JOURNAL OF G EOPHYSICAL RESE ARCH. VO L. 94 . NO . A7. PAG E 8973-8991 , J ULY I. 1989 A Three-Dimensional Time-Dependent Model of the Polar Wind R. W. SCHUNK AND J. J. SOJKA Center for Atmospheric and Space Sciences, Utah State University, Logan A time-dependent global model of the polar wind was used to study transient polar wind per­ turbations during changing magnetospheric conditions. The model calculates three-dimensional distributions for the NO+, ot, Nt, N+ and 0 + densities and the ion and electron tempera­ tures from diffusion and heat conduction equations at altitudes between 120 and 800 km. At altitudes above 500 km, the time-dependent nonlinear hydrodynamic equations for 0 + and H+ are solved self-consistently with the ionospheric equations. The model takes account of supersonic ion outflow, shock formation, and ion energization during a plasma expansion event. During the simulation, the magnetic activity level changed from quiet to active and back to quiet again over a 4.5-hour period. The study indicates the following: (1) Plasma pressure changes due to Te , Ti or electron density variations produce perturbations in the polar wind. In particular, plasma flux tube motion through the auroral oval and high electric field regions produces transient large-scale ion upflows and downflows. At certain times and in certain regions both inside and outside the auroral oval, H+-O+ counterstreaming can occur, (2) The density structure in the polar wind is considerably more complicated than in the ionosphere because of both horizontal plasma convec­ tion and changing vertical propagation speeds due to spatially varying ionospheric temperatures, (3) During increasing magnetic activity, there is an overall increase in Te , Ti and the electron density in the F-region, but there is a time delay in the buildup of the electron density that is . as long as five hours at high altitudes, (4) During increasing magnetic activity, there is an overall increase in the polar wind outflow from the ionosphere, while the reverse is true for declining activity, (5) In certain regions, however, localized ionospheric holes can develop during increasing magnetic activity, and in these regions the polar wind outflow rate is reduced, (6) During changing magnetic activity, the temporal evolution of the ion density morphology at high altitudes can be different from, and even opposite to, that at low altitudes. 1. INTRODUCTION Burch, 1985; Persoon et al., 1983] . Also, theoretical mod­ In the early 1960s, it was recognized that the interaction elling has shown that the polar \\' ind is collision-dominated of the solar wind with the Earth's dipole magnetic field acts at low altitudes (;5 2000 km) and collisionless at high al­ to significantly modify the magnetic field configuration in a titudes. The collision-dominated characteristics of the flow vast region close to the Earth [Axford and Hines, 1961] . The have been extensively studied with the aid of hydrodynamic dynamo action associated with the flow of solar wind plasma models [Banks and Holzer, 1968, 1969; Marubashi, 1970; across magnetic field lines generates an intense current sys­ Raitt et al., 1975, 1977; Schunk et al. , 1978]. When colli­ tem, which acts to compress the Earth's magnetic field on sions prevail, the temperature (or pressure) distribution is the dayside and stretch it into a long comet-like tail on the isotropic and the heat flow is proportional to the tempera­ nightside. The magnetic field lines that form the tail origi­ ture gradient. In the collisionless regime, on the other hand, nate in the Earth's polar regions, and since the pressure in the temperature distribution is anisotropic and the mathe­ ~he ionosphere is much greater than that in the distant tail, matical formulation of the polar wind is considerably more It was suggested that a continual escape of thermal plasma complicated. This collisionless regime has been modelled (H+ and He+) should occur along these 'open' field lines with hydromagnetic [Holzer et al., 1971] , kinetic [Lemaire, [Bauer, 1966; Dessler and Michel, 1966]. 1972; Lemaire and Scherer, 1970, 1973], and semi-kinetic The early suggestions of light ion outflow were based on a [Barakat and Schunk, 1983, 1984] equations. Also, gen­ t.hermal evaporation process. Via thermal evaporation, the eralized transport equations have been used that include ~~ht ions would escape the topside ' ionosphere with veloc­ both collision-dominated and collisionless characteristics of Ities close to their thermal velocities and then flow along the ion outflow, and hence, provide for continuity from the magnetic field lines to the magnetospheric tail. However, it collision-dominated to collisionless regimes [Schunk and was. Subsequently argued that the outflow should be super­ Watkins, 1981, 1982; Demars and Schunk, 1986, 1987; Gan­ BOme and it was termed the 'polar wind' in analogy to the guli, 1986; Ganguli and Palmadesso, 1987; Ganguli et al. , ~lar wind [Axford, 1968]. A simple hydrodynamic descrip­ 1987] . t~on was then used that emphasized the supersonic nature All of the above studies of the 'classical' polar wind were 0. the flow and the basic polar wind characteristics were elu­ for 'steady state' conditions, with the emphasis on elucidat­ Cl~ted [Banks and Holzer, 1968, 1969; Marubashi, 1970]. ing physical processes. As a result of these studies, signif­ I he supersonic nature of the polar wind has now been icant progress has been made in understanding the basic Cearly established by both direct and indirect methods [Hoff­ polar wind characteristics for a wide range of conditions [cf. man and Dodson, 1980; Nagai et al., 1984; Gurgiolo and Schunk, 1986, 1988] . More recently, attention has been fo­ cussed on studying the temporal characteristics of the polar wind. However, because of the severe numerical difficulties Copyright 1989 by the American Geophysical Union. associated with solving the more complicated sets of trans­ ~~per number 89JA00211. port equations [ef. Schunk, 1977; Demars and Schunk, 1979; 48-0227/89/89JA-00211$05.00 Barakat and Schunk, 1982], the initial time-dependent mod- 8973 8974 SCHUNK AND SOJKA: THREE· DIMENSIONAL POLAR WIND els of the classical polar wind were based on a hydrodynamic sumption that local heating and cooling processes dOminate formulation [Singh and Schunk, 1985; Gombosi et al., 1985 , (valid below 500 km). Flux tubes of plasma were followed 1986; Gombosi and Schunk, 1988]. as they moved in response to convect ion electric fields. A Singh and Schunk [1985] studied the temporal evolution further extension of the model to include the minor ions N+ of density perturbations in the supersonic collisionless polar and He+ , an updated photochemical scheme, and the mass wind, including extended density depletions and localized spectrometer/incoherent scatter (MSIS) atmospheric model density bumps and holes. For this study, the H+ continu­ is described in Schunk and Raitt [1980]. ity and momentum equations were solved without allowance The addition of plasma convection and particle precipita. for collisions and assuming constant, isotropic ion and elec­ tion models is described in Sojka et al. [1981a , b) . More re­ tron temperatures of 3560 K. Also, the effects of localized cently, the ionospheric model has been extended by SchUnk ion heating on the polar wind were studied by Gombosi et and Sojka [1982a] to include ion thermal conduction and al. [1985, 1986] and by Gombosi and Killeen [1987]. Both diffusion-thermal heat flow , so that the ion temperature is high-altitude and low-altitude ion heating events were con­ now rigorously calculated at all altitudes between 120-800 sidered. In these studies, the full hydrodynamic continuity, km. The adopted ion energy equation and conductivities are momentum, and energy equations for H+ , 0+, and electrons those given by Conrad and Schunk [1979]. Also, the electron were solved including collisional conductivities and assum­ energy equation has been included recently by Schunk et al. ing isotropic, but variable, ion and electron temperatures. [1986], and consequently, the electron temperature is now More recently, Gombosi and Schunk [1988] conducted a rigorously calculated at all altitudes. The electron energy comparative study of plasma expansion events in the polar equation and the heating and cooling rates were taken from wind. The temporal characteristics of the polar wind were Schunk and Nagy [1978], and the conductivities were taken studied with both a full set of hydrodynamic equations and from Schunk and Walker [1970]. a simplified set of collisionless equations that took account . of the extremely large ion temperature anisotropies that de­ 2.2. High-Altitude Hydrodynamic Model velop at high altitudes [ef. Holzer et al. , 1971; Lemaire and The high-altitude model is based on a numerical solution Scherer, 1973]. These temperature anisotropies were shown of the time-dependent coupled continuity and momentum to be stable with respect to the excitation of electrostatic equations for H+ and 0+ ions. The equations are solved waves by Barakat and Schunk [1987]. The two different po­ along a diverging 'open' magnetic flux tube with boundary lar wind models were solved with different numerical tech­ conditions specified at low altitudes and outflow conditions niques and the results were compared for a range of idealized imposed at high altitudes. The specific equations adopted expansion scenarios. The models were also used to study are as follows: the temporal response of the polar wind to varying electron temperature conditions. (1) All of the time-dependent polar wind studies described above were based on one-dimensional models applied to a single location, with the temporal variations driven by as­ sumed inputs. In this paper, we present a time-dependent, three-dimensional, multi-ion model of the polar wind. The model covers the altitude range of from 120 to 9,000 km and takes account of supersonic ion outflow, shock formation, +p·--+nCME ·k (IIT. -T....1.) --1aA \ r2 \ \ t A ar and ion energization during plasma expansion events.