POOLS OF IONS TRAPPED BELOW THE SURFACE OF SUPERFLUID-HELIUM - MODES OF RESPONSE IN A STEADY VERTICAL MAGNETIC-FIELD

The paper is concerned with two-dimensional classical fluids and solids composed of charged particles that interact only through Coulomb forces. An example of this type of system, and one with which the paper is particularly concerned, is a circular pool of either positive or negative ions trapped just below the free surface of superfluid helium. A calculation is presented of the modes of response of such a system in its own plane when exposed to an oscillating electric potential, especially in the long-wavelength limit and in the presence of a steady magnetic field applied in a direction normal to the plane of the system. The calculations are relevant to the experimental detection and study of these modes, which include shear modes in the crystal phase and viscous modes in the fluid phase.