Maxwellian Electron Distribution Research Articles

Obliquely propagating ion-acoustic double layers in a multicomponent magnetized plasma

Considering the appropriate coordinate transformation and charge separation effect, the reductive perturbation method is used to derive a mKdV equation for a multi-component magnetized plasma having two Maxwellian electron distributions and two warm adiabatic ion distributions. The double layer solution of the mKdV equation is discussed in detail. It is found that the width of the double layer increases as we increase the obliqueness θ, where θ is the angle between wave vector and magnetic field, while the effect of obliqueness on the amplitude of the double layer is negligible. The effect of finite ion temperature is to increase (decrease) the amplitude of compressive (rarefactive) double layer and decrease (increase) its width. The effect of the concentration of second ion impurity, concentration and the temperature ratios of two electron species on the amplitude and width of the double layer is also studied.

The plasma-sheath boundary with fast monoenergetic electrons

The behaviour of the plasma-sheath boundary in the presence of monoenergetic electrons is examined theoretically. A Tonks-Langmuir type model is used to investigate the nature of the quasineutral solution for a plasma containing a Maxwellian bulk electron distribution along with an independent source of high-energy monoenergetic electrons. Results indicate that the presence of fast monoenergetic electrons leads to a larger variation of the space potential across the plasma. In addition, it is found that quasineutrality does not break down when the density of monoenergetic electrons in the remote plasma exceeds a critical value (28.5% of the bulk plasma density).

Thomson scattering diagnostic for the microwave tokamak experiment

The Thomson scattering diagnostic system (TSS) on the microwave tokamak experiment (MTX) at LLNL routinely monitors electron temperature (Te) and density. Typical measured values at the plasma center under clean conditions are 900±70 eV and 1–2×1014 (±30%) cm−3. The TSS apparatus is compact, with all elements mounted on one sturdy, two-level optics table. Because of this, we maintain with minimum effort the alignment of both the ruby-laser input optics and the scattered-light collecting optics. Undesired background signals, e.g., plasma light as well as ruby-laser light scattered off obstacles and walls, are generally small compared with the Thomson-scattered signals we normally detect. In the MTX Te region, the TSS data are definitely fitted better when relativistic effects are included in the equations. Besides determining the temperature of the Maxwellian electron distribution, the system is designed to detect electron heating from GW-level free-electron laser (FEL) pulses by measuring large wavelength shifts of the scattered laser photons. TSS data suggest that we may indeed be able to detect these electrons, which can have energies up to 10 keV, according to computer simulation.

A computer program for the free-free and bound-free Gaunt factors of Rydberg systems

A computer code for the calculation of the quantum mechanical free-free and bound-free Gaunt factors of Rydberg system is described. FORTRAN sources are given which are numerically stable for a wide range of photon and electron energies. Temperature averaged values of the free-free Gaunt factors are also computed for a Maxwellian electron distribution.

The collision term for collisional ionization and three-body recombination

The collision term of the electron distribution function for collisional ionization and three-body recombination is derived in terms of transition functions that specify explicitly the velocities of the three electrons involved in these inelastic processes. Making the simplifying assumption that after an ionization collision all allowed energies and all directions of the two outgoing electrons are equally probable, an approximate collision term is obtained in terms of the total cross section for collisional ionization. The special case of a Maxwellian electron distribution function serves as a test for this collision term and is considered in detail.

Electron impact excitation of neon-like S VII from its ground state

The R-matrix method is used to obtain electron impact collision strengths for various transitions from the ground state of neon-like S VII. The calculation includes the first fifteen target eigenstates in the R-matrix expansion of the total wavefunction. Effective collision strengths are given for electron temperature in the range (5*104-106 K) by assuming a Maxwellian electron velocity distribution for the incident electrons.

An R-matrix calculation of the electron impact excitation of the fine-structure levels in neon-like selenium (Se XXV)

The authors present calculations based on the R-matrix method for electron impact excitation of Ne-like selenium. In these elaborate calculations, the 27 fine-structure levels arising from the four lowest configurations 2s22p6, 2s22p53s, 2s22p53p and 2s22p53d are included. Terms of the Breit-Pauli Hamiltonian are explicitly included in determining both the target and the scattering wavefunction. All target levels included in the calculations are represented by configuration interaction wavefunctions using the 1s, 2s, 2p 3s, 3p and 3d orbitals. The collision strengths are compared with previous theoretical results. For many transitions they found complicated resonance structures in the excitation cross sections. The excitation cross sections are integrated over a Maxwellian distribution of electron energies to give electron excitation rate coefficients; the rates for transitions from the ground state to each fine-structure level are tabulated and are compared with results from distorted-wave calculations. At low temperatures (Tc=500 eV) some of their rates are six times larger than earlier calculations. They also present estimates of the relative populations of the (2p53p)1D2 and 1S0 levels of Se XXV at Tc=1000 eV and at various electron densities.

Electron-impact excitation of Ti XIV from its ground state using R-matrix method

The R-matrix method is used to calculate electron impact collision strengths for various transitions in Ti XIV from its ground state (2P°). Extensive configuration interaction wavefunctions are used to represent the lowest twelve target states which are included in the calculations. Finally effective collision strengths have been calculated for electron temperature in the range (5 × 104-106K) by assuming a Maxwellian electron velocity distribution of the incident electrons.

Magnetic surfaces and striations during pellet ablation

At present, the striations observed on the Hα or Hβ emission signal of ablated pellets are not well understood. An attractive explanation of these striations would be a limitation of the ablation process due to the smaller amount of energy available on resonant magnetic surfaces. To evaluate the ability of the latter to produce the observed features, a model has been developed which takes into account the Maxwellian distribution of electrons, the proportion of trapped particles, the geometric effects linked with the shear and the finite lifetime of the filaments. In tokamaks, it is found that this model is unable to reproduce the observed striations for smooth q-profiles but that the general shape of the Hα (or Hβ) signal can be fitted by introducing local flattenings (e.g. small magnetic islands) around resonant surfaces. In low shear stellarators, striations (rather shallow) due to rational q-values can exist in the absence of magnetic islands, but only if a suprathermal electron tail is present.

Electron-impact excitation of Mg IV using the R-matrix method

The R-matrix method is used to calculate electron impact collision strengths for transitions in Mg IV from its ground state (2Po) to the eleven lowest excited states. Configuration interaction wavefunctions are used to represent the twelve target states which are included in the calculation. The effect of resonances converging onto these excited states is included in the calculations. Finally, collision rates have been calculated from the ground state to the excited states by assuming a Maxwellian electron distribution for the incident electrons. These are tabulated over a wide temperature range. This is the first detailed calculation for this ion in which the effects of exchange, channel couplings and short-range correlations are properly taken into account.

Generalized adiabatic theory applied to the magnetotail current sheet

We use the generalized first adiabatic invariant, an extension of the magnetic moment for regions of large field gradients, to treat particles in the magnetotail current sheet. The equations of motion can be expressed in terms of drift parameters which vary slowly and smoothly at the drift rate, not at the gyration rate. The analysis leads to boundaries in phase space which form a generalized loss cone and separate particles drifting into and out of the layer from particles trapped within the layer. These boundaries can be used in the moment integrals for densities and currents when the drifting particles differ in temperature, or in other properties, from the trapped population, as has been suggested by observations. We give examples of how different kinds of particle orbits contribute to the spatial profiles of density and current and thus to the field structure of the current sheet. We find that the parallel pressure of the drifting particles must exceed the transverse pressure for self-consistent solutions to exist, and based on this result, we give examples of fully self-consistent solutions using bi-Maxwellian ion and Maxwellian electron distributions. We give a proof, using generalized adiabatic theory, of Cowley's (1978a) theorem that particles trapped in the current layer experience zero net drift.

Generation of an electromagnetic field by photoemission of electrons from the surface of conducting targets into a plasma

The problem of finding steady-state fields generated by steady-state emission from the surface of planar targets into a plasma with given (unperturbed) parameters is solved. Analytic expressions are derived for the steady-state field and the dipole moment per unit area of a double layer for the case of a Maxwellian velocity distribution of the emitted electrons and an emission temperature equal to that of the unperturbed plasma. A comparison is made with the solution for emission into a vacuum.

Dielectronic-recombination rate coefficients of hydrogenlike ions in high-temperature low-density plasmas.

Dielectronic-recombination rate coefficients of selected hydrogenlike ions (Z=10, 14, 18, 20, 22, 26, and 28) have been calculated at various plasma temperatures (${\mathrm{kT}}_{e}$=0.6--10 keV) using the Hartree-Fock-Slater atomic model and assuming a Maxwellian velocity distribution for the free electrons. The effects of configuration interaction and spin-orbit coupling are included in all intermediate resonance states \ensuremath{\Vert}2lnl'SLJ〉 for n\ensuremath{\le}4. Configuration average rates have been used to calculate dielectronic-recombination rate coefficients for n=5--8, and 1/${n}^{3}$ scaling law for all higher-lying states. The results from the present calculations are compared with available theoretical and experimental values of dielectronic-recombination rate coefficients.

An analytical solution of a collisional-radiative model for nonequilibrium argon plasmas

The general analytical solution of a collisional-radiative model, including atom–atom inelastic collisions, for nonequilibrium, partially ionized, steady-state plasmas is presented. This is applied to argon plasmas and the results are compared with previous numerical calculations. The model includes three atomic energy levels; the ground level, one excited level, and continuum, and assumes a Maxwellian electron and atom distribution functions. All rates for collisional and radiative processes are expressed as analytical functions. The model is solved algebraically to obtain analytical expressions for the electron and excited atom densities as a function of the plasma parameters. In the limit of an optically thick plasma the solution agrees with results for complete thermodynamic equilibrium. Solutions are presented for a wide range of conditions (3000≤Te≤24 000 K, 105≤Ne≤NA cm−3, 1014≤NA≤1018 cm−3).

Quasilinear heating of electrons in the earth's plasmasphere

In the framework of a quasilinear theory we examine the interaction between thermal electrons and ion-cyclotron waves (ICW) in the outer plasmasphere of the earth. For this type of ‘wave-particle’ interaction, a simplification of the quasilinear diffusion integral in a magneto-active plasma under plasmaspheric conditions is given. Under the assumption of a Maxwellian distribution of electrons we have calculated the collision frequency and the heating source as the electrons are scattered by ICW. The obtained values of intrinsic parameters of the outer plasmasphere may exceed greatly, accordingly, the Coulomb frequency of collisions and the heating source due to suprathermal electrons. ICW-heating causes the ionosphereward thermal flux to increase, and this must lead to an increase in electron temperature in lower-lying plasmaspheric regions and in the subauroral ionosphere. A quantitative estimation of the electron temperature for the ‘hot zone’, made in this paper, is consistent with available experimental data.

Electron impact excitation of Fe XVIII from its ground state

The R-matrix method is used to calculate electron impact collision strengths for transitions in fluorine-like Fe XVIII from its ground 2PO state. All states of the form 2p5, 2s2p6, 2p43l are included as target states and are represented by configuration interaction wavefunctions constructed in LS coupling. Effective collision strengths are calculated for transitions between the fine-structure levels of the ground state and those of the excited states by employing a transformation of the LS-coupled reactance matrices using term coupling coefficients, and by assuming a Maxwellian velocity distribution for the incident electrons.

Electron impact excitation of S VIII from its ground state

The R-matrix method is used to calculate electron-impact collision strengths for transitions in S VIII from its ground state (2Po). Configuration interaction wavefunctions are used to represent the twelve target states which are included in the calculation. Finally, the effective collision strengths have been calculated for electron temperatures in the range 5*104-106 K by assuming a Maxwellian electron velocity distribution for the incident electrons. This is the first detailed calculation for this ion in which the effects of exchange, channel couplings and short-range correlation are properly taken into account.

Electron-impact excitation of He-like ions: Mg XI.

The collision strengths for the electron-impact excitation of inelastic transitions in Mg xi have been calculated by use of the R-matrix method. Eleven lowest LS target states 1${s}^{2}$ ${}^{1}$S, 1s2s ${}^{1}$,3S, 1s2p ${}^{1}$,3P\ifmmode^\circ\else\textdegree\fi{}, 1s3s ${\mathrm{}}^{1}$,3S, 1s3p ${\mathrm{}}^{1}$,3P\ifmmode^\circ\else\textdegree\fi{}, and 1s3d ${\mathrm{}}^{1}$,3D are included in the expansion of the total wave function. These target states are represented by accurate configuration-interaction wave functions. The lower partial-wave (L\ensuremath{\le}8) results obtained in the R-matrix method are supplemented by higher partial waves obtained in the close coupling with exchange terms omitted (L=9\char21{}15), Coulomb-Born (L=16\char21{}36), and Coulomb-Bethe (Lg36) approximations. Rydberg series of resonances converging to n=2 and 3 thresholds are considered in the calculations. Results are obtained over a wide electron energy range (97.66\char21{}350.0 Ry) and are compared, where possible, with the previously available five-state Coulomb-exchange distorted-wave approximation results of Bednell. These collision strengths are then integrated with the assumption of a Maxwellian distribution of electron energies to obtain effective collision strengths for temperatures between ${10}^{5}$ and 4\ifmmode\times\else\texttimes\fi{}${10}^{7}$ K.

Cyclotron emission from white dwarf accretion columns

We calculate the cyclotron absorption coefficient for a Maxwellian velocity distribution of electrons over a wide range of temperatures and frequencies following the method described by Chanmugam. These results are used to determine the range of parameters for a white dwarf accretion column in which a simple steady-state bombardment solution can be found, where the dominant radiative-loss mechanism is optically thick cyclotron radiation. We show that for an acceptable choice of accretion parameters a bombardment solution exists with a temperature ~10 keV, somewhat lower than the shock temperature Ts≃30 keV. We also demonstrate that for parameters for which a simple bombardment model is not valid, the electron temperature (and therefore the observed temperature) will never reach the shock temperature. This leads to a lower hard/soft X-ray ratio than that obtained from the adiabatic shock model – and could thus ease the soft X-ray problem associated with AM Herculis stars.

Time-resolved measurements of nonthermal x-ray emission of Ti

The observation of heliumlike titanium spectra with 20 ms temporal resolution during high-power injection of electron cyclotron heating (ECH) of up to 250 ms pulse length into the Doublet III tokamak is reported. The prominent lines in the spectra and the observed dielectronic satellite lines from the autoionizing lithiumlike ionization states are given. The intensity of the resonance line 1s2 1S0 - 1s 2p 1P1 is found to be extremely sensitive to the ECH power. Time-resolved line ratios are also presented. It is concluded that a significant departure from a Maxwellian distribution of electrons exists in the present ECH plasmas.