  Recently, we have revealed an intrinsic instability of metals due to surface
plasma waves (SPWs) and raised the prospect of using it to create lossless
SPWs. The counter-intuitive nature of this finding prompts one to ask, why had
not this instability been disclosed before, given the long history of this
subject? If this instability does exist, how far is it from reality? The
present work is devoted to answering these questions. To this end, we derive a
unified macroscopic theory of SPWs that applies to any type of electron
dynamics, be they local or non-local, classical or quantum-mechanical. In light
of this theory, we analyze the behaviors of SPWs according to several electron
dynamics models, including the widely used local dielectric model (DM), the
hydrodynamic model (HDM) and the specular reflection model (SRM), in addition
to the less common semi-classical model (SCM). We find that, in order to unveil
the instability, one must (i) self-consistently treat surface effects without
any of the usually imposed auxiliary conditions and (ii) include translation
symmetry breaking effects in electron dynamics. As far as we are concerned,
none existing work had fulfilled both (i) and (ii). To assess the possibility
of realizing the instability, we analyze two very important factors: the
dielectric interfacing the metal and inter-band transitions, which both were
ignored in our recent work. Whereas inter-band absorption -- together with
Landau damping -- is shown adverse to the instability, a dielectric brings it
closer to occurrence. One may even attain it in common plasmonic materials such
as silver under not so tough conditions.
