Generation of proton beams at switchback boundary-like rotational discontinuities in the solar wind

TL;DR

This work demonstrates that switchback-like, RD-boundaries in a 2D hybrid PIC framework can trap a significant proton population downstream, creating a field-aligned beam with $T_ot/T_\fect ~ 4$ that excites left-hand ion cyclotron waves. The beam formation is driven by a relatively static electric field near the RD, primarily from the convective term in the generalized Ohm’s law, and is supported by test-particle experiments showing electric potential as the dominant trapping mechanism. Linear dispersion analysis with the observed beam parameters reproduces the instability characteristics, indicating the beam acts as the seed for ICW growth within the RD transition layer. The results suggest RD sub-structures and their embedded currents can actively shape proton kinetics and wave activity in the inner heliosphere, with implications for proton heating and switchback dynamics observed by missions like PSP and Solar Orbiter; however, the 2D nature and boundary setup call for 3D studies and more realistic initial VDFs to fully capture solar wind conditions.

Abstract

Alfvénic rotational discontinuities (RDs) are abundant in the inner heliosphere and can be used to model the boundary of switchbacks, i.e. Alfvénic magnetic kinks. To investigate the effects of RDs on proton kinetics, we model a pair of switchback-boundary-like RDs with a hybrid Particle-In-Cell (PIC) approach in a 2D system. We find that, at one of the boundary RDs, a significant population of protons remains trapped over long times, creating a secondary beam-like component with temperature anisotropy $T_\perp/T_\|\gtrsim4$ in the proton velocity distribution function that excites ion cyclotron waves within the downstream portion of the transition layer. Further analysis suggests that the static electric field in the vicinity of the RD is the key factor in trapping the protons. This work indicates that switchback boundaries could represent a viable environment for the creation of proton beams in the heliosphere; it also highlights the need to investigate RD sub-structures, especially the embedded current systems of interplanetary RDs. Finally, this paper underscores the importance of high-resolution observations of the solar wind velocity distributions around RDs.

Figures (7)

• Figure 1: The initial settings of the magnetic field and the proton bulk velocity. The variables are in code units.
• Figure 2: Key variables in the simulation. (a) The magnitude of magnetic field, (b)-(d) the three components of the magnetic field, (e)-(g) the three components of the ion bulk velocity, (h) the proton number density, (i)-(k) the three components of the electric field, (l)-(n) parallel, perpendicular and isotropic ion beta.
• Figure 3: Excitation, growth, and damping of the left-hand polarized ICWs due to wave-particle interactions in the presence of a proton beam. (a)-(e): Spatial distribution of $B_y$ at $114d_i<y<120d_i$ where the wave activity dominates, and the green lines are cuts of $B_y$ sampled along the white dashed line. (f)-(j): Proton VDFs sampled within $114.0 d_i<y<120.0d_i$ and $6.0d_i<x<12.0d_i$ (marked with magenta dashed squares). The white dashed line marks roughly the location of the "bean" population in panel(f) as an example. Two panels in the same row correspond to the same simulation time. An animation of the left column, i.e. panels (a)-(e), is available. The video runs for approximately 6 seconds and covers the simulation time interval from $t=120 \Omega_{ci}^{-1}$ to $250 \Omega_{ci}^{-1}$. It demonstrates the continuous leftward propagation of the waves, clearly illustrating the dynamic process of wave amplitude growth and subsequent damping that is represented by the snapshots in the static figure.
• Figure 4: (a) The ratio of the fitted beam number density to the fitted core number density, as a function of time. (b) Red dashed line and red dots: fitted drift velocity of the proton core; blue solid line and blue dots: fitted drift velocity of the proton beam; black solid line and black squares: the difference between the fitted beam drift velocity and the fitted core drift velocity. (c) Red solid line and red dots: fitted parallel thermal speed of the proton core; red dashed line and red circles: fitted perpendicular thermal speed of the proton core; blue solid line and blue solid squares: fitted parallel speed of the proton beam; blue dashed line and blue hollow squared: fitted perpendicular speed of the proton beam. (d) The real frequency, as a function of wavenumber, of the wave branches with maximum growth rates at different times (marked with the colorbar). (e) The imaginary frequency, as a function of the wavenumber, of the same wave branches in (d). The red dashed line in (d) and (e) refers to the estimated wavenumber in the simulation.
• Figure 5: (a) Velocity distribution of downsampled traced particles at $t=125\Omega_{ci}^{-1}$. These particles are sampled from the same region as in Figure \ref{['fig3: waveFieldAndVDF']}f-j. (b) Distribution of $y$-positions of traced particles at $t=100\Omega_{ci}^{-1}$. The black vertical dashed line corresponds to the location of the RD of interest. (c)-(d) Sampled particle trajectories from the "beam" and "core" groups. The colors on trajectories indicate time. The black solid lines show the local magnetic field geometry.