Is surface plasma wave intrinsically amplifiable
We show that the answer is in the affirmative. Within Drude-Boltzmann 
theory, we calculate the properties of long wavelength surface plasma 
waves (SPWs) existing on the surface of clean metals. We find that even 
without extrinsic supply such waves can amplify themselves. The energy is 
supplied the very moment when SPW is launched and it is stored in electrons lying 
beneath the surface within a layer as thick as the electronic mean free path. 
The result holds irrespective of surface smoothness. The intrinsic 
amplification rate $\gamma_{in}$ reveals the size of the 
Fermi surface. We find $\gamma_{in} \sim \omega_s\left(1-\kappa\tan^{-1}(\kappa^{-1})\right)$, 
where $\omega_s$ is the SPW frequency and $\kappa = kv_F/\omega_s$ with 
$k$ being the wave number and $v_F$ the Fermi velocity. Emphasizing the 
evolution of the charge density rather than the associated electric 
field, our approach offers an intuitive perspective on the origin of SPWs.