Velocity-Space Signatures of Energy Transfer for Ion-Acoustic Instabilities

TL;DR

This work tackles energy transfer in ion-ion acoustic instabilities (IIAI) in the solar wind and develops a framework for identifying IIAI signatures with single-point spacecraft data. It employs fully kinetic 1D-1V Vlasov-Poisson simulations of core and beam protons along with electrons and analyzes energy transfer through the Landau resonance condition $v_{\parallel} = v_{res} = \omega/k$, linking secular transfer to instability growth rate $\gamma$ and resonance location. The key finding is that beam protons primarily drive the instability, transferring energy secularly to core protons (and modestly to electrons), while electrons exhibit predominantly oscillatory exchange; velocity-space FPC maps reveal robust resonant signatures that can guide PSP and Solar Orbiter observations, though current cadences limit direct observation of the fastest phases. The results provide a practical, resonance-aware framework for recognizing IIAI in inner-heliospheric measurements and clarify how parameter changes shift resonance and energy partition.

Abstract

Context. Observations by Parker Solar Probe (PSP) of electrostatic waves suggest that electrostatic instabilities, including the ion-ion-acoustic instability (IIAI) frequently observed in the inner heliosphere, play an important role in plasma heating and particle acceleration. Aims. Our aim is to explore the application of single spacecraft diagnostics to the IIAI, in anticipation of application to the current missions operating in the inner heliosphere, e.g. PSP and Solar Orbiter. Methods. We apply the field-particle correlation (FPC) technique to fully kinetic simulations of IIAI. We characterize the conversion of energy between the electric field and particle species, allowing the differentiation between oscillatory and secular energy transfer to and from the particles and highlighting the role of resonant energy exchange. We then identify the characteristic IIAI signatures for the proton and electron distributions, and relate them to our previous knowledge of IIAI onset and energy exchange mechanisms. Results. Applying the FPC technique to our simulations run in parameters regime compatible with solar wind conditions, we have identified IIAI signatures that would enable efficient recognition of IIAI in observations. This task is left for future missions, since the time scale over which IIAI signatures develop is too fast for the sampling rates of current missions.

Figures (14)

• Figure 1: Normalized growth rate, $\gamma/\omega_{pc}$ vs. normalized wavenumber $k \lambda_{Dc}$ from Eq. \ref{['DR']} for the IIAI with parameters given by Table \ref{['tab:runs']}. Panel a, b, and c depict Series 1, 2 and 3, respectively, with the fiducial run shown by the gray curve. These theoretical expectations are compared with simulation results in Table \ref{['comparison']}. The vertical dashed lines refer to the simulated wavenumber ($k\lambda_{Dc}=0.126$).
• Figure 2: Evolution of the electric field amplitude as a function of time for the simulation runs described in Table \ref{['tab:runs']}. In Table \ref{['comparison']}, we compare the growth rate measured here, illustrated with black lines, with linear theory.
• Figure 3: Energy evolution in the fiducial run. Upper panel: (Solid lines) energy variation of the different particle populations, the total energy, and of the electric field energy (inset) calculated as Eq. \ref{['normal']}. (Dashed lines): energy variation for the particle populations calculated as Eq. \ref{['barw']}. Lower panel: $\mathbf{\mathcal{P}_s/ \mathcal{P}_{s0}}$ for the three particle populations and for the total energy. The horizontal solid magenta line at zero separates positive and negative values of $\mathbf{\mathcal{P}}$ and $\mathbf{\mathcal{E}}$.
• Figure 4: The change in the particles, field, and total kinetic energy (solid lines,$\mathcal{P}$), and the net energy exchange rate (dashed lines,$\mathcal{E}$), for Series 1 (first row), Series 2 (second row), and Series 3 (third row) runs in Table \ref{['tab:runs']}. Same as in Fig. \ref{['fig:Eng_Fiducial']}, with the horizontal zero line indicating the separation between positive and negative values.
• Figure 5: $\int dv\,FPC$ for a range of correlation intervals of RUN Fiducial at $x/\lambda_{Dc}=0$.