Properties of the ideal Ginzburg-Landau vortex lattice

The magnetization curves $M(H)$ for ideal type-II superconductors and the maximum, minimum, and saddle-point magnetic fields of the vortex lattice are calculated from Ginzburg-Landau theory for the entire ranges of applied magnetic fields Hc1<~H<~Hc2 or induction 0<~B<~μ₀Hc2 and Ginzburg-Landau parameters 2^-1/2<~κ<~1000. Results for the triangular and square flux-line lattices are compared with the results of the circular cell approximation. The exact magnetic field $B(x,y)$ and magnetization M(H,κ) are compared with often used approximate expressions, some of which deviate considerably or have limited validity. Useful limiting expressions and analytical interpolation formulas are presented.