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

TL;DR

This paper introduces the first analytical formulas to accurately predict heating rates of spherical nonneutral plasmas in a Paul trap, validated by simulations and mean-field solutions.

Contribution

The authors derive explicit analytical heating formulas for nonneutral plasmas in a Paul trap, covering all sizes, particle numbers, and control parameters near the phase transition.

Findings

Excellent agreement between analytical formulas and molecular-dynamics simulations

Numerical mean-field solutions are consistent with simulations and analytical results

First analytical heating formulas with broad applicability and reasonable accuracy

Abstract

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