Quadrupole excitation of ions in linear quadrupole ion traps with added octopole fields

Abstract

Modeling and experimental studies of quadrupole excitation of ions in linear quadrupole traps with added octopole fields are described. An approximate solution to the equations of motion of ions trapped in a quadrupole with added octopole and dodecapole fields, with quadrupole excitation and damping is given. The solutions give the steady-state or stationary amplitudes of oscillation with different excitation frequencies. Trajectory calculations of the oscillation amplitudes are also presented. The calculations show that there can be large changes in the amplitude of ion oscillation with small changes in excitation frequency, on both the low and high-frequency sides of a resonance. Results of experiments with quadrupole excitation of reserpine ions in linear quadrupole traps with 2.0%, 2.6%, and 4.0% added octopole fields are given. It is found that as the excitation frequency is changed, two resonances are generally . For tandem mass spectrometry, where ions are excited at their resonant frequencies in the presence of a collision gas to induce fragmentation, the addition of field distortions, described by the addition of higher multipoles to the potential, can increase the fragmentation efficiency, particularly at low pressures [2,3]. The spatial part of the potential in a linear quadrupole with field distortions can be written as a superposition of multipoleswhere Re[func] is the real part of the complex function func and A N is the dimensionless amplitude of a 2N-pole field. If no dc voltages are applied between the rods, the time-dependent potential iswhere V rf V V is the zero to peak rf voltage pole to ground, r 0 the field radius, x r , y r , are Cartesian coordinates, and t r time. The addition of higher multipoles can lead to nonlinear dynamics, giving sudden changes in the amplitude of ion oscillation with small changes in excitation frequency. These effects have been described in detail for dipole excitation of ions in a linear quadrupole trap with a 4% added octopole field [2a].Trapped ions can also be excited by quadrupole excitation, sometimes called parametric excitation [4]. With quadrupole excitation, the excitation electric field strength is proportional to the distance off axis. In a pure quadrupole field, ions are excited when the excitation angular frequency ex iswhere n ϭ 0, Ϯ1, Ϯ2 . . ., K ϭ 1, 2, 3, . . ., ⍀ is the angular frequency of the trapping radiofrequency field, and ␤ is a function of the Mathieu parameter q given bywith e the charge of an electron, and z the number of charges on an ion. The effects of nonlinear dynamics can also be seen with quadrupole excitation. Werth and coworkers have reported large changes in oscillation amplitude and strongly asymmetric resonances with parametric excitation of ions in 3D Paul traps [5][6][7] and electrons in Penning traps [8,9]. These effects were attributed to the higher order fields of the traps.Address reprint requests to Dr.

Mass analysis with islands of stability with linear quadrupoles incorporating higher order multipole fields

“…With the addition of nonlinear multipole fields to a quadrupole field, the matrix method is no longer strictly applicable to the calculation of stability, because eqs 3 and 4 have nonlinear terms and are no longer Hill equations. For example, theory and experiments show that with quadrupole excitation in linear quadrupoles with added octopole fields, the x and y frequencies differ slightly, so the island boundaries will not exactly match those calculated for a pure quadrupole field [26]. However, it has been found by simulations [20] and experiments [16,17,21] that the overall trend of island formation is still the same for quadrupoles incorporating weak higher order multipoles.…”

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

“…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]. However, the employed PW method neglects all the higher-frequency harmonics of ion motion, which gives rise to low accuracy and little applicability.…”

Ion trap mass analysis at high pressure: A theoretical view

“…In the pressure regions below several mTorr, discrete ionmolecule collision models [4,41,49] are preferred. However, damping term treatments for pressure effects have been shown to be effective at relatively high pressures for characterizing ion trap performance, including mass resolution [45,55], the stability diagram [47], and ion nonlinear resonance phenomena [46,56].…”