Impact of nonthermal electron distributions on the triggering of the ion-ion acoustic instability near the Sun: Kinetic simulations

TL;DR

This paper investigates whether nonthermal electron distributions alter the onset of the ion-ion acoustic instability (IIAI) in solar wind conditions near the Sun, using kinetic simulations and analytical dispersion analysis. It tests two non-Maxwellian electron models—a $\kappa$-distribution and a core–strahl distribution—within Parker Solar Probe–like parameters and validates growth rates against kinetic theory. The main findings are that $\kappa$-distributions tend to stabilize IIAI (growth rates decrease as $\kappa$ decreases), while core–strahl electrons can destabilize the instability, with an effective temperature $T_{\text{eff}}$ faithfully capturing the core-strahl effect. However, the strahl densities required to strongly destabilize the IIAI in this setup exceed typical solar wind values, suggesting that observed IIAI activity may also require external drivers or larger $T_e/T_c$; the results offer a practical framework for stability assessment of future PSP observations.

Abstract

Context. In a previous paper (Afify et al. 2024), we have investigated the stability threshold of the ion-ion acoustic instability (IIAI) in parameter regimes compatible with recent Parker Solar Probe (PSP, (Fox et al. 2016)) observations, in the presence of a Maxwellian electron distribution. We found that observed parameters are close to the instability threshold, but IIAI requires a higher electron temperature than observed. Aims. As electron distributions in the solar wind present clear non-Maxwellian features, we investigate here if deviations from the Maxwellian distribution could explain the observed IIAI. We address specifically the kappa ( $κ$ ) and core-strahl distributions for the electrons. Methods. We perform analytical studies and kinetic simulations using a Vlasov-Poisson code in a parameter regime relevant to PSP observations. The simulated growth rates are validated against kinetic theory. Results. We show that the IIAI threshold changes in the presence of $κ$ or core-strahl electron distributions, but not significantly. In the latter case, the expression of an effective temperature for an equivalent Maxwellian electron distribution given in Jones et al. (1975) is confirmed by simulations. Such an effective temperature could simplify stability assessment of future observations.

Figures (10)

• Figure 1: Electron and proton distribution functions. Left panel: $\kappa$ electron distributions with $T_e/T_c=10$, $\kappa=20$ (black curve), $\kappa=7$ (blue curve), and $\kappa=5$ (red curve). Right panel: total proton distribution consisting of two Maxwellians (core and beam), with $V_{d}/ v_{th,c}= 5$, $T_b/ T_c= 1.0$, and $n_b/n_c=0.05$.
• Figure 2: Dispersion and growth characteristics of the IIAI. (Left panel): Dispersion relation for the IIAI with $\kappa$-distributed electrons and $V_d/v_{th,c}=5$, $n_b/n_c=0.05$, $T_e/ T_c=10$, $T_b/T_c=1$. The black, blue, and red lines are $\kappa= 20, 7,$ and $5$ respectively. (Right panel): Normalized maximum growth rates, $\gamma_{max}/ \omega_{pc}$, as a function of the $\kappa$ for different proton core-beam drift speeds $V_d/v_{th,c}=4.33$ (green line), $4.75$ (red line), $5.0$ (black line), and $5.5$ (blue line). Remaining parameters ($n_b/n_c$, $T_e/ T_c$, and $T_b/T_c$) are the same as in panel a.
• Figure 3: Temporal evolution of the maximum electric field value for the three simulations with $\kappa$ distributed electrons. Derived growth rates (black lines) are $\gamma/ \omega_{pc}=0.0161, 0.0101,$ and $0.0053$ respectively. Simulation parameters are given in Table \ref{['kappa_parameters']}.
• Figure 4: Snapshots of the proton distributions at time $\omega_{pc}t= 300$, when all simulations are approaching the end of the linear phase, from simulations with electron $\kappa$ indices $\kappa = 20, \;7, \;5$. Left: beam phase-space distribution. Middle and right: beam and core velocity distributions, respectively, averaged in $x$ (blue lines), cut at $x/\lambda_{Dc}=0$ (orange line) and at $x/\lambda_{Dc}=25$ (green line). The vertical dashed lines indicate the theoretical estimates of the resonant velocity.
• Figure 5: As in Figure \ref{['kappa-300']}, at $\omega_{pc}t = 1000$ when all instabilities have saturated.