Energy distributions of an ion in a radio-frequency trap immersed in a buffer gas under the influence of additional external forces

An ion held in a radio-frequency trap interacting with a uniform buffer gas of neutral atoms develops a steady-state energy distribution characterized by a power-law tail at high energies instead of the exponential decay characteristic of thermal equilibrium. We have previously shown that the Tsallis statistics frequently used as an empirical model for this distribution is a good approximation when the ion is heated due to a combination of micromotion interruption and exchange of kinetic energy with the buffer gas [Rouse and Willitsch, Phys. Rev. Lett. 118, 143401 (2017)]. Here, we extend our treatment to include the heating due to additional motion of the ion caused by external forces, including the "excess micromotion" induced by uniform electric fields and rf phase offsets. We show that this also leads to a Tsallis distribution with a potentially different power-law exponent from that observed in the absence of this additional forced motion, with the difference increasing as the ratio of the mass of the neutral atoms to that of the ion decreases. Our results indicate that unless the excess micromotion is minimized to a very high degree, then even a system with very light neutrals and a heavy ion does not exhibit a thermal distribution.