Analytical Solution of Magnetically Dominated Astrophysical Jets and
  Winds: Jet Launching, Acceleration, and Collimation
  We present an analytical solution of a highly magnetized jet/wind flow. The
left side of the general force-free jet/wind equation (the "pulsar" equation)
is separated into a rotating and a nonrotating term. The two equations with
either term can be solved analytically, and the two solutions match each other
very well. Therefore, we obtain a general approximate solution of a
magnetically dominated jet/wind, which covers from the nonrelativistic to
relativistic regimes, with the drift velocity well matching the cold plasma
velocity. The acceleration of a jet includes three stages. (1) The jet flow is
located within the Alfv\'{e}n critical surface (i.e. the light cylinder), has a
nonrelativistic speed, and is dominated by toroidal motion. (2) The jet is
beyond the Alfv\'{e}n critical surface where the flow is dominated by poloidal
motion and becomes relativistic. The total velocity in these two stages follows
the same law $v\Gamma=\Omega R$. (3) The evolution law is replaced by
$v\Gamma\approx1/\left(\theta\sqrt{2-\nu}\right)$, where $\theta$ is the
half-opening angle of the jet and $0\leq\nu\leq2$ is a free parameter
determined by the magnetic field configuration. This is because the earlier
efficient acceleration finally breaks the causality connection between
different parts in the jet, preventing a global solution. The jet has to carry
local charges and currents to support an electromagnetic balance. This
approximate solution is consistent with known theoretical results and numerical
simulations, and it is more convenient to directly compare with observations.
This theory may be used to constrain the spin of black holes in astrophysical
jets.
