Undamped electrostatic plasma waves

Electrostatic waves in a collision-free unmagnetized plasma of electrons with fixed ions areinvestigated for electron equilibrium velocity distribution functions that deviate slightly fromMaxwellian. Of interest are undamped waves that are the small amplitude limit of nonlinearexcitations, such as electron acoustic waves (EAWs). A deviation consisting of a small plateau, aregion with zero velocity derivative over a width that is a very small fraction of the electronthermal speed, is shown to give rise to new undamped modes, which here are namedcorner modes.The presence of the plateau turns off Landau damping and allows oscillations with phase speedswithin the plateau. These undamped waves are obtained in a wide region of theðk;xRÞplane(xRbeing the real part of the wave frequency andkthe wavenumber), away from the well-known“thumb curve” for Langmuir waves and EAWs based on the Maxwellian. Results of nonlinearVlasov-Poisson simulations that corroborate the existence of these modes are described. It is alsoshown that deviations caused by fattening the tail of the distribution shift roots off of the thumbcurve toward lowerk-values and chopping the tail shifts them toward higherk-values. In addition,a rule of thumb is obtained for assessing how the existence of a plateau shifts roots off of thethumb curve. Suggestions are made for interpreting experimental observations of electrostaticwaves, such as recent ones in nonneutral plasmas.