= Alfvén Mach number
{c}
{title2=$M_A=u/v_A$}
The Alfvén Mach number compares a characteristic flow speed with the <Alfvén speed> $v_A=B/\sqrt{\mu_0\rho}$. In an <axisymmetric magnetohydrodynamic wind>, the relevant poloidal quantity is $M_{Ap}=|\mathbf u_p|\sqrt{\mu_0\rho}/|\mathbf B_p|$. With <magnetohydrodynamic mass loading> $\rho\mathbf u_p=\kappa\mathbf B_p$, its square is $\mu_0\kappa^2/\rho$. The <Alfvén surface> is the locus $M_{Ap}=1$, and a smooth crossing requires the corresponding <Alfvén-surface regularity condition for an axisymmetric wind>. The total-speed and poloidal-speed definitions should be distinguished when there is substantial rotation or a strong <toroidal magnetic field>.
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