  Direct current in confined two-dimensional (2d) electron systems can become
unstable with respect to the excitation of plasmons. Numerous experiments and
simulations hint that structural asymmetry somehow promotes plasmon generation,
but a constitutive relation between asymmetry and instability has been missing.
We provide such relation in the present paper and show that bounded perfect 2d
electron fluids in asymmetric structures are unstable under arbitrarily weak
drive currents. To this end, we develop a perturbation theory for hydrodynamic
plasmons and evaluate corrections to their eigenfrequency induced by carrier
drift, scattering, and viscosity. We show that plasmon gain continuously
increases with degree of plasmon mode asymmetry until it surrenders to viscous
dissipation that also benefits from asymmetry. The developed formalism allows
us to put a lower bound on the instability threshold current, which corresponds
to the Reynolds number $R_{\min} = 2\sqrt{3}$ for one-dimensional plasmons in
2d channel under constant voltage bias.
