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Many solar wind observations at 1 au indicate that the proton (as well as electron) temperature anisotropy is limited. The data distribution in the (A(a), beta(a),(parallel to))-plane have a rhombic-shaped form around beta(a),(parallel to) similar to 1. The boundaries of the temperature anisotropy at beta(a),(parallel to) > 1 can be well explained by the threshold conditions of the mirror (whistler) and oblique proton (electron) firehose instabilities in a bi-Maxwellian plasma, whereas the physical mechanism of the similar restriction at beta(a),(parallel to) < 1 is still under debate. One possible option is Coulomb collisions, which we revisit in the current work. We derive the relaxation rate nu(A)(aa) of the temperature anisotropy in a bi-Maxwellian plasma that we then study analytically and by observed proton data from WIND. We found that nu(A)(pp) increases toward small beta(p),(parallel to) < 1. We matched the data distribution in the (A(p), beta(p),(parallel to))-plane with the constant contour nu(A)(pp) = 2.8 . 10(-6) s(-1), corresponding to the minimum value for collisions to play a role. This contour fits rather well the left boundary of the rhombic-shaped data distribution in the (A(p), beta(p),(parallel to))-plane. Thus, Coulomb collisions are an interesting candidate for explaining the limitations of the temperature anisotropy in the solar wind with small beta(a),(parallel to) < 1 at 1 au.
Due to the relatively low rate of particle-particle collisions in the solar wind, kinetic instabilities (e.g., the mirror and firehose) play an important role in regulating large deviations from temperature isotropy. These instabilities operate in the high beta(parallel to) > 1 plasmas, and cannot explain the other limits of the temperature anisotropy reported by observations in the low beta beta(parallel to) < 1 regimes. However, the instability conditions are drastically modified in the presence of streaming (or counterstreaming) components, which are ubiquitous in space plasmas. These effects have been analyzed for the solar wind conditions in a large interval of heliospheric distances, 0.3-2.5 AU. It was found that proton counter-streams are much more crucial for plasma stability than electron ones. Moreover, new instability thresholds can potentially explain all observed bounds on the temperature anisotropy, and also the level of differential streaming in the solar wind.
An interesting feature of solar wind fluctuations is the occasional presence of a well-pronounced peak near the spectral knee. These peaks are well investigated in the context of magnetic field fluctuations in the magnetosheath and they are typically related to kinetic plasma instabilities. Recently, similar peaks were observed in the spectrum of ion flux fluctuations of the solar wind and magnetosheath. In this paper, we propose a simple analytical model to describe such peaks in the ion flux spectrum based on the linear theory of plasma fluctuations. We compare our predictions with a sample observation in the solar wind. For the given observation, the peak requires similar to 10 minutes to grow up to the observed level that agrees with the quasi-linear relaxation time. Moreover, our model well reproduces the form of the measured peak in the ion flux spectrum. The observed lifetime of the peak is about 50 minutes, which is relatively close to the nonlinear Landau damping time of 30-40 minutes. Overall, our model proposes a plausible scenario explaining the observation.
The general electromagnetic fluctuation theory is a powerful tool to analyze the magnetic fluctuation spectrum of a plasma. Recent works utilizing this theory for a magnetized non-relativistic isotropic Maxwellian electron-proton plasma have demonstrated that the equilibrium ratio of vertical bar delta B vertical bar/B-0 can be as high as 10(-12). This value results from the balance between spontaneous emission of fluctuations and their damping, and it is considerably smaller than the observed value vertical bar delta B vertical bar/B-0 in the solar wind at 1 au, where 10(-3) less than or similar to vertical bar delta B vertical bar/B-0 less than or similar to 10(-1). In the present manuscript, we consider an anisotropic bi-Maxwellian distribution function to investigate the effect of plasma instabilities on the magnetic field fluctuations. We demonstrate that these instabilities strongly amplify the magnetic field fluctuations and provide a sufficient mechanism to explain the observed value of vertical bar delta B vertical bar/B-0 in the solar wind at 1 au.