Recent experiments on mesoscopic samples and theoretical considerations lea
d us to analyze multiply charged (n > 1) vortex solutions of the Ginzburg-L
andau equations for arbitrary values of the Landau-Ginzburg parameter kappa
. For n>> 1, they have a simple structure and a free energy F similar ton.
In order to relate this behavior to the classic Abrikosov result F similar
ton(2) when kappa-->+infinity, we consider the limit where both n>>1 and ka
ppa >> 1, and obtain a scaling function of the variable kappa /n that descr
ibes the crossover between these two behaviors of F. It is then shown that
a small-n expansion can also be performed and the first two terms of this e
xpansion are calculated. Finally, large and small n expansions are given fo
r recently computed phenomenological exponents characterizing the free ener
gy growth with kappa of a giant vortex.