Phase-Coherent Measurement of Particle Distributions in Electron Acoustic Waves.

Phase-coherent velocity distribution functions $f ({\mathrm v}_z )$ are measured by Laser Induced Fluorescence, for standing ``electron acoustic'' waves in pure ion plasmas. These (mis-named) waves are the lower-frequency branch of standard electrostatic plasma waves, with phase velocity ${\mathrm v}_\phi \approx 1.3 \bar{\mathrm v}$. The waves are necessarily nonlinear so as to flatten the distribution at ${\mathrm v}_\phi$, thereby voiding the otherwise strong Landau damping. Our measurements are performed on $m_\theta \! = \! 0$, $m_z \! = \! 1$ waves driven to moderately large amplitude, i.e. $ e \delta \phi \geq \! 0.1 T$. Received LIF photons are accumulated in 8 phase bins, according to the instantaneous received phase of the wall electric field. The phase-coherent $f ({\mathrm v}_z )$ shows 1)~particle sloshing, $\delta \langle {\mathrm v} \rangle$, as expected; 2)~phase reversal of $\delta f$ at ${\mathrm v} \! = \! 0$ and ${\mathrm v} \! = \! {\mathrm v}_\phi$, in general correspondence with the linear perspective of $\delta f \! = \! ( \delta f_0 / \partial {\mathrm v} )/ ( {\mathrm v} - {\mathrm v}_\phi )$; and 3)~plateaux around ${\mathrm v}_\phi$ with velocity widths as expected from wave-trapping theory. Measurements will be compared to traveling wave trapping theory and to standing wave particle simulations.