2.2 Solar wind electrons

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Figure 1: Top: Electron velocity distribution function in the solar wind as measured by the plasma instrument on the Helios spacecraft at 1 AU. Note the distinct bulge along the magnetic field, which is the so-called strahl, a suprathermal population carrying the heat flux together with the halo, the hotter isotropic component which is slightly displaced with respect to the maximum of the core part (indicated in red) (after Pilipp et al., 1987bJump To The Next Citation Point). Below: Radial decline (increase) of the number of strahl (halo) electrons with heliocentric distance from the Sun according to the Helios, WIND and Ulysses measurements (after Maksimovic et al., 2005Jump To The Next Citation Point).

Because of their small masses, electrons are less important than ions for the solar wind dynamics. Yet, they ensure quasineutrality, constitute an electric field through their thermal pressure gradient and carry heat in the skewness of the thermal bulk and the suprathermal tail of their VDFs, which are determined mainly by the large-scale interplanetary magnetic field and the self-generated electrostatic potential, by Coulomb collisions in the thermal energy range at a few 10 eV, and by various kinds of wave-particle interactions. The electrons are subsonic, i.e. their mean thermal speed considerably exceeds the solar wind (ion) bulk speed. Suprathermal electrons (at several 100 eV) may be considered as test particles that quickly explore the global structure of the heliospheric magnetic field, which consists usually of open field lines mostly anchored in coronal holes (CHs), but may temporarily attain the shape of magnetic bottles or closed loops.

Figure 1View Image shows in the upper frame a typical solar wind electron VDF measured in a fast stream at 1 AU, after Pilipp et al. (1987aJump To The Next Citation Point). A strong heat flux tail is clearly visible as a distinct bulge (the “Strahl”, Rosenbauer et al., 1977Jump To The Next Citation Point) in the VDF along the magnetic field direction (indicated by a dashed line). The main colder core population is surrounded by hotter halo electrons that amount to a few (typically four) percent in relative number density. The lower frame of Figure 1View Image after Maksimovic et al. (2005Jump To The Next Citation Point) indicates that the strahl is declining with radial distance from the Sun, whereas the halo is relatively increasing, perhaps by scattering of strahl electrons.

The collisional free path λc is according to Table 1 much larger than the temperature gradient scale height L. A polynomial expansion of the electron VDF about a local Maxwellian is found to badly converge (see also Dum et al., 1980Jump To The Next Citation Point), and thus an expansion like in the subsequent Equations (23View Equation) or (26View Equation) is certainly not appropriate for solar wind electrons. The reason is that they are global players and reflect, as is obvious from their strongly skewed VDF, the large-scale inhomogeneity of the solar wind and coronal boundary conditions, as well as local collisional processes that shape the central part of their VDF. This was emphasised long time ago by Scudder and Olbert (1979aJump To The Next Citation Point,bJump To The Next Citation Point) in analytical model calculations.

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Figure 2: Electron velocity distribution functions as energy spectra (top) and velocity space contours (bottom) for fast (left), intermediate (middle) and slow (right) solar wind. Isodensity contours are in steps by a factor of 10. Note the core-halo structure and the strahl of suprathermal electrons in fast solar wind (after Pilipp et al., 1987aJump To The Next Citation Point).

In detailed kinetic simulations, Lie-Svendsen et al. (1997Jump To The Next Citation Point) numerically integrated an approximate kinetic equation derived from the basic Boltzmann Equation (9View Equation) to be discussed later, and could reproduce essential features of the observed VDFs. They concluded that electrons do not matter dynamically in solar wind acceleration. The radial evolution of thermal electrons due to expansion and collisions was studied in the fluid picture by Phillips and Gosling (1990). As we will discuss below, Landi and Pantellini (2001Jump To The Next Citation Point) recently carried out fully kinetic simulations of electrons in a coronal hole and the associated solar wind. We come back to these theoretical issues in Section 7, where kinetic models for the corona and solar wind are discussed.

The magnetic field topology has a strong influence on the shapes of the velocity distributions, which can observationally be considered to be composed of three main components, a cold and almost isotropic collisional core, a hot variably-skewed halo population, and in fast solar wind often a narrow field-aligned strahl. The basic electron characteristics were first measured and described by Feldman et al. (1975Jump To The Next Citation Point). A comprehensive modern review was given by Feldman and Marsch (1997Jump To The Next Citation Point). The VFDs have often been modelled by only two convecting bi-Maxwellians as illustrated in the top part of Figure 2View Image, taken from the Helios observations published by Pilipp et al. (1987aJump To The Next Citation Point). On open field lines in the fast wind, the VDF usually develops a high-energy extension with a very narrow pitch-angle distribution only 10 – 20 degrees wide. This electron strahl population responds sensitively to the local magnetic field orientation.

Common observations of the same plasma parcel of the wind by instruments on different spacecrafts, when being radially aligned, allows one to characterise the radial gradients of electron thermal parameters. The core temperature is found to vary widely between isothermal and adiabatic, while the halo temperature behaves more isothermally. The halo density falls off more steeply in dense plasma. Electron parameters have been studied by Ulysses in the distance range from 1 to 4 AU (McComas et al., 1992Jump To The Next Citation Point), where the halo is found to represent always about 4% of the total electron number. Since there is no reason for this ratio to be constant if the halo and core particles were completely separated, it appears that halo particles are not entirely decoupled from the core.

Solar wind electron parameters, in comparison with other measurements made on Ulysses, have also been derived from quasi-thermal noise spectroscopy, a novel method which was introduced by Meyer-Vernet and Perche (1989) and then exploited by Maksimovic et al. (1995) and Issautier et al. (1996).

Solar cycle variations in the electron heat flux have been studied by Scime et al. (2001Jump To The Next Citation Point), who did not find any significant dependence of the heat flux on the cycle or heliographic latitude. On average, the heat flux radially varies according to a power-law scaling, −2.9 qe ∼ R, but there is no significant correlation of its magnitude with the solar wind speed. Concerning the electron temperature in the ambient solar wind, typical values and a lower bound were inferred from ISEE data at 1 AU in a paper by Newbury et al. (1998). In particular, the temperature ratio, Te∕Tp was investigated and found to depend systematically on the wind speed. The average ratio declines from about 4 at 300 km s–1 to about 0.5 at 700 km s–1.

The break-point energy in the electron spectra of Figure 2View Image scales on average like seven times the core temperature, a result which was predicted by a kinetic theory for the electrons when being mediated by Coulomb collisions alone (Scudder and Olbert, 1979aJump To The Next Citation Point,bJump To The Next Citation Point). Such value of the break-point energy is also consistent with its interpretation as being equal to the electrostatic interplanetary potential that traps thermal electrons. Typical values of the interplanetary potential Φe at 1 AU are 50 – 100 eV (Pilipp et al., 1987aJump To The Next Citation Point,bJump To The Next Citation Point). For the importance of Φe(r) see the following Subsection 3.3 and the discussion in the paper by Maksimovic et al. (2001). Concerning the radial profile of the mean electron temperature, Meyer-Vernet and Issautier (1998) presented a kinetic model to obtain what they called the generic radial temperature variation derived from collisionless kinetics. Empirically (Marsch, 1991aJump To The Next Citation Point), the temperature varies between almost isothermal and adiabatic behaviour (that implies r−4∕3 scaling with distance r).

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