Frequency Variability of Electron Acoustic Waves.

``Electron Acoustic Waves'' (EAW) are non-linear electrostatic plasma modes, with a phase velocity comparable to the thermal velocity\footnote{F. Valentini et al., {\it Phys. Plas.} {\bf 13}, 052303 (2007).} ${\mathrm v}_\phi \approx 1.3 \bar{\mathrm v}$. EAWs can be excited in neutralized plasmas,\footnote{Sircombe et al., {\it Plas. Phys. Cont. Fus.} {\bf 48}, 1141 (2006).} pure electron plasmas and pure ion plasmas. Here, we present measurements of the ``thumb shape'' dispersion relation of EAW and Trivelpiece-Gould (TG) plasma modes in a pure magnesium ion plasma. Near the end of the thumb ($r_p / \lambda_D < 3$), modes can be excited at almost any frequency, contrasting with the theoretical dispersion relation. The surprise here is that an ``off-resonant'' drive readily modifies the velocity distribution so as to make the drive {\it resonant}. These plasma modes can also be excited by a chirped down frequency burst, similar to the one described by the Berkeley group.\footnote{Bertsche et al., {\it Phys. Rev. Lett.} {\bf 91}, 265003 (2003).} The chirped excitation creates extreme modification of $f ({\mathrm v}_z )$, and can be tailored to support a plasma mode at almost any frequency. We also observe that the resonant frequency of both EAW and TG plasma modes decreases with mode amplitude, in a fully reversible manner; but this effect has no theoretical explanation.