Power-Law Distributions for a Trapped Ion Interacting with a Classical Buffer Gas

Abstract

Classical collisions with an ideal gas generate non-Maxwellian distribution functions for a single ion in a radio frequency ion trap. The distributions have power-law tails whose exponent depends on the ratio of buffer gas to ion mass. This provides a statistical explanation for the previously observed transition from cooling to heating. Monte Carlo results approximate a Tsallis distribution over a wide range of parameters and have ab initio agreement with experiment.

References in corpus (11)

• A linear radiofrequency ion trap for accumulation, bunching, and emittance improvement of radioactive ion beams
• Mesoscopic molecular ions in Bose-Einstein condensates
• Power-law tails from multiplicative noise
• Quantum theory of ultracold atom-ion collisions
• Power-law tail distributions and nonergodicity
• Probing isotope effects in chemical reactions using single ions
• Radiative charge transfer lifetime of the excited state of (NaCa)${}^{+}$
• Controlled collisions of a single atom and ion guided by movable trapping potentials
• Observation of single collisionally cooled trapped ions in a buffer gas
• Evaporation of buffer gas-thermalized anions out of a multipole rf ion trap
• A linear RFQ ion trap for the Enriched Xenon Observatory

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