1. Complications to Electron Landau Damping in the Solar Wind Waves of interest have v phase|| ≈ v A v A ≈ 54 km/s 0.5m e v A 2 ≈ 8×10 -3 eV  Very very low-energy electrons Landau resonate. Borovsky and Gary, Electron-ion Coulomb scattering and the electron Landau damping of Alfven waves in the solar wind, J. Geophys. Res., 116, A07107, 2011. This low energy leads to 3 complications: (1). Alfven wave parallel voltages >> resonant energy of electrons.  very broad resonance  Linear Vlasov does not work for calculating Landau-damping rates.

2. Complications to Electron Landau Damping in the Solar Wind (2). Slow electrons Coulomb scatter rapidly off solar-wind protons. (At 1 AU the timescale for electrons to collisionally scatter into and out of resonance is measured in seconds.) a)  collision <<  wave,  Landau  Might not want to use the collisionless Vlasov equation. b) Wave does not locally evolve the electron distribution function.  Quasi-linear theory is insufficient. (3). E || of Alfven waves < heliospheric electric field.  Must consider whether E heliosphere disrupts Landau damping. Note also: Ion beams near v A complicate Landau damping.  Ion Landau damping (even at low  ) may not be ignorable.