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.

中文翻译：

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磁控天体物理射流和风的解析解：射流发射、加速和准直

我们提出了一个高度磁化的射流/风流的分析解决方案。一般无力射流/风方程（“脉冲星”方程）的左侧被分成旋转项和非旋转项。带有任一项的两个方程都可以解析求解，并且这两个解非常匹配。因此，我们获得了磁主导射流/风的一般近似解，它涵盖了从非相对论到相对论的领域，漂移速度与冷等离子体速度很好地匹配。射流的加速包括三个阶段。(1) 射流位于Alfv\'{e}n 临界面（即光柱）内，具有非相对论速度，以环形运动为主。(2) 射流超出了Alfv\' {e}n 临界表面，其中流动以极向运动为主并变为相对论。这两个阶段的总速度遵循相同的规律 $v\Gamma=\Omega R$。(3) 演化规律用$v\Gamma\approx1/\left(\theta\sqrt{2-\nu}\right)$代替，其中$\theta$为射流的半开角，$0 \leq\nu\leq2$ 是由磁场配置决定的自由参数。这是因为较早的有效加速最终打破了喷流中不同部分之间的因果关系，阻止了全局解决方案。喷气机必须携带局部电荷和电流以支持电磁平衡。这种近似解与已知的理论结果和数值模拟一致，更便于直接与观测值对比。