  An ion held in a radiofrequency trap interacting with a uniform buffer gas of
neutral atoms develops a steady-state energy distribution characterised 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 [I. Rouse and
S. 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 minimised to a very high
degree, then even a system with very light neutrals and a heavy ion does not
exhibit a thermal distribution.
