Perturber Number Density Research Articles

The propagation of ion-acoustic waves carrying orbital angular momentum in the electron–positron–ion plasmas

Ion-acoustic (IA) waves carrying orbital angular momentum (OAM) are investigated in an unmagnetized, uniform, and collisionless electron–positron–ion (e–p–i) plasma system. Employing the hydrodynamic theory, the paraxial equation in term of ion perturbed number density is derived and discussed about its Laguerre–Gaussian (LG) beam solutions. Obtaining an approximate solution for the electrostatic potential, the IA wave characteristics including helical electric field structure, energy density, and OAM density are theoretically studied. Based on the numerical analysis, the effects of positron concentration, radial and angular mode number as well as beam waist on the obtained potential profile are investigated. It is shown that the depth (height) and width of the LG potential profile wells (barriers) are considerably modify by the variation of positron concentration.

Multi-symplectic scheme for the coupled Schrödinger—Boussinesq equations

In this paper, a multi-symplectic Hamiltonian formulation is presented for the coupled Schrödinger—Boussinesq equations (CSBE). Then, a multi-symplectic scheme of the CSBE is derived. The discrete conservation laws of the Langmuir plasmon number and total perturbed number density are also proved. Numerical experiments show that the multi-symplectic scheme simulates the solitary waves for a long time, and preserves the conservation laws well.

Temperature effects on the perturber induced shift of dopant ionization energies in He and Ne

In this Letter, temperature effects on the perturber induced shift Δ D ( ρ P ) [ ρ P ≡ perturber number density ] of the dopant ionization energy in the repulsive gases Ne and He are investigated at low to medium perturber number densities (i.e., ρ P ⩽ 6.0 × 10 21 cm - 3 ). We show that these effects arise from changes in the ensemble averaged dopant/perturber polarization energy rather than from changes in the energy of the quasi-free electron.

A pressure measurement method for high‐temperature rock vapor plumes using atomic line broadening

Knowledge of pressure conditions is essential in understanding phase changes and chemical reactions. Although several methods have been proposed for the measurement of pressure in impact‐induced vapor plumes, they are somewhat unreliable. In this study, we developed a pressure measurement method for vapor clouds based on spectral line broadening. Under the nearest neighbor approximation, it is possible to analytically express the full width at half maximum as a function of the perturber number density. On the basis of these relations and spectroscopic constants of atomic emission lines of Fe I at 381.58 nm and Ca I at 646.26 nm, quadratic Stark broadening is the dominant broadening mechanism if the degree of ionization exceeds 1%. Resonance broadening and van der Waals broadening should be considered if the degree of ionization is less than 1%. Taking into account the appropriate broadening mechanisms, it is possible to accurately measure the pressure in vapor clouds. We conducted laser ablation experiments using the proposed pressure measurement method in combination with the Boltzmann plot method for temperature. The obtained pressures and temperatures are consistent with an adiabatic expansion. This strongly suggests that the proposed method can measure pressure of vapor clouds accurately. Because thermodynamic quantities can be determined when both pressure and temperature are known, the proposed method enables a complete thermodynamic description of vapor clouds, thereby serving as a powerful tool in investigating the thermodynamic and chemical properties of impact‐ and laser‐induced vapor clouds.

Energy of the excess electron in methane and ethane near the critical point

Field ionization measurements of trimethylamine in methane and triethylamine in ethane are presented as a function of perturber number density at various noncritical temperatures and near the perturber critical isotherm. Critical point effects are observed that are similar to those seen in atomic fluids. A two-Yukawa potential is shown to model the perturber/perturber interactions accurately by calculating the phase diagram of the perturber fluids, and using this potential the local Wigner–Seitz model for the energy of the excess electron is successfully applied to these molecular systems.

Unified Impact Theory for Velocity-Changing Effects and Speed Dependencies in Neutral Species Lineshapes

A dipole correlation function which incorporates velocity-changing (motional narrowing) effects and the effects of speed-dependent Lorentz relaxation rates into otherwise Voigt profile correlation functions is developed, based partly upon previous work by the author. For the first time simple closed expressions, which lend themselves to elementary calculation beginning only with the relevant parts of intermolecular interaction energies, are developed for the cubic time-dependent term within the exponent describing the decay of the correlation function. This term is of first order in perturber number density, as are the Lorentz parameters, and is complex, thereby allowing for narrowing, changing in shape and asymmetry in the line profile. “Soft” and “hard” collisions play no explicit role, though both are variously present for each line. Quartic time dependencies are also discussed, though they are thought to be negligible in nonhydrogen molecular spectroscopy. Finally, some comments are added about a relevant technique for hydrogen spectra.

CH3I low-n Rydberg states in supercritical atomic fluids near the critical point

Vacuum ultraviolet photoabsorption spectra of CH3I 6s and 6s′ Rydberg states doped into supercritical argon, krypton, and xenon perturbers were measured from low density to the density of the triple point liquid at noncritical temperatures and on an isotherm near the perturber critical temperature. A full line shape analysis of these spectra was performed using a single set of intermolecular potential parameters for each dopant/perturber system. The resulting perturber induced shift of the simulated adiabatic transition of the 6s and 6s′ Rydberg states is presented as a function of perturber number density, and this shift illustrates a perturber critical point effect on the excitation energies of the molecular low-n Rydberg states.

Energy of the quasi-free electron in argon, krypton and xenon

Recent field ionization measurements of various high- n molecular Rydberg states doped into argon, krypton and xenon perturbers are presented as a function of perturber number density up to the density of the triple point liquid. These data are modeled to within ± 0.3 % of experiment on both critical and noncritical isotherms using a new theoretical treatment that includes: (i) the polarization of the perturber by the dopant cation, (ii) the polarization of the perturber by the quasi-free electron that arises from field ionization of the dopant, and (iii) the kinetic energy of the quasi-free electron. The polarization terms are determined by a standard statistical mechanical treatment. However, the kinetic energy of the quasi-free electron is calculated within a new local Wigner–Seitz model that contains only one adjustable parameter. This treatment provides an accurate model of the energy of the bottom of the conduction band ( V 0 ) in argon, krypton and xenon from the dilute gas up to the density of the triple point liquid, on both critical and noncritical isotherms.

Energy of the quasifree electron in argon and krypton

Field ionization measurements of ${\mathrm{CH}}_{3}\mathrm{I}$ and ${\mathrm{C}}_{2}{\mathrm{H}}_{5}\mathrm{I}$ dopant high-$n$ molecular Rydberg states in argon and krypton perturbers are presented as a function of perturber number density along various isotherms up to the density of the triple point liquid. Using these data, a new local Wigner-Seitz model for the density-dependent energy ${V}_{0}({\ensuremath{\rho}}_{\mathrm{P}})$ of a quasifree electron in argon and krypton is developed. This model, which contains only one adjustable parameter, uses a local Wigner-Seitz radius derived from the local number density rather than from the bulk number density, includes a statistical mechanical calculation of both the ion/medium polarization energy and the electron/medium polarization energy, and includes the thermal kinetic energy of the quasifree electron. Using this model, ${V}_{0}({\ensuremath{\rho}}_{\mathrm{P}})$ and the perturber-induced energy shift of the dopant ionization potential ${\ensuremath{\Delta}}_{\mathrm{D}}({\ensuremath{\rho}}_{\mathrm{P}})$ are calculated to within $\ifmmode\pm\else\textpm\fi{}0.1%$ of experiment. Previously reported ${V}_{0}({\ensuremath{\rho}}_{\mathrm{P}})$ data for xenon are also shown to be interpretable within this new model.

Photoionization spectra ofCH3I and C2H5I perturbed byCF4 and c-C4F8: electron scattering in halocarbon gases

Photoionization spectra of CH3I and C2H5I doped into perturberhalocarbon gases CF4 (up to a perturber number density of 6.1×1020 cm-3) and c-C4F8 (up to a perturber numberdensity of2.42×1019 cm-3) disclosed a redshift of the dopantautoionizingfeatures that depends linearly on the perturber number density. In the caseof CF4, which is transparent in the spectral region of interest, thisredshift was verified from the dopant photoabsorption features as well.From the perturber-induced energy shifts of the dopant Rydberg states andionization energies, the zero-kinetic-energy electron scattering lengthsfor CF4 and c-C4F8 were found to be -0.180±0.003 nm and-0.618±0.012 nm, respectively. To the best of our knowledge, theseare thefirst measurements of zero-kinetic-energy electron scattering lengthsfor both CF4 and c-C4F8. From these zero-kinetic-energyelectron scattering lengths, we find that the zero-kinetic-energy electronscattering cross sections are σ = 4.1±0.2×10-15 cm2 and 4.8±0.2×10-14 cm2 forCF4 and c-C4F8, respectively.

Pressure studies of subthreshold photoionization: CH 3I perturbed by CF 4 and c-C 4F 8

Subthreshold photoionization spectra of CH 3I perturbed by CF 4 and c-C 4F 8 for variable CH 3I number density ρ CH 3I and perturber number density ρ P are presented. The ρ CH 3I and ρ P dependence of the subthreshold structure is discussed in terms of the excited-state processes of electron attachment and associative ionization. The effective rate constants for these processes are determined from the variation in the subthreshold photocurrent as a function of ρ CH 3I and ρ P. These constants are then analyzed with respect to the properties of the excited CH 3I Rydberg state. The variation in the effective rate constants is discussed in terms of ground-state perturber properties.

Pressure studies of subthreshold photoionization: CH 3I, C 2H 5I and C 6H 6 perturbed by Ar and SF 6

Subthreshold photoionization spectra of CH 3I doped into Ar and SF 6, and C 2H 5I and C 6H 6 doped into SF 6, are reported for variations in both the dopant number density ρ D and perturber number density ρ P. The ρ D and ρ P dependence of the subthreshold structure is discussed in terms of the excited state processes of electron attachment and associative ionization. The variation in the subthreshold photocurrent as a function of ρ D and ρ P leads to the determination of the effective rate constants for these processes. These constants are then analyzed with respect to the properties of the excited dopant Rydberg state. For CH 3I, the variations in the effective rate constants are discussed in terms of ground-state dopant and perturber properties.

Photoionization spectra of CH 3I perturbed by SF 6: electron scattering in SF 6 gas

A photoionization study of CH 3I in the presence of SF 6 perturbers (up to the perturber density 9.75×10 19 cm −3) disclosed a red shift of autoionizing features that depends linearly on the perturber number density. From the perturber induced energy shifts of the CH 3I nd′ Rydbergs ( n=9, 10, 11, 12), the electron scattering length of SF 6 was found to be A=−0.484 nm, which accords with previously reported (but less precise) cross-section data. An assessment is made of the validity of the impact approximation used in the data analysis presented here.

Consequences of particle conservation along a flux surface for magnetotail tearing

The energy principle for magnetotail tearing is reexamined using conservation of electron particle number along a flux surface as a means of calculating the volume‐integrated perturbed number density 〈 n1 〉, where n1 is the perturbed electron number density and the angle brackets denote integration along a field line. It is shown that if the electron response is magnetohydrodynamic, then 〈 n1 〉 can be calculated as a function of the perturbation vector potential component A1y (assuming magnetotail coordinates) independent of the potential components A1x and A1z and independent of the scalar potential ϕ. This result holds as long as the equilibrium and the tearing perturbations are two‐dimensional, independent of the y coordinate. In the case of a parabolic field model, the resulting 〈 n1 〉 exactly matches the results obtained previously by Lembége and Pellat [1982], who used the kinetic drift equation to calculate the electron response. Thus the compressional stabilization of the tearing mode is a direct consequence of, and can be completely calculated from, the conservation of electron particle number along the field line. Further, it is shown that 〈 n1 〉 is independent of By, the guide component of the magnetic field, so the inclusion of a guide field does not alter the tearing stabilization condition.

Pressure shifts and electron scattering lengths in atomic and molecular gases

Photoabsorption or photoionization spectra of CH3I are discussed as a function of perturber pressure for 11 different binary gas mixtures consisting of CH3I and each one of 11 different gaseous perturbers. Five of the perturbers were rare gases and six were nondipolar molecules. The energy shifts of CH3I Rydberg states become independent of n, the principal quantum number, for n≥10. The energy shifts for n≥10 vary in a linear fashion with perturber number density. The electron scattering lengths for the perturbers are extracted from the shifts using Fermi theory in which the polarization term is that of Alekseev and Sobel’man. These scattering lengths are compared with those from swarm and time-of-flight experiments. It is found that the uncorrected shift scattering lengths correspond to the zero energy or near-zero energy scattering lengths obtained from extrapolated swarm and time-of-flight data. It is found that plots of scattering length vs polarizability α (ᾱ for molecules) define two linearities, one for the rare gases and one for molecules, CO2 being an exception to the latter linearity (presumably because of its large quadrupole moment). For a given polarizability, it is also found that molecules exhibit a larger scattering length than the rare gases. These results are discussed and consequences for scattering cross sections are elaborated.

Medium effects on valence and low-n Rydberg states: NO in argon and krypton

Absorption and total fluorescence spectra of NO transitions perturbed by argon and krypton at various densities from the dilute gas to the low temperature solid are reported for photon energies 6≤hν≤9 eV. The valence transitions shift monotonically to lower photon energies with increasing perturber number density. The Rydberg transitions to n=3 (A 2Σ+, C 2Π, D 2Σ+) exhibit a moderate red shift at low perturber densities followed by an increasing blue shift with increasing density. Both valence and Rydberg transition energies vary smoothly and continuously with perturber number density even upon the liquid–solid phase transition. For fluid argon the experimental energy shifts are analyzed employing the semiclassical theory for line broadening.

Density effects on high-n molecular Rydberg states: CH3I in He, Ne, Ar, and Kr.

Absorption studies of the high-n Rydberg states of ${\mathrm{CH}}_{3}$I perturbed by varying number densities of He, Ne, Ar, and Kr (up to 23.0, 24.0, 11.3, and 6.6\ifmmode\times\else\texttimes\fi{}${10}^{20}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$, respectively) are reported. Energy shifts, which increase with increasing perturber number density, are observed and analyzed for both discrete [nd${(}^{2}$${E}_{3/2}$)] and autoionizing [nd'${(}^{2}$${E}_{1/2}$)] states. These shifts vary linearly with the perturber number density for principal quantum numbers n\ensuremath{\ge}10. Moreover, depending upon the nature of the perturber, these shifts are to the blue region (He), slightly to the blue region (or nearly zero) (Ne), or the red region (Ar and Kr). We explain these results quantitatively on the basis of the electron scattering length in the various rare gases, as well as on the polarization of the medium by ${\mathrm{CH}}_{3}$${\mathrm{I}}^{+}$. For low perturber number densities, it is well known that the Fermi model of perturber effects on high-n Rydberg states is invalid. The present experimental results show, for the first time, that this model also fails at high number densities. On the other hand, the energy shifts can be reproduced quantitatively by extending a model developed by Alekseev and Sobel'man to high number densities.

Density effects on high-n molecular Rydberg states: CH3I in argon.

Absorption spectra of the high-n molecular Rydberg states of ${\mathrm{CH}}_{3}$I, perturbed by varying number densities of argon (up to \ensuremath{\sim}11\ifmmode\times\else\texttimes\fi{}${10}^{20}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$), are reported. Red shifts, which increase with increasing argon number density, are observed for both discrete and autoionizing states. These red shifts vary linearly with the perturber number density for principal quantum numbers n\ensuremath{\ge}10. We explain these results quantitatively on the basis of the electron scattering length in argon, as well as the polarization of the medium by ${\mathrm{CH}}_{3}$${\mathrm{I}}^{+}$.

A direct method for modifying certain phase-integral approximations of arbitrary order: Nanny Fröman and Per Olof Fröman. Institute of Theoretical Physics, University of Uppsala, Uppsala, Sweden

Recent field ionization measurements of various high-n molecular Rydberg states doped into argon, krypton and xenon perturbers are presented as a function of perturber number density up to the density of the triple point liquid. These data are modeled to within ±0.3% of experiment on both critical and noncritical isotherms using a new theoretical treatment that includes: (i) the polarization of the perturber by the dopant cation, (ii) the polarization of the perturber by the quasi-free electron that arises from field ionization of the dopant, and (iii) the kinetic energy of the quasi-free electron. The polarization terms are determined by a standard statistical mechanical treatment. However, the kinetic energy of the quasi-free electron is calculated within a new local Wigner–Seitz model that contains only one adjustable parameter. This treatment provides an accurate model of the energy of the bottom of the conduction band (V0) in argon, krypton and xenon from the dilute gas up to the density of the triple point liquid, on both critical and noncritical isotherms.