Electromagnetic Signatures of Kinetic Alfvén Wave Turbulence at Ion Inertial Scales in Earth's High-$\beta$ Magnetosheath

Abstract

We present a multi-diagnostic electromagnetic analysis of a dayside magnetosheath interval observed by the Magnetospheric Multiscale (MMS) mission on 2015 December 28 at high ion beta (${\beta }_i=14.4$), using burst-mode measurements. We combine the scale-dependent electric-to-magnetic field ratio, the parallel electric field, the magnetic compressibility, the wave-normal angle and circular-polarization measure, and the ion--electron frozen-in residuals. The electric-to-magnetic field ratio rises with wavenumber with a log--log slope of +0.92, whereas the ideal advection contribution remains flat, supporting dispersive fluctuations. A wave-normal angle of $75^{\circ }$ and a circular-polarization measure centred near zero support quasi-perpendicular propagation, while the compressibility and the ion temperature anisotropy do not support mirror-mode dominance. A continuous broken power-law fit gives $f_{\mathrm{break}}=0.48\pm 0.06$ Hz, corresponding to $k_{\perp }{d}_i=0.85\pm 0.11$ and $k_{\perp }{\rho }_i=3.23\pm 0.42$. Because $d_i$ and ${\rho }_i$ are well separated at this ${\beta }_i$, the break is more consistent with the ion inertial scale than with the ion gyroscale. Four-spacecraft phase differencing independently supports the Doppler conversion around the break. Above the break, the kinetic-range index is $-2.86\pm 0.06$ (stat) $\pm 0.18$ (fit window), closer to the weakly damped dispersive limit than to the strongly damped limit, with a fluid-scale index of $-1.81\pm 0.08$ below it. The observations are consistent with quasi-perpendicular KAW-like turbulence, but do not uniquely identify the mode; the spectral index constrains the cascade rather than the dissipation mechanism.

21 pages, 8 figures, 3 tables. Revised version