Abstract
The inertial range spectrum of ideal (collisionless/dissipationless) MHD turbulence is analysed in view of the transition from the large-scale Iroshnikov-Kraichnan-like (IK) to the meso-scale Kolmogorov (K) range under the assumption that the ultimate dissipation which terminates the Kolmogorov range is provided by collisionless reconnection in thin turbulence-generated current sheets. Kolmogorov's dissipation scale is identified with the electron inertial scale, as suggested by collisionless particle-in-cell simulations of reconnection. Transition between the IK- and K-ranges occurs at the ion inertial length allowing determination of the IK-coefficient. With the electron inertial scale the K-dissipation scale, stationarity of the spectrum implies a relation between the energy injection and dissipation rates. Application to solar wind is critically discussed.
Highlights
Collisionless turbulence [for reviews cf., e.g., 1–3] is abundant in space, from stellar winds to interstellar and intergalactic matter
In MHD turbulence the large-scale magnetic field B is frozen to the plasma
With this philosophy in mind [for our purposes ignoring the effects of anisotropy, cf., e.g., 8, 10, 11, 24, 25] we determine which shape collisionless MHD turbulence spectra assume under conditions where the energy is injected at scale λi ≪ lin ≪ L much exceeding the ion inertial length though still shorter than the macroscale L of the plasma
Summary
Collisionless turbulence [for reviews cf., e.g., 1–3] is abundant in space, from stellar winds (with solar wind the only accessible paradigm) to interstellar and intergalactic matter. Collisionless particle-in-cell (pic) simulations [cf., 17] established reconnection being based on demagnetised electron, electron inertia and generation of local non-diagonality in the electron pressure tensor (predicted in Hesse and Winske 18; Hesse et al 19) due to thermal electron meandering in the current layer resulting in large electron-shear viscosity. This was simulationally confirmed [20] yielding the lower-hybrid frequency ωlh [21] as robust absolute upper limit on the dissipation rate for the magnetic energy that is fed into formation of small-scale currents [cf., 22, for astrophysical application].
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