Analytic study of two-ring patterns of vortices in a Penning trap

The equilibrium configuration and the stability of vortex patterns made of point vortices equally distributed on two circumferences in a bounded system are studied. Such patterns appear worth studying from a theoretical point of view, as they have been observed experimentally in nonneutral plasmas confined by a Penning trap. The results presented in the paper prove that stable configurations of two rings of point vortices can exist.