Solar Electron Beam Velocities That Grow Langmuir Waves in the Inner Heliosphere

Solar accelerated electron beams, a component of space weather, are emitted by eruptive events at the Sun. They interact with the ambient plasma to grow Langmuir waves, which subsequently produce radio emission, changing the electrons’ motion through space. Solar electron beam–plasma interactions are simulated using a quasilinear approach to kinetic theory to probe the variations in the maximum electron velocity [ Ξ ] responsible for Langmuir wave growth between the Sun’s surface and 50 R ⊙ above the surface. We find that it peaks at 5 R ⊙ at 0.38 c and decreases as r^-0.5 to 0.16 c at 50 R ⊙ . The role of the initial beam density [ n_beam ] and velocity spectral index [ α ] on the energy density of the beam and Ξ is extensively studied. We show that a high spectral index yields a lower Ξ , while a high n_beam yields a higher Ξ , and vice versa. We observe at different energy channels that below 60 keV, electrons arrive up to 0.75 minutes earlier than expected at 13 R ⊙ while higher energy electrons propagate scatter free in the plasma. A special focus on the associated Type III radio burst shows that the energy range [ Δ E ] of electrons producing Langmuir waves evolves from 7 keV to 1 keV between 0 and 28 R ⊙ . Understanding the transport effect on the electron beam kinetics and arrival time at Earth has space weather implications. The results of this simulation can be tested against readily available in-situ data from Solar Orbiter and Parker Solar Probe .