ANALYSIS OF A SKIMMER FOR A HIGH-INTENSITY MOLECULAR BEAM USING A THREE-FLUID MODEL
Analysis of skimmer for high intensity molecular beam using three-fluid model
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Analysis of skimmer for high intensity molecular beam using three-fluid model
It is commonly assumed in models of the solar wind-interstellar neutral hydrogen interaction that the ionized interstellar particles are quickly assimilated into the solar wind proton population and 'become indistinguishable' from the original solar wind. This assumption leads to the prediction that the solar wind proton temperature should increase with radius in the outer heliosphere. This temperature increase has not been observed. It is pointed out that assimilation of the interstellar particles to the point of indistinguishability takes place on the very long Coulomb collision time scale, and is not expected to occur within the heliosphere. Results are presented of a three-fluid model of the solar wind which consists of comoving thermal populations of protons of solar origin, protons produced by ionization of interstellar hydrogen, and electrons. The steady-state results yield a solar wind with a 'core' proton distribution which cools adiabatically, and a 'halo' of interstellar pickup protons which is maintained near 10 to the 7th K by the energy input of continued ionization and pickup. Such a distribution will not be observed to manifest the temperature increase at large heliocentric distances which is predicted from a one-fluid analysis. Further time-dependent calculations show a strong correlation between the densities of the solar wind and the interstellar pickup protons. It is suggested that the interstellar pickup population may be observable by the Voyager plasma instruments in low resolution mode during periods of high solar wind density and low solar wind temperature.
High energy, high intensity molecular beam flow is analyzed, using a skimmer which is a small inlet where the beam is separated from the core flow
Solar wind model with electrons, protons and alpha particles coupled by electric field and expanding due to pressure gradient and solar gravitation
Observations show that, when alpha particles and other minor ions in the solar wind plasma encounter fast shocks, they are heated more than protons and their bulk motion is decelerated less than protons. These effects have been studied using a three-fluid model, and the model predictions have been compared with observations. The comparison indicates that, for supercritical fast shocks, the three-fluid model can explain cross-shock minor ion heating which is significantly greater than that of protons. When the ratio of specific heats for minor ions, gamma (alpha), equals 2, both the lesser cross-shock deceleration and the greater heating of minor ions than of protons can be predicted by the model; thus, the minor ion heating through the shock transition region is consistent with the involvement of two degrees of freedom. Because the analysis is formulated in the de Heffmann-Teller frame of reference, the method is not valid for perpendicular shocks or when the angle is large. These results agree with the few extant observations and might be confirmed by further observations at the earth's bow shock.
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Wave equations for disturbances in partly ionized gas due to current sources determined, using three-fluid model
A detailed model for a photospheric dynamo has been presented by Henoux and Somov (1987), who used the three-fluid model to treat the properties of the weakly ionized plasma. Only the equations for the two ionized components were solved. The equation for the neutral component is considered, and it is argued that the model is unacceptable becaused of an implied impossibly large unbalanced stress on the neutral gas. It is argued more generally that all existing photospheric dynamo models are untenable.
The solution was obtained without approximating the dispersion relation. This was made possible by the use of a computer method for carrying out the extremely large number of algebraic manipulations involved. The three-fluid model employed accounts for the interaction of the electron, ion, and neutral species. The solution for the e-folding distance describes the damping characteristics of each wave mode. Each of the e-folding solutions corresponds to one of the phase velocity solutions.
A self-consistent, three-fluid model of plasma transport and implanted ion acceleration in the unshocked solar wind is presented. The solar wind plasma is depleted by charge exchange with the expanding cometary exosphere, while implanted protons and heavy ions are produced by photoionization and charge transfer and lost by charge exchange. A generalized transport equation describing convection, adiabatic and diffusive velocity change, and the appropriate production terms is used to describe the evolution of the two cometary ion components, while the moments of the Boltzmann equation are used to calculate the solar wind density and pressure. The flow velocity is obtained self-consistently by combining the conservation equations of the three ion species. The results imply that second-order Fermi acceleration can explain the implanted spectra observed in the unshocked solar wind. Comparison of measured and calculated distribution indicates that spatial diffusion of implanted ions probably plays an important role in forming the energetic particle environment in the shock vicinity.
The coronal slow shock was predicted to exist embedded in large coronal holes at 4 to 10 solar radii. A three-fluid model was used to study the jumps in minor ions propertes across the coronal slow shock. The jump conditions were formulated in the de Hoffmann-Teller frame of reference. The Rankine-Hugoniot solution determines the MHD flow and the magnetic field across the shocks. For each minor ion species, the fluid equations for the conservation of mass, momentum, and energy can be solved to determine the velocity and the temperature of the ions across the shock. A simularity solution was also obtained for heavy ions. The results show that on the downstream side of the coronal slow shock the ion temperatures are nearly proportional to the ion masses for He, O, Si, and Fe in agreement with observed ion temperatures in the inner solar wind. This indicates that the possibly existing coronal slow shock can be responsible for the observed heating of minor ions in the solar wind.
The coronal slow shock has been predicted to exist embedded in large coronal holes at 4-10 solar radii. In this paper, a three-fluid model is used to study the jumps in minor ion properties across a slow shock such as the coronal slow shock. The jump conditions are formulated in the de Hoffmann-Teller frame of reference. The Rankine-Hugoniot solution determines the MHD flow and the magnetic field across the shocks. For each minor ion species, the fluid equations for the conservation of mass, momentum, and energy can be solved to determine the velocity and the temperature of the ions across the shock. Also obtained is a similarity solution for heavy ions. The results show that, on the downstream side of the slow shock, the ion temperatures are nearly proportional to the ion masses for He, O, Si, and Fe, in agreement with observed ion temperatures in the inner solar wind. This indicates that the possibly existing coronal slow shock can be responsible for the observed heating of minor ions in the solar wind.
This paper presents a numerical study of the time evolution of plane, cosmic-ray modified shocks with magnetic field parallel to the shock normal, based on the diffusive shock acceleration formalism and including the effects from the finite propagation speed and energy of Alfven waves responsible for controlling the transport of the cosmic rays. The simulations discussed are based on a three-fluid model for the dynamics, but a more complete formalism is laid out for future work. The results of the simulations confirm earlier steady state analyses that found these Alfven transport effects to be potentially important when the upstream Alfven speed and the gas sound speed are comparable, i.e., when the plasma and magnetic pressures are similar. It is also clear, however, that the impact of Alfven transport effects, which tend to slow shock evolution and reduce the time asymptotic cosmic-ray pressure in the shock, is strongly dependent upon uncertain details in the transport models. Both cosmic-ray advection tied to streaming Alfven waves and dissipation of wave energy are important to include in the models. Further, Alfven transport properties on both sides of the shock are also influential.
Mathematical models of wave propagation in three-fluid plasma and numerical solutions to dispersion and propagation properties
Continuum source molecular beam facility, examining effect of source-skimmer distance variation on flux and spatial distribution of beam in collimation chamber downstream
Time evolution of plane, cosmic-ray modified shocks was simulated numerically for the case with parallel magnetic fields. Computations were done in a 'three-fluid' dynamical model incorporating cosmic-ray and Alfven wave energy transport equations. Nonlinear feedback from the cosmic-rays and Alfven waves is included in the equation of motion for the underlying plasma, as is the finite propagation speed and energy dissipation of the Alfven waves. Exploratory results confirm earlier, steady state analyses that found these Alfven transport effects to be potentially important when the upstream Alfven speed and gas sound speeds are comparable. As noted earlier Alfven transport effects tend to reduce the transfer of energy through a shock from gas to energetic particles. These studies show as well that the time scale for modification of the shock is altered in nonlinear ways. It is clear, however, that the consequences of Alfven transport are strongly model dependent and that both advection of cosmic-rays by the waves and dissipation of wave energy in the plasma will be important to model correctly when quantitative results are needed. Comparison is made between simulations based on a constant diffusion coefficient and more realistic diffusion models allowing the diffusion coefficient to vary in response to changes in Alfven wave intensity. No really substantive differences were found between them.
Time evolution of plane, cosmic-ray modified shocks has been simulated numerically for the case with parallel magnetic fields. Computations were done in a 'three-fluid' dynamical model incorporating cosmic-ray and Alfven-wave energy transport equations. Nonlinear feedback from the cosmic rays and Alfven waves is included in the equation of motion for the underlying plasma, as is the finite propagation speed and energy dissipation of the Alfven waves. Exploratory results confirm earlier, steady state analyses that found these Alfven transport effects to be potentially important when the upstream Alfven speed and gas sound speeds are comparable. As noted earlier, Alfven transport effects tend to reduce the transfer of energy through a shock from gas to energetic particles. These studies show as well that the timescale for modification of the shock is altered in nonlinear ways. It is clear, however, that the consequences of Alfven transport are strongly model dependent and that both advection of cosmic rays by the waves and dissipation of wave energy in the plasma will be important to model correctly when quantitative results are needed. Comparison is made between simulations based on a constant diffusion coefficient and more realistic diffusion models allowing the diffusion coefficient to vary in response to changes in Alfven wave intensity. No really substantive differences were found between them.
This work presents an investigation of the properties of the one-dimensional, two-fluid turbulence-driven solar wind model introduced by Hollweg and Johnson (1988). It is found that the model has serious difficulties in reproducing the observed high-speed wind at 1 AU. In particular, the model proton temperatures are lower than those observed by a factor of 2 or more, and the highest temperature models yield excessive wave intensities at 1 AU. It appears that the problem stems from the specific spatial distribution of heat deposition in the model. Thus this study does not rule out a turbulence-driven fast solar wind, since other forms of the turbulent evolution could probably achieve better results. A three-fluid version of the model is also presented to show that the addition of alpha particles does not significantly reduce the extreme proton temperatures displayed near the sun by the Hollweg and Johnson work. Finally, it is suggested that the additional heating needs to be located well beyond the critical point, implying that the heating mechanism for the fast solar wind is likely not the same as that heating the solar corona.