Instabilities of an electron cloud in a Penning trap

We have measured the storage instabilities of electrons in a Penning trap at low magnetic fields. These measurements are carried out as a function of the trapping voltage, for different magnetic fields. It is seen that these instabilities occur at the same positions when the trapping voltage is expressed as a percentage of the maximum voltage, given by the stability limit. The characteristic frequencies at which these instabilities occur, obey a relation that is given by nzÏz + n+Ï+ + nÏ = 0, where Ïz, Ï+ and Ï- are the axial, perturbed cyclotron and the magnetron frequencies of the trapped electrons respectively, and the n's are integers. The reason for these instabilities are attributed to higher order static perturbations in the trapping potential