Engineering topics

Zank, G. P.

Publications and source records attributed to Zank, G. P..

At least 37 records · Page 2

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 NTRS1995

Structure of mass-loading shocks. 2: Comparison of theory and observation at comet Halley

The multifluid diffusive model of G. P. Zank et al. (1994), which describes the interaction of the solar wind with a cometary plasma in the outer coma, has been used to model the structure of the Halley bow shock. The theoretical results are compared to in situ observations made by Giotto. We compare the solar wind and cometary ion number densities and pressures upstream and through the quasi-perpendicular and quasi-parallel shocks (observed on the inbound and outbound legs of the encounter, respectively). In general, good agreement is found between theory and observations in terms of shock structure, strength, and location, especially for the quasi-parallel shock. The comparison between tha quasi-perpendicular shock observations and theory is complicated by the apparently nonstationary behavior of the shock, a feature which has been remarked upon by other investigators. The cometary bow shock appears to be an excellent example of an energetic-particle-mediated shock where the energetic particles comprise less than 10% of the total number density.

Zank, G. P.↗

NASA NTRS1995

Contact and pressure balance structures in two-fluid cosmic-ray hydrodynamics

The role of cosmic-ray-modified contact discontinuities and pressure balance structures in two-fluid cosmic-ray hydrodynamics in one Cartesian space dimension are investigated by means of analytic and numerical solution examples, as well as by weakly nonlinear asymptotics. The fundamental wave modes of the two-fluid cosmic-ray hydrodynamic equations in the long-wavelength limit consist of the backward and forward propagating cosmic-ray-modified sound waves, with sound speed dependent on both the cosmic-ray and thermal gas pressures; the contact discontinuity; and a pressure balance mode in which the sum ofthe cosmic ray and thermal gas pressure perturbations is zero. The pressure balance mode, like the contact discontinuity is advected with the background flow. The interaction of the pressure balance mode with the contact discontinuity is investigated by means of the method of multiple scales. The thermal gas and cosmic-ray pressure perturbations satisfy a linear diffusion equation, and entropy perturbations arising from nonisentropic initial conditions for the thermal gas are frozen into the fluid. The contact discontinuity and pressure balance eigenmodes both admit nonzero perturbations in the thermal gas, whereas the cosmic-ray-modified sound waves are isentropic. The total entropy perturbation is shared between the contact discontinuity and pressure balance eigenmodes, and examples are given in which there is a transfer of entropy between the two modes. In particular, N-wave type density disturbances are obtained which arise as a result of the entropy transfer between the two modes. A weakly nonlinear geometric optics perturbation expansion is used to study the long timescale evolution of the short-wavelength entropy wave and the thermal gas sound waves in a slowly varying, large-scale background flow. The weakly nonlinear geometric optics expansion is also used to generalize previous studies of squeezing instability for short-wavelength sound waves in the two fluid model, by including a weakly nonlinear wave steepening term that leads to shock formation, as well as the effect of long time and space dependence of the background flow. Implications of cosmic-ray-modified pressure balance structures and contact discontinuities in models of the interaction of traveling interplanetary shocks and compression and rarefraction waves with the solar wind termination shock are briefly discussed.

Webb, G. M.↗

NASA NTRS1995

The termination shock: Physical processes

A brief overview of the physics thought to determine the properties of the heliospheric termination shock is given and the central role of hot interstellar pick-up ions and cosmic rays is emphasized.

Zank, G. P.↗

NASA NTRS1994

Transport theory and the WKB approximation for interplanetary MHD fluctuations

An alternative approach, based on a multiple scale analysis, is presented in order to reconcile the traditional Wentzel-Kramer-Brillouin (WKB) approach to the modeling of interplanetary fluctuations in a mildly inhomogeneous large-scale flow with a more recently developed transport theory. This enables us to compare directly, at a formal level, the inherent structure of the two models. In the case of noninteracting, incompressible (Alven) waves, the principle difference between the two models is the presence of leading-order couplings (called 'mixing effects') in the non-WKB turbulence model which are absent in a WKB development. Within the context of linearized MHD, two cases have been identified for which the leading order non-WJB 'mixing term' does not vanish at zero wavelength. For these cases the WKB expansion is divergent, whereas the multiple-scale theory is well behaved. We have thus established that the WKB results are contained within the multiple-scale theory, but leading order mixing effects, which are likely to have important observational consequences, can never be recovered in the WKB style expansion. Properties of the higher-order terms in each expansion are also discussed, leading to the conclusion that the non-WKB hierarchy may be applicable even when the scale separation parameter is not small.

Matthaeus, William H.↗

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 NTRS1994

Radio emissions and the heliospheric termination shock

With the Voyager spacecrafts' discovery of low-frequency radio emissions from the depths of the outer heliosphere has come the realization that the boundaries between our heliosphere and the local interstellar medium have been detected. A model is presented here that can account for the observed radio emissions, based upon a termination shock modified by the dynamical effect of galactic and anomalous cosmic rays. Frequency and time domain properties of both continuum and transient radio events are explained, and new estimates for the distance to the termination shock (approximately 60-70 astronomical units) and the heliopause (less than or approximately 90 AU) are given.

Zank, G. P.↗

NASA NTRS1994

Time-dependent evolution of cosmic-ray-modified shock structure: Transition to steady state

Steady state solutions to the two-fluid equations of cosmic-ray-modified shock structure were investigated first by Drury and Volk (1981). Their analysis revealed, among other properties, that there exist regions of upstream parameter space where the equations possess three different downstream solutions for a given upstream state. In this paper we investigate whether or not all these solutions can occur as time-asymptotic states in a physically realistic evolution. To do this, we investigate the time-dependent evolution of the two-fluid cosmic-ray equations in going from a specified initial condition to a steady state. Our results indicate that the time-asymptotic solution is strictly single-valued, and it undergoes a transition from weakly to strongly cosmic-ray-modified at a critical value of the upstream cosmic ray energy density. The expansion of supernova remnant shocks is considered as an example, and it is shown that the strong to weak transition is in fact more likely. The third intermediate solution is shown to influence the time-dependent evolution of the shock, but it is not found to be a stable time-asymptotic state. Timescales for convergence to these states and their implications for the efficiency of shock acceleration are considered. We also investigate the effects of a recently introduced model for the injection of seed particles into the shock accelerated cosmic-ray population. The injection is found to result in a more strongly cosmic-ray-dominated shock, which supports our conclusion that for most classes of intermediate and strong cosmic-ray-modified shocks, the downstream cosmic-ray pressure component is at least as large as the thermal gas pressure, independent of the upstream state. As a result, cosmic rays almost always play a significant role in determining the shock structure and dissipation and they cannot be regarded as test particles.

Donohue, D. J.↗

NASA NTRS1994

The structure of mass-loading shocks. 1: Comets

A new multifluid model to describe the solar wind-cometary ion plasma in the outer cometary coma is derived. This model is distinguished from previous multifluid models in that wave-particle effects are included explicitly. By considering hydrodynamic timescales, self-consistent dissipative terms (which correspond to the spatial diffusion of cometary ions) are derived, thereby allowing the structure of a cometary bow shock to be resolved. In the hypersonic limit, our diffusive multifluid model reveals an attractive connection to the one-fluid model formulated by Biermann et al. (1967), a connection which serves as an important guide when investigating our more complicated nonhypersonic diffusive model. The detailed model consists of cometary ions diffusing in a warm solar wind which is heated by the dissipation of Alfvenic turbulence (in situ and generated by the initial ring beam distribution). The quasi-parallel cometary shock is found to be at least an order of magnitude thicker than a quasi-perpendicular cometary shock. It is furthermore found that for undisturbed solar wind (sonic) Mach numbers in excess of approximately 6, the cometary bow shock (for both perpendicular and parallel cases) is smoothed completely by the cometary ions and no 'proton' or thermal subshock is necessary. Finally, a detailed comparison of the model with the plasma observations made at Halley by Giotto is undertaken. It is found that the observed shock structure, thickness, location, and plasma parameters compare well with the predictions of the theoretical model, particularly in the case of the quasi-parallel shock.

Zank, G. P.↗

NASA NTRS1993

Steady state and dynamical structure of a cosmic-ray-modified termination shock

A hydrodynamic model is developed for the structure of a cosmic-ray-modified termination shock. The model is based on the two-fluid equations of diffuse shock acceleration (Drury and Volk, 1981). Both the steady state structure of the shock and its interaction with outer heliospheric disturbances are considered. Under the assumption that the solar wind is decelerated by diffusing interstellar cosmic rates, it is shown that the natural state of the termination shock is a gradual deceleration and compression, followed by a discontinuous jump to a downstream state which is dominated by the pressure contribution of the cosmic rays. A representative model is calculated for the steady state which incorporates both interstellar cosmic ray mediation and diffusively accelerated anomalous ions through a proposed thermal leakage mechanism. The interaction of large-scale disturbances with the equilibrium termination shock model is shown to result in some unusual downstream structure, including transmitted shocks and cosmic-ray-modified contact discontinuities. The structure observed may be connected to the 2-kHz outer heliospheric radio emission (Cairns et al., 1992a, b). The time-dependent simulations also demonstrate that interaction with solar wind compressible turbulence (e.g., traveling interplanetary shocks, etc.) could induce the termination shock to continually fluctuate between cosmic-ray-dominated and gas-dynamic states. This fluctuation may represent a partial explanation of the galactic cosmic ray modulation effect and illustrates that the Pioneer and Voyager satellites will encounter an evolving shock whose structure and dynamic properties are strongly influence by the mediation of interstellar and anomalous cosmic rays.

Donohue, D. J.↗

NASA NTRS1993

The structure of mass-loading shocks

A new two-fluid model which describes mass loading in the solar wind (e.g., the interaction of the solar wind with a cometary coma or the local interstellar medium) is presented. The self-consistent back-reaction of the mass-loaded ions is included through their effective scattering in low-frequency MHD turbulence and the invocation of a diffusive approximation. Such an approximation has the advantage of introducing self-consistent dissipation coefficients into the governing equations, thereby facilitating the investigation of the internal structure of shocks in mass-loading environments. To illustrate the utility of the new model, we consider the structure of cometary shocks in the hypersonic one-dimensional limit, finding that the incoming solar wind is slowed by both mass loading and the development of a large cometary ion pressure gradient. The shock is broadened and smoothed by the cometary ions with a thickness of the order of the cometary ion diffusion scale.

Zank, G. P.↗

NASA NTRS1993

Particle injection and the structure of energetic-particle-modified shocks

A macroscopic 'self-consistent' nonlinear two-fluid model is developed for energetic-particle-modeled shocks. The model incorporates particle exchange between a thermal gas and an energetic population via a 'thermal leakage' mechanism. In the model, injection is regarded as a process whereby particles in the cooler thermal core of a total particle distribution are energized sufficiently to cross a 'momentum boundary' into the wings of the distribution. Particles in the wings are identified as 'energetic particles' or 'cosmic rays' and are assumed to propagate according to the diffusive transport equation of cosmic ray theory. Thermal particles are energized either as a result of adiabatic compression in a decelerating flow or directly via anomalous heating within a subshock. It is shown that the nature and model of particle injection directly affects the nature and dynamics of the shock, and hence the efficiency of particle acceleration, and that the shock itself regulates particle injection dynamically.

Zank, G. P.↗

NASA NTRS1993

Nearly incompressible fluids. II - Magnetohydrodynamics, turbulence, and waves

The theory of nearly incompressible (NI) fluid dynamics developed previously for hydrodynamics is extended to magnetohydrodynamics (MHD). Based on a singular expansion technique, modified systems of fluid equations are obtained for which the effects of compressibility are admitted only weakly in terms of the different possible incompressible solutions. NI MHD represents the interface between the compressible and incompressible magnetofluid descriptions in the subsonic regime. It is shown that three distinct NI descriptions exist corresponding to each of the three possible plasma beta regimes. The detailed theory of weakly compressible corrections to the various incompressible MHD descriptions is presented, and the implications for the solar wind are discussed.

Zank, G. P.↗

NASA NTRS1992

Properties of mass-loading shocks. II - Magnetohydrodynamics

The one-dimensional magnetohydrodynamics of mass-loading shocks is examined. These shocks, which are distinct from MHD shocks of classical nonreacting fluid dynamics and of combustion theory and which are characterized by the addition of mass within the shock transition, are to be found at comets and, depending upon circumstances, at nonmagnetized and weakly magnetized planets such as Venus and Mars. A completely general mass-loading form of the Hugoniot equation is derived, and some of the most important differences between mass-loading and nonreacting classical MHD shocks are identified. Two new types of MHD shocks are described which have no classical MHD analogues.

Zank, G. P.↗

NASA NTRS1992

Waves and turbulence in the solar wind

This paper presents an overview of the Zank and Matthaeus (1991) theory of weakly compressible magnetofluid dynamics within the context of solar wind observations, stressing the importance of compressibility in determining the incompressible MHD description appropriate to the solar wind. A new unified model is developed which combines the effects of both the compressibility and the incompressibility, which can be used for investigations of waves and turbulence in the solar wind.

Zank, G. P.↗

NASA NTRS1992

Wave diffraction in weak cosmic-ray-modified shocks

Weakly multidirectional, long-wavelength cosmic-ray-modified shocks are studied via multiple scale perturbation techniques. The effects of diffraction are discussed in terms of Green's function solutions of the linearized 1 + 3D Burgers and 1 + 3D KdVB equations, and also in terms of solutions with singular Dirac delta initial distributions. The solutions show a monotonic decrease of the wave-front curvature with increasing time owing to the effects of wave diffraction. The shape of the wave surface is discussed in terms of solutions S to the wave eikonal equation corresponding to singular initial conditions. For the fast magnetosonic wave propagating in the positive x-direction, the wave phase surface S = 0 has elliptic cross sections with the planes x = constant and has a convex paraboloidal shape. Plane-wave solutions of the 1 + 3D KdVB equation are discussed.

Webb, G. M.↗

NASA NTRS1992

Mass-loading at interplanetary shocks

Mass-loading fronts represent a new class of shocks which is found frequently in the solar system, both at the head of comets and upstream of weakly and nonmagnetized planets, and which has not yet been investigated in great detail. Here, a general theoretical description of mass-loading shocks (MLSs) in the heliosphere is presented and the difference between MLSs and classical nonreacting MHD shock are elucidated. It is found that the momentum contribution of added mass within the shock represents a physically important effect, particularly in the shock strength regime observed at Comets Halley and GZ. The mass-loading MHD Rankine-Hugoniot conditions are not tangentially invariant, so mass-loading fronts are subjected to shearing stresses, greatly curtailing the upstream parameter regime for which stable transitions are possible. The existence of fast and slow mode compound mass-loading fronts is predicted. Other forms of mass-loading fronts exist for which no classical MHD counterparts exist.

Zank, G. P.↗

NASA NTRS1992

Weakly inhomogeneous MHD turbulence and transport of solar wind fluctuations

An evaluation is conducted of recent theories of small-scale MHD turbulence transport in an inhomogeneous background that are pertinent to the evolution of solar wind turbulence. Attention is given to the WKB formalism that has been used in many solar wind-related physics applications, with a view to its shortcomings. Also discussed are the structure of two-scale transport theories, and their relationship to WKB theory in light of multiple-scales analysis.

Matthaeus, W. H.↗