  A ring crystal of ions trapped in a linear multipole trap is studied as a
basis for an optical frequency standard. The equilibrium conditions and cooling
possibilities are discussed through an analytical model and molecular dynamics
simulations. A configuration which reduces the frequency sensitivity to the
fluctuations of the number of trapped ions is proposed. The systematic shifts
for the electric quadrupole transition of calcium ions are evaluated for this
ring configuration. This study shows that a ring of 10 or 20 ions allows to
reach a short term stability better than for a single ion without introducing
limiting long term fluctuations.
