Global Scale-Invariant Dissipation in Collisionless Plasma Turbulence

A higher-order multiscale analysis of the dissipation range of collisionless plasma turbulence is presented using in situ high-frequency magnetic field measurements from the Cluster spacecraft in a stationary interval of fast ambient solar wind. The observations, spanning five decades in temporal scales, show a crossover from multifractal intermittent turbulence in the inertial range to non-Gaussian monoscaling in the dissipation range. This presents a strong observational constraint on theories of dissipation mechanisms in turbulent collisionless plasmas.

Figure 1

PSD plots of components of the magnetic field from both FGM (frequencies lower than 1 Hz) and STAFF-SC (frequencies above 1 Hz). The PSD values for $B_x$ and $B_y$ have been shifted up for clarity. The 95% confidence intervals for all these plots are $\pm 0.03{log}_{10}{\mathrm{nT}}^2{\mathrm{Hz}}^{-1}$. The shaded region denotes the frequency range of STAFF-SC to be studied; the upper limit corresponds to the search-coil signal-to-noise ratio (SNR) of 5 dB; the lower limit to SNR of 10 dB; as estimated from a quiet period (30-06-2007: 15:00–15:20 UT) in the lobes of the magnetotail [37]. At lower frequencies, the STAFF-SC response is attenuated by the instrument calibration filter.

Figure 2

Summary plot illustrating the quiet nature of the solar wind interval under study. Top panel: $E$-field spectrogram from WHISPER on Cluster spacecraft 4 showing steady plasma emissions; center panel: $B$-field components; bottom panel: ion velocities from HIA on Cluster spacecraft 1.

Figure 3

Structure functions of orders: 1-□, 2-▽, 3-★, 4-○, and 5-◇. Open shapes correspond to FGM measurements and filled shapes refer to STAFF-SC. The curves have been shifted along the vertical axis to allow a comparison of the gradients. The shaded area indicates the scales where both FGM and STAFF structure function gradients overlap. Linear fits for the inertial and dissipation ranges are also shown.

Figure 4

Main plot: Scaling exponents $\zeta$ with order $m$; a linear relationship on this plot indicates monoscaling behavior. $\zeta (m)$ obtained from both FGM and STAFF-SC are shown for $B_z$; these show close correspondence. STAFF-SC $B_x$, $B_y$ components are also shown and indicate isotropic scaling. Inset: $\zeta (m)$ vs $m$ for the inertial range using FGM $B_z$; this is concave, consistent with the multifractal nature of the inertial range.

Figure 5

Main plot: PDFs rescaled using Eq. (3) ($\delta B_z^s=\delta B_z{\tau }^{-H}$). A Gaussian fit to the data (dashed curve) illustrates the heavy-tailed non-Gaussian nature of the rescaled PDF. Inset: PDFs at different scales $\tau$ before rescaling; inner and outermost curves show the smallest and largest values of $\tau$, respectively.