Landau damping in relativistic plasmas with power-law distributions and applications to solar wind electrons

The relativistic plasma dispersion relation is derived for Langmuir waves in a spatially homogeneous unmagnetized plasma in which the electrons have an isotropic power-law distribution in momentum space. The theory is applied to the study of Langmuir waves in the quiescent solar wind near the orbit of the Earth assuming that the electron distribution function can be approximated as a power-law from thermal energies similar to 10 eV to relativistic energies greater than or similar to 100 keV. Numerical solutions of the dispersion relation show that in the regime of weak Landau damping the phase speeds of the waves match the velocities of the high-energy particles, known in the solar wind literature as the superhalo, which lie in the range 0.09 < v/c < 0.8. While this result raises the question of whether wave-particle interactions with a spectrum of Langmuir waves plays a role in the formation of the superhalo, the observed energy density of the waves near the orbit of the Earth at 1 AU is so small that active acceleration of superhalo electrons by Langmuir waves, if it occurs at all, has ceased by the time the solar wind reaches the Earth.