Maxwellian Electron Distribution Research Articles

Diagnosing the Fine Structure of Electron Energy Within the ECRIT Ion Source**supported by National Natural Science Foundation of China (No. 11475137)

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 sccm, 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/2×1016 m−3 to 10 eV/4×1016 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.

The Spectral Sharpness Angle of Gamma-ray Bursts

We explain the results of Yu et al. (2015b) of the novel sharpness angle measurement to a large number of spectra obtained from the Fermi gamma-ray burst monitor. The sharpness angle is compared to the values obtained from various representative emission models: blackbody, single-electron synchrotron, synchrotron emission from a Maxwellian or power-law electron distribution. It is found that more than 91% of the high temporally and spectrally resolved spectra are inconsistent with any kind of optically thin synchrotron emission model alone. It is also found that the limiting case, a single temperature Maxwellian synchrotron function, can only contribute up to 58+23 -18% of the peak flux. These results show that even the sharpest but non-realistic case, the single-electron synchrotron function, cannot explain a large fraction of the observed spectra. Since any combination of physically possible synchrotron spectra added together will always further broaden the spectrum, emission mechanisms other than optically thin synchrotron radiation are likely required in a full explanation of the spectral peaks or breaks of the GRB prompt emission phase.

Implications of the pulsar wind nebula scenario for a TeV gamma-ray source VER J2016+371

We present multiwavelength studies of a TeV gamma-ray source VER J2016+371 suggested to be associated with a supernova remnant CTB 87 (G74.9+1.2) and based on X-ray and radio morphologies, CTB 87 is identified as an evolved pulsar wind nebula. A source in the vicinity of VER J2016+371 is also detected at GeV energies by Fermi Gamma Ray Space Telescope suggesting a likely counterpart at GeV energies. We find that a broken power-law (BPL) distribution of electrons can explain the observed data at radio, X-ray and TeV energies, however, is not sufficient to explain the data at MeV--GeV energies. A Maxwellian distribution of electrons along with the BPL distribution of electrons in low magnetic fields can explain the observed multiwavelength data spanned from radio to TeV energies suggesting this as the most likely scenario for this source. We also find that although the hadronic model can explain the observed GeV--TeV data for the ambient matter density of $\sim 20~ \rm cm^{-3}$, no observational support for such high ambient density makes this hadronic scenario unlikely for this source.

Nonlinear propagation of dust-ion-acoustic solitary waves in an unmagnetized dusty plasma with trapped particle distribution

The nonlinear propagation of dust-ion-acoustic (DIA) solitary waves (SWs) in an unmagnetized four-component dusty plasma containing electrons and negative ions obeying vortex-like (trapped) velocity distribution, cold mobile positive ions and arbitrarily charged stationary dust has been theoretically investigated. The properties of small but finite amplitude DIASWs are studied by employing the reductive perturbation technique. It has been found that owing to the departure from the Maxwellian electron and Maxwellian negative ion distribution to a vortex-like one, the dynamics of such DIASWs is governed by a modified Korteweg–de Vries (mKdV) equation which admits SW solution under certain conditions. The basic properties (speed, amplitude, width, etc.) of such DIASWs are found to be significantly modified by the presence of trapped electron and trapped negative ions. The implications of our results to space and laboratory dusty electronegative plasmas (DENPs) are briefly discussed.

The sharpness of gamma-ray burst prompt emission spectra

We aim to obtain a measure of the curvature of time-resolved spectra that can be compared directly to theory. This tests the ability of models such as synchrotron emission to explain the peaks or breaks of GBM prompt emission spectra. We take the burst sample from the official Fermi GBM GRB time-resolved spectral catalog. We re-fit all spectra with a measured peak or break energy in the catalog best-fit models in various energy ranges, which cover the curvature around the spectral peak or break, resulting in a total of 1,113 spectra being analysed. We compute the sharpness angles under the peak or break of the triangle constructed under the model fit curves and compare to the values obtained from various representative emission models: blackbody, single-electron synchrotron, synchrotron emission from a Maxwellian or power-law electron distribution. We find that 35% of the time-resolved spectra are inconsistent with the single-electron synchrotron function, and 91% are inconsistent with the Maxwellian synchrotron function. The single temperature, single emission time and location blackbody function is found to be sharper than all the spectra. No general evolutionary trend of the sharpness angle is observed, neither per burst nor for the whole population. It is found that the limiting case, a single temperature Maxwellian synchrotron function, can only contribute up to $58^{+23}_{-18}$% of the peak flux. Our results show that even the sharpest but non-realistic case, the single-electron synchrotron function, cannot explain a large fraction of the observed GRB prompt spectra. Because of the fact that any combination of physically possible synchrotron spectra added together will always further broaden the spectrum, emission mechanisms other than optically thin synchrotron radiation are likely required in a full explanation of the spectral peaks or breaks of the GRB prompt emission phase.

Precipitation of electrons into the upper atmosphere of a hot-jupiter exoplanet

A kinetic model enabling investigation of the penetration and degradation of a flux of electrons into high-latitude regions of the hydrogen-dominant upper atmosphere of an exoplanet by means of numerical solution of the Boltzmann equation has been developed. It is shown for the case of a dipolar magnetic field that a one-dimensional model makes it possible to obtain a correct solution to this problem. Computations of the precipitation of a flux of electrons from the magnetosphere into the atmosphere of a typical hot Jupiter and the atmosphere of the planet Jupiter in our Solar system have been carried out. The computations assume a Maxwellian velocity distribution for electrons with three characteristic energies, E 0 = 1, 10, and 100 keV. The efficiency of heating the atmosphere of a typical hot Jupiter and the planet Jupiter are considered. The heating efficiency displays only a weak dependence on the characteristic energy of the precipitating electrons. The heating efficiency for the upper atmosphere of Jupiter is also independent of the height, and lies in the range 7–9%. The heating efficiency for the atmosphere of a hot Jupiter depends appreciably on height, and varies from 7 to 18%. In the case of a hot Jupiter, the energy-absorption peaks for electrons with low kinetic energies lie in the region of higher heating efficiencies, substantially strengthening the contribution from precipitating electrons to the total heating of the atmosphere.

Temperature-averaged and total free-free Gaunt factors forκand Maxwellian distributions of electrons

Aims. Optically thin plasmas may deviate from thermal equilibrium and thus, electrons (and ions) are no longer described by the Maxwellian distribution. Instead they can be described by $\kappa$-distributions. The free-free spectrum and radiative losses depend on the temperature-averaged (over the electrons distribution) and total Gaunt factors, respectively. Thus, there is a need to calculate and make available these factors to be used by any software that deals with plasma emission. Methods. We recalculated the free-free Gaunt factor for a wide range of energies and frequencies using hypergeometric functions of complex arguments and the Clenshaw recurrence formula technique combined with approximations whenever the difference between the initial and final electron energies is smaller than $10^{-10}$ in units of $z^2Ry$. We used double and quadruple precisions. The temperature- averaged and total Gaunt factors calculations make use of the Gauss-Laguerre integration with 128 nodes. Results. The temperature-averaged and total Gaunt factors depend on the $\kappa$ parameter, which shows increasing deviations (with respect to the results obtained with the use of the Maxwellian distribution) with decreasing $\kappa$. Tables of these Gaunt factors are provided.

Vlasov tokamak equilibria with sheared toroidal flow and anisotropic pressure

By choosing appropriate deformed Maxwellian ion and electron distribution functions depending on the two particle constants of motion, i.e., the energy and toroidal angular momentum, we reduce the Vlasov axisymmetric equilibrium problem for quasineutral plasmas to a transcendental Grad-Shafranov-like equation. This equation is then solved numerically under the Dirichlet boundary condition for an analytically prescribed boundary possessing a lower X-point to construct tokamak equilibria with toroidal sheared ion flow and anisotropic pressure. Depending on the deformation of the distribution functions, these steady states can have toroidal current densities either peaked on the magnetic axis or hollow. These two kinds of equilibria may be regarded as a bifurcation in connection with symmetry properties of the distribution functions on the magnetic axis.

Time-resolved study of the extreme-ultraviolet emission and plasma dynamics of a sub-Joule, fast capillary discharge

In this work, we discuss experimental observations on the dynamics of a fast, low energy capillary discharge when operated in argon and its properties as an intense source of extreme-ultraviolet (EUV) radiation. The discharge pre-ionization and self-triggering were accomplished by the use of the hollow cathode effect. This allowed a compact size and low inductance discharge with multi-kA current level and a quarter-period of ∼10 ns at sub-Joule energy level. We used the novel moiré and schlieren diagnostics with a 12 ps laser to obtain the time evolution of the line electron density and to study the plasma dynamics. EUV spectroscopy and filtered diodes were also implemented to estimate the plasma temperature and density throughout the evolution of the discharge. EUV source size was measured by using a filtered slit-wire camera. We observed that EUV emission starts from a compressed plasma on axis during the second quarter-period of the current and continues until the fifth quarter-period. Ionization levels from Ar VII to X were observed. By comparing the EUV emission spectra with synthetic spectra, we found that at the onset of emission (∼7 ns), the plasma is well fitted by a single Maxwellian electron distribution function with Te ∼ 12 eV and ne ∼ 1017 cm−3. Close to peak emission (∼13 ns), plasma temperature and density increase to ∼20 eV and ne ∼ 1018 cm−3, respectively. However, in order to successfully match the experimental data, a two component electron distribution function was necessary. Later in time, a smaller fraction in the high energy component and higher temperature suggests homogenization of the plasma. The moiré and schlieren diagnostics showed multiple radial compression-waves merging on axis throughout the discharge; they are an important heating mechanism that leads to a period of severe turbulence at peak EUV emission. It was also observed that emission ceases when the axial maximum of the electron density collapses.

Influence of supersonic ions and nonlocal electron kinetics on the sheath voltage in an expanding plasma

We present the investigation of the sheath potential in an expanding plasma. The properties of the expanding plasma are measured by means of a Langmuir probe. The obtained data is used to calculate the sheath potential and the electron distribution function. We show that the sheath voltage is typically about 40% lower than in a case that neglects supersonic ions and assumes a Maxwellian electron distribution. We explain the magnitude of the measured sheath potential by balancing the ion flux density calculated with an analytical model for the expanding plasma and the electron flux density calculated with the electron distribution function.

Plasma immersion ion implantation characteristics with q-nonextensive electron velocity distribution

The plasma immersion ion implantation process is investigated in the presence ofq–nonextensive electrons by using a one-dimensional fluid model. The effect of the nonextensivity parameter,q, on the plasma parameters and sheath dynamics during the implantation process is studied. The results show that the implantation dose can be enhanced in the presence of energetic electrons at the tail of the distribution function. Different parameters of plasma such as sheath thickness, ion velocity and ion density show more change at the larger values of theq–parameter. Furthermore, the results of simulation tend to what is predicted by the Maxwellian electron distribution function (q= 1).

The width of gamma-ray burst spectra

The emission processes active in the highly relativistic jets of gamma-ray bursts (GRBs) remain unknown. In this paper we propose a new measure to describe spectra: the width of the $EF_E$ spectrum, a quantity dependent only on finding a good fit to the data. We apply this to the full sample of GRBs observed by Fermi/GBM and CGRO/BATSE. The results from the two instruments are fully consistent. We find that the median widths of spectra from long and short GRBs are significantly different (chance probability $<10^{-6}$). The width does not correlate with either duration or hardness, and this is thus a new, independent distinction between the two classes. Comparing the measured spectra with widths of spectra from fundamental emission processes -- synchrotron and blackbody radiation -- the results indicate that a large fraction of GRB spectra are too narrow to be explained by synchrotron radiation from a distribution of electron energies: for example, 78% of long GRBs and 85% of short GRBs are incompatible with the minimum width of standard slow cooling synchrotron emission from a Maxwellian distribution of electrons, with fast cooling spectra predicting even wider spectra. Photospheric emission can explain the spectra if mechanisms are invoked to give a spectrum much broader than a blackbody.

Effect of the q-nonextensive electron velocity distribution on a magnetized plasma sheath

In this work, a sheath model has been developed to investigate the effect of the q-nonextensive electron velocity distribution on the different characteristics of a magnetized plasma. By using Segdeev potential method, a modified Bohm criterion for a magnetized plasma with the nonextensive electron velocity distribution is derived. The sheath model is then used to analyze numerically the sheath structure under different q, the parameter quantifying the nonextensivity degree of the system. The results show that as the q-parameter decreases, the floating potential becomes more negative. The sheath length increases at the lower values of the q-parameter due to the increase in the electron population at the high-energy tail of the distribution function. As q-parameter decreases, the effective temperature of the electrons increases which results in a more extended plasma sheath. The ion velocity and density profiles for the different nonextensivity degrees of the system reflect the gyro-motion of the ions in the presence of the magnetic field. Furthermore, the results coincide with those given by the Maxwellian electron distribution function, when q tends to 1.

The effects of solar wind velocity distributions on the refilling of the lunar wake: ARTEMIS observations and comparisons to one‐dimensional theory

AbstractThe lunar plasma wake refills from all directions, with processes operating both parallel and perpendicular to the magnetic field. The resulting wake structure depends sensitively on the properties of the flowing plasma, including the form of the ion and electron velocity distributions. In this manuscript, we discuss theoretical approximations for the refilling of the lunar wake along the magnetic field. While an often‐used treatment for the parallel refilling assumes cold ions, one can derive solutions for arbitrary ion velocity distributions. Similarly, though the most tractable theory utilizes Maxwellian electrons, one can derive solutions for other types of distributions. We discuss the theoretical framework for various one‐dimensional solutions, spanning the full range from cold‐ion theories to gas‐dynamic solutions, and utilizing both Maxwellian and kappa electron distributions. We compare these solutions to ARTEMIS observations of the lunar wake, for time periods with appropriate plasma parameters. We also present cases that reveal the inherent limitations of one‐dimensional approximations, including those related to electron anisotropies and those related to perpendicular processes associated with both fluid flow and ion gyro‐motion.

A criterion of field reversal in a short glow discharge and its dependence on the parameters of the fluid model used

A criterion of field reversal in the near-cathode plasma of short glow discharge is considered. This criterion is shown to be extremely sensitive to the choice of the fluid-discharge model used (in particular, the choice of a Maxwellian or nonequilibrium electron-distribution function).

Modulational instability of electron-acoustic waves in magnetized plasma in presence of excess superthermal electrons

Modulational instability of finite amplitude electron-acoustic waves along external magnetic field is investigated in plasma composed of inertial cold electrons, hot inertialess superthermal electrons and stationary ions. Reductive perturbation technique is used to derive the three-dimensional nonlinear Schrodinger equation which governs the slow modulation of electron acoustic wave packets. Accounting for effects of hot electron to cold electron number density ratio (α), normalized electron-cyclotron frequency (ω c ) as well as the electron superthermal parameter (κ e ) new regimes for modulational instability of electron acoustic waves are obtained and analyzed. The presence of superthermal electrons modifies conditions for modulational instability to occur, as well as associated threshold and growth rate. Concentration of superthermal electrons (i.e., the deviation from a Maxwellian electron distribution) may control or even suppress modulational instability. In contrast to one-dimensional unmagnetized plasmas, instability growth rate is shown to suppress increasing values of k.

Observation and modeling of magnetospheric cold electron heating by electromagnetic ion cyclotron waves

A cold electron heating event associated with electromagnetic ion cyclotron (EMIC) waves is observed and modeled. The observational data of particles and waves are collected by the Time History of Events and Macroscale Interactions during Substorms spacecraft at magnetic local time 17.0–17.2. During this event, intense He+ band EMIC waves with the peak frequency 0.25 Hz are excited, corresponding to the observed phase space density (PSD) of distinct anisotropic ions. Meanwhile, substantial enhancements in energy flux of cold (1–10 eV) electrons are observed in the same period. The energy flux of electrons below 10 eV is increased by several to tens of times. We use a sum of kappa distribution components to fit the observed ion PSD and then calculate the wave growth rate driven by the anisotropic hot protons. The calculated result is in good agreement with the in situ observation. Then, we investigate whether the excited EMIC waves can transfer energy to cold electrons by Landau resonant absorption and yield electron heating. Using the typical Maxwellian distribution for cold electrons, we evaluate the wave damping rates resulted from the cold electrons in gyroresonance with EMIC waves. The simulating results show that the strong wave growth region in the He+ band induced by anisotropic ions corresponds to the strong wave damping region driven by cold electrons. Moreover, cold electrons can be heated efficiently at large wave normal angles. The current results provide a direct observational evidence for EMIC‐driven cold electron heating—a potential mechanism responsible for stable auroral red arc.

Mackenzie's Demon with instabilities

MacKenzie's Maxwell Demon, consisting of positively biased thin wires, heats plasma electrons without significantly affecting the plasma potential. Experiments were performed on the Maxwell Demon in a multi-dipole confined filament discharge. It is shown that given adequate bias, the Demon reduces a bi-Maxwellian electron distribution function to a single Maxwellian electron distribution function. It is shown that a small planar electrode can perform identical heating as the Demon, provided that the electrode has the area of approximately three times the Demon's conductive surface area. The instability that limits the Demon's operation is investigated. Time-resolved measurements of changes in global electron temperature, plasma density and plasma potential within a cycle of the instability are considered. It is found that the Demon's instability is a repeating pulsed anode spot. Density measurements indicate that the frequency of the instability is dependent on plasma production and loss rates. The neutral pressure dependence of the anode spot instability is measured and modeled for the first time.

Electron density and electron temperature measurement in a bi-Maxwellian electron distribution using a derivative method of Langmuir probes

In plasma diagnostics with a single Langmuir probe, the electron temperature Te is usually obtained from the slope of the logarithm of the electron current or from the electron energy probability functions of current (I)-voltage (V) curve. Recently, Chen [F. F. Chen, Phys. Plasmas 8, 3029 (2001)] suggested a derivative analysis method to obtain Te by the ratio between the probe current and the derivative of the probe current at a plasma potential where the ion current becomes zero. Based on this method, electron temperatures and electron densities were measured and compared with those from the electron energy distribution function (EEDF) measurement in Maxwellian and bi-Maxwellian electron distribution conditions. In a bi-Maxwellian electron distribution, we found the electron temperature Te obtained from the method is always lower than the effective temperatures Teff derived from EEDFs. The theoretical analysis for this is presented.

Nonlinear propagation of dust-acoustic solitary waves in a dusty plasma with arbitrarily charged dust and trapped electrons

A theoretical investigation of dust-acoustic solitary waves in three-component unmagnetized dusty plasma consisting of trapped electrons, Maxwellian ions, and arbitrarily charged cold mobile dust was done. It has been found that, owing to the departure from the Maxwellian electron distribution to a vortex-like one, the dynamics of small but finite amplitude dust-acoustic (DA) waves is governed by a nonlinear equation of modified Korteweg–de Vries (mKdV) type (instead of KdV). The reductive perturbation method was employed to study the basic features (amplitude, width, speed, etc.) of DA solitary waves which are significantly modified by the presence of trapped electrons. The implications of our results in space and laboratory plasmas are briefly discussed.