Optimal Ion Trapping Experiment

Published

May 10, 2007

Author(s)

Kevin J. Coakley

Abstract

In each run of an experiment, ions are confined in a trap for duration {\tau}. After the trapping stage, ions are purged and detected. The detector provides incomplete information because it goes dead after detecting the first trapped ion. There is a dead time {\delta} between the end of the trapping stage in one run and the beginning of the next trapping stage in the next run. Based on the fraction of runs where no ions are detected, I estimate the trapping rate {\lambda} by the method of maximum likelihood. I present asymptotically valid formulas for the bias, variance, and mean-square-error of this maximum likelihood estimate computed from a subsample of all possible realizations of the data. This subsample excludes an exceedingly rare realization of the data that yields an infinite estimate. Based on nominal values of {\lambda} and the dead time {\delta}, I determine the optimal trapping stage duration {\tau} by minimizing the mean-square-error of the estimate.

Citation

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

Pub Type

Journals

Keywords

ion traps, probability theory, statistics

Citation

Coakley, K. (2007), Optimal Ion Trapping Experiment, Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) (Accessed September 12, 2024)