On the phase dependence of the interconversion of the motional modes in a Penning trap by quadrupolar excitation

The interconversion of the radial motional modes in a Penning trap (magnetron and cyclotron modes) by an external quadrupolar rf-field with a frequency near the true cyclotron frequency ωc plays an important role in the measurement cycle of Penning trap mass spectrometry. Ions to be measured are prepared in a state of magnetron motion which is then resonantly converted into cyclotron motion. The data analysis is usually carried out under the assumption that the initial motional state of the ions has been a pure magnetron state. In reality, however, a small component of cyclotron motion is always present in the ion's initial motional state. This component introduces a dependence on the initial phases of the quadrupolar rf-field and of the magnetron and cyclotron oscillators. This paper explores how excitation curves, conversion times and conversion line shapes depend on these phases and on the initial radius of the cyclotron motion. Since most experiments cannot control all of these phases the data must be interpreted in terms of phase-averaged quantities. These are slightly more general than those for pure magnetron motion. Most importantly, there are no shifts of the maxima and minima of phase-averaged conversion profiles compared to those predicted with pure magnetron motion in the initial state, so that the mass determinations are not affected. The theory predicts experimental data points to fall not on a mathematical curve, as for pure magnetron motion in the initial state, but within bands about the phase-averaged curves, with a finite width roughly proportional to the radius of the initial cyclotron motion. The scattering of data points can give rise to a loss of contrast of measured conversion line shapes. The component of cyclotron motion in the initial state introduces an additional parameter into the analytical expressions for conventional and Ramsey type excitation that could in some cases be useful for data fitting.

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► Quadrupolar rf-fields with a frequency near the cyclotron frequency ωc convert magnetron motion into cyclotron motion.
► Starting from pure magnetron motion one obtains symmetric and phase-independent conversion profiles.
► With a non-zero cyclotron component in the initial motional state conversion profiles become asymmetric and phase dependent.
► However, conversion profiles averaged over the phase parameter are symmetric about ωc.
► Conversion profiles become increasingly fuzzy as the initial cyclotron component increases.