Acceleration and Dissipation in Relativistic Winds

I argue that ideal MHD relativistic winds are always limited in practice to asymptotic 4-velocity $\gamma_\infty \approx \sigma_0^{1/3}$ and asymptotic magnetization $\sigma \sim \sigma_0^{2/3} \gg 1$, where $\sigma_0$ is the wind magnetization with respect to the rest energy density, evaluated at the light cylinder of the rotating, magnetized compact object that drives the flow. This suggests that the observed low value of he asymptotic $\sigma$ in the equatorial sectors of the winds driving Pulsar Wind Nebulae and the associated high values of the asymptotic 4-velocity are a consequence of magentic dissipation in the wind zone.