Secondary drift-driven instabilities in the presence of a parallel-propagating electromagnetic ion cyclotron wave and cold multi-component ions

This paper utilizes fully kinetic particle-in-cell simulations and linear theory to demonstrate that parallel-propagating electromagnetic ion cyclotron (EMIC) waves can drive secondary lower-hybrid instabilities in multi-component plasmas, leading to anisotropic heating of cold ions and electrons even at low wave amplitudes.

The Gist

Imagine Earth's magnetic field as a giant, invisible playground. Inside this playground, there are different groups of "players": fast, energetic protons (the hot ions), slow-moving protons (the cold ions), heavy oxygen ions, and electrons. Usually, the fast players are bouncing around wildly, creating a kind of magnetic "noise" called an EMIC wave.

For a long time, scientists knew this noise could knock the fast players out of the playground (scattering them). But they weren't sure how this noise affected the slow, cold players, partly because it's hard to see the cold players up close (spacecraft often get "charged up" like a balloon rubbed on hair, pushing the cold ions away before they can be measured).

This paper acts like a high-speed camera simulation to see what happens when the EMIC wave interacts with these cold players. Here is the story of what they found:

The Setup: A Wave and a Drift

Think of the EMIC wave as a giant, rhythmic sway in the magnetic field. As this wave sways back and forth, it pushes on the different types of particles. Because the particles have different weights (masses), they don't all sway at the same speed.

• The heavy oxygen ions and the light protons get pushed in slightly different directions.
• This creates a relative drift, like two people on a moving walkway trying to walk at different speeds. One is walking forward, the other backward, creating friction or tension between them.

The Surprise: Secondary Ripples

The paper discovered that this "friction" between the drifting particles doesn't just sit there. It triggers secondary instabilities.

• The Analogy: Imagine you are rowing a boat (the EMIC wave) on a calm lake. The rowing creates a big wake. But if you row hard enough, that wake creates smaller, faster, chaotic ripples on the surface of the water. These smaller ripples are the "secondary instabilities."
• In this case, the "ripples" are new, smaller waves (called lower-hybrid waves) that appear because the heavy oxygen ions and the light protons are drifting past each other at different speeds.

The Two Main Characters

The simulation found two main types of these "ripples" doing the work:

1. The Ion-Ion Cross-Field Instability (The Heavy Hitter):

   • This happens when the heavy oxygen ions and the light protons drift past each other.
   • What it does: It acts like a rapid heater. It takes the cold protons and oxygen ions and heats them up very quickly, but mostly in a direction sideways (perpendicular) to the magnetic field. It's like spinning a top; the energy goes into spinning it faster, not moving it forward.
   • Speed: This happens very fast, in just a few seconds (about 50 spins of a proton).

2. The Modified Two-Stream Instability (The Slow Cooker):

   • This happens between the electrons and the ions.
   • What it does: It heats up the electrons in all directions (both sideways and forward). It also adds a little bit of sideways heat to the protons.
   • Speed: This one is much slower to start up compared to the first one.

The Result: A Energy Swap

The most important finding is that these secondary ripples act as a transfer station for energy.

• The fast, hot protons originally created the big EMIC wave.
• The big EMIC wave created the drift.
• The drift created the secondary ripples.
• The ripples then took energy from the big wave and dumped it into the cold particles, warming them up.

Because the cold particles absorbed so much energy, the big EMIC wave actually lost strength (its amplitude dropped by about 32%). It's like the big wave got tired because it was spending all its energy heating up the cold crowd.

The Big Picture

The paper concludes that even if the main EMIC wave is weak, as long as the cold particles stay cold, these secondary ripples will still appear and heat things up.

• Timeframe: This heating happens very quickly (in seconds), whereas other known heating methods take hours.
• Impact: This process changes how energy moves in Earth's magnetosphere. It suggests that cold ions play a bigger role in "taming" the energetic waves than previously thought, acting as a sponge that soaks up energy and slows the waves down.

In short, the paper shows that when a magnetic wave moves through a mix of hot and cold particles, it doesn't just pass through; it creates a chaotic dance that quickly warms up the cold particles and slows the wave down, all through a mechanism of "drifting" and "rippling" that happens in the blink of an eye.

Technical Summary

Technical Summary: Secondary Drift-Driven Instabilities in Multi-Component Plasmas with EMIC Waves

Problem Statement
Electromagnetic ion cyclotron (EMIC) waves are ubiquitous in Earth's inner magnetosphere, driven by anisotropic hot ring-current protons. While their role in scattering hot ions and relativistic electrons is well-established, their interaction with the cold plasma population (energies < 100 eV) remains poorly understood. This gap is partly due to observational limitations caused by spacecraft charging, which prevents cold ions from reaching onboard detectors. Previous research has identified that the electric field of parallel-propagating EMIC waves can drive inter-species perpendicular polarization drifts. In multi-component plasmas, these drifts are theorized to excite secondary lower-hybrid instabilities, specifically the Modified Two-Stream Instability (MTSI) and the ion-ion cross-field instability. However, the quantitative impact of these secondary instabilities on the primary EMIC wave and the resulting heating of cold multi-component plasmas (specifically protons and heavy ions like oxygen) has not been fully characterized using fully kinetic simulations.

Methodology
The authors employ a fully kinetic, nonlinear, two-dimensional, three-velocity (2D3V) Particle-in-Cell (PIC) simulation using the VPIC code to investigate these interactions. The simulation models a homogeneous plasma containing:

• Cold electrons and cold protons (dense core).
• Cold singly-charged oxygen ions ($O^+$).
• A tenuous, anisotropic hot proton population ($T_{\perp} > T_{\parallel}$) that serves as the free energy source for the primary EMIC wave.

The setup utilizes a reduced proton-to-electron mass ratio ($m_p/m_e = 400$) and a realistic oxygen-to-proton mass ratio ($16$). The primary EMIC wave is seeded via a helical magnetic perturbation. The study focuses on a parameter regime where secondary lower-frequency instabilities dominate, specifically suppressing higher-frequency beam-cyclotron and acoustic-like modes by ensuring low primary wave amplitudes and comparable electron/cold ion temperatures.

Complementing the simulations, the authors develop a linear theory for the secondary electrostatic drift-driven instabilities. They derive dispersion relations for the MTSI and the ion-ion cross-field instability in a co-drifting frame, analyzing the growth rates and frequencies as functions of the primary EMIC wave amplitude and frequency.

Key Contributions and Results

1. Validation of Linear Theory and Instability Thresholds:
   The linear theory predicts that the dominant secondary instability depends on the primary EMIC wave's amplitude and frequency. For the parameters used (driver frequency $\omega_0 \approx 0.5\Omega_{cp}$), the ion-ion cross-field instability (driven by the relative drift between protons and oxygen) is predicted to dominate at lower amplitudes, while the electron-proton MTSI becomes dominant at higher amplitudes. The PIC simulations confirm this transition, showing that the ion-ion cross-field instability is the primary driver in the studied regime.

2. Anisotropic Heating of Cold Populations:
   The simulations demonstrate that secondary instabilities lead to significant, anisotropic heating of the cold plasma components:

   • Cold Ions ($H^+$ and $O^+$): The rapidly growing ion-ion cross-field instability causes predominantly perpendicular heating. Cold protons experience a temperature increase by a factor of $\sim 5$, and cold oxygen ions by a factor of $\sim 3$ within the simulation timeframe.
   • Electrons: The slower-growing MTSI modes drive heating in both parallel and perpendicular directions, with electron temperatures increasing by factors of $\sim 1.4$ (perpendicular) and $\sim 1.2$ (parallel).

3. Energy Transfer and Wave Evolution:
   The development of secondary modes mediates energy transfer from the hot proton population to the cold species. As the secondary instabilities grow, the amplitude of the primary EMIC wave decreases by approximately 32% (from $\delta B/B_0 \approx 0.022$ to $0.015$). The authors observe that the primary wave saturates earlier than it would in the absence of these secondary processes, suggesting that the secondary instabilities act as a mechanism for early saturation.

4. Temporal Dynamics and Mode Transition:
   The study reveals a distinct temporal evolution. Initially, the ion-ion cross-field instability drives perpendicular ion heating. As the cold ion temperatures rise, the relative drift-to-thermal-velocity ratio decreases, damping the ion-ion cross-field mode. Subsequently, the system transitions to oblique, long-wavelength electron-proton MTSI modes. This shift is accompanied by a change in the spatial structure of the fluctuations from localized, perpendicular modes to extended, quasi-oblique modes.

5. Comparison with Previous Models:
   The paper contrasts these findings with hybrid simulation results (which treat electrons as a fluid). While hybrid models have identified strong perpendicular heating via nonresonant nonlinear mechanisms over long timescales ($\sim 10^3-10^4$ gyroperiods), the fully kinetic approach captures the rapid evolution ($\sim 50$ gyroperiods) of lower-hybrid secondary instabilities. The heating observed in this study is moderate (factors of 2–5) compared to the orders-of-magnitude heating seen in some hybrid studies, but it occurs on significantly shorter timescales (seconds vs. minutes/hours).

Significance
The paper establishes that secondary drift-driven instabilities are a viable and rapid mechanism for energizing cold magnetospheric ions and electrons in the presence of EMIC waves. The authors conclude that these instabilities introduce an additional pathway for energy transfer between hot and cold species, potentially delaying the saturation time of the primary EMIC wave. This has implications for understanding magnetospheric dynamics, including the loss processes of radiation belt particles and the thermalization of the cold plasma population. The work highlights the necessity of fully kinetic simulations to capture lower-hybrid physics that fluid-based (hybrid) models inherently miss.