Observed Low-Plasma-$β$ Temperature Anisotropy Constraint Driven by $α$-Particle Drift

TL;DR

The paper demonstrates that a low-$\beta$ solar wind can be regulated by an Oblique Drift Instability (ODI) driven by drifting $\alpha$-particles or proton beams, which converts drift free energy into heat and prevents $\beta_{\parallel,p}$ from dropping too low near the Alfvén surface. Using linear dispersion solvers (PLUME/PLUMAGE, ALPS) and 2.5D hybrid-PIC simulations, the authors map ODI thresholds across parameter space, showing a near-linear-in-log relationship between drift speed and $\beta_{\parallel,p}$ and providing analytic expressions for the instability boundary. Hybrid simulations reveal a nonlinear energy exchange where alphas radiate energy via oblique modes that protons absorb, heating both populations and enforcing a dynamic low-$\beta$ limit. The results offer a plausible mechanism for PSP observations and a regional heating pathway near the Alfvén surface, complementing existing AIC/mirror thresholds and guiding future observational tests.

Abstract

Some plasma instability thresholds, derived from linear theory, constrain the observed parameters of solar wind velocity distributions, defining boundaries of ``allowed'' plasma parameters. These thresholds typically account for a single source of free energy, such as temperature anisotropy or a drifting secondary component with some dependence on other system parameters, e.g. the ratio of thermal to magnetic pressure, $β$. Excursions beyond these thresholds result in the emission of energy, transferred from particles to coherent electromagnetic waves, acting to push the system toward a more stable configuration. In this work, we use linear theory to define parametric limits for a low-$β$ plasma that contains a drifting proton beam or helium ($α$)-particle population. A sufficiently fast and dense drifting population triggers an Oblique Drift Instability (ODI). This instability decreases the velocity drift between the thermal proton and secondary populations and prevents $β$ from decreasing below a minimum value by heating both the core and drifting populations. Our predictions are of interest for \emph{Parker Solar Probe} observations, as they provide an additional mechanism for perpendicular heating of ions active in the vicinity of \Alfven surface. The ODI also explains the discrepancy between long-standing expectations of measurements of very low-$β$ plasmas with very large temperature anisotropies in the near-Sun environment and in situ observations, where $β$ is consistently measured above a few percent and the secondary populations drifting faster than the bulk of proton population by no more than approximately one \Alfven velocity.

Figures (9)

• Figure 1: The "island" of stability between the forward Alfvén mode unstable in the direction parallel to $\mathbf{B}$--- the proton AIC instability--- and the Oblique Drifting Instability (ODI) at lower $\beta$ for fixed $n_\alpha$ and $\Delta v_{\alpha}$ The size of points increases as $\lg(\gamma_{\mathrm{max}}/\Omega_p)$, covering the range between $10^{-3}$ and $0.3$.
• Figure 2: Overview of the ion contributions to the AIC and ODI instabilities for intervals marked with black rectangle on Fig. \ref{['fig:overview']}, with solid/dashed lines indicating power emission/absorption. Both instabilities emit a forward-propagating Alfvén mode. PLUMAGE growth rate and PLUME power transmission solutions marked with dots and lines, respectively. Note that in the linear approximation $\sum_j P_j \approx \gamma / \omega_r$Stix_1992.
• Figure 3: ODI mode growth rates and propagation angles (as in Fig. \ref{['fig:overview']}) dependence on the velocity drift. The best-fit parametric instability threshold is shown in green.
• Figure 4: ODI instability thresholds for varying $\alpha$-particle densities (solid lines) for $\gamma/\Omega_p=10^{-3}$. Dashed lines provide comparison given by Gary_1993 for the proton-beam induced ODI with beam densities with the same mass flux as the $\alpha$ cases.
• Figure 5: Growth (solid lines, left column) and damping rates (dashed) for proton and $\alpha$ VDFs representative of the young solar wind unstable to the ODI at early (top right) and late (bottom right) times in the simulation. The emitting $\alpha$-particle $(n=-1)$ and absorbing proton $(n=1)$ cyclotron resonances for the most unstable mode are marked by blue and red lines. Particles are scattered along resonance curves (green) for the highlighted wavevector (magenta, left column), leading to wave emission and heating.