  We present a semi-classical analytic model for spherical core-shell surface
plasmon lasers. Within this model, we drop the widely used one-mode
approximations in favor of fully electromagnetic Mie theory. This allows for
incorporation of realistic gain relaxation rates that so far have been
massively underestimated. Especially, higher order modes can undermine and even
reverse the beneficial effects of the strong Purcell effect in such systems.
Our model gives a clear view on gain- and resonator-requirements, as well as on
the output characteristics that will help experimenters to design more
efficient particle-based spasers.
