Axisymmetric magnetohydrodynamic wind (axisymmetric MHD wind)

A steady axisymmetric magnetohydrodynamic wind follows nested magnetic-flux surfaces and has conserved mass loading, field-line angular velocity, angular momentum, entropy, and Bernoulli quantities along each surface.

For ${\mathbf{B}}_p=\nabla \psi \times \nabla \varphi$, surfaces $\psi =\text{constant}$ are poloidal magnetic surfaces and $2\pi \psi$ is magnetic flux up to the choice of axial reference value.

When $\rho {\mathbf{u}}_p=k{\mathbf{B}}_p$, the flux-surface function $k$ is the mass flux per unit poloidal magnetic flux.

Ideal induction in a steady axisymmetric flow makes each magnetic surface rotate with a constant field-line angular velocity $\omega (\psi )$.

The total specific angular momentum transported by matter and magnetic stress isand is constant on each magnetic surface.

An Alfvén surface is where the poloidal flow speed equals the poloidal Alfvén speed. Smooth passage through it imposes a regularity condition relating field-line angular velocity and angular momentum.

Magnetocentrifugal acceleration occurs when matter tied to a rotating inclined magnetic field moves outward under the effective centrifugal force. For a Keplerian disc, cold launching is possible when the field tilts by more than $30^{\circ }$ from the vertical.