Local sound-speed estimate for ring-flow stability
= Local sound-speed estimate for ring-flow stability
{title2=$n^2<\frac{mR^2\mu_0}{\hbar^2}\frac{1-a}{(1+a)^2}$}
Combining zero-current bulk densities with <quantized circulation> gives an approximate winding bound. If equal halves have densities $\rho_0(1-a)$ and $\rho_0(1+a)$, $0<a<1$, the more restrictive local condition is $n^2<(mR^2\mu_0/\hbar^2)(1-a)/(1+a)^2$. A self-consistent finite-current calculation must also allow kinetic pressure to change those densities.