Understanding cold electron impact on parallel-propagating whistler chorus waves via moment-based quasilinear theory

Earth’s magnetosphere hosts a wide range of collisionless particle populations that interact through various wave-particle processes. Among these, cold electrons, with energies below 100eV, often dominate the plasma density but remain poorly characterized due to measurement challenges such as spacecraft charging and photoelectron contamination. Understanding the contribution of these cold populations to wave-particle interaction is of significant interest. Recent kinetic simulations identified a secondary drift-driven instability in which parallel-propagating whistler-mode chorus waves excite oblique electrostatic whistler waves near the resonance cone and Bernstein-mode turbulence. These secondary modes enable a new channel of energy transfer from the parallel-propagating whistler wave to the cold electrons. In this work, we develop a moment-based quasilinear theory of the secondary instabilities to quantify such energy exchange. Our results show that these secondary instabilities persist for a wide range of parameters and, in many cases, lead to nearly complete damping of the primary wave. Such secondary instability might limit the amplitude of parallel-propagating whistler waves in Earth’s magnetosphere and might explain why high-amplitude oblique whistler or electron Bernstein waves are rarely observed simultaneously with high-amplitude field-aligned whistler waves in the inner magnetosphere.

💡 Research Summary

This paper investigates how a population of cold electrons (energies < 100 eV) influences the dynamics of parallel‑propagating (field‑aligned) whistler‑mode chorus waves in Earth’s magnetosphere. While cold electrons often dominate the plasma density, they are poorly characterized because spacecraft charging and photoelectron contamination obscure their measurements. Recent kinetic simulations have shown that the oscillating electric field of a field‑aligned chorus wave drives a polarization drift between cold electrons and ions, which can become larger than the thermal speed of the cold electrons. When this drift exceeds the cold‑electron thermal speed, a secondary drift‑driven instability develops, exciting electrostatic oblique whistler modes near the resonance cone and short‑wavelength electron‑Bernstein modes. These secondary modes provide a new channel for energy transfer from the primary whistler wave to the cold electrons, potentially damping the primary wave.

The authors develop a moment‑based quasilinear theory (QLT) to describe the temporal evolution of this process. Starting from the Vlasov‑Poisson system, they transform into a frame co‑drifting with the cold electrons, derive the linear response of cold electrons (including full Bessel‑function and plasma‑dispersion‑function treatment), and incorporate an unmagnetized ion response. By accounting for sideband coupling (ω ± n ω₀) they obtain a compact dispersion relation det D(k, ω)=0 that yields growth rates for the secondary electrostatic modes. The QLT then takes the lowest three velocity moments (density, bulk velocity, temperature) of each species and derives coupled evolution equations that link the growth of the secondary modes to the damping of the primary whistler wave.

Key theoretical findings include:

1. The growth rate of the secondary instability rises sharply when the cold‑electron drift amplitude |V_Dc| exceeds the cold‑electron thermal speed v_tc, i.e., when the primary wave amplitude satisfies |B_W| ∝ √T_c.
2. Oblique electrostatic whistler modes dominate the damping, providing at least five times stronger energy extraction from the primary wave than the perpendicular short‑wavelength Bernstein modes.
3. For a broad range of parameters (cold‑electron density fraction n_c/n_e ≈ 0.1–0.9, temperature T_c ≈ 0.5–5 eV, primary wave amplitude |B_W|/B₀ ≈ 10⁻⁴–10⁻²) the secondary instability can reduce the magnetic energy of the primary wave by more than 75 % within a few wave periods.
4. Growth rates are larger for lower chorus frequencies (lower‑band chorus) and for higher cold‑electron densities, while the perpendicular modes are only unstable in a limited lower‑band frequency range.

The theory is validated against fully kinetic 2‑D‑3‑V particle‑in‑cell (PIC) simulations that resolve the Debye length and include realistic mass ratios. The simulations reproduce the predicted growth rates, the rapid damping of the primary wave, and the heating of the cold electron population. Parameter scans confirm that even modest primary wave amplitudes (|B_W|/B₀ ≈ 10⁻⁴) can trigger strong secondary growth when the cold‑electron drift exceeds the thermal speed.

Implications for magnetospheric physics are significant. The secondary drift‑driven instability offers a natural explanation for why high‑amplitude, field‑aligned chorus waves are rarely observed together with high‑amplitude oblique whistler or electron‑Bernstein waves in the inner magnetosphere. In regions where cold electrons dominate (e.g., midnight‑to‑dawn sector, plasma‑sheet injection zones), the secondary instability quickly damps any growing field‑aligned chorus, leaving behind strong oblique electrostatic activity and Bernstein‑mode turbulence. This process also provides a pathway for rapid heating of the cold electron population, which can affect radiation‑belt dynamics and the efficacy of proposed radiation‑belt remediation schemes that rely on chorus‑driven precipitation.

Finally, the moment‑based QLT framework introduced here supplies a computationally inexpensive tool for exploring wave‑particle interactions involving multiple species and secondary instabilities. It can be extended to multi‑frequency wave spectra, non‑Maxwellian background distributions (e.g., plateaus), and global magnetospheric models, opening avenues for more accurate predictions of electron loss, wave saturation, and energy partitioning in space plasmas.