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Arguments for kinetic physics in radial variations of solar wind parameters

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 tex2html_wrap_inline462 fall-off predicted by fluid theory, and on more general grounds by global mass conservation.

  figure76
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 tex2html_wrap_inline404 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.

  figure81
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 tex2html_wrap_inline402 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 tex2html_wrap_inline474 . 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 tex2html_wrap_inline476 K at 10 solar radii and then calculate the power law indices tex2html_wrap_inline480 for each species assuming tex2html_wrap_inline482 K and tex2html_wrap_inline484 K at 1 AU (215 solar radii); with tex2html_wrap_inline486 . This calculation yields tex2html_wrap_inline488 and tex2html_wrap_inline490 . Moreover, analyses of observational data suggest that these indices are tex2html_wrap_inline492 between 1 and 10 AU and tex2html_wrap_inline494 for the same range of heliocentric distances. In comparison, the fluid theories in Chapter 7 yield tex2html_wrap_inline496 for adiabatic flow, tex2html_wrap_inline498 from Eq. (7.3), and tex2html_wrap_inline500 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.

  figure99
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.


next up previous
Next: Interstellar pickup ions Up: Kinetic and Small Scale Previous: Type III solar Radio

Iver Cairns
Wed Sep 8 09:24:55 EST 1999