Linear-wave bound on electromagnetic energy equipartition at sub-electron scales in non-relativistic plasmas

TL;DR

This paper explains the observed electromagnetic energy equipartition at sub-electron scales in space plasmas, showing it is unlikely due to linear wave physics and may result from nonlinear effects or measurement noise.

Contribution

The study derives the electric-to-magnetic energy ratio from linear wave polarization and demonstrates its saturation level is far below observed values, highlighting the role of nonlinear dynamics or noise.

Findings

Linear wave theory predicts a ratio much lower than observed.

The universal threshold for equipartition is not satisfied in typical space plasmas.

Instrumental noise and nonlinear effects likely explain the observed equipartition.

Abstract

Recent Magnetospheric Multiscale (MMS) observations report approximate equality between electric and magnetic field energy spectral densities, $\varepsilon_{0} P[\delta E]/2 \approx P[\delta B]/(2\mu_{0})$, at sub-electron scales in reconnection-driven magnetotail turbulence, interpreted as relaxation toward thermodynamic equilibrium. We derive the electric-to-magnetic energy ratio from the linear polarization of kinetic Alfv\'en waves and whistler-mode waves in the two-fluid framework and show that it saturates at $\mathcal{R}_{\infty}=(V_{A}/c)^{2}(m_{i}/m_{e})(\beta_{e}/2)$ deep in the sub-electron regime. Setting $\mathcal{R}_{\infty}=1$ yields the universal threshold $V_{A}/c \gtrsim \sqrt{2/[(m_{i}/m_{e})\beta_{e}]}$, which no non-relativistic space plasma satisfies. For typical magnetotail parameters, $\mathcal{R}_{\infty}\approx 2\times 10^{-3}$, approximately 500 times below the observed value, a discrepancy rooted in the non-relativistic ordering $(V_{A}/c)^{2}\ll 1$. Noise-floor estimates show that Search Coil Magnetometer and Electric Double Probe sensitivity convergence produces a spurious apparent equipartition throughout this regime. The observed equality likely reflects nonlinear dynamics, incoherent superposition of electromagnetic and electrostatic fluctuations, or instrumental noise contamination.