AbstractWe investigate the structure of the wall sheath of a gas discharge near a flat surface at a negative potential for high mean electron energy. It is shown that in the conditions where the mean energy of ions in the plasma is much lower than the mean electron energy, the parameters of the wall sheath weakly depend on the mutual orientation of the normal to the surface and the electric field in the plasma for an arbitrary ratio of the Debye radius to the ion mean free path relative to the resonant charge exchange process. It is found that for inert gases (He, Ar) for ratio E / P of the electric field to pressure exceeding 10 V/(cm Torr) in the plasma, the disregard of ionization in the perturbed wall sheath can lead to substantial errors in the calculation of its parameters. It is shown that the ionization leads to an increase in the electric field in the wall sheath and, as a consequence, to an increase in the mean velocity of ions at the boundary between the quasi-neutral presheath and the part of the perturbed wall sheath in which quasi-neutrality is substantially violated. The parameters of the wall sheath where quasi-neutrality is significantly violated depend on the ionization rate much less strongly than the corresponding parameters of the quasi-neutral presheath. We have determined the relation for concentration of charged particles in the unperturbed plasma from the ion saturation current considering the actual ion energy distribution function in the plasma as well as ionization in the presheath and the part of the perturbed wall sheath in which quasi-neutrality is violated significantly.

Neutral reactive gaseous species in reactors suitable for plasma surface engineering

Neutral reactive gaseous species are often major reactants in plasma reactors suitable for tailoring surface properties of materials with weakly ionized gaseous plasma. The density of such species depends on discharge parameters as well as the properties of treated materials. Cylindrical pots made from copper, stainless steel and Teflon were mounted in a reactor of volume 20 l and the density of O-atoms was measured with a laser-heated fiber-optic catalytic sensor. The distribution of O-atoms at different distances from the pots as well as inside the pots was determined at a constant discharge power and different pressures between 30 Pa and 90 Pa. Gradients up to the value of about 2 × 1020 m−3 per centimeter were observed inside the pots. For the case of the metallic samples, the gradients were about twice as high as in the case of Teflon. The resultant density of O-atoms inside the pots dropped for almost an order of magnitude as compared to the value measured in unperturbed plasma, although glowing plasma spread inside the pots. The results were explained by heterogeneous surface recombination of O-atoms to parent molecules. The rather unexpectedly large gradients for the case of Teflon were explained by modification of the surface structure upon synergistic effects of O-atoms and hard UV radiation.

Radial evolution of the solar wind in pure high-speed streams: HELIOS revised observations

Spacecraft observations have shown that the proton temperature in the solar wind falls off with radial distance more slowly than expected for an adiabatic prediction. Usually, previous studies have been focused on the evolution of the solar-wind plasma by using the bulk speed as an order parameter to discriminate different regimes. In contrast, here, we study the radial evolution of pure and homogeneous fast streams (i.e. well-defined streams of coronal-hole plasma that maintain their identity during several solar rotations) by means of re-processed particle data, from the HELIOS satellites between 0.3 and 1 AU. We have identified 16 intervals of unperturbed high-speed coronal hole plasma, from three different sources and measured at different radial distances. The observations show that, for all three streams, (i) the proton density decreases as expected for a radially expanding plasma, unlike previous analysis that found a slower decrease; (ii) the magnetic field deviates from the Parker prediction, with the radial and tangential components decreasing more slowly and quickly than expected, respectively; (iii) the double-adiabatic invariants are violated and an increase of entropy is observed; (iv) the proton-core temperature anisotropy is constrained by mirror mode instability; (v) the collisional frequency is not constant, but decreases as the plasma travels away from the Sun. The present work provides an insight into the heating problem in pure fast solar wind, fitting in the context of the next solar missions, and, especially for Parker Solar Probe, it enables us to predict the high-speed solar-wind environment much closer to the Sun.

Charge of a Particle-Absorbing Sphere in Collisionless Plasma by the Results of a Direct Numerical Experiment

The process of charging of a spherical body absorbing plasma electrons and ions is modeled by directly solving the Vlasov–Poisson equations. The main goal of the numerical experiment is to determine the sphere charge in a stable steady state established on long times in perturbed plasma. Special attention is paid to the contribution of trapped ions moving in finite orbits to the screening of a charged body. The charge of the trapped particle cloud is determined as a function of the body size in a wide parameter range of an initially unperturbed plasma.

Two-fluid solutions for Langmuir probes in collisionless and isothermal plasma, over all space and bias potential

This paper presents solutions for the classical one-dimensional (1D radial and Cartesian) problem of Langmuir probes in a collisionless, isothermal plasma. The method is based on two-fluid equations derived from the first two moments of Vlasov's equation. In contrast to commonly used approximations, electron inertia and ion temperature are not neglected so that the fluid equations are symmetric in terms of electrons and ions. The fluid equations are reduced analytically so that the electric potential is the only remaining spatial function, which is numerically determined using Poisson's equation. The single radial solution applies continuously over the whole region from the probe up to the unperturbed plasma, in contrast to theories which separate the probe boundary region into a charged sheath and a quasi-neutral pre-sheath, and is valid for all values of probe bias potential. Current-voltage characteristics are computed for cylindrical and spherical probes, which exhibit non-saturation of the ion and electron currents. The 1D Cartesian case is also analysed, and the Bohm criterion is recovered only in the limit of large radius probes.