A new acoustic-like mode in an unmagnetized dusty plasma

It is shown that because of the dependence of the plasma potential φ on the dust number density $n_d$ for given background plasma parameters and the dust grain radius, viz. ${\mathrm{\phi =\phi (n}}_d\mathrm{),}$ the dusty plasma is endowed with an effective temperature $T_{\mathrm{eff}}$ which is proportional to ${\mathrm{d\phi /dn}}_d.$ The gradient of the effective pressure $n_{\text{d0}}{T}_{\mathrm{eff}}$ provides a restoring force for a new acoustic-like mode, which is referred to as the dust electro-acoustic (DEA) mode whose phase velocity equals ${\mathrm{(T}}_{\mathrm{eff}}{\mathrm{/m}}_d{)}^{\text{1/2}},$ where $m_d$ is the dust mass. The acoustic-like nature of the DEA mode is interpreted in terms of an effective screening (due to the dust charge fluctuations), called the “Coulomb screening,” with the screening length ${\lambda }_c{\mathrm{=(T}}_{\mathrm{eff}}{\text{/4πn}}_d{q}_d^2{)}^{\text{1/2}},$ where $q_d$ is the dust charge.