Degenerate ion-acoustic wave ($c_s^2\simeq m_e{v}_{Fe}^2/(3m_i)$)

For equal densities of singly charged ions and electrons, a completely degenerate electron equation of state gives $d{P}_e/d{n}_e=m_e{v}_{Fe}^2/3$. Coupling this restoring force to ion inertia yields the sound speed in the title. If both species are degenerate and $m_e\ll m_i$, then $v_{Fi}\ll c_s\ll v_{Fe}$. Ion resonances are absent, while the electron parallel marginal distribution has a small slope at the phase velocity, producing relative Landau damping of order $\sqrt{m_e/m_i}$.