Static properties of a non-neutral9Be+-ion plasma

We report measurements of the static properties of laser-cooled non-neutral ${}_{}{}^9{}_{}{}^{}\mathrm{Be}_{}^{+}{}_{}{}^{}$-ion plasmas stored in Penning traps under a variety of experimental conditions. We have measured the shape, rotation frequency, density, and temperature of the ions as functions of the Penning-trap potential and laser-cooling configuration. Two different traps were used. In one trap, we were able to measure the ion temperature in directions both perpendicular and parallel to the trap magnetic field. In the other trap, ${}_{}{}^{198}{}_{}{}^{}\mathrm{Hg}_{}^{+}{}_{}{}^{}$ ions were stored simultaneously with the ${}_{}{}^9{}_{}{}^{}\mathrm{Be}_{}^{+}{}_{}{}^{}$ ions and their effect on the ${}_{}{}^9{}_{}{}^{}\mathrm{Be}_{}^{+}{}_{}{}^{}$ ions was measured. The experimental measurements are compared with theoretical predictions. Within experimental error, the ion plasmas rotate without shear and exhibit approximate thermal equilibrium. For a single stored species, a static model of the ion plasmas, based on thermal equilibrium, is formulated. When the ion-plasma dimensions are small compared to the trap dimensions, this model predicts that the ion plasmas are spheroidal and have an aspect ratio which is a function of the plasma rotation frequency, and the single-particle cyclotron and axial frequencies. This is verified by measurement. The ion densities and temperatures measured in our experiments show that the plasmas are strongly coupled and should exhibit liquid and solid properties.