  The hamiltonian describing a single fermion in a Penning trap is shown to be
supersymmetric in certain cases. The supersymmetries of interest occur when the
ratio of the cyclotron frequency to the axial frequency is 3/2 and the particle
has anomalous magnetic moment 4/3 or 2/3. At these supersymmetric points, the
spectrum shows uniformly spaced crossed levels. The associated superalgebras
are su(2|1) and su(1|1). The phase space for this problem has an osp(2|6)
structure and contains all the degeneracy superalgebras.
