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Comparison of solar wind driving mechanisms: ion cyclotron resonance versus kinetic suprathermal electron effects Sunny W. Y. Tam and Tom Chang Center for Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Abstract. The combined kinetic effects of two possible solar wind driving mechanisms, ion cyclotron resonance and suprathermal electrons, have been studied in the literature [1]. However, the individual contribution by these two mechanisms was unclear. We compare the two effects in the fast solar wind. Our basic model follows the global kinetic evolution of the solar wind under the influence of ion cyclotron resonance, while taking into account Coulomb collisions, and the ambipolar electric field that is consistent with the particle distributions themselves. The kinetic effects associated with the suprathermal electrons can be included in the model as an option. By comparing our results with and without this option, we conclude that, without considering any wave-particle interactions involving the electrons, the kinetic effects of the suprathermal electrons are relative insignificant in the presence of ion cyclotron resonance in terms of driving the solar wind. INTRODUCTION [11, 12], and has successfully addressed various satellite observations. It has been shown that in the absence of wave-particle interactions, the suprathermal electron population can increase the ambipolar electric field, leading to higher ion velocities in the polar wind. Because the ionospheric polar wind and the solar wind are both outflows along open magnetic field lines, it is worthwhile to study KSEE in the solar wind. The combined kinetic effects of ion cyclotron resonance and the suprathermal electron population have been considered by Tam and Chang [1]. The study associated the ion resonance with some of the solar wind observations, as discussed earlier. The bulk acceleration of the solar wind demonstrated in the study, however, consisted of contributions by both the ion resonance and the suprathermal electron effects. It was therefore unclear to what extent each of the two acceleration mechanisms contributes to the driving of the solar wind. Our goal in this study is to compare the relative importance of the kinetic effects due to suprathermal electrons and ion cyclotron resonance, and to determine which of the mechanisms is mostly responsible for driving the solar wind. Kinetic ion cyclotron resonance has been shown to accelerate the solar wind ions to the observed high-speed range [1, 2]. Qualitative features associated with the resonance are consistent with observations. For example, the resonance involving sunward propagating electromagnetic waves was shown to produce double-peaked proton velocity distributions [1], which had occasionally been observed [3]. In addition, the cyclotron resonance based on observed power spectra [4] was shown to preferentially accelerate the alpha particles over the protons [1], in agreement with the observations by the Helios, Ulysses, and WIND spacecraft [5, 6, 7]. These observed power spectra may be produced by the small-scale reconnections near the coronal region. Recently, Chang [8] has suggested that such type of intermittent turbulence may be associated with the “complexity” generated by the sporadic localized mergings and interactions of the coherent magnetic structures near the coronal holes. Another mechanism that may accelerate the solar wind is due to kinetic suprathermal electron effects (KSEE). Due to the velocity-dependence of the Coulomb collisional depth and the global kinetic nature of the solar wind flow, suprathermal tails may form in the electron distributions, giving rise to an anomalous outward electron heat flux [9]. The idea of this “velocity filtration effect” (VFE) was further pursued by Olbert [10], who suggested that the heat flux contribution by the suprathermal electrons may drive the solar wind. Such an idea has been applied to the ionospheric polar wind with photoelectrons playing the role of the suprathermal population MODEL Our model is adapted from a self-consistent hybrid model for the ionospheric polar wind [11, 12]. It is based on an iterative scheme between fluid and kinetic calculations. A set of fluid equations determines the ambipolar electric field and the properties of the bulk thermal electrons, whose distributions are assumed to be in a drifting CP679, Solar Wind Ten: Proceedings of the Tenth International Solar Wind Conference, edited by M. Velli, R. Bruno, and F. Malara © 2003 American Institute of Physics 0-7354-0148-9/03/$20.00 259 Maxwellian. To solve the fluid equations, we impose the quasi-neutrality and current-free constraints for the solar wind, and make use of the results from the kinetic calculations in the model. The kinetic part of the model consists of multiple components, each describing the global evolution of a particle component along the solar wind. In the basic version of the model, the kinetic approach is applied only to the protons and alpha particles. The distributions of these ions evolve under the influence of Coulomb collisions, an ambipolar electric field, and cyclotron resonance. The results of the kinetic calculations are coupled with the fluid equations. This ensures the consistency of the ambipolar electric field with the particle distributions when an iteration between the fluid and kinetic parts of the model converges. In addition, a convergence of the results enables our kinetic calculations to correctly take into account the Coulomb collisions for the ions, including those among the same ion species. To take into account the effects of cyclotron resonance for a given ion species, we incorporate quasilinear diffusion operators with coefficients D and D into the steady-state collisional kinetic equations for the species: ∂ v g ∂s Cf q ∂ E m ∂v ∂ ∂ D ∂v ∂v v 2 B ∂ 2B ∂ v ∂ v ∂ v v v1 ∂∂v vD ∂ ∂v is an efficiency factor that adjusts the available wave power, and depends on the heliocentric distance r (in the unit of R ). The reasons for these adjustments have been discussed in [1], one of those being consistent with a recent study of wave dissipation near the corona [13]. Equation (1) is solved with a Monte Carlo technique. This technique for describing ion resonant heating was originally applied to the auroral region by Retterer et al. [14]. With this technique, our model is able to incorporate the resonant effect of a given wave spectrum into an otherwise self-consistent solar wind description. Up to this point, we have described the basic constituents of our model. This model enables us to follow the global evolution of the ion distributions along the solar wind flow, including the effect of cyclotron resonance. However, it does not take into account KSEE. To do so, we simply add another kinetic component into the model to describe the suprathermal electron population. The kinetic equation for the suprathermal electrons is similar to Eq. (1), but without the terms that represent wave-particle interactions. The results of this kinetic component, including the heat flux contribution, are coupled into the fluid part of the model. The suprathermal electrons in our model comprises the tail portion of the electron Maxwellian distribution at 1 R , the lower boundary of our model. They satisfy the criteria at 1 R : 12mev2 8Te0 and v 0, where me is the electron mass, and Te0 is the thermal electron temperature. Because the suprathermal electrons originally constitute the high-energy portion of a Maxwellian, rather than a distribution with a significantly enhanced tail, and because we do not consider any interactions between the electrons and the waves, the KSEE in our calculations is essentially the VFE proposed by Scudder and Olbert [9]. By comparing solutions generated with and without the optional suprathermal electron component being included, we can identify the contribution by the VFE in driving the solar wind. f f (1) where s is the distance along the radial magnetic field line, f s v v is the distribution function for the species, q and m are the electric charge and mass respectively, E is the field-aligned ambipolar electric field, g is the gravitational acceleration, B is the magnetic field, B dBds, and C is a Coulomb collisional operator. The expressions for the diffusion coefficients are: D η q2 d ω v 2 PC ω 2π δ ω 4m2 kv Ω (2) q2 d ω Ωk2 PC ω 2π δ ω kv Ω (3) 4m2 where Ω is the gyrofrequency of the species, ω and k are the frequency and wavevector for the resonance with the individual ion, and are related by the cold plasma dispersion relation for left-hand polarized waves. The argument of the δ -function corresponds to the resonance condition. PC is the magnetic field wave power, based on an interpolation/extrapolation scheme of the Helios measurements [4] and taking into account both inward and outward propagation. The assumptions on PC are discussed in more detail in Tam and Chang [1]. Lastly, COMPARISON OF SOLAR WIND DRIVING MECHANISMS D η η η0 exp 1 r05 We have generated two solar wind solutions for the range between 1 R and 1 AU with identical parameters and boundary conditions, one with KSEE, and the other without. Boundary and initial conditions are imposed at 1 R : the boundary thermal electron temperature is 100 eV; initial distributions for the ion species are the upper halves of Maxwellian distributions, whose temperatures are also 100 eV; the densities for the protons and alpha particles are respectively 42 107 and 40 106 cm3 . The parameter η0 that characterizes the strength of the available wave power is 0.016. (4) 260 A noticeable difference between the two solutions is the shape of the total electron distributions. Their reduced distributions in the parallel direction are shown in Fig. 1. We see that the total electron distribution deviates from a Maxwellian when KSEE is included. The formation of a significant tail in the outward portion of the distribution verifies the idea of VFE [9]. The suprathermal electron population influences the ion species mainly through the effect of its heat flux on the ambipolar electric field. With a Maxwellian approximation for the entire electron population, the overall electric potential drop from 1 R to 1 AU is about 700 V. The potential difference increases by about 70 V when KSEE is taken into account. Such an increase suggests that VFE can accelerate the ions in the solar wind. To evaluate the significance of the VFE as a solar wind driving mechanism, we should consider the energy input to the ions. Other physical processes that may deposit energy to the solar wind ions are cyclotron resonance and Coulomb collisions. In fact, like VFE, these other two processes also indirectly affect the ion energy through their influence on the ambipolar electric field. Whether an ion can reach large radial distances in the solar wind depends whether the overall kinetic energy it gains is high enough to overcome the gravitational potential. Therefore, we evaluate the significance of a physical mechanism in driving the solar wind by comparing its contribution to the energy input for the ions with the contributions from all the physical processes combined. Because we are interested in comparing only the processes that may drive the solar wind, we shall exclude the gravitational force in our energy consideration. After all, the gravitational potential profile is invariant under all solar wind conditions, and is independent of the presence of other physical processes. Hence, we define the following FIGURE 2. for protons and alpha particles. Solid: with kinetic suprathermal electron effects; dashed: based on a Maxwellian approximation. quantity for each ion species for our purpose of energy comparison: average kinetic energy + gravitation potential energy per ion. For a given ion species in our model, its increase in along the solar wind flow is due to a combination of energy input from the ambipolar electric field, ion cyclotron resonance, and Coulomb collisions with other species. In particular, the ambipolar electric field also reflects the influence due to ion cyclotron resonance, and Coulomb collisions, and, in the case where KSEE is included, the VFE as well. The profiles of for the protons and alpha particles in our two solar wind solutions are shown in Fig. 2. It appears from the figure that the difference in is very small between the two solutions. Indeed, we find that with KSEE taken into account, the increase in for the protons from 1 R to 1 AU is only 1.5% larger than in the case of a Maxwellian approximation. For the alpha particles, the corresponding difference is 2.4%. The influence by the KSEE on the ion outflow velocities can be seen in Fig. 3. The difference due to VFE is minimal, considering that the kinetic effect only increases the proton speed by 1.5% at 1 AU, and the alpha particle speed by 2.3%. Note that even under a Maxwellian approximation for the overall electron distributions, the ion speeds at 1 AU are as high as 650 km/s in the solution. Thus, the available wave power in these calculations seems to be able to drive the solar wind to the high-speed range. For such a strong wave-driven solar wind, it is clear from our results that VFE plays an insignificant role in the driving and acceleration of the solar wind. Recently, Vocks and Marsch [15] have introduced a semi-kinetic solar wind model to describe the effects of strong ion cyclotron resonant heating. Like this study, FIGURE 1. Reduced electron distributions in the parallel direction at 0.1 AU. Solid: with kinetic suprathermal electron effects; dashed: based on a Maxwellian approximation. 261 driven solar wind. Thus, even though ion cyclotron resonance appears to be the dominant solar wind driving mechanism, it is possible that KSEE can make a considerable contribution to the acceleration of the solar wind. Epilogue. After submission of the manuscript, the authors realized that the modeling technique discussed here seems to satisfy the criteria suggested by Meyer-Vernet et al. [18] for a proper treatment of the overall electron population. ACKNOWLEDGMENTS This work is partially supported by AFOSR, NASA, and NSF. FIGURE 3. Profiles of the proton (u p ) and alpha particle (uα ) outflow velocities. Solid: with kinetic suprathermal electron effects; dashed: based on a Maxwellian approximation. REFERENCES their model describes the wave-particle interaction in the framework of quasilinear theory. However, the treatment of the particles is different in the two models. Their model is based on reduced ion distributions, massless electron fluid, and an assumed electron temperature profile. With the approximations on the electrons, the model does not take into account KSEE. However, as we have shown that the VFE associated with the suprathermal electrons is negligible when strong ion resonant heating is present, the assumptions in [15] regarding the electrons seem to be reasonable approximations. KSEE was proposed to be a solar wind acceleration mechanism under the assumption that no wave-particle interactions were present [10]. Therefore, it is worthwhile for us to investigate the VFE in the scenario of a weak wave-driven solar wind, in which case, the available wave power for ion resonance is not sufficient to drive the outflow to the high-speed velocity range. We reduce η0 to 0.0075, less than half of the strong wavedriven case. With the reduced wave power, and without KSEE, the velocities of both ion species plateau at about 390 km/s. The inclusion of VFE increases the proton speed by only 2.5%, and the alpha particle speed by only 2.8%. 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