= Stress-maximizing magnetorotational channel polarization
{title2=$\langle T_{xy}\rangle=\frac\rho2(|V|^2+|B|^2)>0$}
For complex velocity amplitudes $v_x=v_y=V$ and magnetic amplitudes $b_x=-b_y=B$ in Alfvén-speed units, phase averaging gives the displayed stress. For fixed horizontal velocity energy, equal radial and azimuthal components maximize their positive <Reynolds stress>. Opposite equal magnetic components maximize the outward tension contribution of the <Maxwell stress tensor>, since $-B_xB_y$ is then positive. These conclusions follow from $2|ab|\leq |a|^2+|b|^2$. The vertical channel transports angular momentum outward and extracts energy from decreasing angular velocity.
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