Two ions in a Penning trap: Implications for precision mass spectroscopy

With the goal of increasing the accuracy of Penning-trap mass spectroscopy to a part in ${10}^{11}$, we model the motion of two simultaneously trapped, dissimilar ions. Simultaneous cyclotron resonance on two trapped ions will circumvent the problem of temporal instability in the trapping fields. Conservation of energy and canonical angular momentum require that, in the regime appropriate for mass spectroscopy, the average interion spacing be an approximate constant of the motion. Cyclotron-frequency perturbation from ion-ion repulsion is therefore limited. Orbits that minimize measurement errors from residual field imperfections are shown to be both stable and attainable. Experimental results demonstrating the simultaneous trapping of a single ${\mathrm{N}}_2^{+}$ ion and a single ${\mathrm{CO}}^{+}$ ion are presented.