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Optimal Ion Trapping Experiment



Kevin J. Coakley


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


ion traps, probability theory, statistics


Coakley, K. (2007), Optimal Ion Trapping Experiment, Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) (Accessed May 25, 2024)


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Created May 10, 2007, Updated February 17, 2017