Separable expansion for off-shell two-body t matrix with Coulomb potential.
Separable expansion for off shell two body t matrix with Coulomb potential to solve nonrelativistic three body problem with two body interactions
Chen, J. C. Y.↗
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Local and global processes which impact solar wind electrons
A detailed first principle kinetic theory for solar wind electrons which is neither fluid not exospheric in nature is presented. The global and local properties of the solar wind expansion and coulomb collisions that are reflected in the observed electron velocity distribution function are: its bifurcation, skewness, and the differential temperatures of the thermal and suprathermal subpopulations. Predictions of correlations amongst electron solar wind parameters which were previously reported are shown.
Scudder, J. D.↗
The microscopic state of the solar wind: Links between composition, velocity distributions, waves and turbulence
An overview is given of the microscopic state of the solar wind with emphasis on recent Ulysses high-latitude observations and previous Helios in-ecliptic observations. The possible links between composition, ionization state. velocity distribution functions of electrons, protons and heavy ions. kinetic plasma waves and MHD-scale turbulence are elaborated. Emphasis is placed on a connection of interplanetary kinetic-scale phenomena with their generating microscopic processes in the corona. The fast streams seem to consist of mesoscale pressure-balanced plasma filaments and magnetic flux tubes, reminiscent of the supergranular-size structures building the open corona, from which copious Alfven waves emanate. The wind from the magnetically structured and active corona shows developed compressive turbulence and considerable abundance and ionization state variations. Some modelling attempts to explain the observed element fractionation are briefly reviewed. The causes of the nonthermal particle features. such as proton-ion differential streaming, ion beams. temperature anisotropies, and skewed distributions associated with collisionless heat conduction, are ultimately to be searched in the fact, that the corona is never quiescent but fundamentally variable in space and time. Consequently, the radial evolution of the internal state of the wind resembles at all latitudes a complicated relaxation process, in the course of which the free (in comparison with LTE conditions) particle kinetic energy is converted into plasma waves and MHD turbulence on a wide range of scales. This leads to intermittent wave-particle interactions and unsteady anomalous transport, mixed with the weak effects of the rare Coulomb collisions. Spherical expansion and large-scale inhomogeneity forces the wind to attain microscopically a complex internal state of dynamic statistical equilibrium.
Marsch, E.↗
Three-body Coulomb systems using generalized angular-momentum S states
An expansion of the three-body Coulomb potential in generalized angular-momentum eigenfunctions developed earlier by one of the authors is used to compute energy eigenvalues and eigenfunctions of bound S states of three-body Coulomb systems. The results for He, H(-), e(-)e(+)e(-), and pmu(-)p are compared with the results of other computational approaches.
Whitten, R. C.↗
The role of Coulomb collisions in limiting differential flow and temperature differences in the solar wind
Data obtained by OGO 5 are used to confirm IMP 6 observations of an inverse dependence of the helium-to-hydrogen temperature ratio in the solar wind on the ratio of solar-wind expansion time to the Coulomb-collision equipartition time. The analysis is then extended to determine the relation of the difference between the hydrogen and helium bulk velocities (the differential flow vector) with the ratio between the solar-wind expansion time and the time required for Coulomb collisions to slow down a beam of ions passing through a plasma. It is found that the magnitude of the differential flow vector varies inversely with the time ratio when the latter is small and approaches zero when it is large. These results are shown to suggest a model of continuous preferential heating and acceleration of helium (or cooling and deceleration of hydrogen), which is cancelled or limited by Coulomb collisions by the time the plasma has reached 1 AU. Since the average dependence of the differential flow vector on the time ratio cannot explain all the systematic variations of the vector observed in corotating high-velocity streams, it is concluded that additional helium acceleration probably occurs on the leading edge of such streams.
Neugebauer, M.↗
Radial evolution of solar wind thermal electron distributions due to expansion and collisions
ISEE 3 electron observations near 1 AU show that the solar wind thermal electron temperature anisotropy, T(parallel)/T(perpendicular), is typically 1.0 to 1.5, with densest distributions most nearly isotropic, but is sometimes much higher when density is low. For a small observational subset characterized by high density and low bulk speed, T(perpendicular) can exceed T(parallel). Based on these and other observations, a simple model is proposed for radial evolution of thermal electrons in a structureless solar wind under the influence of Coulomb collisions and geometric expansion in a spiral interplanetary magnetic field. The model, which satisfactorily explains the 1 AU observations, shows that the evolution of electron temperature and T(parallel)/T(perpendicular) is controlled by plasma density, flow speed, and initial temperature, with density the most important factor. The model makes predictions for radial distances other than 1 AU and for high solar latitudes.
Phillips, J. L.↗
ISEE 3 observations of solar wind thermal electrons with T-perpendicular greater than T-parallel
This study presents ISEE 3 observations of anomalous electron distributions for which T-perpendicular exceeds T-parallel in the solar wind near 1 AU. Twelve anomaly events were identified, lasting from 24 min to 6 hours. These events generally share the following characteristics: (1) high plasma density, (2) low solar wind speed, (3) magnetic field which is nearly transverse to the flow, and (4) low electron and ion temperatures. The processes of solar wind adiabatic expansion and isotropization via Coulomb collisions could be expected to lead to such anomalous anisotropies under conditions similar to those observed. However, these conditions actually produce T-perpendicular greater than T-parallel for only a small fraction of the time, suggesting that other mechanisms are also important in regulating solar wind electron distributions.
Phillips, J. L.↗
Solar wind thermal electrons from 1.15 to 5.34 AU - Ulysses observations
Using unique 3-d velocity space measurements by the Ulysses solar wind plasma experiment from 1.15 to 5.34 AU, we assess the radial gradient in thermal electron temperature. Until 3.8 AU, the gradient was steeper than previously reported but flatter than adiabatic; after 3.8 AU the gradient flattened. Trends in the observed electron distribution shapes qualitatively support predictions for regulation by Coulomb collisions and by expansion in a spiral IMF.
Phillips, J. L.↗
Ulysses near-ecliptic observations of differential flow between protons and alphas in the solar wind
The evolution of differential streaming between protons and alpha particles in the solar wind was observed with the solar wind plasma experiment on the Ulysses spacecraft over the solar range of 1.15 to 5.40 AU between November 18, 1990, and May 5, 1992. The correlation of the difference in ion speeds, Delta V = the absolute value of V(sub alpha) - the absolute value of V(sub p), with the proton speed V(sub p) observed by other spacecraft at solar distances less than or equal to 1 AU disappeared at approximately 2 AU. At solar distances greater than or equal to 2.85 AU, the largest values of both V(sub alpha p) = the absolute value of V(sub alpha p) = the absolute value of V(sub alpha) - V(sub p) and the absolute value of Delta V were found in the interaction regions on the leading edges of high-speed streams. The differential streaming was typically enhanced just downstream of strong forward and reverse shocks, and large negative values of Delta V were frequently encountered in the interaction regions. A correlation between V(sub alpha p) and the ratio tau(sub zero)/tau(sub e) of Coulomb collision time to expansion time was observed at all distances, but it is suggested that at the larger values of tau(sub zero)/tau(sub e) observed correlation may arise from enhanced production of differential streaming by processes that also increase the entropy of the solar wind protons.
Neugebauer, M.↗
Impact expansions in classical and semiclassical scattering.
Impact expansions and interference patterns in atomic scattering theory for cases of forward scattering, backscatter, inversion problem and screened Coulomb potential approximation
SERIES EXPANSION↗
Thermodynamic Structure of Collision-Dominated Expanding Plasma: Heating of Interplanetary Coronal Mass Injections
We investigate the thermodynamic structure of interplanetary coronal mass ejections (ICMEs) using combined surveys of the ejecta between 0.3 and 20 AU. ICMEs are shown to have a moderate expansion in the solar wind compared with theoretical predictions. The expansion seems to be governed by a polytrope with gamma approx. 1.3 in this distance range. We find that Coulomb collisions are important contributors to the ion-ion equilibration process in the ICME plasma. The alpha-proton differential speed quickly drops to below 10 km/s due to strong Coulomb collisions. However, the two species of particles are far from thermal equilibrium with a temperature ratio T(sub alpha/T(sub p) = 4-6, suggestive of a preferential heating of alpha particles. The plasma heating rate as a function of heliocentric &stance required for the temperature profile is deduced by taking into account the expansion and energy transfer between protons and alphas via Coulomb collisions. The turbulence dissipation rate is also inferred from the inertial range power spectrum of magnetic fluctuations within ICMEs. Comparison of the turbulence dissipation rate with the required heating rate shows that turbulence dissipation seems sufficient to explain the ICME heating. Sources powering the turbulence are also investigated by examining the instabilities induced by temperature anisotropies and energy deposition by pickup ions.
Liu, Y.↗
On the equation of state of solar wind ions derived from Helios measurements
The radial evolution of such adiabatic invariants as the ion magnetic moments are studied on the basis of solar wind ion velocity distribution observations made by the Helios spacecraft between 0.3 and 1 AU. Significant differences between proton and alpha-particle parameters in wind velocity dependence are noted, and adiabaticity is on the average found to be violated. This violation is interpreted as evidence that protons are heated perpendicular to the field in fast streams. The contribution of the differential streaming energy to the total internal energy of the ions is also considered, and average heliocentric radial profiles for the ion heat fluxes are presented together with an examination of a possible ion heat flux role in the supply of thermal energy during the winds radial expansion. The present findings suggest that wave-particle interactions, and/or Coulomb collisions, are required to explain solar wind ion thermal energy states and radial temperature profiles.
Marsch, E.↗
Effect of Coulomb interaction on time of flight of cold antiprotons launched from an ion trap
Time-of-flight spectra for Maxwell-Boltzman (MB) distributions of antiprotons initially held in an ion trap and detected after being launched through a 50-cm-long shielding drift tube have been calculated. The distributions used are of temperature 0.4-40 K, cubic length 0.003-3.0 cm, and number 10-100 particles. The mutual Coulomb repulsion of the particles causes a reduction in the number of late arrival particles expected from the MB velocity distribution. The Coulomb energy is not equally divided among the particles during the expansion. The energy is transferred preferentially to the outer particles so that the reduction in the number of slow particles is not necessarily large. The reduction factor is found to be greater than unity when the potential energy of the trapped ions is greater than about 5 percent of the ions' kinetic energy and is about 2 for the launch parameters of the Los Alamos antiproton gravity experiment.
Camp, J. B.↗
Potentials for three-body systems.
Coulomb, Gaussian and harmonic oscillator potentials for particle pairs in three body system, using S wave expansion
Whitten, R. C.↗
A theory of local and global processes which affect solar wind electrons. I - The origin of typical 1 AU velocity distribution functions - Steady state theory
A kinetic theory for the velocity distribution of solar wind electrons which illustrates the global and local properties of the solar wind expansion is proposed. By means of the Boltzmann equation with the Krook collision operator accounting for Coulomb collisions, it is found that Coulomb collisions determine the population and shape of the electron distribution function in both the thermal and suprathermal energy regimes. For suprathermal electrons, the cumulative effects of Coulomb interactions are shown to take place on the scale of the heliosphere itself, whereas the Coulomb interactions of thermal electrons occur on a local scale near the point of observation (1 AU). The bifurcation of the electron distribution between thermal and suprathermal electrons is localized to the deep solar corona (1 to 10 solar radii).
Scudder, J. D.↗
The effects of vacuum polarization on thermonuclear reaction rates
Added to the pure Coulomb potential, the contribution from vacuum polarization increases the barrier, reducing the wave function (u) for reacting nuclei within the range of nuclear forces. The cross section and reaction rate are then reduced accordingly by a factor proportional to u squared. The effect is treated by evaluating the vacuum polarization potential as a small correction to the Coulomb term, then computing u in a WKB formulation. The calculation is done analytically employing the small r power-series expansion for the Uehling potential to express the final result in terms of convenient parameters. At a temperature of 1.4 x 10 to the 7th K the (negative) correction is 1.3 percent for the fundamental fusion process p + p yields d + e(+) + nu.
Gould, Robert J.↗
Axial expansion of the electron pulse in a free-electron laser
The necessity of including longitudinal electrostatic fields in free electron laser theory is investigated. A simple model is proposed which examines the axial expansion of a free electron beam of finite length, and criteria are obtained for including macroscopic fields. It is shown that longitudinal Coulomb forces do not pose a problem in current free electron laser experiments. Transverse space-charge spreading is neglected, and negligible emittance is assumed.
Speziale, T.↗
A reexamination of two-fluid solar wind models
The two-fluid solar-wind equations have been solved by a method which is approximately 50 times faster than any previously developed, through the use of asymptotic expansions which are self-consistently iterated upon to find a solution that passes through the critical point. The energy assumptions in two-fluid solar-wind models are reexamined, and the conclusions are as follows: (1) proton thermal conduction may not be neglected, (2) the Coulomb logarithm must be calculated as a function of radius, and (3) the electron and proton temperatures at the base need not be equal, even when the time scale for energy exchange between the species is an order of magnitude smaller than the expansion time at the base. It is possible to reproduce reasonable quiet-time solar-wind parameters at 1 AU, but only if the proton temperature is approximately twice the electron temperature at 1 solar radius. This may indicate that extended proton heating is important in the outer solar corona. Winds with velocities at 1 AU of 450 km/s are generated without nonthermal energy deposition but require high proton temperatures as well as very low densities at the base. Higher-velocity solutions are not possible in a spherically symmetric geometry for reasonable particle fluxes at 1 AU, and it is suggested that these higher-velocity states probably require additional heating, acceleration mechanisms, or nonradial flow.
Nerney, S.↗