Origin of the Fast Solar Wind:
From an Electron - Driven Wind to Cyclotron Resonances
Joseph V. Hollweg
Space Science Center, University of New Hampshire, Durham, NH 03824 USA
Abstract. Even before the discovery of the fast solar wind in the mid - 1970s, it was known that even the average solar wind
could not be well explained by models in which electron heat conduction was the energy source and the electron pressure
gradient was the principal accelerating force. The outward - propagating Alfvén waves discovered around 1970 were thought
for a while to provide the sought - after additional energy and momentum, but their wave pressure ultimately failed to explain
the rapid acceleration of the fast wind close to the Sun in coronal holes. By the late 1970s, various in situ data were
suggesting that protons and heavy ions were being heated and accelerated by the ion - cyclotron resonance far from the Sun.
This notion was soon applied to the acceleration region in coronal holes close to the Sun. The models which resulted
suggested that the fast wind could be driven mainly by the proton pressure gradient (which is mainly the mirror force if the
anisotropy is large), and that the high temperatures and flow speeds of heavy ions could originate within a few solar radii of
the coronal base; these models also emphasized the importance of treating the extended coronal heating and solar wind
acceleration on an equal footing. By the mid 1990s, SOHO, especially the UVCS (Ultraviolet Coronagraph Spectrometer),
provided remarkable data which have given great impetus to studies of the ion cyclotron resonance as the principal
mechanism for heating the plasma in coronal holes, and ultimately driving the fast wind. We will discuss the basic ideas
behind current research, emphasizing the particle kinetics. We will discuss remaining problems such as the source of the ion
- cyclotron resonant waves (direct launching, turbulence, microinstabilities), problems concerning OVI and MgX, the roles of
inward - propagating waves and instabilities, the importance of oblique propagation, and the electron heating. Some
alternatives, such as shock heating and turbulence - driven magnetic reconnection, will also be reviewed.
ELECTRON - DRIVEN WINDS
coronal holes, and in the distant solar wind as well.
Parker's point was driven home in 1966 and 1968 by
Hartle and Sturrock [4, 5], who produced the first two fluid models of the wind, with separate energy
equations for the electrons and protons. As in Parker's
models, all coronal heating was assumed to take place
in a thin layer near the base. This produced a high base
temperature, > 106 K, which served as an inner
boundary condition.
Because protons are poor
conductors of heat, their temperature dropped very
rapidly to only a few x 10 3 K at 1 AU, in contrast to the
observed proton temperatures, Tp , of about 2 x 105 K in
high - speed streams (see Feldman's 1976 article [6]
describing the properties of the high - speed wind).
The flow speeds predicted by Hartle and Sturrock were
much too slow: some 250 km s-1 compared to observed
values of 700 - 800 km s-1 in the fast wind. The authors
concluded "Departures [are] attributed to heating by a
flux of non - thermal energy".
Parker's [1] original model of the solar wind was
motivated by the observation that electrons conduct heat
so effectively that a static corona would have a pressure
far from the Sun greatly in excess of the interstellar
pressure. Such a corona could not be contained, and
thus could not be static. In effect, these early solar wind
models were driven mainly by the electron pressure
gradient, which was maintained at a high level by the
slow decline of the electron temperature, which was
itself a consequence of the efficient electron heat
conduction out of the hot corona at the base. However,
in his 1965 review [2], Parker recognized that such
models were not fully successful in accounting for the
observed properties of the wind. He stated "The model
for the hypothetical conduction corona leads to a
temperature falling too rapidly with radial distance from
the Sun, indicating that the actual solar corona is
probably actively heated for some considerable distance
by the dissipation of waves." It now appears he may
well have been right. Not only is the electron
temperature in coronal holes low, < 106 K [3], but
available evidence points to the action of waves in
WAVE - DRIVEN WINDS
In 1969 and 1971, Belcher and co - workers [7, 8]
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
14
provided strikingly clear evidence that Alfvén waves are
ubiquitous in the solar wind, especially in the high speed streams (see also [9, 10] for earlier indications).
The waves were found to propagate predominantly
outward from the Sun, suggesting a solar source. Were
these the waves mentioned by Parker? Were they
Hartle and Sturrock's "flux of non - thermal energy"?
In 1971 Alazraki and Couturier [11] and Belcher
[12] realized that the Alfvén waves could contribute to
the acceleration of the wind via the wave pressure
gradient (also called the ponderomotive force), ∇<δB2 >/8π (in cgs units which we use throughout),
where δB is the magnetic fluctuation, and the angle
brackets denote a time (or ensemble) average. In 1973
Hollweg [13] showed how the waves could be
incorporated into the energy balance, allowing for wave
damping, and he produced some detailed two - fluid
models which looked promising when compared with
the observed solar wind near 1 AU. Such "wave driven" solar wind models were soon explored further
by many others (see [14] for a review).
These models were incomplete in one major respect:
They had to guess how the Alfvén waves might be
damped, since they do not readily undergo Landau or
transit - time damping [15, 16]. At first it was simply
postulated that the waves damp by saturating at some
maximum level of <δB2 >/Bo 2 (B o is the ambient
magnetic field); much later Roberts [17] provided
evidence that this does not occur. Wave damping via a
turbulent cascade was proposed in the early 1980s [18,
19], and that idea has been predominant ever since;
more on this later.
Wave - driven models were generally very
successful in reproducing observed properties of the
wind far from the Sun. But by the early 1990's it was
realized that they had difficulties close to the Sun,
where observations were indicating that the wind
accelerates faster than the wave - driven models could
explain. Radio observations (e.g. [20]) suggested rapid
acceleration, but they might have been measuring
propagating disturbances rather than the solar wind flow
(that is now the prevailing view). At about the same
time, improved observations of densities in polar
coronal holes became available (e.g. [21]). With
knowledge of the mass flux (obtained from Ulysses),
the coronal velocities could be deduced. They were
indeed found to be very fast close to the Sun, implying a
sonic critical point inside 3rs (rs is the solar radius).
Wave - driven models could not explain such rapid
acceleration, because the ponderomotive force only
became significant at greater distances, beyond 3r s [14].
The heavy ions, especially He++, presented further
difficulties. They tend to flow faster than the protons by
about the Alfvén speed, v A, and they tend to be roughly
mass - proportionally hotter than the protons. The most
likely explanation seemed to be heating and acceleration
by the cyclotron resonance; see [22 - 27] for some early
discussions.
There were already available other hints that
cyclotron resonances were at work. Here we refer to the
excellent review by Marsch [28]. His Figure 8.31
shows that the proton magnetic moment increases with
heliocentric distance r between 0.3 and 1 AU, implying
heating perpendicular to Bo ; figure 8.25 shows the same
for He++. Moreover, Marsch's Figure 8.1 shows proton
distribution functions whose "cores" are anisotropic in
the sense T⊥ > T || (T is temperature, and the subscripts
indicate directions relative to Bo ). Perpendicular
heating is again implied, with the cyclotron resonance
being the most apparent candidate.
Three - fluid (electrons, protons, He++) models
which incorporated the cyclotron resonance succeeded
qualitatively but failed in detail [25, 29]. An essential
difficulty was the fact that once the ions flow
significantly faster than the protons, they tend to drop
out of resonance with no further acceleration and
heating. In retrospect, these models may also have
failed because the cyclotron resonances were assumed
to act only far from the Sun.
PROTON - DRIVEN WINDS
By the mid - 80's, some of these ideas were applied
to the acceleration region of the solar wind by Hollweg
[30] and Hollweg and Johnson [31]. The basic idea was
that the Sun launches a flux of low - frequency Alfvén
waves which damp via a turbulent cascade to high
frequencies where the energy is absorbed by the protons
(He++ was omitted). The volumetric heating Q was
essentially Kolmogorov: Q = ρ<δV2 >/L c, where ρ is
density, δV is the wave velocity fluctuation, and Lc is
the correlation length transverse to Bo . The wave
propagation was handled in the WKB limit. This means
that there was an internal inconsistency, since the
nonlinear terms cancel for WKB Alfvén waves, and no
turbulence can occur (for correct treatments see
Dmitruk and Matthaeus, this volume, and [32, 33].
Nonetheless, the model could give the required rapid
acceleration close to the Sun. A noteworthy feature of
the model was that the protons were substantially hotter
than the electrons, with Tp ≈ 4 x 10 6 K at (3 - 4)rs . It
was mainly the proton pressure gradient which led to
the rapid acceleration; we therefore call this model
"proton - driven". The then available data argued
against such high proton temperatures and the model
15
1.2
was rejected.
Isenberg [34] extended the model to include He++.
Quasilinear theory was used to apportion the cascaded
energy between the protons and He++, but it was
necessary to assume the form of the power spectrum in
the resonant range. The model produced many features
of the acceleration region which we now know to be at
least qualitatively in accord with the UVCS/SOHO
observations of coronal holes (e.g. [35, 36]): protons
hotter than electrons, He++ (and other ions) more than
mass - proportionally hotter than the protons, rapid
acceleration driven mainly by the proton pressure
gradient, He++ already flowing faster than the protons
close to the Sun. Again, this model was rejected
because of the high Tp , but it anticipated the
UVCS/SOHO discoveries of hot and fast coronal
protons and ions.
UVCS/SOHO also indicated that 0 +5 is heated
primarily perpendicular to B o [37], again implicating
cyclotron heating. Moreover, the UVCS/SOHO results
[35, 36] show that the ion heating extends far into the
corona, even beyond the sonic critical point, in strong
contrast to the early models in which all the heating was
in a thin shell at the base: coronal heating and solar
wind acceleration must be treated together.
Before closing this section, we note that solar wind
models with hot protons and ions were investigated
years ago by Ryan and Axford [38]. Esser, Habbal, and
co - workers [39 - 41] also explored the consequences
of hot coronal protons, and showed explicitly that high speed streams could be produced by the coronal proton
pressure gradient, with no additional momentum input
from the wave pressure gradient. All of these papers
used ad hoc heating functions, however, rather than
attempting to model the effects of a specific physical
heating (and acceleration) mechanism.
1.0
Protons
v || = – 0.1 vA
ω/Ωp
0.8
0.6
Ion - cyclotron mode;
cold e - p plasma
O+5
0.4
5/16
0.2
In the proton frame
0
0
0.5
1.0
1.5
k || v A/Ωp
2.0
FIGURE 1. The heavy curve is the dispersion relation. The
thin lines represent the resonance condition (1). The solid thin
lines show that only backward moving protons can resonate.
The dashed lines show that both forward and backward
moving oxygen can resonate, but that no resonance is possible
if the oxygen moves too fast.
energy secularly, depending on the phase relative to the
electric field. In a random field, phase will be random,
and the particle will random walk in velocity space.
Random walks imply diffusion so a collection of
particles will diffuse in velocity space.
The heavy curve in Figure 1 is the dispersion
relation for parallel - propagating ion - cyclotron waves
in a cold electron - proton plasma, as viewed in the bulk
proton frame. The thin solid lines are equation (1) for
the protons, for two values of v|| . The intersection of (1)
with the dispersion relation gives ω and k || of the
resonant wave. If v || > 0, there is no intersection; a
proton moving with the wave cannot be in resonance.
For v || < 0 there can be resonance. Roughly speaking,
only half of the proton distribution can resonate with ion
- cyclotron waves. If the waves are propagating away
from the Sun, only sunward moving protons (as seen in
the bulk proton frame) can resonate.
The situation is more favorable for heavy ions, in
several respects. The dashed lines show equation (1)
for 0+5 (Ω = 5Ωp /16). The lower two dashed lines
show that both forward and backward moving 0 +5 can
be in resonance. However, the upper dashed line shows
that 0 +5 can drop out of resonance if it moves too fast
(v|| >
~ 0.3 vA). Note too that heavy ions can resonate
with waves having lower k|| than found for the protons.
This too gives ions an advantage, since we expect more
wave power at lower k|| , and because lower - k|| waves
have higher phase speeds. (He++ is abundant enough to
THE CYCLOTRON RESONANCE
Consider a wave with angular frequency ω and
wavenumber k|| propagating parallel to B o . A particle
with gyrofrequency Ω will see a constant electric field
when
ω – k || v || = ± Ω ;
v || = 0.1 vA
(1)
v|| is the particle's velocity along Bo , the (+) refers to
waves which are circularly polarized in the sense of the
particle's gyration, while the (–) refers to the opposite
sense of polarization. Space limits us to consideration
only of ion - cyclotron waves, i.e. the (+).
When (1) is satisfied, the particle gains or loses
16
0+5 behavior is difficult to understand. Once oxygen's
v⊥ exceeds that of the protons, it experiences a greater
mirror acceleration and a greater adiabatic cooling.
Moreover, as the oxygen accelerates, it resonates with
higher k|| waves, which have less power and slower
phase speeds. The oxygen can even drop out of
resonance when its speed becomes fast enough (Figure
1). These factors work against the fairly steady increase
of the oxygen temperature with r. In fact, models such
as in [42, 48] behave in the way described above: the
temperature at first increases rapidly, mirroring then
gives rapid acceleration, and the temperature then drops
as adiabatic cooling overwhelms resonant heating.
Isenberg ([49] and this volume) suggests a possible
solution involving both outward and sunward propagating waves. By redrawing Figure 2 with circles
corresponding to both propagation directions, it can
readily be seen that a proton can resonate with either
propagation direction, but not both simultaneously. An
oxygen ion can simultaneously resonate with both types
of waves. Thus oxygen can undergo second - order
Fermi acceleration, while protons cannot. This may be
the extra ingredient needed to explain the 0+5 data.
Mg+9 also presents a problem. Even though 0 +5 and
Mg+9 have very nearly the same charge - to - mass
ratios, q/m, the former is definitely more than mass proportionally hotter than the protons, while the latter is
only mass - proportionally hotter [50]. Why species
with nearly the same q/m behave so differently is a
challenge to the cyclotron heating scenario. Cranmer
[43] notes that the second most abundant coronal ion
(after He++) is 0+6, which has the same q/m, and thus
the same Ω, as Mg+9 . He suggests that 0+6 depletes
wave power in the vicinity of the 0 +6 and Mg+9
resonance, leaving little power for Mg+9 , without
affecting the power available to 0+5 . This idea needs
detailed evaluation. We note, however, that it will fail
if 0 +6 and Mg+9 have different v|| 's; see equation (1).
v ⊥/vA
1.0
+5
O
fusio
n
0.5
pitch
-ang
le dif
protons
–0.2
0
0.3 0.4
v /v 0.7 0.8
|| A
FIGURE 2. Particle motion in v||-v⊥ space due to resonance.
affect the dispersion relation significantly, but there is
insufficient room for a discussion. See recent reviews
[42, 43] as well as [44 - 47]).
Figure 2 shows the ion advantage in a different way.
If there is a single wave (or if we ignore dispersion), a
particle will conserve energy in the wave frame. In that
frame it will move on a circle such that v⊥2 + v|| 2 =
constant. The figure shows two such circles. The 0+5
circle has a greater radius than the proton circle,
qualitatively reflecting the fact that 0+5 resonates with
faster - moving waves than the protons. The dark arcs
show the portions of the circles within which the
particles can be in resonance. If we imagine a group of
particles starting with small values of v⊥, they will
diffuse upwards, tending to uniformly fill the dark arcs.
This will give perpendicular heating. Note that the ions
can attain larger v⊥ than the protons, implying more
than mass proportional perpendicular temperatures, in
qualitative agreement with the UVCS/SOHO results for
0+5 . Note too that as the particles diffuse upwards, they
also move to the right, increasing v|| . Resonant heating
implies resonant acceleration; simple models [42, 48]
suggest that the resonant acceleration cannot be
overlooked, even though the magnetic mirror
acceleration is usually substantially larger. Finally, note
that the mirror acceleration is v⊥2 dlogBo /dr; if the ions
attain larger values of v ⊥, they will experience a greater
acceleration from mirroring.
(See Isenberg, this
volume, for further variations of Figure 2.)
We point out two difficulties with this picture. The
first concerns 0+5 , which is observed to have T ⊥
increasing with r out to 3.5rs (the outer limit of the data
in [35], while the protons have T⊥ nearly constant. This
WHENCE THE CYCLOTRON WAVES?
Although many workers agree that ion - cyclotron
waves can explain a variety of observations, there is
substantial disagreement on where these high - ω, high
- k|| waves come from. There are two principal theories.
The models in references [19, 30, 31, 34, 42, 48, 51 54], among others, assume that the Sun launches low
frequency waves, and that the high - frequency
cyclotron waves are produced by a turbulent cascade.
This is motivated by in situ observations (e.g. [55])
showing most power at low frequencies, with power law
power spectra at higher frequencies, suggestive of
17
turbulent cascades. Radio science data (e.g. [56]) show
that density fluctuations in the corona, as close as r ≈
5rs , have similar power spectra.
One question that arises in this context is whether
there is sufficient low - frequency power to drive the
high - speed wind. Hollweg et al. [57] studied Faraday
rotation fluctuations on the signal from Helios. These
were caused by coronal magnetic fluctuations, which
were associated with Alfvén waves. They concluded
that there was enough power to drive the wind.
Andreev et al. [58] obtained similar results. However,
other observers disagree. For example, Mancuso and
Spangler [59] look at Faraday rotation fluctuations on
natural radio sources. They conclude that the power in
the corona is insufficient to drive the wind. The
differences seem to arise because the observed
fluctuations depend on the sizes of the scattering
elements, and how many there are along the line of
sight. This requires knowledge of the correlation scale,
which has to be guessed; different authors have made
different guesses. It is also fair to say that no studies
have properly accounted for dissipation, in extrapolating
from the observation region back to the Sun.
Turbulence faces another problem. MHD turbulence
tends to produce high k ⊥, not high k || (see papers by
Dmitruk and Matthaeus, and by Milano et al., this
volume). The cascaded energy then dissipates via
reconnection, not via cyclotron resonance. If this is
what is happening, we have to start from scratch and ask
whether reconnection can explain the ion heating seen
by UVCS/SOHO. But before we change the paradigm,
be aware that in situ data do show wave power at high
k|| , even though there is a preference for high k ⊥ (e.g.
[60]).
In this context we inform the reader of a neglected
paper by Ulrich [61]. He found evidence for upward propagating Alfvén waves in the chromosphere, with
periods in a broad range around five minutes. The
upward Poynting flux was about 3 x 107 erg cm-2 s -1.
This is far in excess of the energy requirements of the
fast wind (few times 105 erg cm -2 s-1 at the coronal
base), but it is comparable to the energy requirements of
active regions, which is where the observations were
made. Perhaps the fast wind is supplied by five minute
waves, but that would still require a turbulent cascade.
An entirely different approach postulates that small
reconnection events on the Sun launch the required
energy in the kilohertz range [62 - 65]. The waves
would be below the cyclotron resonance where they are
launched, but would be resonant at greater heights
where Ω is less. This is often called the "sweeping
mechanism", since the resonant frequency sweeps from
high values to lower values as the waves get further
from the Sun.
Tu and Marsch [64, 65] presented some detailed
calculations based on this idea. They postulated a wave
power spectrum which was adjusted to deposit the
required energies at various heliocentric distances.
They assumed parallel - propagating waves, which is of
course not realistic in a structured solar atmosphere.
Hollweg [66] asked what would be different if that
assumption were relaxed. He noted that obliquely
propagating waves would be compressive, and used the
model's magnetic power spectrum to estimate the
spectrum of density fluctuations in the corona. The
estimated spectrum was found to be much larger than
density spectra inferred from radio scattering (IPS).
This probably means that magnetic spectra such as
those used in the sweeping models are not there.
However, the oblique waves damp, via Landau and
transit - time damping on the electrons, and this might
explain why the large density fluctuations are not
observed. This needs to be worked out in detail, but our
guess is that if the Sun launches high - frequency waves
propagating at many angles to B o , and if the oblique
waves damp, then too much electron heating would
result, and the electrons would carry more heat flux than
observed.
Are there alternatives? Recently there has been a
flurry of activity looking at whether instabilities can
drive the high - frequency waves. These instabilities are
generally highly oblique to B o , some may be
electrostatic, and some may propagate sunward. The
driving mechanisms looked at include cross - field
currents [67, 68], large but intermittent electron heat
flux ([69], and Markovskii and Hollweg, this volume),
and proton beams launched by reconnection events [70].
This review would not be complete without
mentioning a totally different view. Lee and Wu [71]
showed how obliquely - propagating fast shocks can
preferentially heat heavy ions such as 0 +5 . The trouble
here is that the shocks need to be strong, with velocity
jumps greater than about 0.3 vA. These velocity jumps
should show up as line broadening in the UVCS/SOHO
data. In coronal holes vA can be very large, and the
shock - related line broadening could be comparable to
or even larger than the observed broadening. Much
more detailed modeling needs to be done to assess
whether this mechanism can explain the line widths
observed by UVCS/SOHO.
CONCLUSIONS
In the years since the discovery of the solar wind, we
have progressed from an electron - driven wind, through
18
a wave - driven wind, to a proton - driven wind which is
accelerated mainly by the proton pressure gradient
(which is equivalent to the mirror force if Tp⊥ >> T p||).
We now know that the coronal heating is not confined
to a thin layer at the coronal base; the heating extends
throughout the acceleration region, implying that
coronal heating and wind acceleration need to be treated
on an equal footing. And we now realize that, in
coronal holes at least, the heating works mainly on the
protons and ions. That the heating is mainly transverse
to Bo has been verified for one ion, 0+5 ; it seems likely
that this will turn out to be a general result. The heating
is not Ohmic dissipation, in contrast to what many
workers believe to be the case elsewhere in the solar
atmosphere. Will it turn out that other regions are
heated in the same way as coronal holes?
Even if one accepts the cyclotron heating paradigm,
there is still much to be done. What is the source of the
waves: turbulent cascade, direct launching, or local
instabilities? How important is oblique propagation,
which has received very little attention [72]? What is
the mix of outward and sunward - propagating waves?
Are sunward - propagating waves produced mainly by
instabilities, or by reflections? How important is second
- order Fermi acceleration? Perhaps the most important
area for future development, and probably the most
difficult, is full kinetic solutions. This aspect is still in
its infancy ([49, 73 - 76] and Isenberg, this volume).
Perhaps one of the most difficult features to incorporate
will be the self - consistent evolutions of the particle
distribution functions and the waves, including
instabilities; intuition based on bi - Maxwellians is
misleading (Isenberg, this volume).
We again warn the reader that some models based on
MHD turbulent cascades ultimately dissipate their
energy via reconnection. If true, this would necessitate
a complete rethinking of the coronal heating and solar
wind acceleration problem.
Finally, we have to say something about the
electrons. Their pressure gradient may contribute less
to accelerating the wind than that of the protons, but it is
not negligible either. They determine the charge states
which emerge out of the corona, they are responsible for
the electromagnetic radiation emerging from the corona
and transition region, and their downward heat
conduction has much to do with how the corona joins
with the lower layers. For these reasons it is obviously
important to get a grasp on the electron energy equation,
which still proves elusive: we still do not have a good
prescription for the electron heat conduction. The
electron energy equation is important for another reason
as well. If we knew the level of electron heating we
would have one further constraint on the physical
processes going on in the corona; recall our discussion
of the sweeping models of Tu and Marsch. At present
the electrons can not be used in this fashion because
their energy equation is not understood.
ACKNOWLEDGEMENTS
The author acknowledges valuable conversations
with P. A. Isenberg, M. A. Lee, S. A. Markovskii, and
S. R. Cranmer. This work was supported by the NASA
Sun - Earth Connections Theory Program under grants
NAG5 - 8228 and NAG5 - 11797 to the University of
New Hampshire.
REFERENCES
1. Parker, E. N., Astrophys. J. 128, 664 (1958).
2. Parker, E. N., Space Science Rev. 4, 666 (1965).
3. Wilhelm, K., Marsch, E., Dwivedi, B. N. et al., Astrophys.
J. 500, 1023 (1998).
4. Sturrock, P. A., and Hartle, R. E., Phys. Rev. Lett. 16, 628
(1966).
5. Hartle, R. E., and Sturrock, P. A., Astrophys. J. 151, 1155
(1968).
6. Feldman, W. C., Asbridge, J. R., Bame, S. J. et al., J.
Geophys. Res. 81, 5054 (1976).
7. Belcher, J. W., Davis, L., Jr., and Smith, E. J., J. Geophys.
Res. 74, 2302 (1969).
8. Belcher, J. W., and Davis, L., Jr., J. Geophys. Res. 76, 3534
(1971).
9. Coleman, P. J., Jr., Phys. Rev. Lett. 17, 207 (1966).
10. Unti, T. W. J., and Neugebauer, M., Phys. Fluids 11, 563
(1968).
11. Alazraki, G., and Couturier, P., Astron. Astrophys. 13, 380
(1971).
12. Belcher, J. W., Astrophys. J. 168, 509 (1971).
13. Hollweg, J. V., Astrophys. J. 181, 547 (1973).
14. Hollweg, J. V., Rev. Geophys. 16, 689 (1978).
15. Barnes, A., Astrophys. J. 154, 751 (1968).
16. Barnes, A., Astrophys. J. 157, 479 (1969).
17. Roberts, D. A., J. Geophys. Res. 94, 6899 (1989).
18. Tu, C.-Y., Pu, Z.-Y., and Wei, F.-S., J. Geophys. Res. 89,
9695 (1984).
19. Tu, C.-Y., Solar Phys. 109, 149 (1987).
20. Grall, R. R., Coles, W. A., Klinglesmith, M. T. et al.,
Nature 379, 429 (1995).
21. Guhathakurta, M., and Fisher, R., Astrophys. J. 499, L215
(1998).
22. Abraham-Shrauner, B., and Feldman, W. C., J. Geophys.
Res. 82, 618 (1977).
23. Dusenbery, P. B., and Hollweg, J. V., J. Geophys. Res. 86,
153 (1981).
24. Hollweg, J. V., and Turner, J. M., J. Geophys. Res. 83, 97
(1978).
25. Isenberg, P. A., and Hollweg, J. V., J. Geophys. Res. 88,
3923 (1983).
26. Marsch, E., Goertz, C. K., and Richter, K., J. Geophys.
Res. 87, 5030 (1982).
19
27. McKenzie, J. F., and Marsch, E., Astrophys. Space Sci. 81,
295 (1982).
28. Marsch, E., "Kinetic physics of the solar wind plasma", in
Physics of the Inner Heliosphere, 2, Particles, Waves and
Turbulence, edited by R. Schwenn, and E. Marsch,
Springer-Verlag, Berlin, 1991, p. 45.
29. Isenberg, P. A., J. Geophys. Res. 89, 6613 (1984).
30. Hollweg, J. V., J. Geophys. Res. 91, 4111 (1986).
31. Hollweg, J. V., and Johnson, W., J. Geophys. Res. 93,
9547 (1988).
32. Dmitruk, P., Milano, L. J., and Matthaeus, W. H.,
Astrophys. J. 548, 482 (2001).
33. Dmitruk, P., Matthaeus, W. H., Milano, L. J. et al.,
Astrophys. J., in press (2002).
34. Isenberg, P. A., J. Geophys. Res. 95, 6437 (1990).
35. Kohl, J. L., and al., e., Astrophys. J. 501, L127 (1998).
36. Cranmer, S. R., and al., e., Astrophys. J. 511, 481 (1999).
37. Antonucci, E., Dodero, M. A., and Giordano, S., Solar
Phys. 197, 115 (2000).
38. Ryan, J. M., and Axford, W. I., J. Geophys. 41, 221
(1975).
39. Esser, R., and Habbal, S. R., Geophys. Res. Lett. 22, 2661
(1995).
40. Esser, R., and Habbal, S. R., "Modeling high flow speeds
in the inner corona", in Solar Wind Eight, edited by D.
Winterhalter, J. Gosling, S. R. Habbal, W. S. Kurth, and M.
Neugebauer, AIP, New York, 1996, p. 133.
41. Esser, R., Habbal, H. R., Coles, W. A. et al., J. Geophys.
Res. 102, 7063 (1997).
42. Hollweg, J. V., and Isenberg, P. A., J. Geophys. Res., in
press (2002).
43. Cranmer, S. R., Space Sci. Rev., in press (2002).
44. Gomberoff, L., and Elgueta, R., J. Geophys. Res. 96, 9801
(1991).
45. Gomberoff, L., Gratton, F. T., and Gnavi, G.,
"Acceleration and heating of heavy ions in high speed solar
wind streams", in Solar Wind Eight, edited by D.
Winterhalter, J. T. Gosling, S. R. Habbal, W. S. Kurth, and
M. Neugebauer, Amer. Inst. Physics, New York, 1996, p.
319.
46. Gomberoff, L., Gratton, F. T., and Gnavi, G., J. Geophys.
Res. 101, 15661 (1996).
47. Gomberoff, L., and Astudillo, H., "Ion heating and
acceleration in the solar wind", in Solar Wind Nine, edited
by S. R. Habbal, R. Esser, J. V. Hollweg, and P. A.
Isenberg, Amer. Inst. Phys., New York, 1999, p. 461.
48. Hollweg, J. V., J. Geophys. Res. 105, 15699 (2000).
49. Isenberg, P. A., Space Sci. Rev. 95, 119 (2001).
50. Esser, R., Fineschi, S., Dobrzycka, D. et al., Astrophys. J.
510, L63 (1999).
51. Tu, C.-Y., J. Geophys. Res. 93, 7 (1988).
52. Li, X., Habbal, S. R., Hollweg, J. V. et al., J. Geophys.
Res. 104, 2521 (1999).
53. Hu, Y. Q., Habbal, S. R., and Li, X., J. Geophys. Res. 104,
24819 (1999).
54. Hu, Y. Q., Esser, R., and Habbal, S. R., J. Geophys. Res.
105, 5093 (2000).
55. Marsch, E., and Tu, C.-Y., J. Geophys. Res. 95, 8211
(1990).
56. Coles, W. A., and Harmon, J. K., Astrophys. J. 337, 1023
(1989).
57. Hollweg, J. V., Bird, M., Volland, H. et al., J. Geophys.
Res. 87, 1 (1982).
58. Andreev, V. E., Efimov, A. I., Samoznaev, L. N. et al.,
Solar Phys. 176, 387 (1997).
59. Mancuso, S., and Spangler, S. R., Astrophys. J. 525, 195
(1999).
60. Leamon, R. J., Smith, C. W., Ness, N. F. et al., J.
Geophys. Res. 103, 4775 (1998).
61. Ulrich, R. K., Astrophys. J. 465, 436 (1996).
62. Axford, W. I., and McKenzie, J. F., "The acceleration of
the solar wind", in Solar Wind Eight, edited by D.
Winterhalter, J. T. Gosling, S. R. Habbal, W. S. Kurth, and
M. Neugebauer, Amer. Inst. Phys., New York, 1996, p. 72.
63. McKenzie, J. F., Banaszkiewicz, M., and Axford, W. I.,
Astron. Astrophys. 303, 45 (1995).
64. Tu, C.-Y., and Marsch, E., Solar Phys. 171, 363 (1997).
65. Marsch, E., and Tu, C.-Y., Astron. Astrophys. 319, L17
(1997).
66. Hollweg, J. V., J. Geophys. Res. 105, 7573 (2000).
67. Markovskii, S. A., Astrophys. J. 557, 337 (2001).
68. Markovskii, S. A., and Hollweg, J. V., J. Geophys. Res., in
press (2002).
69. Markovskii, S. A., and Hollweg, J. V., Geophys. Res. Lett.,
in press (2002).
70. Voitenko, Y., and Goossens, M., Solar Phys. 206, 285
(2002).
71. Lee, L. C., and Wu, B. H., Astrophys. J. 535, 1014 (2000).
72. Hollweg, J. V., and Markovskii, S. A., J. Geophys. Res., in
press (2002).
73. Tam, S. W. Y., and Chang, T., Geophys. Res. Lett. 26,
3189 (1999).
74. Tam, S. W. Y., and Chang, T., Geophys. Res. Lett. 28,
1351 (2001).
75. Isenberg, P. A., Lee, M. A., and Hollweg, J. V., J.
Geophys. Res. 106, 5649 (2001).
76. Isenberg, P. A., J. Geophys. Res. 106, 29249 (2001).
20