The electron-acoustic mode

This paper examines electrostatic modes in an unmagnetized, homogeneous, Vlasov plasma with three Maxwellian components: ions, hot electrons, and cool electrons. In such a plasma, the electron-acoustic mode with frequencies between the ion and electron plasma frequencies may propagate with light damping. The conditions that allow propagation of this mode, which is distinct from the well-known ion-acoustic and Langmuir waves, are given in detail; approximate necessary conditions are 10≲Th/Tc and 0<nc<0.8ne, where the subscripts c, h, and e refer to the cool and hot electron components and the total electron population, respectively.