= Upper critical magnetic field
{title2=$B_{c2}=\mu_0H_{c2}=\Phi_0/(2\pi\xi^2)$}
Linearize the stated model about $\psi=0$ in a uniform <magnetic field>. The kinetic operator has the <Landau level> ground energy $\hbar|q|B/(2m_*)$. Its cancellation with $\alpha<0$ gives
$$
B_{c2}=\frac{2m_*|\alpha|}{\hbar|q|}
=\frac{\hbar}{|q|\xi^2}=\frac{\Phi_0}{2\pi\xi^2}.
$$
This is the bulk orbital field scale of this model; it excludes spin-polarization limits and uses the normal-state relation $B_{c2}=\mu_0H_{c2}$. For the chosen $\xi=10\,\mathrm{nm}$, it is about \b[$3.29\,\mathrm T$]. With $\lambda=100\,\mathrm{nm}$, $\kappa=10$. Counting triangular cells at $B_{c2}$ would give $a/\xi=\sqrt{4\pi/\sqrt3}\simeq2.69$, but it is the linearized field equation, rather than disks of an arbitrarily chosen core radius touching, that supplied the transition criterion.
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