Many global aspects of the solar wind flow are well described by the fluid theory developed and used in Lectures 4-8 and 11. However, even some of these global aspects point to a need to directly consider the kinetic and not fluid nature of the plasma. These points are now illustrated in some detail.
Figure 12.9 [Belcher et al., 1993] shows that the solar wind plasma density follows the
simple 
fall-off predicted by fluid theory, and on more general grounds
by global mass conservation.
Figure 12.9: The solar wind plasma density as a function of heliocentric distance R [Belcher et al.,
1993].
Similarly, Parker's theory for the solar wind predicts that
asymptotes to a constant value within about 10 solar radii and then remains
constant further from the Sun. Richardson et al. [1995] show that this result is
consistent with Voyager data (except perhaps beyond 20 AU where mass loading by
interstellar pickup ions may cause a small slowdown - see below). Similarly the magnetic
field is well described by Parker's MHD theory, as shown in Figure 12.10 [Burlaga et al., 1998]
taking into account solar cycle variations in the solar wind speed at the spacecraft
location. Thus, the zeroth and first moments of the particle distribution function and the
magnetic field follow the predictions of MHD theory very well.
Figure 12.10: Voyager 1 observations of the magnetic field strength versus time (solid dots) and
Parker's prediction (solid curve) taking into account variable solar wind speed and variable
source fields in the photosphere [Burlaga et al., 1998]. The dotted curves show Parker's
predictions for
variable source fields but constant solar wind speeds of 800 and 400 km s 
for the
bottom and top curves, respectively.
The situation is different for the second moments (e.g., temperatures) of the solar wind electrons
and ions, although the different results of competing scientific teams suggest that no
consensus has been reached on these issues. The first and most obvious illustration of this is
that the ratio of electron to ion temperature in the solar wind near 1 AU is typically
. If these species
were strongly thermally coupled then they would have identical temperatures.
This difference in temperature at 1 AU compared with very similar temperatures in the corona
suggests that the temperatures of ions and electrons fall off differently. To see this assume that
both species have temperatures of 
K at 10 solar radii and then calculate the power
law indices 
for each species assuming 
K and
K at 1 AU (215 solar radii); with 
.
This calculation yields 
and 
. Moreover, analyses of
observational data suggest that these indices are 
between 1 and 10 AU and
for the same range of heliocentric distances. In comparison, the
fluid theories in Chapter 7
yield 
for adiabatic flow, 
from Eq. (7.3), and 
for isothermal flow. How can these differences be explained in the context of MHD or two-fluid
theory?
The non-fluid nature of the electron distribution is illustrated in Figure 12.11, where it can be seen that the distribution is well-represented as the sum of two approximately Maxwellian components: a relatively dense and cold ``core'' component and a relatively hot and dilute ``halo'' component.
Figure 12.11: A cut through a solar wind electron distribution along the magnetic field
direction [Feldman, 1979]. The two solid curves are two bi-Maxwellian functions
which best fit the core and halo electrons at low and intermediate energies,
respectively.
The core and halo electrons drift relative to one another, resulting in a net heat flux outward away from the Sun. The detailed variations of the solar wind heat flux and the core and halo distributions are not yet understood. The way forward, however, is widely believed to require the use of kinetic physics and wave-particle interactions.