[Paper Review] Interplay of Turbulence and Proton-Microinstability Growth in Space Plasmas

R. Bandyopadhyay, Ramiz A. Qudsi+14 more|arXiv (Cornell University)|Jun 18, 2020

Ionosphere and magnetosphere dynamics43 references4 citations

TL;DR

This study investigates the competition between turbulence and proton microinstability growth in space plasmas by comparing linear instability growth rates with local nonlinear time scales. It finds that while most regions exhibit faster nonlinear times, extreme anisotropy conditions near the edges of the observed parameter space show instability growth rates comparable to or exceeding nonlinear times, explaining why linear microinstability theory successfully predicts observed anisotropy limits despite turbulent nonlinearity.

ABSTRACT

Numerous prior studies have shown that as proton beta increases, a narrower range of proton temperature anisotropy values is observed. This effect has often been ascribed to the actions of kinetic microinstabilities because the distribution of observational data aligns with contours of constant instability growth rates in the beta-anisotropy plane. However, the linear Vlasov theory of instabilities assumes a uniform background in which perturbations grow. The established success of linear-microinstability theories suggests that the conditions in regions of extreme temperature anisotropy may remain uniform for a long enough time so that the instabilities have the chance to grow to sufficient amplitude. Turbulence, on the other hand, is intrinsically non-uniform and non-linear. Thin current sheets and other coherent structures generated in a turbulent plasma, may destroy the uniformity fast enough. It is therefore not a-priori obvious whether the presence of intermittency and coherent structures favors or disfavors instabilities. To address this question, we examined the statistical distribution of growth rates associated with proton temperature-anisotropy driven microinstabilities and local nonlinear time scales in turbulent plasmas. Linear growth rates are, on average, substantially less than the local nonlinear rates. However, at the regions of extreme values of temperature anisotropy, near the "edges" of the populated part of the proton temperature anisotropy-parallel beta plane, the instability growth rates are comparable or faster than the turbulence time scales. These results provide a possible answer to the question as to why the linear theory appears to work in limiting plasma excursions in anisotropy and plasma beta.

Motivation & Objective

• To resolve the paradox of why linear microinstability theory accurately predicts observed proton temperature anisotropy limits despite the presence of strong turbulence.
• To assess whether turbulence-induced intermittency and coherent structures suppress or enhance proton microinstability growth.
• To compare local linear instability growth rates with local nonlinear time scales in turbulent plasmas across multiple observational and simulation datasets.
• To evaluate the validity of linear Vlasov theory in realistic, non-uniform turbulent environments where nonlinearity and intermittency are significant.
• To determine under what conditions microinstabilities can grow fast enough to regulate proton temperature anisotropy in the presence of turbulence.

Proposed method

• Computed linear growth rates for proton temperature-anisotropy driven microinstabilities using the Vlasov-Maxwell model and bi-Maxwellian velocity distribution functions.
• Estimated local nonlinear time scales from turbulent energy cascade rates derived from in-situ measurements (MMS, Wind) and 3D particle-in-cell (PIC) simulations.
• Performed spatially resolved comparisons of linear growth rates (Γ_max) and nonlinear time scales (ω_nl) across three distinct plasma regimes: solar wind, magnetosheath, and simulated turbulent plasmas.
• Used bi-Maxwellian fitting to observed proton velocity distribution functions from MMS and Wind spacecraft data to extract R_p and β_∥p for analysis.
• Applied statistical analysis to determine the fraction of data points where Γ_max > ω_nl, identifying conditions favorable for microinstability growth.
• Validated results across observational data (MMS, Wind) and 3D PIC simulations to ensure robustness across different plasma regimes and modeling approaches.

Experimental results

Research questions

• RQ1 In turbulent space plasmas, do nonlinear time scales typically exceed or fall below the growth rates of proton microinstabilities?
• RQ2 Under what conditions—specifically in regions of extreme proton temperature anisotropy—do microinstability growth rates become comparable to or faster than nonlinear time scales?
• RQ3 Why does linear microinstability theory successfully predict observed limits on proton temperature anisotropy despite the presence of strong turbulence and non-uniformity?
• RQ4 How does the presence of coherent structures and intermittency in turbulent plasmas affect the lifetime and amplitude of microinstabilities?
• RQ5 To what extent do simplified assumptions—such as bi-Maxwellian velocity distributions—impact the accuracy of linear instability predictions in real space plasmas?

Key findings

• On average, local nonlinear time scales (ω_nl) are substantially faster than the maximum linear growth rates (Γ_max) of proton microinstabilities across all datasets.
• In regions of extreme proton temperature anisotropy, particularly near the edges of the observed (R_p, β_∥p) parameter space, Γ_max becomes comparable to or exceeds ω_nl.
• For the MMS data, 28% of samples showed positive growth rates (Γ_max > 0), and 4% had Γ_max > ω_nl; for Wind data, 16% had Γ_max > 0 and 12% had Γ_max > ω_nl.
• In 3D PIC simulations, 16% of data points were unstable (Γ_max > 0), with 11% showing Γ_max > ω_nl, indicating that extreme anisotropy conditions are where instabilities can effectively compete with turbulence.
• The results suggest that microinstabilities are most likely to regulate temperature anisotropy precisely in the most extreme, edge-of-observation regions, explaining the success of linear theory in predicting observed boundaries.
• The study highlights that while turbulence generally suppresses long-lived linear instabilities, localized conditions of high anisotropy allow instabilities to grow rapidly and potentially disrupt the turbulent cascade.