Doppler imaging of plasma modes in a Penning trap.

We describe a technique and present results for imaging the modes of a laser-cooled plasma of 9 Be + ions in a Penning trap. The modes are excited by sinusoidally time-varying potentials applied to the trap electrodes. They are imaged by changes in the ion resonance fluorescence produced by Doppler shifts from the coherent ion velocities of the mode. For the geometry and conditions of this experiment, the mode frequencies and eigenfunctions have been calculated analytically. A comparison between theory and experiment for some of the azimuthally symmetric modes shows good agreement.