4.2 Validity of classical electron heat flux in the transition region

Proton and more so electron heat conduction reduce the maximal corona temperature, and consequently the initial solar wind acceleration. However, high temperatures also yield a long Coulomb mean free path, thus bringing into question the application of the classical heat flux law, particularly in the presence of strong waves which can affect the ions on much shorter scales. Whereas this problem of a possible breakdown of classical collision-dominated transport in the solar corona has found not much attention as far as protons, alpha particles and minor ions are concerned, there has for a long time been a debate about the validity of the Spitzer–Härm electron heat conduction (Spitzer and Härm, 1953Jump To The Next Citation Point), or the validity of Fourier’s law according to which heat flows down the temperature gradient.

Lie-Svendsen et al. (1999) studied the transport of thermal energy in the solar transition region (TR), to find out if there the classical description,

q = − κ T 5∕2∇T , (29 ) e e e e
of electron heat conduction is applicable. Here Te is the electron temperature, and κe the heat conductivity. Using an approximation in which test electrons moved in a prescribed Maxwellian electron-proton plasma, they validated this approach by a comparison of their with known results (Spitzer and Härm, 1953Jump To The Next Citation Point) in the collision-dominated regime, where the Spitzer–Härm relation (29View Equation) applied. They obtained electron VDFs in good agreement with that theory, showing that classical theory is sufficient to describe heat transport in the TR. Only when the pressure (density) was reduced to unrealistically low values, while the temperature profile remained unchanged, a significant fraction of the heat flux was carried by suprathermal electrons from the corona. But even then the total heat flux was never found to exceed the classical value.

However, this conclusion is in striking disagreement with other more recent results described in the subsequent section, but also the older results obtained by Shoub (1983), who solved numerically the Landau–Fokker–Planck equation for a kinetic transition region model and found that sizable high-energy tails developed in the electron distribution even for very low Knudsen number, 𝜖 = 10−3. This result was affirmed by Landi and Pantellini (2001Jump To The Next Citation Point) and Dorelli and Scudder (2003Jump To The Next Citation Point), who emphasised the importance of suprathermal electrons in coronal plasma conditions.

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