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arXiv · 2604.18472

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

Vivek Shrivastav·Mani K Chettri·Britan Singh·Hemam D. Singh·Rupak Mukherjee
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Abstract

Recent Magnetospheric Multiscale (MMS) observations report approximate equality between electric and magnetic field energy spectral densities, $\varepsilon_{0} P[δE]/2 \approx P[δB]/(2μ_{0})$, 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 Alfvén waves and whistler-mode waves in the two-fluid framework and show that it saturates at $\mathcal{R}_{\infty}=(V_{A}/c)^{2}(m_{i}/m_{e})(β_{e}/2)$ deep in the sub-electron regime. Setting $\mathcal{R}_{\infty}=1$ yields the universal threshold $V_{A}/c \gtrsim \sqrt{2/[(m_{i}/m_{e})β_{e}]}$, 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.

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Vivek Shrivastav, Mani K Chettri, Britan Singh, Hemam D. Singh, Rupak Mukherjee. 2026-04-20. Linear-wave bound on electromagnetic energy equipartition at sub-electron scales in non-relativistic plasmas. https://arxiv.org/abs/2604.18472

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