A Coulomb crystal formed in a linear Paul trap by Doppler cooling with a single axial laser often shows undesired oscillatory behavior in the direction perpendicular to the trap axis. This transverse oscillation is found to include two distinct coherent motions; in addition to the well-known micromotion driven by external error fields, there exists another natural oscillatory component. The latter oscillation is a kind of statistical phenomenon that takes place even in the absence of any mechanical errors. A detailed theoretical study is performed to clarify the basic characteristics of these overlapping coherent motions. A simple cooling scheme is proposed to minimize the transverse oscillation amplitude of a Coulomb crystal without use of extra lasers. The validity of theoretical predictions made in the present paper is confirmed through molecular dynamics simulations assuming the three-dimensional electrode geometry of a typical Paul trap.
Muroo et al. (Thu,) studied this question.