Maxwellian Electron Distribution Research Articles

Observation of Electron Plasma Waves in Plasma of Two-Temperature Electrons

Propagation of electron plasma waves in a large and unmagnetized plasma containing two Maxwellian distributions of electrons is studied experimentally. Two kinds of plasma sources which supply electrons of different temperature are used. The temperature ratio is about 3 and the density ratio of hot to cool electrons is varied from 0 to 0.5. A small contamination of hot electrons enhances the Landau damping of the principal mode known as the Bohm-Gross mode. When the density of hot electrons is larger than about 0.2, two modes are observed. The results agree with theoretical dispersion relations when excitation efficiencies of the modes are considered.

Electron impact excitation of transition among states with configurations 2p2, 2s2p3and 2p4in O III

The authors have calculated the collision strength for 43 semi-forbidden transitions among the states having configurations 1s22s22p2, 1s22s2p3 and 1s22p4 in O III using the R-matrix method. Configuration interaction wavefunctions are used to represent the twelve target states which are included in the calculation. Collision strengths averaged over Maxwellian distribution of electrons are calculated for these transitions over a wide temperature range and the results are compared with other work.

Lonization waves in low-temperature plasmas

The ionizational instability, which results in the excitation of moving and standing striations, is one of the most common instabilities in low-temperature plasmas. Phenomena analogous to striations are encountered not only in a variety of fields in physics but also in related sciences, such as chemistry, biology, and ecology. Striations are thus of general scientific interest. This paper reviews experimental and theoretical research on striations published for the most part over the past decade and thus after the 1968 publication of the reviews by Nedospasov, Pekarek, and Oleson and Cooper. New and more comprehensive scaling laws are used for a systematic description of the regions in which moving and stationary striations exist in inert and molecular gases. From the standpoint of the general theory of oscillations these striations may be thought of as a particular case of a very distinctive wave process with unusual properties. It is thus useful to describe the striations by an oscillation approach involving the methods of wave theory. The kinetic theory of striations has been developed markedly in recent years, but the usefulness of the hydrodynamic theory of striations, modified appropriately, has not yet been exhausted, at least with regard to a qualitative explanation of the experimental properties of striations. The linear and nonlinear hydrodynamic theories for the formation of moving and stationary striations at intermediate and high currents, incorporating such factors as the deviation from a Maxwellian electron distribution function, oscillations in the density of metastable atoms, and wave reflection from boundaries, yield several results: the conditions for the spontaneous excitation of striations, the shape of the striations, an explanation for the existence of a striation-free region, an explanation for the excitation of one or several types of striations, confirmation of Novak's rule stating that the potential drop over the length of a striation remains constant, etc. The nonlinearity of the system proves important in the study of such questions as the asynchronous suppression of striations and the excitation of stationary striations in inert and molecular gases.

Electron impact excitation of helium-like ions

Distorted wave calculations of electron impact excitation of the 1 1 S→2 1 S , 2 1P transitions in helium-like ions are reported. Collision strengths averaged over a Maxwellian distribution of electrons are calculated for these transitions in the electron temperature range (0.1−25)×10 6 K.

Quasi-Linear Dynamics of a Hot Maxwellian Electron Distribution Released from a Localized Region in a Homogeneous Plasma

To investigate by numerical analysis the transition towards the asymptotic regime postulated by Ryutov and Sagdeev (1970) in their study of the expansion of a hot electron cloud through a plasma, a physically consistent system of one-dimensional quasi-linear equations has been solved on a Cyber 7600. The results obtained for various conditions of injection were all found in qualitative agreement with the simple analytic description of Ryutov and Sagdeev, in spite of the serious deficiencies of their analysis. Although the aims and techniques of the present study are quite distinct from published numerical works by Takakura and Shibahashi (1976) and Magelssen (1976), all the results point towards the same conclusion: plasmon emission, due to advective instability at the front of the electronic disturbance, is followed by strong reabsorption through a reverse advective process at the rear. In the present note, only the case of a localized hot electronic distribution (initially Maxwellian with Te = 108 K) is considered. The effect of plasmon-plasmon scattering, which can also be included in the programmes, is mentioned in the conclusion.

Study on voltage contrast in SEM

Voltage contrast in the SEM is a contactless technique for the study of potentials and potential distributions. Its applications include the examination of static and dynamic voltage signals on semiconductor devices, the direct observation of grain boundaries on polycrystalline semiconductors, and the detection of acoustic wave signals on a piezoelectric material. The quality of a recorded micrograph and the minimum detectable voltage are both limited by the noise level associated with the electron–beam and the detector system. In general, the electron–beam current must be increased to apoint at which the noise level in the collected signal is acceptable. A relationship between the minimum detectable voltage and the beam current has been established for any specific recording condition. The theory assumes a Maxwellian energy distribution of the secondary electrons. Furthermore, the collector system is assumed to act like a simple energy filter which accepts only secondary electrons having an energy higher than Ef. The theoretical results also indicate that the highest detection sensitivity can be achieved when the collector system is designed so tht Ef is around 2.6 eV for an ’’average’’ metal. A relationship between the electron beam current and the expanded SNR caused by a voltage difference has been obtained experimentally. There was a satisfactory agreement between theoretical predictions and experimental results. The experiment was conducted in an SEM which is equipped with a standard scintillator–photomultiplier detector.

Observation of Beam-Induced Currents in a Toroidal Plasma

We report the observation of a reverse electron current excited when fast ions are trapped in a toroidal plasma. The induced electron current was measured in the Culham superconducting Levitron as a function of electron temperature and found to be larger than that predicted assuming a shifted Maxwellian electron distribution.

Anisotropy of Electrons in a Turbulently Heated Plasma

The observed anisotropy of hot electrons in a turbulently heated plasma is consistent with a Maxwellian electron distribution shifted in the direction of the applied electric field.

Moment-generated radiative-transfer functions for relativistic Maxwellian electrons

Coupling the relativistic expressions for various momentum moments of Maxwellian electron distributions to an invariant representation of Compton photon scattering permits fast and accurate approximations of the effective transfer kernels appearing in the photon transport equation. The method is detailed, earlier approaches are discussed, and numerical results and comparisons are presented.

Electron Cyclotron Harmonic Waves Excited in a Helical Electron Beam-Plasma System

The instabilities of electron cyclotron harmonic waves due to the anisotropy of the electron velocity distribution produced by the injection of the electron beam perpendicular to the magnetic field. A strong spontaneous emission growing up 60 dB above background noise appears near the electron cyclotron harmonics. This instability cannot be launched or sychronized by external modulation. The amplitude is usually not steady in time, but switches off and on in time intervals of 10∼100 µsec. It grows exponentially in time initially, saturates and disappears. This instability can be explained by dispersion relations of electron cyclotron harmonic waves propagating perpendicular to the magnetic field in a plasma with a mixture of ring and Maxwellian electron distributions. The measured growth rate is smaller by 2 to 5 times than the theoretical ones.

Electron temperature and Zeff measurements in the hot plasma of TFR by soft-X-ray analysis

A hot plasma can be analysed by means of soft-X-ray fluxes using various absorbers. In the first part of the paper, the method of calculation of the flux as a function of Te, Zeff, ne and their profiles is given. The problem of relativistic corrections in the evaluation of the Gaunt factor is also considered. As an example, in a 200-kA discharge in TFR, the measured fluxes are compared to those calculated for a Maxwellian electron distribution function. From this comparison, the electron temperature is determined and information on the impurity content in the plasma is obtained, in agreement with other independent measurements.

Thomson scattering measurements from a current carrying plasma and the determination of local current density in a Tokamak (T.T.F.2)

Measurements of Thomson scattering in a Tokamak with a component of the scattering vector k along the current direction, give scattered spectra with a red or a blue shift according to the direction of the current. Assuming a displaced Maxwellian electron distribution function it has been possible to determine the local electron drift velocity and hence the local current density. An increase in time of current density on axis, followed by a sudden decrease has been observed: this is probably due to the relaxation following a thermal instability.

Relativistic Compton scattering from a relativistic maxwellian distribution of electrons

Using an earlier developed relativistic differential cross section formula for Compton scattering of photons from a given momentum distribution of electrons, an expression for the differential cross section is derived for the case of a relativistic Boltzmann distribution.

The Influence of Deviations from the Maxwellian Electron Distribution on the Population densities in a low Temperature Monatomic Plasma

Abstract A selfconsistent solution with respect to both free and bound electron energy states is presented for a low temperature monatomic plasma. The deviations from a Maxwellian electron distribution under the action of unbalanced resonance transitions of the plasma atoms are incorporated in analytical form using a recursion formula, which links the high energy tail of the electron distribution function to its low energy part. The unbalance of the resonance level may be due to diffusion processes and/or radiation escape, which reflect the influence of the plasma boundaries. The population densities of the bound electron energy states are numerically determined by an iteration procedure. The calculations were performed for a cesium plasma both without and with consideration of resonance level diffusion and ambipolar diffusion. As is to be expected, the effect of a disturbance of the electron distribution on the population densities increases with decreasing electron density and increasing electron temperature.

Damping and saturation of electron plasma wave echoes

A description is given of theoretical and experimental work on the damping of a second−order electron plasma wave echo due to velocity space diffusion in a low temperature magnetoplasma. Sufficient precision was obtained to verify the theoretically predicted cubic rather than quadratic or quartic dependence of the damping on exciter separation. Compared with the damping predicted for Coulomb collisions in a thermal plasma in an infinite magnetic field, the magnitude of the damping was approximately as predicted, while the velocity dependence of the damping was weaker than predicted. The discrepancy is consistent with the actual non−Maxwellian electron distribution of the plasma. In conjunction with the damping work, echo amplitude saturation was measured as a function of the velocity of the electrons contributing to the echo. Good agreement was obtained with the predicted J1 Bessel function amplitude dependence, as well as a demonstration that saturation did not influence the damping results.

Electron vibrational energy transfer under MHD combustion generator conditions

An analysis of the energy transfer rate between an electron gas and the vibrational modes of diatomic gases has been made. The electron vibrational energy transfer rate may be characterized by δ v , the electron vibrational energy loss factor. For MHD combustion generator conditions, the electron vibrational energy transfer rate dominates and δ v is approximately equal to δ, the total electron energy loss factor. Detailed numerical predictions have been obtained for N 2 and CO. These results indicate that the energy transfer rate is strongly dependent upon the electron velocity distribution function. In particular, for a Maxwellian electron distribution function (which prevails in MHD combustion generators) δ v has been found to exceed published experimental values of δ by a factor as large as 50 for N 2. Consideration of the conditions under which the experimental values of δ were obtained shows that the electron distribution function was non-Maxwellian. An analytical re-determination of δ v and δ, using appropriate non-Maxwellian distribution functions, resolves the discrepancy between the calculated values of δ v and the measured values of δ.

Relativistic Compton Scattering by the Discrete Ordinates Method

This research effort determined how to numerically represent the scattering kernel for x-ray scattering from a relativistic Maxwellian distribution of electrons in a multigroup discrete Sn treatmen...

On the possibility of amplification of acoustic waves in the presence of plasma oscillations in strong electric fields in semiconductors Karnatak University, Dharwar, Mysore State

AbstractA kinetic method is developed of the acoustic wave amplification in a strong electric field in semiconductors with a simple parabolic band. A displaced Maxwellian distribution for electrons is assumed. It is found that the influence of the plasma oscillations on the acoustic wave amplification is significant and in the low electric field region the maximum value of the amplification factor is identical with the published result. In the strong field region the amplification factor takes a negative value because of the direct electric field term although the drift term may also contribute if the electron drift velocity exceeds the sound velocity.

Compton scattering from a maxwellian distribution of electrons in the discrete S n method

This paper summarizes an effort which calculated group-averaged Legendre coefficients to numerically represent the scattering kernel for X-ray scattering from a relativistic Maxwellian distribution of electrons in a multigroup discrete S n treatment of the equation of radiative transfer. An ordinary four-term Legendre polynomial expansion of the scattering kernel was used in the study. Ten sets of 134-group-averaged Wien weighted equilibrium cross section coefficients were calculated for electron temperatures between 0.5 and 20 keV, with photon energies between 0.05 and 400 keV. The first Legendre coefficients satisfy conservation and detailed balance at equilibrium neglecting induced effects. These 134-group cross sections can be collapsed to any desired few-group cross-section sets using any appropriate weighting function and are suitable for use in X-ray transport studies using a discrete S n transport code.

The Solar Flare Plasma: Observation and Interpretation

AbstractIn the past several years, X-ray observations of the Sun made from rockets and satellites have demonstrated the existence of high temperature (~20 × 106 – ~100 × 106 K), low density plasmas associated with solar flare phenomena. In the hard X-ray range (λ≲ 1 Å), spectra of the flaring plasma have been obtained using proportional and scintillation counter detectors. It is possible from these data to determine the evolution of the hard X-ray flare spectrum as the burst progresses; and by assuming either a non-thermal or thermal (Maxwellian) electron distribution function, characteristic plasma parameters such as emission measure and temperature (for a thermal interpretation) can be determined. Thermal interpretations of hard X-ray data require temperatures of ~100 × 106 K.Incontrasi, the soft X-ray flare spectrum (1 Å<λ<30Å) exhibits line emission from hydrogenlike and helium-like ions, e.g. Ne, Mg, Al, Si, … Fe, that indicates electron energies more characteristic of temperatures of ~20 × 106 K. Furthermore, line intensity ratios obtained during the course of an event show that the flare plasma can only be described satisfactorily by assuming a source composed of several different temperature regions; and that the emission measures and temperatures of these regions appear to change as the flare evolves. Temperatures are determined from line ratios of hydrogen-like to helium-like ions for a number of different elements, e.g., S, Si, and Mg, and from the slope of the X-ray continuum which is assumed to be due to free-free and free-bound emission. There is no obvious indication in soft X-ray flare spectra of non-thermal processes, although accurate continuum measurements are difficult with the data obtained to date because of higher order diffraction effects due to the use of crystal spectrometers.Soft X-ray flare spectra also show satellite lines of the hydrogen-like and helium-like ions, notably the 1s22s2S-1s2s2p2P transition of the lithium-like ion, and support the contention that in low density plasmas these lines are formed by dielectronic recombination to the helium-like ion. Also, series of allowed transitions of hydrogen-like and helium-like ions are strong, e.g., the Lyman series of S up to Lyman-ε, and ratios of the higher member lines to the Lyman-α line can be compared with theoretical calculations of the relative line strengths obtained by assuming various processes of line formation.This review will discuss the X-ray spectrum of solar flares from ~250 keV to ~0.4 keV, but will be primarily concerned with the soft X-ray spectrum and the interpretation of emission lines and continuum features that lie in this spectral range.