\Omega r$, where $r$ is the distance from the rotation axis; (small deviation occur only at the bounding surface of the superfluid). On the global hydrodynamic scales a transition to a continuum vortex distribution can be carried out on the right-hand side of Eq. (\[eq:AS:curlv\]) by defining vortex densities $n_{\tau}=
\sum_{j} \delta^{(2)} ({\bf x}-{\bf x}_{\tau j})$. Since for rigid-body rotations the curl of ${\bf v}_n$ is simply $2\Omega$, the number density of vortices in the neutron superfluid is related to the macroscopic angular velocity of the neutron condensate by the familiar Feynman formula $$\begin{aligned}
\label{eq:AS:nn}
n_n = \frac{2m_n\Omega}{\pi\hbar}.\end{aligned}$$ For typical pulsar periods, $0.05 < P < 0.5$ s, $n_n\simeq 6.3.\times 10^3 \, P^{-1}\sim 10^4$-$10^5$ per cm$^2$. The minute difference between the superfluid and normal angular velocities in a neutron star decelerating under external breaking torques is neglected here. For a charged superfluid Eq. (\[eq:AS:curlv\]) can be transformed to a contour integral over a path where ${\bf v}_p=0$, as the super-current is screened beyond the magnetic field penetration depth $\lambda$. Again, going over to the continuum vortex limit we find $$\begin{aligned}
\label{eq:AS:np}
n_p =\frac{B}{\Phi_0}\simeq  5\times 10^{18}
{~~\rm cm}^{-2}.\end{aligned}$$ Note that the number of proton vortices per neutron vortex is $n_p/n_n\sim 10^{13}-10^{14}$ 