Formation Of Electron Distribution Function Research Articles

Specificities of the Nonlocal EDF Formation in a Dusty Plasma With the Different Spatial Distribution of the Microparticle Density

The formation of a nonlocal electron distribution function (EDF) in an argon dusty plasma of a dc glow discharge has been studied in a wide range of microparticle densities and their different spatial distributions inside a dusty cloud have also been explored. It is shown that the spatial profile of charges and the ambipolar potential can vary greatly, both with a change in the absolute values of the density of dust particles and the type of their spatial distribution. In turn, changes in the profiles of the ambipolar potential lead to strong differences in the nonlocal EDF at different points of the tube radius. This is most clearly seen at high densities of dust particles when nonmonotonic profiles of the potential distribution and reversal of the sign of the ambipolar field are formed. In this extreme case, great changes in the nonlocal EDF are observed not only at the discharge periphery but also inside the dust cloud.

Dayside Low Energy Electron Precipitation Driven by Hiss Waves in the Presence of Ionospheric Photoelectrons

AbstractAs was demonstrated by many observations, hiss waves are often to observed in the dayside plasmasphere and plumes. Previous studies of hiss waves have been focused on the scattering of energetic electrons of 10–1,000 keV energies and only recently this focus was shifted to the energies below several keV down to the energies of tens of eV. These studies, however, did not include electrons of ionospheric origin photo‐ and secondary‐ electrons. The major focus of our study is dayside low energy electron precipitation driven by hiss waves in the presence of ionospheric photo‐ and secondary‐ electrons. It is found that photoelectrons play an important role in hiss waves driven low energy electron precipitation phenomena. They are serving as the seed population that is required to study the low energy (below 1 keV) electrons using different kinetic approaches that are considered in this study. Our approach is based two kinetic codes: the SuperThermal Electron Transport (STET) and Fokker Plank (F‐P) models. The STET code couples magnetospheric hiss‐driven electron precipitation dynamic with ionosphere and forms the low energy MI coupling input to the F‐P code. The latter finalizes the formation of electron distribution function at magnetospheric altitudes via Landau resonant heating and forms the combined electron distribution function that is driven by Magnetosphere‐Ionosphere (MI) energy interplay processes.

Formation of inverse EDF in glow discharges with an inhomogeneous electric field

The formation mechanisms of an inverse electron distribution function (EDF) in gas-discharge plasma are investigated. An approximate analytical model of an inverse EDF in an inhomogeneous electric field and the formation criteria are presented. It is shown that the regions of EDF inversion in classical glow discharges are located in the transition regions to the right and left of the positive column in areas with significant gradients of the electron density. An interesting feature of the EDF behavior in the vicinity of the second reversal point of the electric field is discovered in the numerical simulation results. At least one of the second-order partial derivatives in the solution of the Boltzmann kinetic equation for the isotropic part of the EDF has a discontinuity at this point.

Influence of metastable atoms on the formation of nonlocal EDF, electron reaction rates, and transport coefficients in argon plasma

The influence of metastable atoms on formation of the nonlocal electron distribution function (EDF) and other characteristics of gas-discharge plasma in argon is investigated in this paper. Superelastic collisions of electrons with metastable atoms strongly affect the shape of the EDF, the behavior of reaction rate constants, and other plasma characteristics. An interesting phenomenon of EDF replication emerges with a period of excitation threshold; this effect can increase the rate constants of excitation and ionization processes by several orders of magnitude, especially at the periphery of the plasma volume. Thus, collisions between electrons and metastable atoms are important in the formation of a nonlocal EDF, and neglecting them can lead to large errors in calculations of plasma characteristics.

Ambipolar field role in formation of electron distribution function in gas discharge plasma

It is shown that the local approximation for electron distribution function (EDF) determination at plasma periphery, where the ambipolar field is dominant, is not applicable even at high pressures when the characteristic plasma size exceeds the energy relaxation length of the electrons R > λε. Therefore, consistent results can be obtained only when solving the complete kinetic equation in both energy and spatial variables (i.e. it is necessary to solve nonlocal kinetic equation).

Electron distribution function formation in regions of diffuse aurora

AbstractThe precipitation of high‐energy magnetospheric electrons (E ∼ 600 eV–10 KeV) in the diffuse aurora contributes significant energy flux into the Earth's ionosphere. To fully understand the formation of this flux at the upper ionospheric boundary, ∼700–800 km, it is important to consider the coupled ionosphere‐magnetosphere system. In the diffuse aurora, precipitating electrons initially injected from the plasma sheet via wave‐particle interaction processes degrade in the atmosphere toward lower energies and produce secondary electrons via impact ionization of the neutral atmosphere. These precipitating electrons can be additionally reflected upward from the two conjugate ionospheres, leading to a series of multiple reflections through the magnetosphere. These reflections greatly influence the initially precipitating flux at the upper ionospheric boundary (700–800 km) and the resultant population of secondary electrons and electrons cascading toward lower energies. In this paper, we present the solution of the Boltzman‐Landau kinetic equation that uniformly describes the entire electron distribution function in the diffuse aurora, including the affiliated production of secondary electrons (E < 600 eV) and its energy interplay in the magnetosphere and two conjugated ionospheres. This solution takes into account, for the first time, the formation of the electron distribution function in the diffuse auroral region, beginning with the primary injection of plasma sheet electrons via both electrostatic electron cyclotron harmonic waves and whistler mode chorus waves to the loss cone, and including their subsequent multiple atmospheric reflections in the two magnetically conjugated ionospheres. It is demonstrated that magnetosphere‐ionosphere coupling is key in forming the electron distribution function in the diffuse auroral region.

ECE and ECH application for investigation of plasma self-organization at T-10 tokamak

A behaviour of the high energy electrons appointed by their ECE simultaneously on two first harmonics are used for the electron distribution function analysis. Experiments were fulfilled in Ohmic regime and with on-axis ECH. The explored spectrum of emission from the extreme column periphery comes into existence after a relaxation of the primary flow of electrons with energy more than 1 MeV on the plasma waves. Maximum energy of the generated electrons does not vary during all discharge time also as the spectrum shape of i ts emission. The form of spectrum does not depend on electron temperature and density but its character width is directly proportional to the value of magnetic field. The appointed connection of the dynamical features between the peripheral high energy ele ctrons and the periodical kinetic instability in the central plasma area (mode m/n=1/1) confirms an existence of the wave transport from the center to the plasma edge. The set of experimental data corresponds to the theory of the stationary electron distribution function formation by the potential plasma waves which apparently are the main mechanism of plasma self-organization in tokamak.

Peculiarities of the resonant structure of the electron distribution function in S-, P- and R-striations

S-, P- and R-striations, which can be observed in an inert gas dc discharge at low pressures and small current densities, are considered. Mechanisms of the resonant formation of the electron distribution function (EDF) in S-, P-, Q- and R-striation-like fields are discussed on the basis of an accurate numerical solution of the Boltzmann kinetic equation and from the standpoint of the analytical theory. For S-, P- and Q-resonances, the EDF has the form of maxima of equal magnitudes. The maxima move in the plane (energy, coordinate) along the resonance trajectories. In the case of R-resonance, alternation of the magnitudes of these maxima takes place. The cause of such behavior of the EDF is elucidated. The experimental investigation of the EDF in R-striations in neon has also been carried out. The probe voltage–current characteristics were measured in each striation phase. The EDFs were determined by the second derivative of the probe characteristics. The ill-posed problem of the computation of the second derivative was solved by the Tikhonov regularization method. Comparison of the results of the measurements with the calculations shows the adequacy of the developed theoretical notions about the resonant character of the EDF formation for both integer S-, P- and Q-resonances and non-integer R-resonance.

Resonant formation of the electron distribution function in striation-like electric fields

The resonant behavior of the electron distribution function (EDF) in spatially periodic striation-like fields is analyzed in application to the discharge in neon at low pressures and small current. Numerical solution of the Boltzmann kinetic equation is interpreted from the standpoint of Tsendin’s analytical theory [3] using decomposition into two factors, one of which depends only on the total energy. Features of the EDF formation are considered for both integer resonances (which follow from theory [3]) and non-integer resonances.

The structure of the electron distribution function in R striations

The electron distribution function (EDF) in R striations of a low-pressure dc discharge in neon has been measured using probe techniques. The results of measurements satisfactorily agree with calculations performed using a model that describes the EDF formation in R striations as a resonance with the spatial period of two-thirds of the S striation length.

About the EDF formation in a capacitively coupled argon plasma

The formation of the electron distribution function (EDF) in the bulk plasma of a capacitively coupled radio-frequency (rf) discharge in argon generated in the plasma-chemical reactor PULVA-INP is investigated experimentally and theoretically. Measurements of the EDF and internal plasma parameters were performed by means of a Langmuir probe at pressures of 0.5–100 Pa and discharge powers of 5–100 W. The observed EDFs have revealed a two-temperature behaviour at low pressures and evolved into a Maxwellian distribution at high gas pressures and large discharge powers. Theoretical determination of the EDF is based on the numerical solution of the Boltzmann kinetic equation in the local and non-local approaches under experimental conditions. The model includes elastic and inelastic electron–atom collisions and electron–electron interactions. Low electron temperatures and relatively high ionization degrees are the features of the PULVA-INP rf discharge. This leads to significant influence of the electron–electron collisions on the EDF formation. The modelled and measured distributions show good agreement in a wide range of discharge parameters, except for a range of low gas pressures, where the stochastic electron heating is intense. Additionally, mechanisms of the EDF formation in the dc and rf discharge were compared under similar discharge conditions.

Resonance effects in the electron distribution function formation in spatially periodic fields in inert gases.

The calculations of the electron distribution function (EDF) in striationlike, sinusoidally modulated electric fields were performed to determine the dependence on spatial period length. The calculations were done for a discharge in neon at pR=2 Torr cm, i/R=5 mA/cm, and electric field E/p=1.9 V cm(-1) Torr(-1). The presence of the resonances in the EDF and macroscopic parameters has been demonstrated. These resonances correspond to S and P striations observed in experiments. An interpretation of the results is proposed based on an analytical approximation of the numerical solution. Decomposition of EDF into two factors-amplitude and body-is carried out. The amplitude of the EDF is shown to be resonantly dependent on the value of the spatial period. One maximum in the EDF is formed at the value of the spatial period corresponding to the S striation, and two maxima at the value which corresponds to the P striation. The experimental measurements of the EDF in S and P striations with high spatial resolution showed agreement between the theoretical and the experimental results. Resonance effects in the EDF formation are considered based on the linear theory in the weakly modulated electric fields.

On the formation ofelectron velocity distribution functions in striation-like fields

Peculiarities of the formation of electron distribution functions in spatially periodicstriation-like fields in a neon dc glow discharge are analysed on the basis of anaccurate solution of the Boltzmann kinetic equation, taking into account elastic andinelastic collisions, as well as spatial gradients. Mean axial electric fields andstriation lengths are measured in a wide range of pressures. The transition from thelocal formation of electron distribution function through the weakly nonlocal case atadvanced pressures to the distinctly nonlocal formation at low pressures is demonstrated.The phase shifts between the electron density and rates of excitation and ionization dueto nonlocal effects and finiteness of the lifetime of excited atoms are illustrated.Comparison between numerical and approximate analytical solutions is performed for thelimiting cases of low and advanced pressures, when the kinetic equation can be solvedanalytically by means of the small parameter expansion.

On the bunching effect of electrons in spatially periodic resonance fields

The spatial relaxation of the electron distribution function (EDF) in uniform and spatially periodic electric fields is considered. The analysis is based on the Boltzmann kinetic equation containing spatial gradients and operators of elastic and inelastic collisions. We demonstrate that the presence of a discrete spectrum of excited states due to the process of electron back scattering leads to the appearance of a quasicontinuous flux of energy in the elastic region, similar to the flux created by means of energy loss in elastic impacts. In the absence of channels of energy dissipation connected with energy loss in elastic impacts and in the presence of several excited states, information about the initial EDF injected in a field of arbitrary configuration, can be transmitted over an unlimited distance.The process of the relaxation has the nature of undamped oscillations. The introduction of channels of energy dissipation results in a damped oscillatory relaxation character of the EDF injected into a uniform field and in the establishment of a homogeneous EDF in this field. The relaxation of an EDF injected into a spatially periodic resonance field results in the distribution function having specific maxima which change in energy and coordinates along the resonance paths in accordance with the potential distribution (the so-called bunching effect). This effect can be used for the interpretation of EDF formation in S- and P-striations in inert gas discharges at low pressures and currents.

Fast modelling of low-pressure radio-frequency collisional capacitively coupled discharge and investigation of the formation of a non-Maxwellian electron distribution function

The principles of fast modelling (FM) of a low-pressure radio-frequency capacitively coupled discharge are presented. They are based on averaging over fast electron and ion motions and on eliminating a small spatial scale, the Debye radius. As a result, the solution of a self-consistent system of the electron kinetic equation, Poisson and ion continuity equations takes approximately 10 min on a 486 PC. The calculation of discharge parameters has been performed for a wide range of current and pressure. The comparison with full-scale Monte Carlo calculations and experimental data has been performed. The performed comparisons demonstrate that the developed method of fast modelling has a good accuracy for calculating the global parameters such as central plasma density, applied voltage, sheath thickness, ionization rate, etc, and the profiles of plasma density and the electric fields. The accuracy of the electron distribution function (EDF) calculation is high when the EDF form is not enriched by slow electrons, and seems satisfactory in the case of a strongly peaked EDF. The results are in qualitatively good agreement with the experiment. The quantitative agreement is mainly within a factor of two. This discrepancy can be attributed to the fact that the EDF form is very sensitive to the details of plasma description, e.g. small variation of cross-sections results in considerable changes in the EDF. The mechanism of non-Maxwellian EDF formation due to non-locality effects has been analysed. The evolution of the low-pressure radio-frequency collisional capacitively coupled discharge with current and pressure variation has been investigated.