= Corotating energy invariant of an axisymmetric magnetic wind
{title2=$\epsilon_J=|\mathbf u|^2/2+\Phi-\omega Ru_\phi$}
For a pressure-free flowing <poloidal flux surface>, subtracting its angular <velocity> times the azimuthal momentum equation from the mechanical energy equation shows that $\epsilon_J$ is constant. It equals poloidal kinetic energy plus $(u_\phi-R\omega)^2/2+\Phi-R^2\omega^2/2$. This is the total <magnetohydrodynamic Bernoulli invariant> minus $\omega$ times the total <magnetohydrodynamic angular-momentum invariant>, not the total energy alone.
Back to article page
