This work continues the studies on searching for plasma media with the inverse electron energy distribution function(EEDF)and providing recommendations for setting up subsequent experiments.The inverse EEDF is a distr...This work continues the studies on searching for plasma media with the inverse electron energy distribution function(EEDF)and providing recommendations for setting up subsequent experiments.The inverse EEDF is a distribution function that increases with an increase in energy at zero electron energy.The inverse EEDF plays a central role in the problem of negative conductivity.Based on the previously obtained criterion for the formation of an inverse EEDF in a spatially inhomogeneous plasma,a heuristic method is proposed that allows one to avoid resource-intensive calculations for spatially two-dimensional(2D)kinetic modeling on a large array of different glow discharges.It is shown that the conditions for EEDF inversion can be realized in two-chamber discharge structures due to violating the known Boltzmann distribution for electron density.The theoretical conclusions are validated by numerical modeling of lowpressure two-chamber inductively-coupled plasma(ICP)discharges in the COMSOL Multiphysics environment.As a result,areas of conditions with inverse EEDF were found for subsequent detailed kinetic analysis and experimental studies.展开更多
Since the position of the electron in a hydrogen atom cannot be determined, the region in which it resides is said to be determined stochastically and forms an electron cloud. The probability density function of the s...Since the position of the electron in a hydrogen atom cannot be determined, the region in which it resides is said to be determined stochastically and forms an electron cloud. The probability density function of the single electron in 1s orbit is expressed as φ2, a function of distance from the nucleus. However, the probability of existence of the electron is expressed as a radial distribution function at an arbitrary distance from the nucleus, so it is estimated as the probability of the entire spherical shape of that radius. In this study, it has been found that the electron existence probability approximates the radial distribution function by assuming that the probability of existence of the electron being in the vicinity of the nucleus follows a normal distribution for arbitrary x-, y-, and z-axis directions. This implies that the probability of existence of the electron, which has been known only from the distance information, would follow a normal distribution independently in the three directions. When the electrons’ motion is extremely restricted in a certain direction by the magnetic field of both tokamak and helical fusion reactors, the probability of existence of the electron increases with proximity to the nucleus, and as a result, it is less likely to be liberated from the nucleus. Therefore, more and more energy is required to free the nucleus from the electron in order to generate plasma.展开更多
In general,as the radio frequency(RF)power increases in a capacitively coupled plasma(CCP),the power transfer efficiency decreases because the resistance of the CCP decreases.In this work,a parallel resonance circuit ...In general,as the radio frequency(RF)power increases in a capacitively coupled plasma(CCP),the power transfer efficiency decreases because the resistance of the CCP decreases.In this work,a parallel resonance circuit is applied to improve the power transfer efficiency at high RF power,and the effect of the parallel resonance on the electron energy distribution function(EEDF)is investigated in a 60 MHz CCP.The CCP consists of a power feed line,the electrodes,and plasma.The reactance of the CCP is positive at 60 MHz and acts like an inductive load.A vacuum variable capacitor(VVC)is connected in parallel with the inductive load,and then the parallel resonance between the VVC and the inductive load can be achieved.As the capacitance of the VVC approaches the parallel resonance condition,the equivalent resistance of the parallel circuit is considerably larger than that without the VVC,and the current flowing through the matching network is greatly reduced.Therefore,the power transfer efficiency of the discharge is improved from 76%,70%,and 68%to 81%,77%,and 76%at RF powers of 100 W,150 W,and 200 W,respectively.At parallel resonance conditions,the electron heating in bulk plasma is enhanced,which cannot be achieved without the VVC even at the higher RF powers.This enhancement of electron heating results in the evolution of the shape of the EEDF from a biMaxwellian distribution to a distribution with the smaller temperature difference between high-energy electrons and low-energy electrons.Due to the parallel resonance effect,the electron density increases by approximately 4%,18%,and 21%at RF powers of 100 W,150 W,and 200 W,respectively.展开更多
A conservative transport operator in space (v//,r) and moment equations are used to describe the combined effects of a stochastic magnetic field and a radial ambipolar electric field on the electrons. The transport o...A conservative transport operator in space (v//,r) and moment equations are used to describe the combined effects of a stochastic magnetic field and a radial ambipolar electric field on the electrons. The transport operator is coupled with Fokker-planck and Ohmic heating terms to compute the electron distribution function. A physical picture exhibits the possible importance of the turbulent magnetic field on the suprathermal electrons, which may be concerned with plasma confinement.展开更多
Controlling charge polarity in the semiconducting single-walled carbon nanotubes(CNTs) by substitutional doping is a difficult work due to their extremely strong C–C bonding. In this work, an inner doping strategy is...Controlling charge polarity in the semiconducting single-walled carbon nanotubes(CNTs) by substitutional doping is a difficult work due to their extremely strong C–C bonding. In this work, an inner doping strategy is explored by filling CNTs with one-dimensional(1D)-TM_(6)Te_(6) nanowires to form TM_(6)Te_(6)@CNT-(16,0) 1D van der Waals heterostructures(1D-vd WHs). The systematic first-principles studies on the electronic properties of 1D-vd WHs show that N-type doping CNTs can be formed by charge transfer from TM_(6)Te_(6) nanowires to CNTs, without introducing additional carrier scattering.Particularly, contribution from both T M(e.g., Sc and Y) and Te atoms strengthens the charge transfer. The outside CNTs further confine the dispersion of Te-p orbitals in nanowires that deforms the C-π states at the bottom of the conduction band to quasi sp^(3) hybridization. Our study provides an inner doping strategy that can effectively confine the charge polarity of CNTs and further broaden its applications in some novel nano-devices.展开更多
This paper presents a self-contained description on the configuration of propagator method(PM)to calculate the electron velocity distribution function(EVDF) of electron swarms in gases under DC electric and magnetic f...This paper presents a self-contained description on the configuration of propagator method(PM)to calculate the electron velocity distribution function(EVDF) of electron swarms in gases under DC electric and magnetic fields crossed at a right angle. Velocity space is divided into cells with respect to three polar coordinates v,θ and f. The number of electrons in each cell is stored in three-dimensional arrays. The changes of electron velocity due to acceleration by the electric and magnetic fields and scattering by gas molecules are treated as intercellular electron transfers on the basis of the Boltzmann equation and are represented using operators called the propagators or Green’s functions. The collision propagator, assuming isotropic scattering, is basically unchanged from conventional PMs performed under electric fields without magnetic fields. On the other hand, the acceleration propagator is customized for rotational acceleration under the action of the Lorentz force. The acceleration propagator specific to the present cell configuration is analytically derived. The mean electron energy and average electron velocity vector in a model gas and SF6 were derived from the EVDF as a demonstration of the PM under the Hall deflection and they were in a fine agreement with those obtained by Monte Carlo simulations. A strategy for fast relaxation is discussed, and extension of the PM for the EVDF under AC electric and DC/AC magnetic fields is outlined as well.展开更多
In many physical situations where a laser or electron beam passes through a dense plasma,hot low-density electron populations can be generated,resulting in a particle distribution function consisting of a dense cold p...In many physical situations where a laser or electron beam passes through a dense plasma,hot low-density electron populations can be generated,resulting in a particle distribution function consisting of a dense cold population and a small hot population.Presence of such low-density electron distributions can alter the wave damping rate.A kinetic model is employed to study the Landau damping of Langmuir waves when a small hot electron population is present in the dense cold electron population with non-Maxwellian distribution functions.Departure of plasma from Maxwellian distributions significantly alters the damping rates as compared to the Maxwellian plasma.Strong damping is found for highly nonMaxwellian distributions as well as plasmas with a higher density and hot electron population.Existence of weak damping is also established when the distribution contains broadened flat tops at the low energies or tends to be Maxwellian.These results may be applied in both experimental and space physics regimes.展开更多
The electron energy distribution function （EEDF） for a magnetically filtered dusty plasma is studied in a dusty double plasma device where the electron energy can be varied from 0.15 eV to ～ 2.8 eV and plasma densi...The electron energy distribution function （EEDF） for a magnetically filtered dusty plasma is studied in a dusty double plasma device where the electron energy can be varied from 0.15 eV to ～ 2.8 eV and plasma density from 10 6 cm-3 to 10 9cm-3 . The characteristics of EEDF for these ranges of plasma parameters are investigated in a pristine plasma as well as in a dusty plasma. The results show that in the presence of dust, there is a drastic modification in EEDF patterns in a plasma with higher electron temperature and density than those in a low temperature and low density plasma produced by the magnetic filter.展开更多
We have developed a computational model which quantitatively studies the Electron Energy Distribution Function (EEDF) in laser excited lithium vapor at 2s→3d two-photon resonance. A kinetic model has been constructed...We have developed a computational model which quantitatively studies the Electron Energy Distribution Function (EEDF) in laser excited lithium vapor at 2s→3d two-photon resonance. A kinetic model has been constructed which includes essentially all the important collisional ionization, photoionization, electron collisions and radiative interactions that come into play when lithium vapor (density range 1013?- 1014 cm-3) is subject to a sudden pulse of intense laser radiation (power range 105?- 106 W·cm-2) at wavelength 639.1 nm and pulse duration 20 ns. The applied computer simulation model is based on the numerical solution of the time-dependent Boltzman equation and a set of rate equations that describe the rate of change of the formed excited states populations. Using the measured values for the cross-sections and rate coefficients of each physical process considered in the model available in literature, relations are obtained as a function of the electron energy and included in the computational model. We have also studied the time evolution and the laser power dependences of the ion population (atomic and molecular ions) as well as the electron density which are produced during the interaction. The energy spectra of the electrons emerging from the interaction contains a number of peaks corresponding to the low-energy electrons produced by photoionization and collisional ionization such as assosicative and Penning ionization processes. The non-equilibrium shape of these electrons occurs due to relaxation of fast electrons produced by super-elastic collisions with residual excited lithium atoms. Moreover, a reasonable agreement between McGeoch results and our calculations for the temporal behaviour of the electron density is obtained.展开更多
Here we derive a new charge distribution function for an electron by using as an equation of motion a segment of charge whose self energy interaction is due to electric field potential. Our method is based on the cons...Here we derive a new charge distribution function for an electron by using as an equation of motion a segment of charge whose self energy interaction is due to electric field potential. Our method is based on the consideration that a charged distribution function should be represented as an eigenfunction of electron mass energy. We compare our electron charge distribution function to that of Weinberg’s η(r) and our charged electron radius to that obtained by Kim.展开更多
In this paper we show that two significant phenomena of magnetospheric chorus emission can be explained by the participation of beam-like electron structures,created by Landau-resonant interaction with growing oblique...In this paper we show that two significant phenomena of magnetospheric chorus emission can be explained by the participation of beam-like electron structures,created by Landau-resonant interaction with growing oblique whistler waves.The first concerns the widely observed spectral gap near half the electron cyclotron frequency Ωe;the second is related to the observation of very obliquely propagating lower-band waves that cannot be directly generated by temperature anisotropy.Concerning the gap,kinetic dispersion theory reveals that interference of the beam-related cyclotron mode ω~Ωe-kVb with the conventional whistler mode leads to mode splitting and the appearance of a ’forbidden’ area in the ω-k space.Thereby the beam velocity appears as an essential parameter.It is directly related to the phase velocity of the most unstable whistler wave mode,which is close to VAe/2 for sufficiently hot electrons(VAe is the electron Alfven velocity).To clarify the second point,we show that Landau-resonant beams with Vb Vb<VAe/2,which arise in cold plasmas from unstable upper-band waves,are able to generate lower-band whistler mode waves at very oblique propagation(θ≥60°).Our studies demonstrate the important role of Landau-resonant electrons in nonlinear whistler wave generation in the magnetosphere.展开更多
The ion source of the electron cyclotron resonance ion thruster （ECRIT） extracts ions from its ECR plasma to generate thrust, and has the property of low gas consumption （2 seem, standard-state cubic centimeter per...The ion source of the electron cyclotron resonance ion thruster （ECRIT） extracts ions from its ECR plasma to generate thrust, and has the property of low gas consumption （2 seem, standard-state cubic centimeter per minute） and high durability. Due to the indispensable effects of the primary electron in gas discharge, it is important to experimentally clarify the electron energy structure within the ion source of the ECRIT through analyzing the electron energy distribution function （EEDF） of the plasma inside the thruster. In this article the Langmuir probe diagnosing method was used to diagnose the EEDF, from which the effective electron temperature, plasma density and the electron energy probability function （EEPF） were deduced. The experimental results show that the magnetic field influences the curves of EEDF and EEPF and make the effective plasma parameter nonuniform. The diagnosed electron temperature and density from sample points increased from 4 eV/2 ×10^16 m-3 to 10 eV/4×10^16 m-3 with increasing distances from both the axis and the screen grid of the ion source. Electron temperature and density peaking near the wall coincided with the discharge process. However, a double Maxwellian electron distribution was unexpectedly observed at the position near the axis of the ion source and about 30 mm from the screen grid. Besides, the double Maxwellian electron distribution was more likely to emerge at high power and a low gas flow rate. These phenomena were believed to relate to the arrangements of the gas inlets and the magnetic field where the double Maxwellian electron distribution exits. The results of this research may enhance the understanding of the plasma generation process in the ion source of this type and help to improve its performance.展开更多
In the present paper, we shall rigorously re-establish the result of the single-particle function of a quantum dot system at finite temperature. Unlike the proof given in our previous work （Phys. Rev. B 74 195414 （2...In the present paper, we shall rigorously re-establish the result of the single-particle function of a quantum dot system at finite temperature. Unlike the proof given in our previous work （Phys. Rev. B 74 195414 （2006））, we take a different approach, which does not exploit the explicit expression of the Gibbs distribution function. Instead, we only assume that the statistical distribution function of the quantum dot system is thermodynamically stable. As a result, we are able to show clearly that the electronic structure in the quantum dot system is completely determined by its thermodynamic stability. Furthermore, the weaker requirements on the statistical distribution function also make it possible to apply the same method to the quantum dot systems in non-equilibrium states.展开更多
In order to calculate the electron energy distribution in the fuel rod gap of a VVER- 1000 nuclear reactor, the Fokker-Planck equation （FPE） governing the non-equilibrium behavior of electrons passing through the fu...In order to calculate the electron energy distribution in the fuel rod gap of a VVER- 1000 nuclear reactor, the Fokker-Planck equation （FPE） governing the non-equilibrium behavior of electrons passing through the fuel-rod gap as an absorber has been solved in this paper. Besides, the Monte Carlo Geant4 code was employed to simulate the electron migration in the fuel-rod gap and the energy distribution of electrons was found. As for the results, the accuracy of the FPE was compared to the Geant4 code outcomes and a satisfactory agreement was found. Also, different percentage of the volatile and noble gas fission fragments produced in fission reactions in fuel rod, i.e. Krypton, Xenon, Iodine, Bromine, Rubidium and Cesium were employed so as to investigate their effects on the electrons＇ energy distribution. The present results show that most of the electrons in the fuel rod＇s gap were within the thermal energy limitation and the tail of the electron energy distribution was far from a Maxwellian distribution. The interesting outcome was that the electron energy distribution is slightly increased due to the accumulation of fission fragments in the gap. It should be noted that solving the FPE for the energy straggling electrons that are penetrating into the fuel-rod gap in the VVER-1000 nuclear reactor has been carried out for the first time using an analytical approach.展开更多
The electron energy distribution function （EEDF）, predicted by the Boltzmann equation solver BOLSIG＋ based on the two-term approximation, is introduced into the fluid model for simulating the high-power microwave ...The electron energy distribution function （EEDF）, predicted by the Boltzmann equation solver BOLSIG＋ based on the two-term approximation, is introduced into the fluid model for simulating the high-power microwave （HPM） breakdown in argon, nitrogen, and air, and its validity is examined by comparing with the results of particle-in-cell Monte Carlo collision （PIC/MCC） simulations as well as the experimental data. Numerical results show that, the breakdown time of the fluid model with the Maxwellian EEDF matches that of the PIC/MCC simulations in nitrogen; however, in argon under high pressures, the results from the Maxwellian EEDF were poor. This is due to an overestimation of the energy tail of the Maxwellian EEDF in argon breakdown. The prediction of the fluid model with the BOLSIG＋ EEDF, however, agrees very well with the PIC/MCC prediction in nitrogen and argon over a wide range of pressures. The accuracy of the fluid model with the BOLSIG＋ EEDF is also verified by the experimental results of the air breakdown.展开更多
In this work, the effects of superthermal and trapped electrons on the oblique propa- gation of nonlinear dust-acoustic waves in a magnetized dusty （complex） plasma are investigated. The dynamic of electrons is simu...In this work, the effects of superthermal and trapped electrons on the oblique propa- gation of nonlinear dust-acoustic waves in a magnetized dusty （complex） plasma are investigated. The dynamic of electrons is simulated by the generalized Lorentzian （k） distribution function （DF）. The dust grains are cold and their dynamics are simulated by hydrodynamic equations. Using the standard reductive perturbation technique （RPT） a nonlinear modified Korteweg-de Vries （mKdV） equation is derived. Two types of solitary waves; fast and slow dust acoustic solitons, exist in this plasma. Calculations reveal that compressive solitary structures are likely to propagate in this plasma where dust grains are negatively （or positively） charged. The properties of dust acoustic solitons （DASs） are also investigated numerically.展开更多
We present a theoretical investigation of plasma generation in sodium vapor induced by laser radiation tuned to the first resonance line (3S-3P) at λ = 589 ns. A set of rate equations that describe the rate of change...We present a theoretical investigation of plasma generation in sodium vapor induced by laser radiation tuned to the first resonance line (3S-3P) at λ = 589 ns. A set of rate equations that describe the rate of change of the ground and excited states population as well as the temporal variation of the electron energy distribution function (EEDF), beside the formed atomic ion Na+, molecular ion ?and tri-atomic ions are solved numerically. The calculations are carried out at different laser energy and different sodium atomic vapor densities under the experimental conditions of Tapalian and Smith (1993) to test the existence of the formed tri-atomic ions. The numerical calculations of the electron energy distribution function (EEDF) show that a deviation from the Maxwellian distribution due to the super elastic collisions effect. In addition to the competition between associative ionization (3P-3P), associative ionization (3P-3D) and Molnar-Horn- beck ionization processes for producing , the calculations have also shown that the atomic ions Na+ are formed through the Penning ionization and photoionization processes. These results are found to be consistent with the experimental observations.展开更多
A numerical investigation of laser wavelength dependence on the threshold intensity of spark ignition in molecular hydrogen over a wide pressure range is presented. A modified electron cascade model (Gamal et al., 199...A numerical investigation of laser wavelength dependence on the threshold intensity of spark ignition in molecular hydrogen over a wide pressure range is presented. A modified electron cascade model (Gamal et al., 1993) is applied under the experimental conditions that carried out by Phuoc (2000) to determine the threshold intensity dependence on gas pressure for spark ignition in hydrogen combustion using two laser wavelengths namely;1064 nm and 532 nm. The model involves the solution of the time dependent Boltzmann equation for the electron energy distribution function (EEDF) and a set of rate equations that describe the change of the formed excited molecules population. The model takes into account most of the physical processes that expected to occur in the interaction region. The results showed good agreement between the calculated thresholds for spark ignition and those measured ones for both wavelengths, where the threshold intensities corresponding to the short wavelength (532 nm) are found to be higher than those calculated for the longer one (1064 nm). This result indicates the depletion of the high density of low energy electrons generated through multi-photon ionization at the short wavelength via electron diffusion and vibrational excitation. The study of the EEDF and its parameters (viz, the temporal evolution of: the electron density, ionization rate electron mean energy, …) revealed the important role played by each physical process to the spark ignition as a function of both laser wavelength and gas pressure. More over the study of the time variation of the EEDF explains the characteristics of the ignited spark at the two wavelengths for the tested pressure values.展开更多
基金supported by the National Key R&D Program of China(No.2022YFE0204100)National Natural Science Foundation of China(Nos.12205067 and 12375199)the Fundamental Research Funds for the Central University(No.HIT.D?J.2023178)。
文摘This work continues the studies on searching for plasma media with the inverse electron energy distribution function(EEDF)and providing recommendations for setting up subsequent experiments.The inverse EEDF is a distribution function that increases with an increase in energy at zero electron energy.The inverse EEDF plays a central role in the problem of negative conductivity.Based on the previously obtained criterion for the formation of an inverse EEDF in a spatially inhomogeneous plasma,a heuristic method is proposed that allows one to avoid resource-intensive calculations for spatially two-dimensional(2D)kinetic modeling on a large array of different glow discharges.It is shown that the conditions for EEDF inversion can be realized in two-chamber discharge structures due to violating the known Boltzmann distribution for electron density.The theoretical conclusions are validated by numerical modeling of lowpressure two-chamber inductively-coupled plasma(ICP)discharges in the COMSOL Multiphysics environment.As a result,areas of conditions with inverse EEDF were found for subsequent detailed kinetic analysis and experimental studies.
文摘Since the position of the electron in a hydrogen atom cannot be determined, the region in which it resides is said to be determined stochastically and forms an electron cloud. The probability density function of the single electron in 1s orbit is expressed as φ2, a function of distance from the nucleus. However, the probability of existence of the electron is expressed as a radial distribution function at an arbitrary distance from the nucleus, so it is estimated as the probability of the entire spherical shape of that radius. In this study, it has been found that the electron existence probability approximates the radial distribution function by assuming that the probability of existence of the electron being in the vicinity of the nucleus follows a normal distribution for arbitrary x-, y-, and z-axis directions. This implies that the probability of existence of the electron, which has been known only from the distance information, would follow a normal distribution independently in the three directions. When the electrons’ motion is extremely restricted in a certain direction by the magnetic field of both tokamak and helical fusion reactors, the probability of existence of the electron increases with proximity to the nucleus, and as a result, it is less likely to be liberated from the nucleus. Therefore, more and more energy is required to free the nucleus from the electron in order to generate plasma.
基金supported by the National Research Foundation of Korea(Nos.NRF-2019M1A7A1A03087579 and NRF-2021R1I1A1A01050312)the Ministry of Trade,Industry&Energy(Nos.20011226 and 20009415)。
文摘In general,as the radio frequency(RF)power increases in a capacitively coupled plasma(CCP),the power transfer efficiency decreases because the resistance of the CCP decreases.In this work,a parallel resonance circuit is applied to improve the power transfer efficiency at high RF power,and the effect of the parallel resonance on the electron energy distribution function(EEDF)is investigated in a 60 MHz CCP.The CCP consists of a power feed line,the electrodes,and plasma.The reactance of the CCP is positive at 60 MHz and acts like an inductive load.A vacuum variable capacitor(VVC)is connected in parallel with the inductive load,and then the parallel resonance between the VVC and the inductive load can be achieved.As the capacitance of the VVC approaches the parallel resonance condition,the equivalent resistance of the parallel circuit is considerably larger than that without the VVC,and the current flowing through the matching network is greatly reduced.Therefore,the power transfer efficiency of the discharge is improved from 76%,70%,and 68%to 81%,77%,and 76%at RF powers of 100 W,150 W,and 200 W,respectively.At parallel resonance conditions,the electron heating in bulk plasma is enhanced,which cannot be achieved without the VVC even at the higher RF powers.This enhancement of electron heating results in the evolution of the shape of the EEDF from a biMaxwellian distribution to a distribution with the smaller temperature difference between high-energy electrons and low-energy electrons.Due to the parallel resonance effect,the electron density increases by approximately 4%,18%,and 21%at RF powers of 100 W,150 W,and 200 W,respectively.
文摘A conservative transport operator in space (v//,r) and moment equations are used to describe the combined effects of a stochastic magnetic field and a radial ambipolar electric field on the electrons. The transport operator is coupled with Fokker-planck and Ohmic heating terms to compute the electron distribution function. A physical picture exhibits the possible importance of the turbulent magnetic field on the suprathermal electrons, which may be concerned with plasma confinement.
基金Project supported by the National Natural Science Foundation of China (Grant No. 92477205)。
文摘Controlling charge polarity in the semiconducting single-walled carbon nanotubes(CNTs) by substitutional doping is a difficult work due to their extremely strong C–C bonding. In this work, an inner doping strategy is explored by filling CNTs with one-dimensional(1D)-TM_(6)Te_(6) nanowires to form TM_(6)Te_(6)@CNT-(16,0) 1D van der Waals heterostructures(1D-vd WHs). The systematic first-principles studies on the electronic properties of 1D-vd WHs show that N-type doping CNTs can be formed by charge transfer from TM_(6)Te_(6) nanowires to CNTs, without introducing additional carrier scattering.Particularly, contribution from both T M(e.g., Sc and Y) and Te atoms strengthens the charge transfer. The outside CNTs further confine the dispersion of Te-p orbitals in nanowires that deforms the C-π states at the bottom of the conduction band to quasi sp^(3) hybridization. Our study provides an inner doping strategy that can effectively confine the charge polarity of CNTs and further broaden its applications in some novel nano-devices.
文摘This paper presents a self-contained description on the configuration of propagator method(PM)to calculate the electron velocity distribution function(EVDF) of electron swarms in gases under DC electric and magnetic fields crossed at a right angle. Velocity space is divided into cells with respect to three polar coordinates v,θ and f. The number of electrons in each cell is stored in three-dimensional arrays. The changes of electron velocity due to acceleration by the electric and magnetic fields and scattering by gas molecules are treated as intercellular electron transfers on the basis of the Boltzmann equation and are represented using operators called the propagators or Green’s functions. The collision propagator, assuming isotropic scattering, is basically unchanged from conventional PMs performed under electric fields without magnetic fields. On the other hand, the acceleration propagator is customized for rotational acceleration under the action of the Lorentz force. The acceleration propagator specific to the present cell configuration is analytically derived. The mean electron energy and average electron velocity vector in a model gas and SF6 were derived from the EVDF as a demonstration of the PM under the Hall deflection and they were in a fine agreement with those obtained by Monte Carlo simulations. A strategy for fast relaxation is discussed, and extension of the PM for the EVDF under AC electric and DC/AC magnetic fields is outlined as well.
基金Project supported by the National Natural Science Foundation of China (Grant No. 40931054)the National Basic Research Program of China (Grant No. 2011CB811404)the Higher Education Commission of China (Grant No. 20-1886/R&D/10)
文摘In many physical situations where a laser or electron beam passes through a dense plasma,hot low-density electron populations can be generated,resulting in a particle distribution function consisting of a dense cold population and a small hot population.Presence of such low-density electron distributions can alter the wave damping rate.A kinetic model is employed to study the Landau damping of Langmuir waves when a small hot electron population is present in the dense cold electron population with non-Maxwellian distribution functions.Departure of plasma from Maxwellian distributions significantly alters the damping rates as compared to the Maxwellian plasma.Strong damping is found for highly nonMaxwellian distributions as well as plasmas with a higher density and hot electron population.Existence of weak damping is also established when the distribution contains broadened flat tops at the low energies or tends to be Maxwellian.These results may be applied in both experimental and space physics regimes.
文摘The electron energy distribution function （EEDF） for a magnetically filtered dusty plasma is studied in a dusty double plasma device where the electron energy can be varied from 0.15 eV to ～ 2.8 eV and plasma density from 10 6 cm-3 to 10 9cm-3 . The characteristics of EEDF for these ranges of plasma parameters are investigated in a pristine plasma as well as in a dusty plasma. The results show that in the presence of dust, there is a drastic modification in EEDF patterns in a plasma with higher electron temperature and density than those in a low temperature and low density plasma produced by the magnetic filter.
文摘We have developed a computational model which quantitatively studies the Electron Energy Distribution Function (EEDF) in laser excited lithium vapor at 2s→3d two-photon resonance. A kinetic model has been constructed which includes essentially all the important collisional ionization, photoionization, electron collisions and radiative interactions that come into play when lithium vapor (density range 1013?- 1014 cm-3) is subject to a sudden pulse of intense laser radiation (power range 105?- 106 W·cm-2) at wavelength 639.1 nm and pulse duration 20 ns. The applied computer simulation model is based on the numerical solution of the time-dependent Boltzman equation and a set of rate equations that describe the rate of change of the formed excited states populations. Using the measured values for the cross-sections and rate coefficients of each physical process considered in the model available in literature, relations are obtained as a function of the electron energy and included in the computational model. We have also studied the time evolution and the laser power dependences of the ion population (atomic and molecular ions) as well as the electron density which are produced during the interaction. The energy spectra of the electrons emerging from the interaction contains a number of peaks corresponding to the low-energy electrons produced by photoionization and collisional ionization such as assosicative and Penning ionization processes. The non-equilibrium shape of these electrons occurs due to relaxation of fast electrons produced by super-elastic collisions with residual excited lithium atoms. Moreover, a reasonable agreement between McGeoch results and our calculations for the temporal behaviour of the electron density is obtained.
文摘Here we derive a new charge distribution function for an electron by using as an equation of motion a segment of charge whose self energy interaction is due to electric field potential. Our method is based on the consideration that a charged distribution function should be represented as an eigenfunction of electron mass energy. We compare our electron charge distribution function to that of Weinberg’s η(r) and our charged electron radius to that obtained by Kim.
文摘In this paper we show that two significant phenomena of magnetospheric chorus emission can be explained by the participation of beam-like electron structures,created by Landau-resonant interaction with growing oblique whistler waves.The first concerns the widely observed spectral gap near half the electron cyclotron frequency Ωe;the second is related to the observation of very obliquely propagating lower-band waves that cannot be directly generated by temperature anisotropy.Concerning the gap,kinetic dispersion theory reveals that interference of the beam-related cyclotron mode ω~Ωe-kVb with the conventional whistler mode leads to mode splitting and the appearance of a ’forbidden’ area in the ω-k space.Thereby the beam velocity appears as an essential parameter.It is directly related to the phase velocity of the most unstable whistler wave mode,which is close to VAe/2 for sufficiently hot electrons(VAe is the electron Alfven velocity).To clarify the second point,we show that Landau-resonant beams with Vb Vb<VAe/2,which arise in cold plasmas from unstable upper-band waves,are able to generate lower-band whistler mode waves at very oblique propagation(θ≥60°).Our studies demonstrate the important role of Landau-resonant electrons in nonlinear whistler wave generation in the magnetosphere.
基金supported by National Natural Science Foundation of China(No.11475137)
文摘The ion source of the electron cyclotron resonance ion thruster （ECRIT） extracts ions from its ECR plasma to generate thrust, and has the property of low gas consumption （2 seem, standard-state cubic centimeter per minute） and high durability. Due to the indispensable effects of the primary electron in gas discharge, it is important to experimentally clarify the electron energy structure within the ion source of the ECRIT through analyzing the electron energy distribution function （EEDF） of the plasma inside the thruster. In this article the Langmuir probe diagnosing method was used to diagnose the EEDF, from which the effective electron temperature, plasma density and the electron energy probability function （EEPF） were deduced. The experimental results show that the magnetic field influences the curves of EEDF and EEPF and make the effective plasma parameter nonuniform. The diagnosed electron temperature and density from sample points increased from 4 eV/2 ×10^16 m-3 to 10 eV/4×10^16 m-3 with increasing distances from both the axis and the screen grid of the ion source. Electron temperature and density peaking near the wall coincided with the discharge process. However, a double Maxwellian electron distribution was unexpectedly observed at the position near the axis of the ion source and about 30 mm from the screen grid. Besides, the double Maxwellian electron distribution was more likely to emerge at high power and a low gas flow rate. These phenomena were believed to relate to the arrangements of the gas inlets and the magnetic field where the double Maxwellian electron distribution exits. The results of this research may enhance the understanding of the plasma generation process in the ion source of this type and help to improve its performance.
基金Project supported by the National Science Foundation of China (Grant Nos. 10874003 and 11074004)the National Basic Research Program of China (Grant No. 2009CB939901)
文摘In the present paper, we shall rigorously re-establish the result of the single-particle function of a quantum dot system at finite temperature. Unlike the proof given in our previous work （Phys. Rev. B 74 195414 （2006））, we take a different approach, which does not exploit the explicit expression of the Gibbs distribution function. Instead, we only assume that the statistical distribution function of the quantum dot system is thermodynamically stable. As a result, we are able to show clearly that the electronic structure in the quantum dot system is completely determined by its thermodynamic stability. Furthermore, the weaker requirements on the statistical distribution function also make it possible to apply the same method to the quantum dot systems in non-equilibrium states.
文摘In order to calculate the electron energy distribution in the fuel rod gap of a VVER- 1000 nuclear reactor, the Fokker-Planck equation （FPE） governing the non-equilibrium behavior of electrons passing through the fuel-rod gap as an absorber has been solved in this paper. Besides, the Monte Carlo Geant4 code was employed to simulate the electron migration in the fuel-rod gap and the energy distribution of electrons was found. As for the results, the accuracy of the FPE was compared to the Geant4 code outcomes and a satisfactory agreement was found. Also, different percentage of the volatile and noble gas fission fragments produced in fission reactions in fuel rod, i.e. Krypton, Xenon, Iodine, Bromine, Rubidium and Cesium were employed so as to investigate their effects on the electrons＇ energy distribution. The present results show that most of the electrons in the fuel rod＇s gap were within the thermal energy limitation and the tail of the electron energy distribution was far from a Maxwellian distribution. The interesting outcome was that the electron energy distribution is slightly increased due to the accumulation of fission fragments in the gap. It should be noted that solving the FPE for the energy straggling electrons that are penetrating into the fuel-rod gap in the VVER-1000 nuclear reactor has been carried out for the first time using an analytical approach.
基金the National Natural Science Foundation of China，the Fundamental Research Funds for the Central Universities，the Open Project of Beijing National Laboratory for Molecular Sciences，the Program for Innovative Research Team of Guizhou Province of China，the University Development Fund of Guizhou Province，the Talent Special Fund of Guizhou Province
基金Project supported by the National Basic Research Program of China(Grant No.2013CB328904)the Fundamental Research Funds for the Central Universities,Chinathe Open Research Fund of Key Laboratory of Cognitive Radio and Information Processing of Ministry of Education of China
文摘The electron energy distribution function （EEDF）, predicted by the Boltzmann equation solver BOLSIG＋ based on the two-term approximation, is introduced into the fluid model for simulating the high-power microwave （HPM） breakdown in argon, nitrogen, and air, and its validity is examined by comparing with the results of particle-in-cell Monte Carlo collision （PIC/MCC） simulations as well as the experimental data. Numerical results show that, the breakdown time of the fluid model with the Maxwellian EEDF matches that of the PIC/MCC simulations in nitrogen; however, in argon under high pressures, the results from the Maxwellian EEDF were poor. This is due to an overestimation of the energy tail of the Maxwellian EEDF in argon breakdown. The prediction of the fluid model with the BOLSIG＋ EEDF, however, agrees very well with the PIC/MCC prediction in nitrogen and argon over a wide range of pressures. The accuracy of the fluid model with the BOLSIG＋ EEDF is also verified by the experimental results of the air breakdown.
文摘In this work, the effects of superthermal and trapped electrons on the oblique propa- gation of nonlinear dust-acoustic waves in a magnetized dusty （complex） plasma are investigated. The dynamic of electrons is simulated by the generalized Lorentzian （k） distribution function （DF）. The dust grains are cold and their dynamics are simulated by hydrodynamic equations. Using the standard reductive perturbation technique （RPT） a nonlinear modified Korteweg-de Vries （mKdV） equation is derived. Two types of solitary waves; fast and slow dust acoustic solitons, exist in this plasma. Calculations reveal that compressive solitary structures are likely to propagate in this plasma where dust grains are negatively （or positively） charged. The properties of dust acoustic solitons （DASs） are also investigated numerically.
文摘We present a theoretical investigation of plasma generation in sodium vapor induced by laser radiation tuned to the first resonance line (3S-3P) at λ = 589 ns. A set of rate equations that describe the rate of change of the ground and excited states population as well as the temporal variation of the electron energy distribution function (EEDF), beside the formed atomic ion Na+, molecular ion ?and tri-atomic ions are solved numerically. The calculations are carried out at different laser energy and different sodium atomic vapor densities under the experimental conditions of Tapalian and Smith (1993) to test the existence of the formed tri-atomic ions. The numerical calculations of the electron energy distribution function (EEDF) show that a deviation from the Maxwellian distribution due to the super elastic collisions effect. In addition to the competition between associative ionization (3P-3P), associative ionization (3P-3D) and Molnar-Horn- beck ionization processes for producing , the calculations have also shown that the atomic ions Na+ are formed through the Penning ionization and photoionization processes. These results are found to be consistent with the experimental observations.
文摘A numerical investigation of laser wavelength dependence on the threshold intensity of spark ignition in molecular hydrogen over a wide pressure range is presented. A modified electron cascade model (Gamal et al., 1993) is applied under the experimental conditions that carried out by Phuoc (2000) to determine the threshold intensity dependence on gas pressure for spark ignition in hydrogen combustion using two laser wavelengths namely;1064 nm and 532 nm. The model involves the solution of the time dependent Boltzmann equation for the electron energy distribution function (EEDF) and a set of rate equations that describe the change of the formed excited molecules population. The model takes into account most of the physical processes that expected to occur in the interaction region. The results showed good agreement between the calculated thresholds for spark ignition and those measured ones for both wavelengths, where the threshold intensities corresponding to the short wavelength (532 nm) are found to be higher than those calculated for the longer one (1064 nm). This result indicates the depletion of the high density of low energy electrons generated through multi-photon ionization at the short wavelength via electron diffusion and vibrational excitation. The study of the EEDF and its parameters (viz, the temporal evolution of: the electron density, ionization rate electron mean energy, …) revealed the important role played by each physical process to the spark ignition as a function of both laser wavelength and gas pressure. More over the study of the time variation of the EEDF explains the characteristics of the ignited spark at the two wavelengths for the tested pressure values.
