Inertial-Range Suppression and Ponderomotive Density Cavitation in Broadband Sub-Alfvénic Turbulence under Plasma Sheet Boundary Layer Conditions

Abstract

Kinetic Alfvén waves (KAWs) are among the most pervasive electromagnetic fluctuations in magnetized astrophysical plasmas, from Earth's magnetospheric boundary layers to the turbulent intracluster medium of galaxy clusters. Their ponderomotive coupling to compressive density fluctuations remains incompletely understood in the broadband turbulent regime. We present two-dimensional pseudospectral simulations of the modified nonlinear Schrödinger--magnetosonic (MNLS--MS) system governing KAW envelopes, initialized with a broadband power-law spectrum ($|ψ(\mathbf{k})|^2\propto k^{-5/6}$) spanning many interacting modes, at $β\sim 0.1$--$0.3$ representative of plasma sheet boundary layer (PSBL) conditions. A fourth-order Runge--Kutta scheme on a $256\times 256$ grid integrates the system to $t = 40$ (normalized), with total energy conserved to within $0.085\%$. The nonlinearity parameter $χ_\mathrm{NL} \approx 0.25$ confirms broadband sub-Alfvénic turbulence throughout. Magnetic field intensity and plasma density develop spatially intermittent, filamentary structures within the first few wave periods, consistent with ponderomotive density cavitation and plasma expulsion from wave-intense regions. The magnetic energy spectra show inertial-range suppression, with a rapid transition from injection ($k < 0.3$) to dissipation without an extended power-law cascade, in agreement with the moderate magnetic Reynolds number ($\mathrm{Re} \sim 250$--$370$) of the simulation and the observationally constrained range for PSBL turbulence. These results provide numerical evidence that broadband KAW turbulence self-organizes into coherent density structures at kinetic scales, and that the spectral character of such turbulence is governed primarily by moderate-Reynolds-number constraints rather than by the wave physics alone.

Figures (5)

• Figure 1: Global diagnostic quantities over the full simulation. (a) Total energy evolution showing a drift of only $-0.085\%$, confirming numerical reliability. (b) Energy partition between magnetic (blue) and density (green) components on a logarithmic scale; the magnetic component dominates by roughly two orders of magnitude throughout. (c) Nonlinearity parameter $\chi_\mathrm{NL}$ as a function of time; values near $0.25$, well below the strong-turbulence threshold $\chi_\mathrm{NL} = 1$ (red dashed line), confirm sub-Alfvénic operation.
• Figure 2: Temporal evolution of the magnetic field intensity $|\delta B_y|^2$ (normalized) at $t = 0, 8, 16, 24, 32, 40$. Elongated, filamentary structures emerge from the initial broadband spectrum and persist throughout. Peak intensities reach $\sim 1.6$ in isolated regions while the background stays near zero, indicating notable spatial intermittency characteristic of kinetic-scale turbulence.
• Figure 3: Temporal evolution of the normalized density perturbation $\delta n/n_0$ at $t = 0, 8, 16, 24, 32, 40$. Red regions are density enhancements; blue regions are depletions. Persistent cavities (dark blue, $\delta n/n_0\lesssim -0.3$) form co-spatially with magnetic intensity peaks, consistent with ponderomotive expulsion. Amplitudes $|\delta n/n_0|\sim 0.3$--$0.5$ exceed those found in single-wave-packet runs, reflecting the stronger continuous drive from the broadband initialization.
• Figure 4: One-dimensional profiles of $|\delta B_y|^2$ (normalized). (a) Perpendicular cuts at $z = 15.7$, $31.4$, and $47.1$. (b) Parallel cuts at $x = 15.7$, $31.4$, and $47.1$. Peak intensities reach $\sim 1.0$ in both directions with structure widths of $5$--$15$ normalized units, consistent with ion-scale magnetic structures observed by MMS in the plasma sheet boundary layer.
• Figure 5: Time-averaged magnetic energy spectra. (a) Perpendicular spectrum $E_B(k_\perp)$: energy is concentrated at large injection scales ($k_\perp \lesssim 0.3$) and falls steeply without forming an extended power-law range before reaching the dissipation floor near $k_\perp \sim 2$. (b) Parallel spectrum $E_B(k_\parallel)$: qualitatively similar, with a somewhat less steep transition consistent with weaker damping of field-aligned fluctuations. In both panels the dashed line shows the theoretical inertial-range slope ($k^{-5/3}$ perpendicular; $k^{-7/3}$ parallel) anchored at the injection scale as a reference; the immediate and sustained departure of the simulated spectrum from this slope confirms the absence of an inertial range, consistent with the moderate Reynolds number of PSBL turbulence ($\mathrm{Re}\sim 7$--$110$ from spacecraft observations; see Section \ref{['sec:discussion:Re']}).