The coupling effects of hexapole and octopole fields in quadrupole ion traps: a theoretical study

Abstract

A theoretical method, the harmonic balance method, was introduced to study the coupling effects of hexapole and octopole fields on ion motion in a quadrupole ion trap. Ion motion characteristics, such as ion motion center displacement, ion secular frequency shift, nonlinear resonance curve and buffer gas damping effects, have been studied with the presence of both hexapole and octopole fields. It is found that hexapole fields have bigger impacts on ion motion center displacement, while octopole fields dominate ion secular frequency shift. Furthermore, the nonlinear features originated from hexapole and octopole fields could enhance or cancel each other, which provide us more space in a practical ion trap design process. As an example, an ion trap with improved performance was designed using a specific combination of hexapole and octopole fields. In this ion trap, a hexapole field was used to achieve efficient ion directional ejection, while an octopole field was added to correct the chemical mass shift and resolution degradation introduced by the hexapole field.

A Theoretical Method for Characterizing Nonlinear Effects in Paul Traps with Added Octopole Field

“…In Figure 3a, the ion secular frequencies, β, along the q-axis of the first stability region were calculated under different superimposed octopole fields: ε=0 (black curve), ε=0.1 (red curve), and ε=-0.1 (blue curve). The ion frequency shift effect has been extensively studied based on the PW model [34,39,45,[47][48][49][50][51][52][53][54][55][56][57][58][59][60]; therefore, it is not a surprise to find that compared with the ion secular frequency, β 0 , in the quadrupole field (black curve), the frequencies, β, in the positive (red curve) and negative superimposed octopole fields (blue curve) have positive and negative frequency shifts, Δβ (inset of Figure 3a), respectively. To clearly show the effect, the Δβ as a function of q at ε=0.1 (red curve) and ε=-0.1 (blue curve) is shown in Figure S3 in the Supporting Information.…”

“…The HB method has already been used to solve the NME [47][48][49]. However, in those works, the ion secular harmonic (i.e., C 0 term in Equation 10) is considered to have the main contribution to the ion amplitude; therefore, the higher-frequency harmonics (i.e., C 2n (n≠0) terms in Equation 10) are partially [47] or completely neglected [48,49].…”

“…Generally, two sorts of approximation treatments are most often employed, including the PW method [46] and the perturbation methods. The latter include a variety of methods, such as Poincare-Lighthill-Kuo (PLK) [45], harmonic balance (HB) [47][48][49], LindstedtPoincare [50][51][52][53][54], asymptotic [55], homotopy [56,57], and multiple time scales [58,59]. In most cases, using the perturbation method alone is still difficult to solve the NME; therefore, the perturbation method and the PW method are always used together [48][49][50][51][52][53][54][55][56][57][58][59].…”

Theoretical Study of Dual-Direction Dipolar Excitation of Ions in Linear Ion Traps

“…Moreover, it is well known that ITs with some positive even-order fields might improve performance [33,[39][40][41][42][43][44][45]. For example, the addition of octopole [40][41][42][43][44][45] or dodecapole fields [30,33,39] can compensate for the detrimental field caused by the slot and, therefore, the mass resolution and mass accuracy are enhanced.…”

Nonlinear Ion Harmonics in the Paul Trap with Added Octopole Field: Theoretical Characterization and New Insight into Nonlinear Resonance Effect

“…Generally, among the harmonics, the ion fundamental secular oscillation has the largest amplitude and is therefore the most important [2,3]. By neglecting all the other smallamplitude harmonics, including higher-frequency and nonlinear ones, theoretical methods, such as the most often employed pseudo-potential well (PW) model [19,20], can focus on the nonlinear effects of ion secular motion [10,[21][22][23][24][25][26][27][28].…”