H. G. Demars

Effect of centrifugal acceleration on the polar wind

The ionospheric convection electric fields that occur at high latitudes cause plasma to drift across the cusp region and the polar cap. Since the magnetic field at high latitudes is close to vertical, pointing downward (upward) in the northern (southern) hemisphere, the convecting plasma experiences a centrifugal acceleration as it crosses the polar region because of the diverging magnetic field geometry. The centrifugal force is directly proportional to the mass of the plasma particles, and it is reasonable to ask whether this force has an effect on polar plasma outflow, particularly for the more massive ion O+. To date, a number of studies have addressed this question, but the theoretical models used in these studies were either overly simplified (i.e., neglected processes known to be important in the polar ionosphere) or else did not use appropriate boundary conditions or take account of the time variability of the problem. The results of these prior investigations were often contradictory. In order to overcome the limitations of these earlier studies, we have used a macroscopic particle-in-cell (PIC) code, which is sophisticated in the sense that a broad range of physical processes are incorporated in its description, in conjunction with time-varying boundary conditions obtained from a time-dependent, three-dimensional, hydrodynamic model of the polar ionosphere. This enables us to properly account for the variation of boundary conditions along a flux tube trajectory. Initially, our macroscopic PIC model was solved for steady state conditions. This allowed us to compare results from our code with those of a prior study of centrifugal acceleration that uses a PIC formulation. Also, by obtaining steady state solutions for both low and high electron temperatures, we have been able to directly compare the effects of electron temperature and centrifugal force on the polar plasma outflow, a comparison that a time-dependent simulation might obscure. Then time-dependent PIC solutions were obtained for the plasma in a convecting flux tube, using solutions to a time-dependent, three-dimensional, hydrodynamic model to provide realistic boundary values for the electron and ion temperatures and the H+ and O+ densities and drift velocities along a flux tube trajectory. Both steady state and time-dependent solutions indicate that centrifugal acceleration does not significantly contribute to the loss of plasma from the polar ionosphere.

Solutions to bi-Maxwellian transport equations for the polar wind

Abstract In the past, the polar wind has been simulated using transport equations based on either a Maxwellian or a bi-Maxwellian velocity distribution function. Previous solutions obtained for both the Maxwellian-based 13-moment set of equations and the bi-Maxwellian-based 16-moment set of equations have indicated that these two approaches are in close agreement with each other. However, due to the numerical problems involved in solving the transport equations, the solutions obtained were few in number and represented only a small subset of the possible range of polar wind behavior. In this study, we obtained polar wind solutions for a broad range of O + density, H + drift velocity, electron temperature and H + temperature boundary conditions. We used the bi-Maxwellian-based 16-moment set of transport equations, since this set is expected to be superior to Maxwellian-based equations in describing large temperature anisotropies and heat flows. Our solutions corroborate the earlier results when similar boundary conditions are used. Also, for previously unexplored combinations of boundary conditions, our solutions are often qualitatively different from any obtained before.

Semikinetic and generalized transport models of the polar and solar winds

Thermal space plasmas have generally been modeled either by direct solution of the collisionless Boltzmann equation or by solving a set of transport equations obtained by multiplying the Boltzmann equation by suitable velocity moments and integrating over velocity space. The former approach gives the spatial-temporal variation of the distribution function itself, whereas the latter approach provides only partial information regarding the distribution function through the spatial-temporal variation of a finite number of velocity moments. However, the transport approach can easily incorporate the effects of collisions and chemical reactions into the description, whereas a direct solution of the Boltzmann equation (the kinetic approach), in any but a collisionless regime, has proven to be difficult. A vast body of work has been done in space plasma physics in which either a transport (e.g., hydrodynamic, hydromagnetic, generalized transport) or a kinetic (e.g., fully kinetic, semikinetic) approach has been employed. In order to properly understand the significance of this work, it is critical that a better understanding be gained of the relative merits of the transport and kinetic approaches. As a first step in this direction, a comparison has been made, in as consistent a manner as possible, of a transport (bi-Maxwellian based 16-moment equations) and a semikinetic description of supersonic flow in the solar wind and also of both supersonic and subsonic flows in the polar wind for “steady state” conditions. The study shows: (1) remarkable agreement between the two models for supersonic collisionless flows, even for the higher-order moments; (2) the inadequacy of the semikinetic approach for modeling subsonic flows; and (3) the superiority of the 16-moment transport over the semikinetic approach for modeling the solar wind. Our study provides further evidence that the bi-Maxwellian based transport equations are a useful tool for studying “thermal” space plasmas that develop non-Maxwellian features.

Trapped particles in the polar wind

The flow of plasma along open field lines at high latitudes is highly variable and depends both on conditions in the underlying ionosphere and thermosphere and on the transport of particles and energy from the magnetosphere. Past attempts to model this time variability have, for the most part, examined the response of the plasma on a stationary field line to certain prespecified boundary conditions and heat sources. While such prespecified conditions may bear some resemblance to what occurs naturally, they are artificial and cannot be expected to yield a truly quantitative understanding of the various physical processes that interact to produce the dynamic polar wind. The present study is one in a series of studies that attempts to eliminate this artificiality by coupling the mathematical description of the polar wind to a three-dimensional time-dependent model of the high-latitude ionosphere. In this study, an individual flux tube of plasma is followed as it moves under the influence of combined corotation and convection electric fields. Boundary conditions at the lower end of the flux tube are obtained from the ionosphere model, which takes into account all significant particle species, chemical reactions, and heat sources that contribute to the state of the ionosphere. A multi-ion macroscopic particle-in-cell code is used to model the plasma in the flux tube. A description of the behavior of H+ and O+ for the altitude range from 2000 km to about 8 Earth radii is obtained as the flux tube moves along the trajectory, which traverses regions of the subauroral ionosphere, dayside and nightside ovals, and polar cap. The goal of the study is to determine the extent to which ion trapping can occur in the polar wind and the effects that collisions, wave-particle interactions, centrifugal acceleration, and varying ionospheric conditions have on the trapped ions. The main conclusion of the study is that O+ trapping is important and it acts to increase the O+ density at high altitudes.

Seasonal and solar cycle variations of the polar wind

Until recently, theoretical models of the polar wind were one-dimensional. In these models, reasonable but ad hoc boundary conditions were fed to a mathematical model, which was then solved to provide either a steady state or time-dependent description of the plasma along a particular field line. These models were inherently unable to address the three-dimensional structure of the polar wind. Now, a truly global model of the polar wind has been developed. This model is a three-dimensional, time-dependent, fluid model that self-consistently couples the ionosphere and the polar wind. It describes the plasma dynamics in a large number of high-latitude flux tubes as they move under the combined influence of corotational and convection electric fields. The model incorporates realistic models of the high-latitude convection and auroral electron precipitation. In this study, the global model of the ionosphere and polar wind was used to illuminate the seasonal and solar cycle variability of the polar winds three-dimensional structure. In particular, the three-dimensional distribution of both H+ and O+ ions in the polar wind was examined for both solar maximum and minimum conditions and for both summer and winter solstices, as well as for various levels of geomagnetic activity. Over 1000 flux tubes of plasma are modeled for each set of geophysical conditions considered in this study, providing a horizontal resolution that is much finer than in previous applications of the global model. The modeling results are compared with relevant observational databases.

A multi‐ion generalized transport model of the polar wind

The higher-order generalizations of the equations of standard hydrodynamics, known collectively as generalized transport theories, have been used since the early 1980s to describe the terrestrial polar wind. Inherent in the structure of generalized transport theories is the ability to describe not only interparticle collisions but also certain non-Maxwellian processes, such as heat flow and viscous stress, that are characteristic of any plasma flow that is not collision dominated. Because the polar wind exhibits a transition from collision-dominated to collisionless flow, generalized transport theories possess advantages for polar wind modeling not shared by either collision-dominated models (such as standard hydrodynamics) or collisionless models (such as those based on solving the collisionless Boltzmann equation). In general, previous polar wind models have used generalized transport equations to describe electrons and only one species of ion (H+). If other ion species were included in the models at all, it was in a simplified or semiempirical manner. The model described in this paper is the first polar wind model that uses a generalized transport theory (bi-Maxwellian-based 16-moment theory) to describe all of the species, both major and minor, in the polar wind plasma. In the model, electrons and three ion species (H+, He+, O+) are assumed to be major and several ion species are assumed to be minor (NO+, Fe+, O++). For all species, a complete 16-moment transport formulation is used, so that profiles of density, drift velocity, parallel and perpendicular temperatures, and the field-aligned parallel and perpendicular energy flows are obtained. In the results presented here, emphasis is placed on describing those constituents of the polar wind that have received little attention in past studies. In particular, characteristic solutions are presented for supersonic H+ outflow and for both supersonic and subsonic outflows of the major ion He+. Solutions are also presented for various minor ions, both atomic and molecular and both singly and multiply charged.

Comparison of semikinetic and generalized transport models of the polar wind

A comparison has been made, in as consistent a manner as possible, of a transport (bi-Maxwellian based 16-moment equations) and a semikinetic description of the terrestrial polar wind. The comparison shows a remarkably close agreement in the corresponding predictions for the altitude variation of the density, drift velocity, parallel and perpendicular (to B) temperatures, and the flow of parallel and perpendicular thermal energies. This close agreement provides further evidence that the bi-Maxwellian based transport equations are a powerful tool for studying thermal space plasmas that develop non-Maxwellian features.

Dynamic features of the polar wind in the presence of hot magnetospheric electrons

A time-dependent macroscopic particle-in-cell (mac-PIC) model was used to study the temporal evolution of the polar wind under the influence of a hot electron population. First, the steady state results of the mac-PIC model were found for a wide range of hot/cold electron temperature ratios and compared with the results of the well-established time-independent semikinetic model, and excellent agreement was found. Second, simulations were conducted to study the temporal evolution of a plasma that was originally in a steady state condition, and then a hot electron population was suddenly introduced. The profiles of the plasma moments again displayed discontinuities, which oscillated with a decreasing amplitude until they reached their steady state values. As the hot electron temperature increased, the oscillation amplitude increased, and the altitude of the discontinuity decreased, while the period of oscillation and decay rate remained essentially unchanged. Third, simulations were conducted for plasma flux tubes as they drifted across the subauroral, cusp, polar cap, and auroral regions. It was found that as soon as the plasma entered the polar cap, the signatures of the hot electrons were observed. The strength of these signatures varied with time owing to the variation in the instantaneous values of the density and temperature of the thermal electrons. After the plasma exited the polar cap the signatures of the hot electrons persisted for a while, and a density bump formed. For more energetic hot electrons the signatures of the hot electrons became more pronounced in the polar cap and persisted longer after the flux tube left the polar cap. The results of this study were shown to explain some interesting features of the polar wind that were observed by the POLAR satellite.

Solutions to bi-Maxwellian transport equations for radial solar wind beyond 28 Rs

Abstract There have been numerous attempts to model the solar wind using closed self-consistent sets of transport equations. These models have employed coupled continuity, momentum and energy equations. If stress and heat flow effects have been accounted for at all, it has usually been done in a simplistic and/or empirical fashion. Sets of transport equations that are based on a higher-order approximation to the velocity distribution function can include stress and heat flow equations in a self-consistent way, thus putting the stress and heat flow moments on an equal footing with the number density, drift velocity and temperature. Such equations are capable of describing both collisionless and collision-dominated plasmas as well as the transition between these two regimes. We present solar wind solutions for radial flow between 28 solar radii and 1 a.u. using the bi-Maxwellian based 16-moment set of transport equations. In addition to the number density, drift velocity and parallel and perpendicular temperatures, the 16-moment equations account for the transport of both longitudinal and transverse thermal energies as well as stress. Also, using the 16-moment approximation for the distribution function and assuming plasma parameter values characteristic of the solar wind, we generate contour plots for the proton velocity distribution function and show how the shape of these plots depends on various macroscopic plasma parameters.

Shocks in the polar wind

The occurrence of shock waves in the terrestrial polar wind was predicted many years ago by a time-dependent three-dimensional model based on hydrodynamic equations. These shocks were seen to occur for counterstreaming ion populations and for cases when a convecting flux tube entered a region of sharply increasing electron temperature, such as the dayside cusp. Other studies conducted at about the same time showed that the shocks induced by counterstreaming ion populations may simply be artifacts of the adopted hydrodynamic model. The validity of shocks induced by electron temperature enhancements has remained an open question. Using a macroscopic particle-in-cell (PIC) code, we have verified the hydrodynamic prediction that sudden electron temperature enhancements can launch shock waves in a convecting flux tube of plasma. Our simulation follows a flux tube as it convects antisunward across the dayside auroral oval, the polar cap, and the nightside auroral oval. The electron temperature at 2000 km altitude is assumed to be relatively low (3000 K) in the subauroral ionosphere and in the polar cap but much higher (7000 K) in the dayside and nightside auroral oval. As the flux tube enters the auroral oval, either on the dayside or the nightside, forward and reverse shock pairs in the H+ component of the plasma are created at the bottom of the flux tube and propagate upward until they exit the simulation region at the top. The forward and reverse shock fronts propagate at speeds greater than and less than the drift speed of the H+ gas, respectively.