Alpha Core-Beam Origin in Low-$β$ Solar Wind Plasma: Insights from Fully Kinetic Simulation

TL;DR

This work addresses how alpha-particle beams can form locally in the fast solar wind by exploiting non-linear Landau damping driven by a super-Alfvénic alpha–proton drift. Using a one-dimensional fully kinetic PIC approach (ECsim) complemented by linear theory (DIS-K), the authors identify two unstable modes (FM/W and A/IC) and demonstrate, through long-time simulations, the fragmentation of the alpha distribution into a dense alpha-core and a fast alpha-beam, with the beam achieving super-Alfvénic speeds. The field–particle correlator analysis reveals Landau-resonant energy transfer as the mechanism transferring energy from parallel drift to perpendicular alpha heating, culminating in a metastable core–beam configuration (roughly 40% core and 60% beam, beam drift ~1.8 $c_{A p}$). These results offer a local, kinetic pathway for alpha-beam generation compatible with in-situ solar-wind observations, while highlighting the need for multidimensional studies to capture oblique instabilities and broader parameter space.

Abstract

In-situ observations of the fast solar wind in the inner-heliosphere show that minor ions and ion sub-populations often exhibit distinct drift velocities. Both alpha particles and proton beams stream at speeds that rarely exceed the local Alfvén speed relative to the core protons, suggesting the presence of instabilities that constrain their maximum drift. We aim to propose a mechanism that generates an alpha-particle beam through non-linear Landau damping, primarily driven by the relative super-Alfvénic drift between protons and alpha particles. To investigate this process, we perform one-dimensional, fully kinetic particle-in-cell simulations of a non-equilibrium multi-species plasma, complemented by its linear theory to validate the model during the linear phase. Our results provide clear evidence that the system evolves by producing an alpha-particle beam, thereby suggesting a local mechanism for alpha-beam generation via non-linear Landau damping.

Figures (11)

• Figure 1: Schematic illustration of the simulation setup. The figure shows a portion of velocity phase space containing the electron and ion VDFs, with color intensity indicating particle density. For each species, the plasma-$\beta$ parameter is defined as $\beta_s \doteq 8\pi n_s k_B T_s / B^2$.
• Figure 2: In the first row, panels (a) to (c) respectively show the result of LT for the real frequency $\omega_{r}/\omega_{pp}$, growth rate $\gamma/\omega_{pp}$, and polarization of the unstable eigenmode in the $k_{\parallel}$-$k_{\perp}$ plane, computed using the realistic mass ratio $m_p/m_e = 1836$. In the second row, panels (d) to (f), the same quantities are shown but computed with a reduced mass ratio of $m_p/m_e = 100$. The black triangle indicates the most unstable quasi-parallel propagating eigenmode, while the black dot indicates the most unstable oblique propagating eigenmode. In panels (c) and (f), the white dotted line indicates the contour separating right-hand (RH) from left-hand (LH) polarization.
• Figure 3: Growth rate plotted in the ${k}$-$\theta_{\boldsymbol{k}\boldsymbol{B}}$ plane computed using the reduced proton-to-electron mass ratio. The black triangle marks the parallel propagating unstable eigenmode, while the black dot marks the oblique propagating one.
• Figure 4: Dispersion relation and resonance conditions for the quasi-parallel FM/W eigenmode with $\theta_{\boldsymbol{k}\boldsymbol{B}}^{\star} = 0^{\circ}$ (orange solid line) and for the oblique A/IC eigenmode with $\theta_{\boldsymbol{k}\boldsymbol{B}}^{\star} = 55^{\circ}$ (blue solid line). The dashed red line represents the $n = -1$ resonance condition for as, given by Equation \ref{['eq:alpharesonance']}. Panel (a) shows quantities related to protons: the cyan dot-dashed lines, defined by Equation \ref{['eq:thresholdn1']}, indicate the thresholds for cyclotron resonance, while the green lines, defined by Equation \ref{['eq:thresholdn0']}, indicate those for Landau resonance. Panel (b) shows the corresponding quantities for alphas.
• Figure 5: Time series of relevant kinetic quantities are shown, indicating the three distinct temporal phases of the system’s evolution (vertical dashed lines). These quantities are defined in Section \ref{['sec:results']}. Panel (a): system’s global electromagnetic energy (blue solid line) and global kinetic energy (orange solid line). Panel (b): thermal energy in the parallel direction (brown line), thermal energy in the perpendicular direction (cyan line) and the drift energy (green line), respectively, for protons (dashed lines) and alpha particles (dash–dotted lines). Panel (c): temporal evolution of ion anisotropy; panel (d): temporal evolution of ion drift speed.