Multipole traps for non-neutral plasmas

A multipolar generalization of the Penning trap is presented. The case of l=1 is that of standard Penning trap. For the case of a quadrupolar magnetic field, analytic solutions are presented for cold, confined, one-species plasmas with spheroidal or spherical boundaries; for higher l values analytic solutions are given only for spherically bounded plasmas. By virtue of the sheared flow present for solutions with l>1, the classical Brillouin ratio (stored rest energy of particles/stored magnetic energy) of unity is exceeded and attains a global limit of 2 at infinitely high l