Electrostatic waves in a nonuniform plasma

Approximate expressions describing the Tonks‐Dattner and Buchsbaum‐Hasegawa resonances (at the second electron cyclotron harmonic) in a warm nonuniform plasma are derived by means of a fairly easy analytic continuation technique. Connection formulas are developed for third‐order electric field differential equations derived from kinetic theories and show the coupling of slow and fast waves in the vicinity of a linear turning point. The relatively simple field expressions predict traveling longitudinal waves possessing outwardly directed phase velocities. Internal plasma fields appreciably larger than the excitation field are found when the density nonuniformity supports even mode resonances. The field equations and expressions for the associated impedance variation are compared to numerical integration solutions and show striking similarity to experimental observations.