Theoretical study of the effect of damping force on higher stability regions in a Paul trap

Ziaeian, Iman; Noshad, Houshyar

doi:10.1016/j.ijms.2009.09.003

Cited by 15 publications

(15 citation statements)

References 6 publications

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“…Boundary ejection methods take the advantage of ejecting ions with a mass-selective instability scan, with which the rf amplitude is scanned linearly to cause the secular frequency of ions to increase until they become unstable [2-4], when the ions reach the boundary at a ϭ 0, q eject ϭ 0.908, ␤ z is equal to one, the ion has reached its stability limit. When a buffer gas was first used to improve the resolution of the mass spectrum by Stafford et al [4], the stability boundary would move towards the positive direction on q-axis as bath gas pressure increase [2,5,6]. For the particle under the background at about 40 mTorr, the delay ejection also occurred at a large q value in the audio-frequency ion trap mass spectrometer [7][8][9][10][11].…”

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confidence: 99%

Characteristics of stability boundary and frequency in nonlinear ion trap mass spectrometer

Zhou

Zhu

Xiong

et al. 2010

J. Am. Soc. Mass Spectrom.

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In this article, the Poincare-Lighthill-Kuo (PLK) method is used to derive an analytical expression on the stability boundary and the ion trajectory. A multipole superposition model mainly including octopole component is adopted to represent the inhomogeneities of the field. In this method, both the motional displacement and secular frequency of ions have been expanded to asymptotic series by the scale of nonlinear term , which represents a weak octopole field. By solving the zero and first-order approximate equations, it is found that a frequency shift exists between the ideal and nonlinear conditions. The motional frequency of ions in nonlinear ion trap depends on not only Mathieu parameters, a and q, but also the percentage of the nonlinear field and the initial amplitude of ions. In the same trap, ions have the same mass-to-charge ratio (m/z) but they have different initial amplitudes or velocities. Consequently, they will be ejected at different time through after a mass-selective instability scan. The influences on the mass resolution in quadrupole ion trap, which is coupled with positive or negative octopole fields, have been discussed respectively. where u is the related motional frequency in the axial and radial direction, ⍀ is the frequency of the driven radio-frequency (rf) potential, ␤ u is a parameter dependent on Mathieu parameters a u and q u , and the subscript u refers to axial and radial coordinates. Boundary ejection methods take the advantage of ejecting ions with a mass-selective instability scan, with which the rf amplitude is scanned linearly to cause the secular frequency of ions to increase until they become unstable [2-4], when the ions reach the boundary at a ϭ 0, q eject ϭ 0.908, ␤ z is equal to one, the ion has reached its stability limit. When a buffer gas was first used to improve the resolution of the mass spectrum by Stafford et al. [4], the stability boundary would move towards the positive direction on q-axis as bath gas pressure increase [2,5,6]. For the particle under the background at about 40 mTorr, the delay ejection also occurred at a large q value in the audio-frequency ion trap mass spectrometer [7][8][9][10][11].In practical traps, however, the electric field distribution is nonlinear, and the main causes contributing to field distortions are the misalignment of the trap [12], the truncation of electrodes [12], and the space charge [13,14]. As the existence of high order terms in electric field, the stability boundary deviates from the ideal value and the equation of motion for the ions will be nonlinear Mathieu equation.Most papers [15][16][17][18][19] deal with the time-dependent nonlinear terms with the method of pseudopotential well approximation [20].Using this approximation, high order terms become time-independent, and the nonlinear Mathieu equation is a normal nonlinear equation known as Duffing equation. The solution of such kind of equations has been well-studied [21]. When q u Ͻ 0.4 [2,22], this approximation accords well with the physical truth, some useful...

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Characteristics of stability boundary and frequency in nonlinear ion trap mass spectrometer

Zhou

Zhu

Xiong

et al. 2010

J. Am. Soc. Mass Spectrom.

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“…As a typical stable solution of the equations, the trajectory of an H + ion confined into the trap in the x–z plane and the phase space curve in the z–v z plane, known as the Poincaré plot, were computed. The results are represented in Figs.…”

Section: Resultsmentioning

confidence: 99%

“…It should be noted that applicability of a specific category of ion trap depends on many parameters including trap workability, portability, storage capacity, easy fabrication, external ion injection capacity, interaction with a laser beam and signal‐to‐noise ratio. Every type of ion trap has its own advantages and disadvantages . For instance, the Paul trap and cylindrical ion trap (CIT) suffer from difficulties in miniaturization .…”

Section: Introductionmentioning

confidence: 99%

Theoretical investigation on confinement of ions in a cube‐shaped ion trap

Noshad

Amouhashemi

2015

J. Mass Spectrom.

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The confinement of ions in a cube-shaped ion trap and the mathematical formalism governing the behavior of ions in the trap is investigated theoretically. Afterwards, the stability regions are computed using the fourth-order Rung-Kutta method. Consequently, the influence of the direction of ions, injected into the trap from its center on the stability region, is numerically discussed. Moreover, the maximum angle of injection with respect to the vertical axis of the cube for which the ions could be confined in the trap without invoking any direct current component of voltage (henceforth referred to as limiting angle) was calculated. Strong linear correlation between the angle of injection and the ratio of the stability region areas is confirmed. A nonlinear feature of a cube-shaped ion trap is demonstrated with a focus on the equations of motion for an ion confined into the trap. It is worthwhile to note that the stability region of our cubic ion trap, which has its own boundary conditions and electrodynamics, has been theoretically investigated for the first time. Besides, the limiting angle as well as the aforementioned strong linear correlation has not been reported in the literature previously. Copyright © 2015 John Wiley & Sons, Ltd.

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“…In order to operate the Paul traps, an electric voltage including a direct-current (DC) and a radio-frequency (rf) components is employed to generate a trapping electric field. However, only proper voltages falling within appropriate stability regions can make the ions stable within the trap [16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

“…The main difficulty for operating a Paul trap in higher stability regions, compared with the first stability region, is attributable to the narrowed working area and decreased ion trapping efficiency [28,29]. From the diagram of stability regions (Figure 1), it is obvious that the area of the second stability region is much smaller than that of the first stability region, which means trappable mass range will shrink in higher stability regions [16,17]. In addition, higher DC and rf voltages are required in higher stability regions, which heat the ions and, thus, make them difficult to be trapped [28,29].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Effects in Paul Traps Operated in the Second Stability Region: Analytical Analysis and Numerical Verification

Xiong

Zhou

Zhang

et al. 2014

J. Am. Soc. Mass Spectrom.

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Paul trap working in the second stability region has long been recognized as a possible approach for achieving high-resolution mass spectrometry (MS), which however is still far away from the experimental implementations because of the narrow working area and inefficient ion trapping. Full understanding of the ion motional behavior is helpful for solving the problem. In this article, the ion motion in a superimposed octopole field, which was characterized by the nonlinear Mathieu equation, was solved analytically using Poincare-Lighthill-Kuo (PLK) method. This method equivalently described the nonlinear disturbance by an effective quadrupole field with perturbed Mathieu parameters, a(u) and q(u), which would bring huge convenience in the studies of nonlinear ion dynamics and was, therefore, used for rapid evaluation of the nonlinear effects of ion motion. Fourth-order Runge-Kutta method (4th R-K) indicated the error of PLK for characterizing the frequency shift of ion motion was within 15%.

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Theoretical study of the effect of damping force on higher stability regions in a Paul trap

Cited by 15 publications

References 6 publications

Characteristics of stability boundary and frequency in nonlinear ion trap mass spectrometer

Characteristics of stability boundary and frequency in nonlinear ion trap mass spectrometer

Theoretical investigation on confinement of ions in a cube‐shaped ion trap

Nonlinear Effects in Paul Traps Operated in the Second Stability Region: Analytical Analysis and Numerical Verification

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