Drift approximation and ideal MHD of cold relativistic winds

A critical revision of the essential principles of the physics of relativistic flows of cold plasma is given. We prove that the approximation of ideal magnetic hydrodynamics of the cold plasma is equivalent to the drift approximation of motion of charged particles in an electromagnetic field. The equations of magnetohydrodynamics are obtained from equations for the drift motion of the charged particles. The conditions of application of the equations of ideal magnetohydrodynamics are obtained. In the case of the Crab pulsar the violation of the frozen-in condition can happen at a distance that well exceeds the distance to the termination shock. One fluid MHD can be incorrect at the light cylinder provided that the Lorentz factor of the plasma exceeds $10^{4}$ and the curvature radius of the flow line is comparable with the light cylinder. It is shown that the electric currents in the cold plasma are the result of the inertial drift motion of the charged particles in the crossed electric and magnetic fields.