Magnetosonic critical speed
= Magnetosonic critical speed
{title2=$c_{\mathrm f},c_{\mathrm s}$}
For propagation in a direction with field component $v_{an}$ of the <Alfvén velocity>, the squared <fast magnetosonic wave> and <slow magnetosonic wave> speeds are the roots of $c^4-(c_s^2+v_a^2)c^2+c_s^2v_{an}^2=0$. They are real and nonnegative, and satisfy $c_{\mathrm s}^2\leq v_{an}^2\leq c_{\mathrm f}^2$. A steady acceleration equation can become singular when the flow equals either of these speeds.