The nonlinear excitation of fast magnetosonic waves by phase mixing Al
fven waves in a cold plasma with a smooth inhomogeneity of density acr
oss a uniform magnetic field is considered. If initially fast waves ar
e absent from the system, then nonlinearity leads to their excitation
by transversal gradients in the Alfven wave. The efficiency of the non
linear Alfven-fast magnetosonic wave coupling is strongly increased by
the inhomogeneity of the medium. The fast waves, permanently generate
d by Alfven wave phase mixing, are refracted from the region with tran
sversal gradients of the Alfven speed. This nonlinear process suggests
a mechanism of indirect plasma heating by phase mixing through the ex
citation of obliquely propagating fast waves.