In Situ Observation of Hall Magnetohydrodynamic Cascade in Space Plasma

We present estimates of the turbulent energy-cascade rate derived from a Hall-magnetohydrodynamic (MHD) third-order law. We compute the contribution from the Hall term and the MHD term to the energy flux. Magnetospheric Multiscale (MMS) data accumulated in the magnetosheath and the solar wind are compared with previously established simulation results. Consistent with the simulations, we find that at large (MHD) scales, the MMS observations exhibit a clear inertial range dominated by the MHD flux. In the subion range, the cascade continues at a diminished level via the Hall term, and the change becomes more pronounced as the plasma beta increases. Additionally, the MHD contribution to interscale energy transfer remains important at smaller scales than previously thought. Possible reasons are offered for this unanticipated result.

Figure 1

Magnetic field spectra for the solar-wind (SW, in blue) and magnetosheath (MSH, in red) interval. The solid vertical line represents $k{d}_i=1$ with the wave vector $k\simeq (2\pi f)/|⟨\mathbf{V}⟩|$, where $f$ is the frequency.

Figure 2

MHD ($-Y$) and Hall ($-H/2$) structure function from generalized third-order law [Eq. (3)] from MMS data. Top: solar wind, ${\beta }_i=0.4$. Bottom: magnetosheath, ${\beta }_i=17$. The proton gyroradius ${\rho }_i$ is shown as a dotted vertical line, and the correlation length $L_{\mathrm{corr}}$ is shown as a solid vertical line. A linear scaling with arbitrary offset is shown for reference.

Figure 3

MHD ($-Y$) and Hall ($-H/2$) structure function from generalized third-order law [Eq. (3)] from 2D hybrid-kinetic simulations. Top panel: ${\beta }_i=0.5$. Bottom panel: ${\beta }_i=8$. The dotted vertical line indicates the ion gyroradius ${\rho }_i$, and the solid vertical line indicates the correlation length $L_{\mathrm{corr}}$. A linear scaling with arbitrary offset is shown for reference.

Figure 4

Variation with ion beta of the ratio of the MHD term ($-Y$) to the Hall-MHD term $(-H/2)$ in the third-order cascade rate at lag $\ell =3d_i$, as obtained from simulation and MMS data.