Stability of a Penning trap with a quadrupole rotating electric field

We present theoretical and experimental studies of the center-of-mass (c.m.) stability of ions in a Penning trap with a quadrupole rotating electric field. The rotation frequency of an ion cloud in a Penning trap determines the cloud density and shape, and it can be precisely controlled by a rotating electric field. The quadrupole rotating-field scheme can control pure single-species plasmas in contrast to the dipole field, which is effective only for plasmas composed of two or more species of ions. However, the quadrupole field can modify the trap stability because of the spatial dependence of the electric field. In this study, we theoretically and experimentally determine the c.m. stability condition for ions in a Penning trap with a rotating quadrupole field. The experimental results agree well with the theoretical prediction. In the limit of zero magnetic field we obtain a type of rf trap which uses a rotating quadrupole field and in which the c.m. motion is analytically solvable.