  If a magnetic field is frozen into a plasma that undergoes spherical
compression then the magnetic field B varies with the plasma density \rho
according to B \propto \rho^{2/3}. In the gravitational collapse of
cosmological density perturbations, however, quasi-spherical evolution is very
unlikely. In anisotropic collapses the magnetic field can be a much steeper
function of gas density than in the isotropic case. We investigate the
distribution of amplifications in realistic gravitational collapses from
Gaussian initial fluctuations using the Zel'dovich approximation. Representing
our results using a relation of the form B\propto \rho^{\alpha}, we show that
the median value of \alpha can be much larger than the \alpha=2/3 resulting
from spherical collapse, even if there is no initial correlation between
magnetic field and principal collapse directions. These analytic arguments go
some way towards understanding the results of numerical simulations.
