Explicit, analytical radio-frequency heating formulas for spherically symmetric nonneutral plasmas in a Paul trap

摘要

We present explicit, analytical heating formulas that predict the heatingrates of spherical, nonneutral plasmas stored in a Paul trap as a function ofcloud size $S$, particle number $N$, and Paul-trap control parameter $q$ in thelow-temperature regime close to the cloud $\rightarrow$ crystal phasetransition. We find excellent agreement between our analytical heating formulasand detailed, time-dependent molecular-dynamics simulations of the trappedplasmas. We also present the results of our numerical solutions of atemperature-dependent mean-field equation, which are consistent with ournumerical simulations and our analytical results. This is the first time thatanalytical heating formulas are presented that predict heating rates withreasonable accuracy, uniformly for all $S$, $N$, and $q$.