Modeling Interactions of Narrowband Large Amplitude Whistler-mode Waves with Electrons in the Solar Wind inside ∼0.3 au and at 1 au Using a Particle Tracing Code

Abstract

The discovery of large amplitude narrowband whistler-mode waves at frequencies of tenths of the electron cyclotron frequency in large numbers both inside ∼0.3 au and at ∼1 au provides an answer to longstanding questions about scattering and energization of solar wind electrons. The waves can have rapid nonlinear interactions with electrons over a broad energy range. Counter propagation between electrons and waves is not required for resonance with the obliquely propagating waves in contrast to the case for parallel propagation. Using a full 3D particle tracing code, we have examined interactions of electrons with energies from 0 eV to 2 keV with whistler-mode waves with amplitudes of 20 mV m−1 and propagation angles from 0° to 180° to the background magnetic field. Interactions with wave packets and single waves are both modeled based on observations at ∼0.3 au and 1 au. A test particle simulation approach allows us to examine the particle motion in detail, which reveals kinetic effects of resonant interactions. The simulations demonstrate the key role played by these waves in rapid scattering and energization of electrons. Strong scattering and energization for some initial energy and pitch angle ranges occurs for both counter-propagating and obliquely propagating waves. Strong scattering of strahl electrons counteracts the pitch angle narrowing due to conservation of the first adiabatic invariant as electrons propagate from the Sun into regions of smaller magnetic field. Scattering also produces the hotter isotropic halo. The concomitant limiting of the electron heat flux is also relevant in other astrophysical settings.

The Sunward Electron Deficit: A Telltale Sign of the Sun’s Electric Potential

“…The clear anticorrelation of significant fractional halo densities with the presence of the deficit suggests that the formation of the halo may play an important role in erasing the sunward deficit. A plausible scenario might involve oblique instabilities that rapidly scatter the strahl over a broad angular range (Cattell & Vo 2021), producing the halo and obscuring the deficit simultaneously. However, the fact that the probability of observing the deficit correlates not with the electron heat flux, but with core temperature anisotropy, complicates the story.…”

“…These observed trends naturally motivate the question of whether a single process could simultaneously produce the halo and obscure the sunward deficit. Oblique whistler instabilities provide one natural candidate, as they can rapidly scatter the strahl over a broad angular range to form a halo-like distribution (Cattell & Vo 2021). A multi-stage process whereby oblique whistlers scatter the strahl to form the halo, and then quasi-parallel whistlers redistribute the halo into a more isotropic state (Micera et al 2020), also provides a plausible hypothesis to explain these observations.…”

Stochastic diffusion of electrons interacting with whistler-mode waves in the solar wind

“…We use the relativistic Boris algorithm (Ripperda et al, 2018) to solve (8) numerically with a range of initial conditions. Similar to Cattell and Vo (2021), we study two sets of background parameters typical of solar wind conditions at 0.3 AU and 1 AU. The former, identical to those in Micera et al (2020), which is hereby referred to as M2020, has an electron density n e = 350 cm -3 and a background field B 0 = 60 nT so that ω pe /Ω c = 100 where ω pe = 4πe 2 n e /m is the plasma frequency.…”

“…We find that a time step ∆t/T c = 10 −5 is a good choice which maintains |∆V /V 0 | ∼ 10 −2 (see colorbar limits of Figure 2). The same time step was used in the test particle simulations in Cattell and Vo (2021) and the PIC simulation in M2020. In the fol- lowing section, we study the stochastic motion of electrons in large amplitude waves using this time step.…”

“…We demonstrate the effects of increasing whistler amplitude and propagation angle and show that high amplitude, quasi-parallel whistlers are not as essential to the isotropization of the VDF at 1 AU as they are near the Sun. We also present our numerical methods, which were only briefly outlined in Cattell and Vo (2021). In Section II, we discuss the relevant theory of wave-particle interaction and define the error in phase space volume which is important to simulations of Hamiltonian systems.…”