  An explicit expression for the quadratic density-response function of a
many-electron system is obtained in the framework of the time-dependent
density-functional theory, in terms of the linear and quadratic
density-response functions of noninteracting Kohn-Sham electrons and functional
derivatives of the time-dependent exchange-correlation potential. This is used
to evaluate the quadratic stopping power of a homogeneous electron gas for slow
ions, which is demonstrated to be equivalent to that obtained up to second
order in the ion charge in the framework of a fully nonlinear scattering
approach. Numerical calculations are reported, thereby exploring the range of
validity of quadratic-response theory.
