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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)
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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.
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[17] showed that electron cyclotron resonant heating may
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