Exact scaling laws for helical three-dimensional two-fluid turbulent plasmas

We derive exact scaling laws for a three-dimensional incompressible helical two-fluid plasma, without the assumption of isotropy. For each ideal invariant of the two-fluid model, i.e., the total energy, the electron helicity, and the proton helicity, we derive simple scaling laws in terms of two-point increment correlation functions expressed in terms of the velocity field of each species and the magnetic field. These variables are appropriate for comparison with direct numerical simulation data and with in situ measurements in the near-Earth space over a broad range of spatial scales. Finally, using the exact scaling laws and dimensional analysis we predict the magnetic energy and electron helicity spectra for different ranges of scales.

Figure 1

Schematic magnetic energy spectrum through different scales, from the energy containing wave number ${\lambda }_{\mathcal{F}}^{-1}$ up to the dissipation wave number ${\lambda }_{\mathcal{D}}^{-1}$.