  In the context of magnetic hyperthermia, several physical parameters are used
to optimize the heat generation and these include the nanoparticles
concentration and the magnitude and frequency of the external AC magnetic
field. Here we extend our previous work by computing nonlinear contributions to
the specific absorption rate, while taking into account (weak) inter-particle
dipolar interactions and DC magnetic field. In the previous work, the latter
were shown to enhance the SAR in some specific geometries and setup. We find
that the cubic correction to the AC susceptibility does not modify the
qualitative behavior observed earlier but does bring a non negligible
quantitative change of specific absorption rate, especially at relatively high
AC field intensities. Incidentally, within our approach based on the AC
susceptibility, we revisit the physiological empirical criterion on the upper
limit of the product of the AC magnetic field intensity $H_{0}$ and its
frequency $f$, and provide a physicist's rationale for it.
