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Ideal MHD turbulence: the inertial range spectrum with collisionless dissipation

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.