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A two-fluid solar wind model with Alfven waves - Parameter study and application to observations

The effects of Alfven waves from the inner corona on the solar wind density profile, flow velocity and on the random motion of protons are studied. Different base densities, temperatures, and wave velocity amplitudes, as well as different flow geometries, are considered. The model calculations are compared to simultaneous observations of the electron density profile and the resonantly scattered Lyman alpha line. Present observations, out to 4 solar radii, can be used to place limits on the coronal base density and temperature, and put an upper limit on the wave amplitude. It is pointed out that future observations of the electron density and the Lyman alpha line, out to larger heliocentric distances, and of lines from heavier elements, should be used to place more stringent constraints on the amplitudes of MHD waves in the corona.

Esser, R.

Some physical implications of recent solar wind measurements

The physical implications of the existence at about 1 AU of a quiet solar wind particle flux about 90 percent larger than that suggested in the past is investigated within the framework of the two-fluid solar wind model equations. During the spherically symmetric radial expansion of the quiet solar wind, the particle flux is conserved quantity. It is found that a pure collisional two-fluid model provides good particle density and streaming velocity at 1 AU, but predicts too large an electron temperature and too small a proton temperature. When noncollisional contributions to the transport coefficients are incorporated in the model equations, a complete satisfactory agreement with the available observations is obtained. Upper limits to the effective coupling between electrons and protons, as well as to the effective proton thermal conductivity, and both upper and lower limits to the effective electron thermal conductivity in the quiet solar wind, required to provide agreement with observations, are given.

Cuperman, S.

Dynamics of magnetosphere-ionosphere coupling including turbulent transport

A two dimensional two-fluid MHD model including anomalous resistivity was used to investigate the dynamics of magnetosphere-ionosphere coupling. When a field-aligned current is generated on auroral field lines, the disturbance propagates towards the ionosphere in the form of a kinetic Alfven wave. When the current exceeds a critical value, microscopic turbulence is produced, which modifies the propagation of the Alfven wave. This process is modeled by a nonlinear collision frequency, which increases with the excess of the drift velocity over the critical value. Turbulence leads to absorption and reflection of the Alfven wave, partially decoupling the generator from the ionosphere. The approach to a steady-state is strongly dependent on the presence or absence of the turbulence. The current is self-limiting, since a current in excess of critical causes a diffusion of the magnetic field perturbation and a reduction of current.

Lysak, R. L.

Dynamics of magnetosphere-ionosphere coupling including turbulent transport

The dynamics of magnetosphere-ionosphere coupling has been investigated by means of a two-dimensional two-fluid MHD model including anomalous resistivity. When field-aligned current is generated on auroral field lines, the disturbance propagates toward the ionosphere in the form of a kinetic Alfven wave. When the current exceeds a critical value, microscopic turbulence is produced, which modifies the propagation of the Alfven wave. This process is modeled by a nonlinear collision frequency, which increases with the excess of the drift velocity over the critical value. The system evolves toward an electrostatic structure, with the perpendicular electric field having a shorter scale than the field-aligned current. The approach to a steady state is strongly dependent on the presence or absence of the turbulence and on the boundary conditions imposed in the generator. As current is increased or scale size is decreased, the turbulent region reflects and absorbs most of the Alfven wave energy, decoupling the generator from the ionosphere.

Lysak, R. L.

Chaotic behaviour of high Mach number flows

The stability of the super-Alfvenic flow of a two-fluid plasma model with respect to the Mach number and the angle between the flow direction and the magnetic field is investigated. It is found that, in general, a large scale chaotic region develops around the initial equilibrium of the laminar flow when the Mach number exceeds a certain threshold value. After reaching a maximum the size of this region begins shrinking and goes to zero as the Mach number tends to infinity. As a result high Mach number flows in time independent astrophysical plasmas may lead to the formation of 'quasi-shocks' in the presence of little or no dissipation.

Varvoglis, H.

Hydrodynamical constraints on cosmic-ray acceleration in relativistic shocks

A two-fluid hydrodynamical model governing the transport of cosmic rays in a relativistically moving background plasma is developed. The equations are used to discuss the time asymptotic structure of a relativistic, plane-parallel shock wave significantly modified by first-order Fermi acceleration of cosmic rays. The model allows for an anisotropic cosmic-ray pressure tensor with pressure components parallel and perpendicular to the shock normal. It is surmised that the well-known energy threshold problem for diffusive shock acceleration that downstream particles have a large enough velocity to overtake the shock and subsequently scatter in the upstream medium before returning to the downstream medium may be expressed hydrodynamically by the condition V less than V(cr), where V is the fluid velocity relative to the shock and V(cr) is the relativistic cosmic-ray sound speed. Astrophysical implications of the results are briefly discussed.

Webb, G. M.

Cosmic ray-modified stellar winds. I - Solution topologies and singularities

In the present two-fluid hydrodynamical model for stellar wind flow modification due to its interaction with Galactic cosmic rays, these rays are coupled to the stellar wind by either hydromagnetic wave scattering or background flow irregularity propagation. The background flow is modified by the cosmic rays via their pressure gradient. The system of equations used possesses a line of singularities in (r, u, P sub c)-space, or a two-dimensional hypersurface of singularities in (r, u, P sub c, dP sub c/dr)-space, where r, u, and P sub c are respectively the radial distance from the star, the radial wind flow speed, and the cosmic ray pressure. The singular points may be nodes, foci, or saddle points.

Ko, C. M.

Modified non-linear Burgers' equations and cosmic ray shocks

A reductive perturbation scheme is used to derive a generalized non-linear Burgers' equation, which includes the effects of dispersion, in the long wavelength regime for the two-fluid hydrodynamical model used to describe cosmic ray acceleration by the first-order Fermi process in astrophysical shocks. The generalized Burger's equation is derived for both relativistic and non-relativistic cosmic ray shocks, and describes the time evolution of weak shocks in the theory of diffusive shock acceleration. The inclusion of dispersive effects modifies the phase velocity of the shock obtained from the lower order non-linear Burger's equation through the introduction of higher order terms from the long wavelength dispersion equation. The travelling wave solution of the generalized Burgers' equation for a single shock shows that larger cosmic ray pressures result in broader shock transitions. The results for relativistic shocks show a steepening of the shock as the shock speed approaches the relativistic cosmic ray sound speed. The dependence of the shock speed on the cosmic ray pressure is also discussed.

Zank, G. P.

Particle dispersion in confined turbulent swirling flows

This paper reports a numerical investigation of confined swirling flows of gas-particle mixtures. A recently developed two-fluid, multiple-scale mixing model is applied to study the influence of particles on the intensity of the reverse flows of the gas phase and the effects of swirl on the particle dispersion in an annular expanding chamber under isothermal condition. The calculations were made for different swirl strength of injection of the annular jet into the mixing chamber. Results agree well qualitatively with experimental information available. It is also found that the calculated flow fields depend heavily on the prescription of the inlet flow conditions.

Chen, C. P.

Solar transition region response to variations in the heating rate

The response of a numerical model for the upper chromosphere, transition region, and corona to variations in the energy input has been examined. The numerical model solves the set of one-dimensional two-fluid hydrodynamic equations in a simple vertical magnetic flux tube. The atmosphere responds to both the increase and decrease in energy deposition by smoothly readjusting the temperature gradient and the amount of material in the region of peak radiating efficiency to radiate away energy being deposited. At no time during this readjustment is a departure from a thin laminar transition region structure seen. In addition, a time-dependent description of the nonequilibrium ionization of all of the ionization stages of oxygen has been included. This calculation is coupled with the self-consistent calculations of the dynamical variables. It is found that the nonequilibrium ionization balance calculations for both heating and cooling small loops in the quiet sun predict relative ionic abundances which differ substantially from those which would be predicted by an equilibrium calculation

Mariska, J. T.

A two-region model of the solar wind including azimuthal velocity

The two-region model of the solar wind divides the interplanetary space into two regions: it assumes that the solar wind is one-fluid in an inner region within 0.4 AU and two-fluid in an outer region beyond 0.4 AU. This paper includes the angular motion of the solar wind in the two-region model. The flow in the one-fluid region is governed by the one-fluid magnetohydrodynamic equations. The second and third moment equations of the Vlasov equation together with other conservation equations are used to describe the solar-wind flow in the two-fluid region. The predicted azimuthal velocity at 1 AU is less than 2 km/s. All other macroscopic and microscopic properties from this model are in good agreement with experimental quiet-time observations at 1 AU. The numerical results also confirm that when the azimuthal velocity is included in the analysis, the amount of magnetic-field energy converted into kinetic energy in the solar wind is only a small fraction of the total expansion energy flux and has little effect upon the final radial expansion velocity.

Acuna, M. H.

The electromagnetic interchange mode in a partially ionized collisional plasma

A collisional electromagnetic dispersion relation is derived from two-fluid theory for the interchange mode coupled to the Alfven, acoustic, drift and entropy modes in a partially ionized plasma. The fundamental electromagnetic nature of the interchange model is noted; coupling to the intermediate Alfven mode is strongly stabilizing for finite k sub z. Both ion viscous and ion-neutral stabilization are included, and it was found that collisions destroy the ion finite Larmor radius cutoff at short perpendicular wavelengths.

Hudson, M. K.

Thermofluid analysis of the SSME preburner using a gas-gas diffusion model for oxygen and hydrogen combustion at supercritical pressures

The paper discusses the thermofluid analysis of the Space Shuttle Main Engine (SSME) fuelside preburner. The governing equations have been solved numerically to predict flow, heat transfer, mixing, and combustion. A two-fluid approach is adopted in which oxygen is regarded as one fluid and hydrogen is regarded as the other fluid. The chemical kinetics is assumed to be very fast so that combustion is primarily controlled by the rate of mixing between oxygen and hydrogen. The preburner pressure is much greater than the critical pressures of oxygen and hydrogen; hence, a gas-gas diffusion model (rather than an evaporation model) has been developed to compute the rate of interphase mixing. Empirical correlations have been incorporated to account for the effect of slip on the interphase exchange. A sensitivity study has been performed with various model parameters. It is observed that the model can predict possibility of incomplete combustion and local regions of high temperatures under steady operating conditions. Some of these anomalies have been observed in actual tests, and the numerical model is useful for understanding possible causes and remedies. At least some measurements are needed for quantitative verification of the model.

Prakash, C.

A solar-wind model including proton thermal anisotropy.

A model of the solar wind is presented which divides the interplanetary space into two regions. It assumes that the solar wind is one-fluid in an 'inner region' of radius less than 0.4 A, and two-fluid and collisionless in an 'outer region' of radius greater than 0.4 A. The second and third moment equations of the Vlasov equation together with conservation equations are used to govern the solar wind flow in the outer region. The model produces solutions for all macroscopic quantities as well as for the microscopic proton distribution function, both as functions of heliocentric distances up to 50 A. Calculated results at 1 A include the solar wind velocity, electron temperature, proton temperature, proton thermal anisotropy and magnetic field magnitude. They are in good agreement with observations.

Whang, Y. C.

The collisionless macroscopic Kelvin-Helmholtz instabiity. I Transverse electrostatic mode

The electrostatic limit of the Kelvin-Helmholtz instability in a collisionless plasma is investigated for a magnetic field perpendicular to the velocity flow. A two-fluid eigenvalue analysis of the transverse electrostatic Kelvin-Helmholtz instability is performed using the Chew-Goldberger-Low hydromagnetic equations with first-order finite Larmer radius corrections, establishing that the transverse electrostatic mode reduces to the incompressible transverse MHD mode in the limit of zero ion gyroradius. The linear growth rates are determined and a strong stabilization of the instability for (k-perpendicular) (rho sub i) of 0.2 or greater is observed. The nonlinear stage of the instability displays large vortices whose size is many times the initial velocity shear length. At saturation the simulation is dominated by the longest-wavelength mode permitted in the system. The simulation results can be understood in terms of a simple model which assumes that saturation occurs when the angular frequency of the vortex motion reaches the linear growth rate of the instability.

Prichett, P. L.