Higher order non-linear resonances in a Paul trap

Alheit, R.; Kleineidam, S.; Vedel, Fernande; Vedel, M; Werth, G.

doi:10.1016/0168-1176(96)04380-7

Cited by 88 publications

(60 citation statements)

References 10 publications

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“…(9) and (12) cannot be solved in closed form. Some characteristics of the motion of ions in nonlinear fields have, however, been reported in experimental [15,24,25] and theoretical [7] studies and our analytical study will rely on these features to understand ion dynamics. It was seen that nonlinear resonance occurred when there was a simple rational relationship between the axial, radial and rf drive frequency.…”

Section: Analytical Studymentioning

confidence: 99%

“…These are regions where ions do not experience as strong a trapping field as in other regions and here ion motion has a tendency to become unstable. Such observations have resulted in the characterization of regions and points where the trapping strength is low as "black canyons" and "black holes," respectively [12][13][14][15]. It has been suggested by Wang et al [16] that such a phenomenon occurs on account of nonlinear resonance when axial and radial ion secular frequencies and the rf drive frequency have a simple rational relationship with each other.…”

Section: Introductionmentioning

confidence: 95%

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Escape velocity and resonant ion dynamics in Paul trap mass spectrometers

Abraham¹,

Chatterjee²,

Menon³

2004

International Journal of Mass Spectrometry

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Section: Analytical Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

Escape velocity and resonant ion dynamics in Paul trap mass spectrometers

Abraham¹,

Chatterjee²,

Menon³

2004

International Journal of Mass Spectrometry

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“…In practice, there are many different factors that influence the ion oscillation frequency [17] and which can lead to shifts and shape perturbations of the stability diagram. The nature of these factors sometimes is unknown [18]. In the case of the Mathieu equation, we use the method described above.…”

Section: Ince Diagram For the Mathieu Equationmentioning

confidence: 99%

Matrix methods for the calculation of stability diagrams in quadrupole mass spectrometry

Konenkov

Sudakov

Douglas

2002

J. Am. Soc. Mass Spectrom.

112

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The theory of the computer calculation of the stability of ion motion in periodic quadrupole fields is considered. A matrix approach for the numerical solution of the Hill equation and examples of calculations of stability diagrams are described. The advantage of this method is that it can be used for any periodic waveform. The stability diagrams with periodic rectangular waveform voltages are calculated with this approach. Calculations of the conventional stability diagram of the 3-D ion trap and the first six regions of stability of a mass filter with this method are presented. The stability of the ion motion for the case of a trapping voltage with two or more frequencies is also discussed. It is shown that quadrupole excitation with the rational angular frequency ϭ N⍀/P (where N, P are integers and ⍀ is the angular frequency of the trapping field) leads to splitting of the stability diagram along iso-␤ lines. Each stable region of the unperturbed diagram splits into P stable bands. The widths of the unstable resonance lines depend on the amplitude of the auxiliary voltage and the frequency. With a low auxiliary frequency splitting of the stability diagram is greater near the boundaries of the unperturbed diagram. It is also shown that amplitude modulation of the trapping RF voltage by an auxiliary signal is equivalent to quadrupole excitation with three frequencies. The effect of modulation by a rational frequency is similar to the case of quadrupole excitation, although splitting of the stability diagram differs to some extent. The methods and results of these calculations will be useful for studies of higher stability regions, resonant excitation, and non-sinusoidal trapping voltages. (J Am Soc Mass Spectrom 2002, 13, 597-613)

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“…Brown and Gabrielse [4] have successfully tuned out anharmonicities thereby achieving unprecedented experimental precision in their studies on geonium. Subsequently, several groups [15][16][17][18][19][20] have studied in detail the occurrences of non-linear resonances in Paul traps. Sevugrajan and Menon [21] have used perturbation method to derive an analytical relationship describing the dependence of ion secular frequency on octupole and hexapole superpositions.…”

Section: Introductionmentioning

confidence: 99%

Numerical calculations of potential distribution in non-ideal quadrupole trap and simulations of anharmonic oscillations

Gupta

Rao

2008

Pramana - J Phys

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A quadrupole ion trap consisting of electrode structures symmetric about zaxis is an important tool for conducting several precision experiments. In practice the field inside the trap does not remain purely quadrupolar, and can be calculated using numerical methods. We have used boundary element method to calculate the potential inside the truncated as well as symmetrically misaligned quadrupolar ion trap. The calculated potential values are fitted to multipole expansion and the weights of multipole moments have been evaluated by minimizing the least square deviation. The higher-order multipole contribution in the fabricated hyperbolic electrodes due to truncation and machining imperfections is discussed. Non-linear effects arising due to the superposition of octupole moment manifest as anharmonic oscillations of trapped ions in the non-ideal Paul trap. Theoretical simulations of non-linear effects have been carried out.

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Higher order non-linear resonances in a Paul trap

Cited by 88 publications

References 10 publications

Escape velocity and resonant ion dynamics in Paul trap mass spectrometers

Escape velocity and resonant ion dynamics in Paul trap mass spectrometers

Matrix methods for the calculation of stability diagrams in quadrupole mass spectrometry

Numerical calculations of potential distribution in non-ideal quadrupole trap and simulations of anharmonic oscillations

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