A Dynamic Fluid Kinetic (DyFK) simulation is conducted to study the H+/O+ flows and distribution functions in the high-latitude dynamic transition region, specifically from 1000 km to about 4000 km altitude. Here, the collisional-to-collisionless transition region is that region where Coulomb collisions have significant but not dominant effects on the ion distributions. In this study, a simulation flux tube, which extends from 120 km to 3 RE altitude, is assumed to experience a pulse of auroral effects for approximately 20 minutes, including both soft electron precipitation and transverse wave heating, and then according to different geophysical circumstances, either to relax following the cessation of such auroral effects or to be heated further continuously by waves with power at higher frequencies. Our principal purpose in this investigation is to elicit the characteristic ion distribution functions in the auroral transition region, where both collisions and kinetic processes play significant roles. The characteristics of the simulated O+ and H+ velocity distributions, such as kidney bean shaped H+ distributions, and O+ distributions having cold cores with upward folded conic wings, resemble those observed by satellites at similar altitudes and geographic conditions. From the simulated distribution function results under different geophysical conditions, we find that O+-O+ and O+-H+ collisions, in conjunction with the kinetic and auroral processes, are key factors in the velocity distributions up to 4000 km altitude, especially for the low speed portions, for both O+ and H+ ions.
 In the classical polar wind, in the region between about 1000 and 3000–4000 km altitude, both ion-ion collisions and macroscopic forces are significant but not necessarily dominant influences on the ion transport behavior and characteristic distribution functions. Typically, between 1500 and 2500 km altitude, the polar wind ion characteristics are predicted to transition from collisional dominance to a nearly-collisionless regime [André and Yau, 1997]. At altitudes below this collisional/collisionless transition region, O+ and H+ usually have near-Maxwellian distributions owing to frequent ion-ion collisions [St.-Maurice and Schunk, 1979; Ho et al., 1997]. Above the transition region, non-Maxwellian distributions gradually develop because of the accelerations produced by macroscopic forces and other processes [e.g., Ho et al., 1997; Wilson, 1992]. In the collisional/collisionless transition region the competing processes of collisions, kinetic effects and macroscopic forces play important roles in the developments of the characteristic velocity distribution functions [Wilson, 1995; Barghouthi et al., 1993; Barakat et al., 1995].
 To date, only a limited set of simulations has been conducted to investigate the dynamics of O+ and H+ distribution functions in the collisional/collisionless transition region. Incorporating a static O+ background, Schunk and Watkins [1981, 1982] used a generalized transport model to simulate the electron and proton temperatures from 1500 km to 12000 km altitudes. Their model included H+ self collisions while H+-O+ collisions were ignored. These simulations predicted that above 2500 km the electron perpendicular temperature is higher than the parallel temperature, with both temperatures increasing with altitude. Temperature anisotropies were present in the simulated H+ distributions, while the parallel temperature was enhanced for supersonic flow regions and the perpendicular temperature was enhanced for subsonic flow regions. Barakat and Lemaire  used Monte Carlo methods for a general study of the transition region. They simulated the velocity distribution function of the minor species by tracking the motion of a large number of simulation particles through a collisionally-dominant region, while employing a variable mass ratio for the minor-to-background species. They assumed a local Maxwellian distributed and isothermal background. In the Barakat and Lemaire  model, the gravitational force was simulated by including a critical velocity, the electromagnetic force was ignored, and the non-resonant ion-neutral interactions were simulated through use of both Maxwell molecule collision and hard sphere collision assumptions. Their results showed that the ratio of normalized parallel temperature to normalized perpendicular temperature decreased with altitude, approaching the collisionless region. An asymmetry involving an upward tail of the distribution function was observed. Barghouthi et al.  used similar techniques to study the steady state H+ flow through an O+ background similar in treatment to that employed by Barakat and Lemaire . This improved model incorporated H+-O+ collisions, although H+ self-collisions were neglected, and used a Fokker-Planck representation for Coulomb collisions. The effects of gravity, the polarization electric field, and the divergence of the geomagnetic field were also included in the model. The Barghouthi et al.  results indicated that the H+ distribution changed rapidly from Maxwellian to a “kidney bean” shape in the transition region, and the modeled flow changed from subsonic to supersonic with the sonic point occurring in the transition region [Barghouthi et al., 1993].
 A semikinetic, time-dependent model, tracking the motion of ion gyrocenters, was used to investigate the H+ and O+ outflows through the transition region under different circumstances [Wilson, 1992, 1995; Ho et al., 1995, 1997]. The transition from O+ dominance to H+ dominance was incorporated as the H+ ions passed through the collisional/collisionless transition region by including H+ self-collisions, as well as all of the macroscopic forces (i.e., gravity, ambipolar electric, and mirror). Assuming a static O+ background, Wilson  found that the effects of H+-O+ collisions were evident in the H+ velocity distribution functions at altitudes above the region of H+-O+ collisional dominance, and H+ exhibited significant non-Maxwellian distributions in the transition region. When downward H+ flows with sufficient number densities were present, the H+ bulk flow was constrained to be subsonic and multiple peaks were present in the simulated velocity distribution functions, owing to the low self-collision rate. Similar double-hump H+ distribution functions were present at lower altitudes (starting at about 1100 km) in the simulations of Barakat et al. . Wilson  simulated both H+ and He+ distribution functions in the transition region where collision time scales and length scales were comparable to transport time and length scales, and found that the effects of collisions could be nonlocal, i.e., the velocity distribution function at one location could evolve via collisions that occur at a distant location. Using a dynamic O+ background, Ho et al.  investigated the effects of centrifugal force and frictional heating caused by ionospheric convection in the range 200–6000 km altitude. The resonant charge exchange collisions O+-O and O+-H were also considered in their simulations. The results showed that the distribution functions of H+ and O+ ions and their bulk parameters at collisionless altitudes greatly depended on the collisional and chemical processes (induced by a 200 mV m−1 convection electric field), as well as centrifugal acceleration, at lower altitudes where the collisions were significant. The centrifugal force energized O+ more than H+ because the velocity accelerations for different species tend to be comparable because they are driven by the equal convection speeds [cf. Horwitz and Lockwood, 1985]. The centrifugal force was also found to indirectly influence the H+ distribution function via the H+-O+ collisions. The dynamics of H+ and O+ in the transition region were investigated for varying convection conditions [Ho et al., 1997]. Ho et al.  found that the collisional/collisionless transition region for H+ was more extended in altitude during stronger convection, owing to the effects on the O+ density profile.
 It has long been recognized that auroral processes play important roles in ion acceleration by many in situ observations [e.g., Yau et al., 1983; Pollock et al., 1990; Moore et al., 1996] and complementary simulations [Ganguli and Palmadesso, 1987; Brown et al., 1991; Wu et al., 2002]. Certain previous investigations [e.g., Wu et al., 1999, 2002] have focused on two auroral processes, i.e., soft electron precipitation and wave-induced transverse ion heating, to elicit their effects on auroral ion transport. Soft electron precipitation can effectively ionize the F-region and elevate ionospheric ion supply to higher topside altitudes where the wave-driven transverse ion heating in combination with the magnetic mirror force pumps ions upward [Wu et al., 1999, 2002]. Thus far most simulations which have focused on the collisional/collisionless transition region have been conducted for the nominal polar cap region. Auroral processes have not been, to our knowledge, incorporated into simulation investigations focused on the transition region. In this paper, we present the results of a focused simulation study of the collisional/collisionless transition region under dynamic auroral effects. Two important auroral processes, soft electron precipitation and wave-induced transverse ion heating, are incorporated into our simulation. It may be noted that in the FAST observations of Strangeway et al. , for example, strong evidence has been found for the effects of wave activity and soft electron precipitation being the principal drivers of ionospheric outflows. Although some modeling studies [Cannata and Gombosi, 1989] indicated that H+ should be a minor species throughout the transition region at all altitudes, which might permit the neglect of H+ self-collisions under certain circumstances, the studies of Wilson  indicated that the densities of O+ and H+ can be comparable in the transition region, and Ho et al.  also showed the necessity of considering a dynamic O+ background in terms of influencing the H+ distributions. In the present simulations, H+ self collisions, resonant charge exchange between O+ and H, O+ self collisions, and charge exchange collisions between O+ and O, as well as polarization interactions between O+ and N2, are included in the simulation of the auroral transition region. Macroscopic forces included are the ambipolar electric force, gravity, mirror force, and centrifugal force due to E × B convection. Further details of the model and the present simulation are presented in the next section.
2. Description of the Dynamic Fluid-Kinetic Model
 The Dynamic Fluid-Kinetic (DyFK) model used in the simulations presented here is a time-dependent, one-dimensional high-latitude plasma transport model [Estep et al., 1999]. It couples a truncated version of the field line interhemisphere plasma (FLIP) model [Richards and Torr, 1990] to the generalized semi-kinetic (GSK) model [e.g., Wilson, 1992] across an overlapped boundary region. Using this model, Wu et al.  simulated the auroral plasma outflow driven by transverse ion heating and soft electron precipitation, and further investigated the synergistic effects of parallel potential, transverse ion heating, and soft electron precipitation on auroral ionospheric plasma transport. Tu et al. [2004, 2005] compared, respectively, simulated field-aligned density profiles with Imager for Magnetopause-to-Aurora Global Exploration (IMAGE)/Radio Plasma Imager (RPI) measurements, and simulated the cleft ion fountain effects for comparison with Polar/TIDE altitude in observations.
 In this paper, we simulate the ion flows in a flux tube extended from 120 km to 3 RE altitude with this DyFK model. In the lower, fluid-treatment portion, the densities of the major neutral species and neutral temperatures are provided by the mass spectrometer and incoherent radar (MSIS-86) model [Hedin, 1987], with 3-hour Ap magnetic activity index option, and the neutral wind parameters are obtained from the horizontal wind (HWM-93) model [Hedin et al., 1996]. The upper boundary of this portion is set at 1100 km altitude. The upper boundary conditions for this fluid-treatment region, such as the ion density, parallel velocity, heat flux and the electron temperature, are provided at each time step by results of the advancing GSK treatment. The fluid-treatment portion includes the effects of precipitating auroral electrons on the ionospheric ions and electrons, which is adopted in the simulation of the auroral processes. In the altitude region 800 km – 3 RE of the flux tube, a generalized semi-kinetic (GSK) treatment is used to advance the O+ and H+ gyrocenters. The simulation ions are injected at the lower boundary of the GSK portion using distributions based on the moment parameters resulting from the fluid-treatment results at that altitude for each alternating time step. The simulation ions are subject to the macroscopic forces of field-aligned electric field, gravity, geomagnetic mirror force and centripetal force. The parallel motion of the ions is in part described through the equations:
where mi and qi are the ion mass and charge, E∥ is the field-aligned electric field, G is the gravitational constant, ME is the mass of the earth, r is the geocentric distance, μi = mivi⊥2/(2B) is the magnetic moment, B is the geomagnetic field, VC is the E × B/B2 convection velocity, and is the unit vector in the direction of B. The magnetic field is assumed to be dipolar, which should be sufficiently accurate for the altitude range of this simulation. Each simulation O+ or H+ ion represents about 2.1 × 1010 or 2.4 × 109 real O+ or H+ particles, respectively. In the simulations conducted for this paper, the number of total simulation O+ and H+ particles in the flux tube from 800 km to 3 RE was approximately 5 × 105 and 3 × 105, respectively, allowing relatively smooth velocity distribution functions.
 In addition to the indicated macroscopic forces, the simulation particles are also subject to Coulomb collisions, collisions with neutrals and wave-particle interaction effects. Ion-neutral collisions incorporated in this study include: (1) polarization collisions between O+ and O; (2) polarization collisions between O+ and N2; and (3) O+-O resonant charge exchange (RCE) collisions [Tu et al., 2004]. The Coulomb collisions between O+-O+, H+-H+, and O+-H+ are treated via the Monte Carlo algorithm described by Miller and Combi . This algorithm is similar to that proposed by Takizuka and Abe , which was widely used in previous simulation studies [Wilson, 1992; Barghouthi et al., 1994; Ho et al., 1997]. The advantage of the Miller and Combi Coulomb collision algorithm is that it conserves energy and momentum when the colliding simulation particles have different weights, which is the case of our simulation. The DyFK model tests have shown that the total energy and momentum of O+ and H+ ions are indeed conserved after each Coulomb collision when the newer Miller and Combi Coulomb collision algorithm is used [Tu et al., 2005].
 Ample electromagnetic waves and evidence of wave-particle interactions have been observed in the auroral zone [e.g., Yau et al., 1983; André, 1997]. Various mechanisms for the wave-particle interaction have been discussed [e.g., Norqvist et al., 1998; Lund et al., 2000]. In the present simulation, the wave-induced transverse ion heating rate is calculated following the procedure of Crew et al.  as 2miDi⊥, where
in which ∣E∣2 is the electric spectral density at the ion gyrofrequency Ω(r). The factor η is the ratio of the left handed polarized wave components, which is assumed to be 0.125 [Chang et al., 1986]. A more complete description of the wave-induced ion transverse heating effects incorporated in these simulations has been given by Wu et al. [1999, 2002] and Tu et al. .
 It should be noted that some other investigators have employed a diffusion coefficient Di⊥(r) which is velocity dependent [Barghouthi et al., 1998]. In such cases, perpendicular velocity saturations may appear when the ion Larmor radius is larger than the perpendicular wavelength. The perpendicular broadband extremely low frequency (BBELF) wavelength is, however, difficult to measure, and other authors have used Crew et al.  type wave-particle diffusion coefficients in recent papers [e.g., Bouhram et al., 2003]. Hence, we believe it is reasonable to use the indicated approach to the wave-particle velocity diffusion to illustrate at least semi-quantatively the effects in the transition region.
 The full DyFK simulation flux tube extends from 120 km altitude to 3 RE. For the simulation described in this paper, the flux tube was initially run to a quasi-steady polar wind state. The auroral effects (soft electron precipitation and wave-induced ion transverse heating) were then turned on for 19.2 minutes (this time turns out to be more convenient in running the code than 20 minutes) to simulate the effects of a pulse of auroral processes. During the auroral pulse, the ion transverse heating was assumed to be produced by broadband extremely low frequency (BBELF) electrostatic waves [Norqvist et al., 1998]. Following the phase of auroral effects, the soft electron precipitation was then turned off, and two possible scenarios were explored in our simulation. For the case in which the auroral pulse was associated with a time-dependent burst on a relatively stationary flux tube, the simulation flux tube was assumed to be heated continuously by “lower hybrid” waves such as those observed by DE 1 [Gurnett and Inan, 1988] and Freja [André et al., 1998] for another 40 minutes. We also simulated the flux tube convecting through a region of auroral processes by allowing the flux tube to relax for 40 minutes after the auroral pulse. The foot point of the flux tube was located at 77.58°S, 290.19°E geographically, and 66.56°S, 0.59°E geomagnetically. Other geophysical conditions in the simulation included setting the planetary activity index Ap = 17 and the solar radio activity index F10.7 = 142. The wave spectral density was approximated by
where ∣E0∣2 is the electric field spectral density at frequency ω0 and α is the power law index which was assumed to be 1.7 [Crew et al., 1990]. The wave spectral density was taken to be 0.3 × 10−6 V2 m−2 Hz−1 at 6.5 Hz, which is the O+ gyrofrequency at 1 RE altitude. This value is in the range of Freja and Viking spacecraft observations [André et al., 1998; Oscarsson and Ronnmark, 1990]. We further assumed that the BBELF waves were distributed between 1600 km and 2 RE altitudes during the phase of auroral effects, as used by Wu et al. . During the resonant heating by lower hybrid waves, we assumed that the wave frequency corresponding to the spectral density peak gradually moved higher, up to 400 Hz, while the wave spectral density peak remained 0.3 × 10−6 V2 m−2 Hz−1, as observed by Freja and Viking [André et al., 1998; Oscarsson and Ronnmark, 1990]. The lower hybrid waves were distributed from 1100 km to 1400 km altitude, which is consistent with the observations of DE 1 [Gurnett and Inan, 1988]. The soft electron precipitation stream was assumed to have a Maxwellian energy spectrum with a peak at 100 eV and an energy flux of 1.0 ergs cm−2 s−1 [Richards and Torr, 1990].
3. O+/H+ Distribution Function Features in the Transition Region
 In this section we present simulation results pertaining to O+ and H+ distribution function features in the altitude range from 1000 km to 4000 km altitude for before, during, and subsequent to the period of auroral effects. As noted in the previous section, for this simulation, before the auroral effects were turned on, the flux tube was in a quasi-steady polar wind state. The flux tube then experienced both wave-driven transverse ion heating and soft electron precipitation for 19.2 minutes. Subsequently, the soft electron precipitation was turned off, and the flux tube was either continuously heated by higher frequency waves or allowed to relax for another 40 minutes.
3.1. O+/H+ Distribution Function Characteristics Prior to Auroral Processes
Figure 1 displays the O+ velocity distribution functions for the quasi-steady state case, prior to introduction of auroral effects. It shows 10 gray-scaled distribution function contours for 10 different simulation cells at different altitudes within the transition region. Each contour plot is normalized to a peak value of one, and the magnitude of each successive contour of the distribution function, from the center, reduces by e−1/2, also indicated by the gray scale bar. The altitude range for each cell is indicated at the top of each plot. The distribution functions in each plot are symmetric about the Vperp = 0 line, appropriate to the convecting frame of reference.
 Below 2200 km altitude, O+ distribution function contours are observed in Figure 1 to appear essentially Maxwellian in shape, which indicates sufficiently frequent Coulomb collisions to thermalize and isotropize the ions. The parallel and perpendicular thermal energies (not shown) are similar, about 0.13 to 0.14 eV. Above this altitude, the contours narrow in the perpendicular direction, indicating a cooling of the perpendicular distribution. This perpendicular cooling results from partial magnetic moment conservation, and is similar to the H+ cooling process in perpendicular direction discussed by Wilson . As we can see from Figure 1, the O+ bulk velocity in the steady state is actually downward, although the magnitude is less than 100 m s−1 throughout the altitudes displayed. The O+ bulk velocities, which are slightly downward at this stage, play important roles in the formation of the H+ distribution function, as will be discussed in later sections.
Figure 2, which has a similar format to Figure 1, shows the H+ distribution functions for the same period and altitudes as for the O+ distributions in Figure 1. From the evolution of the H+ distribution at different altitudes, it may be observed that for altitudes below 1200 km for this case, the velocity distribution was approximately drifting Maxwellian with slight asymmetric upward heat flux. The H+ field-aligned bulk velocity was in the range from zero to less than 1 km s−1 upward. In the 1200–2500 km altitude range, the H+ distribution evolved toward having a significant upward bulk drift velocity with a downward stretched tail, indicating a downward heat flux. The peak of the distribution abruptly jumped from about 2 to near 10 km s−1 over the short altitude range between 1500 km to 1900 km. Between about 1500 and 1900 km was also where the heat flux changed rapidly from positive at lower altitudes to negative at higher altitudes (the heat flux profile is not shown here). The H+ heat flux is defined as
where uH+ = ∫vH+f()d, and mH+, nH+ are H+ mass and density, respectively. Therefore, the change of heat flux from upward to downward indicated asymmetries relative to the bulk velocity in the distribution function, i.e., stretched downward tails, developed in this altitude range. With increasing altitude the distribution was gradually depleted of all downward moving particles, and the distribution also narrowed in the perpendicular direction, owing to partial conservation of the first adiabatic invariant. A “kidney bean” distribution gradually developed [Barghouthi et al., 1993]. The H+ distribution peak velocity “jump” may be understood through consideration of the following approximate H+-O+ collision frequency expression [Takizuka and Abe, 1977]:
In this circumstance, ν is the Coulomb collision frequency between H+ and O+ which can change the H+ velocity, nO+ is the background O+ density, mH+, mO+ is the H+, O+ mass, respectively. EH+ = mH+ (VH+ − VO+)2/2 represents the kinetic energy of an H+ ion relative to O+ background bulk velocity, and λ is the Coulomb logarithm, which may be taken to be ∼10, μ(x) is defined as:
where x denotes and = + is the O+ temperature. As an example, the relationship between the H+-O+ collision frequency and H+ kinetic energy is displayed in Figure 4. This is the result at 1500 km altitude in our present simulation. It should be noted that equations (5) and (6) and Figure 4 are computed assuming a Maxwellian distribution for the O+ background. As noted previously, some departures from Maxwellian O+ distribution functions gradually developed with increasing altitude in the transition region. However, these departures should not affect the basic trends suggested in these equations and Figure 4. We can see from Figure 4 that H+ collisions with the O+ background occur more frequently at small relative speeds, as also indicated by the v−4 dependence of the classical Rutherford scattering cross section. For the present case of an O+ background with near zero bulk velocity, the low speed portion of the H+ ion distribution experiences the greatest drag from H+-O+ collisions, see upper first, second, and third plots of Figure 2. Of course, ν is also proportional to the O+ density This density of course declines with altitude, e.g., from 4500 cm−3 at 1500 km altitude to 1800 cm−3 at 1900 km altitude in the present simulation. Hence, with increasing altitude, the H+ ions are increasingly unaffected by the H+-O+ collisional drag. Therefore, the peak velocity of the H+ distribution can often abruptly jump over a limited altitude range: the H+ peak velocity jumped from 2 km s−1 to 10 km s−1 from 1500 km to 1900 km altitude in our case. Even double peaks are evident in the H+ distribution function at some specific altitudes, as shown in the upper fourth plot of Figure 2. The H+ distribution evolution shown in Figure 2 is similar to that in Wilson  except that the jump of the peak of the distribution occurred over a range of altitudes about 400 km lower. The reason is that the self-consistent O+ density under the specific geophysical conditions in the present simulation is about 5 times lower than the static O+ background set by Wilson . Therefore, H+-O+ collisions were less frequent and H+ became “collisionless” at lower altitudes in the present study.
 It should be noted that collisions of O+ and H+ ions with molecular ions, such as N2+, NO+, and O2+ were not included in the Generalized SemiKinetic portion of our simulation flux tube, which is at altitudes above 1100 km altitude. According to the molecular ion measurements from DE 1 spacecraft [Craven et al., 1985], the density of total molecular ions was about 2 cm−3 in the dynamic transition region under active geophysical conditions (Kp ≥ 5). In the relatively quiet geophysical circumstance of our simulation (Kp ≈ 3), the densities of molecular ions were at least 2 orders of magnitude lower than O+ densities, and at least 1 order of magnitude lower than H+ densities. The effect of possible molecular ions within the transition region on the H+ and O+ distribution functions presented in this paper would not change appreciably if O+ and H+ collisions with molecular ions had been incorporated in our simulations.
3.2. O+/H+ Distribution Functions During Auroral Processes
 As described previously, the flux tube was next exposed to 19.2 minutes of auroral effects, including soft electron precipitation and wave-induced transverse ion heating. The parameters of soft electron precipitation and broadband extremely low frequency waves in this simulation have been described in section 2. Figure 3 shows the O+ velocity distribution functions at 9.6 minutes after the initiation of auroral effects. The O+ distributions below 1000 km (not shown here) remained approximately Maxwellian at 9.6 minutes after the initiation of the auroral effects. This is because in the profile of the presumed wave distribution the wave power declines rapidly below 1600 km altitude [Wu et al., 1999]. The wave heating rates for O+ decreased below the wave distribution region, and were negligible at altitudes lower than 1000 km. Beginning at the 1080–1119 km altitude cell, O+ perpendicular heating is increasingly apparent, and the perpendicular temperatures increase with altitude. As a portion of the energized O+ ions from the principal wave heating region moved downward and both mixed and collided with the relatively cold background, an O+ temperature increase was observed at altitudes as low as 1000 km.
 At altitudes above 1200 km, conic distributions exhibiting perpendicular wings increasingly developed, while retaining a cold core central distribution. O+ distribution functions observed by the Freja satellite near 1700 km altitude [cf. André et al., 1998, Figure 2], in which O+ ions were heated by broadband low-frequency waves in the auroral region, revealed similar characteristics to those of the present simulation results: an O+ distribution consisting of a cold core and extended perpendicular wings at higher velocities. The O+ distribution function observed by Freja displayed folding to 10°–15° from the perpendicular direction because the principal heating occurred below the observation point. In the present simulations, which incorporate wave heating at higher altitudes, conic folding toward the magnetic field direction is evident above 2000km altitude. The O+ distributions with cold cores and conic wings, sometimes called “upwelling ion distributions,” develop as altitude increases. These types of distribution functions have been observed by Dynamics Explorer-1 spacecraft in the dayside auroral in similar altitude ranges [Moore et al., 1985, Figure 4]. In the case studied by Moore et al. , O+ was presumably transversely heated at about 3000 km altitude, and the distribution function observed near 5000 km altitude contained conical lobes with a cone half angle of approximately 45°. As shown in Figure 3, the O+ distribution functions obtained in our simulation resemble those observed by DE 1, except that the half angle of the conic wings, about 65°, is wider than that of the observation. Several factors, such as the heating altitude, wave spectral density, and wave altitudinal distribution, influence their attribute. No effort in this simulation was made to adjust those parameters to attain close agreement with the results observed by Moore et al. .
Equations (5) and (6) can also be applied to O+ self-collisions, and a similar relationship between the O+ kinetic energy and the O+ self-collision frequency to Figure 4 can be obtained. In the present simulation, at 2200 km altitude, where the O+ distribution function with cold core and conic wings began to develop, the O+ density was about 1000 cm−3 and the temperature was ∼2200 K. The O+ ions with 1 km s−1 velocity collide with other O+ ions about 4.5 times more frequently that those with 3 km s−1 velocity. Low-energy O+ ions experienced more frequent self-collisions, and tended to thermalize the core of the O+ distribution function. For the higher energy O+ ions, kinetic processes dominated, owing to much less frequent self-collisions.
 The O+ distribution functions at other times during the auroral processes stage are similar to those in Figure 3. However, in the dynamic transition region, the heated O+ ions continuously flow up to higher altitudes, and the flux tube is replenished with relatively cold ionospheric O+ ions. The O+ bulk parameters, such as density, drift velocity, parallel and perpendicular temperatures, and heat flow, fluctuate after the auroral processes onset for 9.6 minutes. The O+ bulk parameters' temporal evolutions during the 19.2 minutes aurora presence are shown in Figure 5. One interesting feature is that the O+ perpendicular temperatures don't increase monotonically as wave-induced transverse heating goes on in the auroral processes phase. Owing to the soft electron precipitation and transverse heating effects, relatively cold ionospheric O+ rises to higher altitudes and increases the O+ densities there. This process increases the O+-O+ collision frequencies, which would tend to thermalize the ions and lead also to an increased downward heat conduction. A similar temporal trend can also be seen in the parallel temperature, as shown by the second plot at the bottom panel of Figure 5. However, comparing with the parameters prior to the auroral processes initiation, the temperature increase due to wave-induced transverse heating is striking: the O+ perpendicular temperature attains values up to 8 eV in the first 5 minutes, and the parallel temperature reaches 0.6 eV at 3000 km altitude, compared to the 0.14 eV prior to the heating effects.
 The corresponding H+ velocity distribution functions at 9.6 minutes after the onset of the auroral processes are displayed in Figures 6. From the third and fourth plots of the upper panel, the peak of the H+ distribution is observed to jump from around 5 km/s to approximately 10 km/s between 1500 km and 1700 km altitude. However, this change in the distribution peak is smaller than the change observed prior to the initiation of the auroral effects, as shown in Figure 2. This difference results because there are higher O+ densities at these altitudes during this period, which impose increased H+-O+ drag on the H+ low-energy distribution portion, and thus decrease the upward H+ velocity of the H+ distribution function peak. During this period, the O+ background is dynamic and its bulk velocities turn to upward and increase with altitude, as shown in Figure 3. The strongest O+-H+ collision drag occurs for H+ ions whose velocities are comparable to the background O+. We have examined H+ distribution functions for the period following that of Figure 6, and find that as H+-O+ drag on the H+ ions with comparable velocities becomes more significant, the phenomenon of the apparent abrupt jump with altitude of the H+ distribution peak disappears: the velocity of the distribution peak appears to gradually increase with altitude.
Figure 7 shows the temporal evolution of the H+ bulk parameters during the auroral effects phase. From Figure 6 and the first plot at the bottom panel of Figure 7, the H+ perpendicular temperature enhancements become apparent from about 1400 km altitude, while the similar temperature effects for O+ start from 1200 km altitude. As seen in Figure 7, following the period of auroral effects, the highest H+ perpendicular temperature attained is about 0.8 eV. The H+ perpendicular temperature during the period of auroral processes is larger than that for before the auroral effects initiation, but is much smaller than the O+ perpendicular temperature, which exceeded 8 eV. This is because under similar conditions the heating rate for H+ is about one order of magnitude lower than that for O+, as well as the fact that H+ ions which have characteristic velocities much higher than those of O+, tend to have much shorter times for transit of the heating region, and therefore experience less heating [Wu et al., 1999; Tu et al., 2004, 2005]. The H+ perpendicular temperature increased monotonically with time, as contrasted with the O+ perpendicular temperature, which increased within the first 5 minutes, then decreased afterwards. The reason for this is that during the auroral processes stage the H+ ions have upward parallel velocities in the range 2–12 km s−1, while the O+ bulk velocity is essentially stationary initially and then increase to 1–5 km s−1 upward. We know that the O+ ions collide more frequently with H+ ions which have lower speeds relative to the O+ background. As O+ drift velocities change from stationary initially to 1–5 km s−1 upward, the principal H+-O+ drag effects on the H+ also shift from the lowest-energy distribution portion to those H+ ions near 5 km s−1. Therefore, the actual H+ bulk velocities decrease with time after 5 minutes into the auroral effects period, as shown in the second upper plot of Figure 7. The middle plot in the bottom panel of Figure 7 shows that the H+ parallel temperature decreases continuously with altitude. This is the adiabatic cooling effect resulting from the accelerating parallel flow [Wilson, 1992]. However, the parallel temperature is higher than that prior to the auroral effects initiation, especially at higher altitudes. This is because the H+-O+ and H+-H+ collisions, as well as the mirror force, convert part of the increased perpendicular energy into parallel energy.
3.3. O+/H+ Distribution Function Characteristics Following the Auroral Processes Stage
 Following the 19.2 minutes period of auroral processes, the ionospheric plasma in the simulation flux tube was allowed to either relax without any further auroral effects or to be continuously heated by “lower hybrid” waves, under the assumptions that the simulation was associated either with the convection of a flux tube through a region of auroral processes and a time-dependent burst of LH waves on a relatively stationary flux tube, respectively. The distribution function characteristics under the different conditions are described in the following two sections.
3.3.1. Convection Into a Polar Cap Region Free of Auroral Effects
 In the scenario that the simulation was associated with the convection of a flux tube through an auroral region, the auroral effects, both soft electron precipitation and wave-induced transverse heating, were turned off and the plasma in the flux tube allowed to relax for about 40 minutes to observe the evolutions of the O+ and H+ distribution functions. Figure 8 shows the O+ distribution functions at 32 minutes, 12.8 minutes after the end of the auroral processes phase. The evolution during this relaxation period largely reversed the developments during the auroral processes stage, as expected. The perpendicular temperatures declined rapidly during this relaxation phase. Within 20 minutes, the perpendicular temperatures throughout the tube declined to values comparable to the temperatures prior to the auroral processes stage. At higher altitudes in the transition region, the vestiges of wave transverse heating, such as perpendicular temperature boost and conic distribution function, persisted longer than at lower altitudes, as the O+ ions experienced larger heating rates at higher altitudes during the presence of auroral processes [Wu et al., 1999]. Also, O+ self collisions are less frequent at higher altitudes due to the smaller O+ densities, and so the O+ ions at higher altitudes take more time to be thermalized.
 From Figure 9, which displays the H+ distribution functions after 12.8 minutes relaxation, the H+ distributions at the lower altitudes, i.e., below 1300 km, were similar to those present before the auroral processes initiation. Comparing Figures 8 and 9, we find that the H+ cooled in the perpendicular direction more rapidly than O+. Two reasons accounted for this: O+ was heated to higher perpendicular temperatures during the auroral processes stage than H+, and, for the same energy, the collision frequency (here we refer to the energy transfer collision frequency which is different from the momentum transfer collision frequency in equation (5)) with the O+ background is higher for H+ (see equation (5)). In the examination of temporal evolutions of the H+ bulk parameters, we found there was a downward H+ heat flux region above 1500 km and this region of downward H+ heat flux shifted to lower altitudes during the relaxation period. From the discussion in section 3.2, we know that a negative H+ heat flux in the polar wind typically is indicative of the characteristic drag effect through O+-H+ collisions during periods of downward O+ drift. As the O+ plume cooled and O+ bulk velocities decreased and turned downward during this relaxation phase, the drag effect became evident at the lower altitudes, and more influential on the lowest-energy portions of the H+ distribution, which contrasts with the auroral effects phase when the background O+ bulk velocities were upward above 2000 km altitude and the downward portion of H+ distribution was depleted above 3000 km altitude.
 As an alternate scenario to that described in section 3.3.1, we also considered a situation in which, after 19.2 minutes auroral pulse, and the soft electron precipitation was terminated, the simulation flux tube experienced further wave-induced transverse heating, but with the wave frequency corresponding to the spectrum peak increased over approximately five minutes to near the lower hybrid frequency and the wave power in this phase was restricted to the altitude range 1100–1400 km. The wave spectrum utilized for this phase is qualitatively similar to that been observed by DE 1 and Freja spacecraft [Gurnett and Inan, 1988; André et al., 1998]. DE 1 also observed low frequency waves in a narrow altitude range around 1000 km altitude [Gurnett and Inan, 1988]. In the present simulation, we assumed that the wave spectral density peaked at 400 Hz, which is approximately four times the H+ gyrofrequency at 1 RE altitude, and the peak spectral density was 0.3 × 10−6 V2 m−2 Hz−1, which is in the range of Freja and Viking observations [André et al., 1998; Oscarsson and Ronnmark, 1990]. Similar to equation (4), we again assumed that the wave spectral density had a power law relation with frequency, and the power index should be negative for the frequency less than 400 Hz.
 Following the 19.2 minutes auroral effects phase, the resonant heating by the low hybrid waves continued for another 40 minutes in our simulation. The O+ and H+ distribution functions toward the end of this second phase are shown in Figures 10 and 11, respectively. From Figure 10, we see that the O+ perpendicular temperatures are much lower than those in Figure 3, which was for during the first auroral effects phase. This is because the O+ heating rate produced by the purported low hybrid waves is significantly lower, about 0.1% of that during the auroral processes. The O+ bulk velocities above 2000 km altitude changed from ∼1 km s−1 upward (see Figures 3 and 5) to approximately stationary, which had important implications in the H+ distribution function formation through the aforementioned H+-O+ drag effects.
 From Figure 11, the H+ perpendicular temperatures are higher than those in Figure 6. For the low hybrid wave power spectrum assumed, the heating rate for H+ is about 10 times that for during the auroral processes phase, when the ions were presumed to be heated by BBELF waves. In Figure 11, above 2000 km altitude, as the upward folding wings gradually developed, the downward H+ particles were not completely depleted, in contrast with the distributions in Figure 6. This difference results because the O+ background is different for these two cases. During the auroral processes phase, as shown in Figure 3, the O+ ions at lower altitudes were energized and higher O+ densities attained higher altitudes, and the O+ bulk velocities changed from near zero to ∼1 km s−1 upward at 2000 km altitudes, and up to 7 km s−1 at 4000 km altitude. The H+–O+ collision drag effects caused those very low-energy H+ ions whose velocities were comparable to the O+ background to also be drifting upward, with velocities still comparable to the O+ background, i.e., 1 – 7 km s−1 upward. Of course, the H+ bulk velocities were much larger in the upward direction, up to 15 km s−1 at 4000 km altitude, because of the combined acceleration of the macroscopic forces. During the lower-hybrid heating period, part of the previously heated and elevated O+ plume begun to fall back. These downgoing O+ ions captured a portion of the H+ distribution through O+-H+ collision drag effects. In those cases where the downward drag effects cancelled the upward accelerations caused by macroscopic forces, that portion of the H+ distribution also turned downward. This is the reason we can see downward stretched distribution tails up to 4000 km altitude in Figure 11.
4. Summary and Discussion
 In this paper we have sought to investigate the features of O+/H+ flows and distribution functions, as well as the roles of Coulomb collisions and kinetic processes, in the high-latitude collisional/collisionless transition region, specifically from 1000 km to 4000 km, by conducting a Dynamic Fluid Kinetic (DyFK) simulation. The simulation flux tube extended from 120 km to 3 RE altitudes in our simulation. It was initially run to a quasi-steady polar wind state. We assumed the flux tube to experience 19.2 minutes of auroral effects, including both soft electron precipitation and wave-induced transverse ion heating, and then allowed the flux tube either to relax or to be continuously heated by lower hybrid waves for another 40 minutes. From the results of our simulation, we concluded that the Coulomb collisions between O+ and O+, O+ and H+ played important roles in the velocity distributions up to 4000 km altitude, especially for the low speed portions.
 During the quasi-steady state prior to the auroral process initiation, the peak velocity of the H+ distribution function jumped from about 2 to near 10 km s−1 over the short altitude range between 1500 km to 1900 km. Because of the near-stationary O+ background and the dependence of the Rutherford collision cross-section on relative speed between colliding ions, the lowest-energy portion of the H+ distribution is most likely to experience drag by O+-H+ collisions. With increasing altitude the O+ background density decreases approximately exponentially, decreased from 4500 cm−3 at 1500 km to 1800 cm−3 at 1900 km altitude in these simulations. Thus, increasingly H+ ions are released from the O+-H+ collision drag, and increasing the other macroscopic forces, such as the ambipolar electric field, become the dominant influences on their motions. In these cases, the peak velocity of the H+ distribution may experience a jump of ∼8 km s−1 over a limited altitude range between 1500 km and 1900 km altitude. At certain altitudes, when collisional drag effects and acceleration by macroscopic forces are comparable, double peaks in the H+ distribution function might develop. This kind of H+ distribution is seen in the simulation cell between 1652 km and 1702 km altitude, i.e., the upper fourth plot of Figure 2.
 During the auroral processes stage, the low-energy O+ ions experienced frequent self-collisions, owing to the inverse relationship between the O+ collision frequency and the O+ kinetic energy (see equations (5) and (6) and Figure 4), and tended to thermalize the core of the O+ distribution function. For the higher speed O+ ions, kinetic processes dominated, owing to much less frequent self-collisions. The extended perpendicular wings involving conical folding toward the magnetic field developed. These distributions resemble “upwelling” ion distribution functions observed by DE-1 spacecraft [Moore et al., 1985].
 The Coulomb collisions between O+ and H+ also played a significant role in the characteristics of the H+ distribution function. During the auroral processes stage, as higher densities of O+ ions were elevated to higher altitudes, e.g., the O+ density at 2500 km altitude increased 3 times after 9.6 minutes auroral effects, the drag effects, especially on the low-energy portion of H+ caused by increased O+-H+ collisions were enhanced. In these cases the H+ peak velocity experienced a less significant, if compared with the stage prior to auroral processes, jump of ∼5 km s−1, and the H+ upward bulk velocity decreased. Following the auroral processes stage, if the ionospheric plasma in the flux tube was heated only by lower hybrid waves, which had weak heating effects on the O+, the previously elevated O+ plume subsided. The effects of O+-H+ collisions were also seen in the H+ distribution functions. The downward-going O+ ions often “captured” part of the low speed H+ ions through these O+-H+ collisions. In these situations, a downward component in the H+ distribution functions was at times evident at altitudes up to 4000 km.
 This work was completed under financial support by NASA grant NNG05GF67G and NSF grant ATM-0505918 to the University of Texas at Arlington.
 Arthur Richmond thanks Imad Barghouthi and Patrik Norqvist for their assistance in evaluating this paper.