Engineering topics

Williams, L. L.

Publications and source records attributed to Williams, L. L..

8 records

NASA NTRS1995

Self-consistent solar wind-LISM interaction including neutrals: A 4-fluid model

We investigate the interaction between the heliosphere and local interstellar medium, including charge-exchange self-consistently between the neutral and ionized components. The system is modelled as consisting of neutral hydrogen, protons and electrons. The electrons are assumed to contribute to the dynamics via a pressure that is everywhere equal to the proton pressure. The fluid equations for the protons and hydrogen are solved self-consistently, assuming the two species interact only via charge exchange. The protons are treated as a single isotropic fluid. The hydrogen is decomposed into three isotropic fluids: hydrogen of interstellar origin with characteristic temperature of approximately 104 K, hydrogen produced via charge exchange in the post-shock solar wind, with characteristic temperature of approximately 105 K, and hydrogen produced via charge exchange in the supersonic solar wind, relatively cool but expanding radially outward with the solar wind speed. Two-Dimensional time-dependent numerical simulations of this system are performed to calculate the number density, temperature and bulk velocity of neutral hydrogen and plasma everywhere in the heliosphere. These quantities are compared to relevant solar wind observations. Implications for the pick-up process in the supersonic solar wind, as well as heating and deceleration of the wind, are addressed.

Williams, L. L.↗

NASA NTRS1995

Heat flux and viscosity of ions in the collisionless solar wind

Between 1 and 2 solar radii, the Coulomb-collision mean free path for thermal ions exceeds the scale height of the solar atmosphere. The expanding solar plasma becomes collisionless and the kinetics of the solar wind are no longer dominated by thermalizing collisions. The usual Braginskii-type expressions for solar wind ion heat flux and viscosity are no longer valid. However, another microscale still exists in the solar wind, dictated by the gyro-radius of ions in the turbulent embedded solar wind magnetic field. Wave-particle interactions will act to isotropize (but not thermalize) particle distributions, and the relevant microscale for this process is the ion gyro-radius. The ion distribution can be modelled as undergoing isotropizing 'collisions,' with the relevant mean free path scaling with gyro-radius. Here, the author presents the heat flux and viscosity expected for solar wind protons which are relaxing to isotropy on a microscale that scales with gyro-radius. The collisionless viscosity and heat flux have a functional dependence different than their collisional analogs. The collisional expressions for ion viscosity and heat flux drastically overestimate the efficiency of diffusive energy and momentum transport actually operative in the solar wind.

Williams, L. L.↗

NASA NTRS1995

Multi-dimensional modelling of the solar wind-LISM interaction including neutrals: A Boltzmann equation approach

The importance of interstellar neutrals in understanding and modelling the global interaction of the solar wind with the local interstellar medium is becoming increasingly apparent. Unfortunately the self-consistent inclusion of a neutral interstellar component into time-dependent, dynamical models is formidably difficult due to the extremely large mean free paths associated with the neutrals and the creation of essentially different neutral distributions from different interaction regions of the solar wind and LISM. In full generality, one has to address the problem by treating the neutrals kinetically with the appropriate extinction and creation source terms. In this paper, a limited set of simulations will be presented in which the solar wind and interstellar plasma is described as a 2D fully compressible time-dependent fluid while the interstellar neutral distribution is derived by solving the appropriate Boltzmann equation directly.

Zank, G. P.↗

NASA NTRS1994

Effect of magnetic field geometry on the wave signature of the pickup of interstellar neutrals

By using the technique of Johnstone et al. (1991), the asymptotic wave spectrum induced by the pickup of interstellar ions in the heliosphere is derived. This approach is independent of quasi-linear theory. The asymptotic wave spectrum is calculated from the standard resonance condition by assuming that the asymptotic ion distribution is bispherical and by using conservation of energy. The calculation places no restriction on either the ratio of Alfven speed to solar wind flow speed or the particle pitch angle. Spectra for various geometries (relative orientations of the magnetic field and solar wind velocity) are calculated. Absolute upper limits to the expected wave enhancements are calculated. These upper limits are compared to the background fluctuation spectrum extrapolated from 0.87 AU, assuming a spectral index of -5/3 and radial dependences of -2 and -3. The heliocentric radial distances at which the peaks in the various geometry-dependent wave spectra are expected to be observable above the background are identified. Peaks due to pickup hydrogen at the proton gyrofrequency are found to be always stronger relative to the background in parallel than in perpendicular geometries. The parallel-geometry excitations consist only of sunward propagating waves. In perpendicular geometries a peak also occurs, this time near 0.1 of the proton gyrofrequency (corresponding to the peak calculated by Lee and Ip (1987)). However, the steep spectral dependence of the ambient wave field makes it unlikely that this peak will be observed inside 20 AU. A similar result holds for the case of pickup-helium induced excitation at the helium gyrofrequency. Inside 10 AU, peaks at these lower frequencies tend to be obscured by the steep frequency dependence (proportional to -5/3) of the ambient spectrum and then are only observable in parallel geometries.

Williams, L. L.↗

NASA NTRS1993

A unified transport equation for both cosmic rays and thermal particles

We present a unified transport equation that is valid for particles of all energies if the particle mean free paths are much smaller than macroscopic fluid length scales. If restricted to particles with random speeds much greater than fluid flow speeds, this equation reduces to the previously discussed extended cosmic-ray transport equation. It is significant that this allows one to describe the acceleration of particles from thermal energies to cosmic-ray energies using one transport equation. This is in contrast to previous transport equations (the Parker equation and the extended cosmic-ray transport equation), which were restricted to fast particles. The close connection to the extended cosmic-ray transport equation is demonstrated.

Williams, L. L.↗

NASA NTRS1993

The telegraph equation in charged particle transport

We present a new derivation of the telegraph equation which modifies its coefficients. First, an infinite order partial differential equation is obtained for the velocity space solid angle-averaged phase-space distribution of particles which underwent at least a few collisions. It is shown that, in the lowest order asymptotic expansion, this equation simplifies to the well-known diffusion equation. The second-order asymptotic expansion for isotropic small-angle scattering results in a modified telegraph equation with a signal propagation speed of v(5/11) exp 1/2 instead of the usual v/3 exp 1/2. Our derivation of a modified telegraph equation follows from an expansion of the Boltzmann equation in the relevant smallness parameters and not from a truncation of an eigenfunction expansion. This equation is consistent with causality. It is shown that, under steady state conditions in a convecting plasma, the telegraph equation may be regarded as a diffusion equation with a modified transport coefficient, which describes a combination of diffusion and cosmic-ray inertia.

Gombosi, T. I.↗

NASA NTRS1992

Viscous and inertial effects at cosmic-ray shocks

To illustrate the effect of the viscous and inertial terms on the structure of cosmic-ray-modified shocks, an analysis of a time-independent 1D shock is presented in which the pressure of the background fluid and the magnetic-field energy density are negligible compared with the cosmic-ray pressure. The effect of the magnetic field on cosmic-ray transport coefficients is retained. The diffusion, viscous and inertial terms work to 'thicken' the shock. When the average magnetic field is negligible and the cosmic-ray transport is isotropic, diffusion is the dominant effect unless the parameters are such that the scattering time becomes comparable to the characteristic times for velocity change in the fluid frame. For a perpendicular shock, where the diffusion is strongly reduced by the magnetic field, the relative magnitude of the viscous effect is increased by a factor about (omega tau) exp 2, leading to the conclusion that cosmic-ray viscosity can be important to the structure of collisionless MHD shocks. In both cases considered, the viscous and inertial terms become important for those parameter ranges where the diffusion approximation begins to break down.

Jokipii, J. R.↗

NASA NTRS1991

Viscosity and inertia in cosmic-ray transport - Effects of an average magnetic field

A generalized transport equation is introduced which describes the transport and propagation of cosmic rays in a magnetized, collisionless medium. The equation is valid if the cosmic-ray distribution function is nearly isotropic in momentum, if the ratio of fluid speed to fluid-flow particle speed is small, and if the ratio of collision time to time for change in the macroscopic flow is small. Five independent cosmic-ray viscosity coefficients are found, and the ralationship of this viscosity to particle orbits in a magnetic field is presented.

Williams, L. L.↗