TY - JOUR

T1 - The true cyclotron frequency for particles and ions in a Penning trap

AU - Gabrielse, G.

N1 - Funding Information:
This work was supported by the NSF, by the AFOSR and by a Humboldt Research Award. Helpful comments from J. Äystö, K. Blaum, G. Bollen, L.S. Brown, J. DiSciacca, N. Guise, J. Hardy, E. Myers, W. Quint, R. Schuch, G. Savard and R.S. Van Dyck, Jr. are gratefully acknowledged.
Copyright:
Copyright 2009 Elsevier B.V., All rights reserved.

PY - 2009/1/15

Y1 - 2009/1/15

N2 - The true cyclotron frequency of a particle or ion, needed for mass spectrometry and other accurate measurements in a Penning trap, cannot be measured directly. It is not one of the oscillation frequencies of the trapped particle, and the three oscillation frequencies that can be measured vary with the misalignment and the harmonic distortion of the trap potential. Two methods to determine the cyclotron frequency are discussed. First, when all three eigenfrequencies of a trapped particle can be measured, the true cyclotron frequency is given by the prescription of the Brown-Gabrielse invariance theorem. This prescription makes possible a surprising number of the most accurate measurements in particle, nuclear and atomic physics because it accounts exactly for the lowest order electrostatic imperfections and magnetic misalignments. Second, when less accuracy is required, as when the masses of unstable nuclei are measured, a single sideband frequency is often measured instead-the frequency of a driving force that optimally couples two of the motions of the ion in the trap. A missing theoretical justification for this alternate method is provided using an expansion of the same invariance theorem. A remarkable suppression of systematic measurement errors is predicted, showing why these are not larger than reported measurement uncertainties, despite the contrary indication of simple estimates.

AB - The true cyclotron frequency of a particle or ion, needed for mass spectrometry and other accurate measurements in a Penning trap, cannot be measured directly. It is not one of the oscillation frequencies of the trapped particle, and the three oscillation frequencies that can be measured vary with the misalignment and the harmonic distortion of the trap potential. Two methods to determine the cyclotron frequency are discussed. First, when all three eigenfrequencies of a trapped particle can be measured, the true cyclotron frequency is given by the prescription of the Brown-Gabrielse invariance theorem. This prescription makes possible a surprising number of the most accurate measurements in particle, nuclear and atomic physics because it accounts exactly for the lowest order electrostatic imperfections and magnetic misalignments. Second, when less accuracy is required, as when the masses of unstable nuclei are measured, a single sideband frequency is often measured instead-the frequency of a driving force that optimally couples two of the motions of the ion in the trap. A missing theoretical justification for this alternate method is provided using an expansion of the same invariance theorem. A remarkable suppression of systematic measurement errors is predicted, showing why these are not larger than reported measurement uncertainties, despite the contrary indication of simple estimates.

KW - Invariance theorem

KW - Mass spectrometry

KW - Penning trap

KW - Quadrupolar excitation

KW - Radionuclides

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U2 - 10.1016/j.ijms.2008.10.015

DO - 10.1016/j.ijms.2008.10.015

M3 - Article

AN - SCOPUS:58149107214

VL - 279

SP - 107

EP - 112

JO - International Journal of Mass Spectrometry

JF - International Journal of Mass Spectrometry

SN - 1387-3806

IS - 2-3

ER -