This article reports on some theoretical studies concerning the impulsional mode of a cylindrical ion trap (CIT) supplied with a periodic impulsional radio frequency (rf) voltage of the form V(ac)cosΩt/(1-kcos2Ωt) with 0 ≤ k < 1. The performance characteristics of CIT impulsional mode, for the twelve stability regions, were computed using fifth order Runge-Kutta method and were compared to the classical sinusoidal mode k = 0. Also, the results show that, for the same equivalent operating point in two stability diagrams (having the same β(z)) the associated modulated secular ion frequencies behavior are the same.
The paper reports on some theoretical studies concerning the impulsional mode of a quadrupole mass filter (QMF) supplied with a new periodic impulsional radio frequency voltagein the form of V(ac)cos(Ωt)⌊1=kcos(1/3Ωt/1-√kcos(2Ωt⌋ with 0 ≤k < 1 (⌊.⌋ means floor function) and eventually compares it to the classical sinusoidal case, k = 0. The physical properties of the confined ions in the r and z directions are illustrated and the fractional mass resolutions m/Δm of the confined ions in the first stability regions of both potential were analyzed for hydrogen isotopes and presented.
The homotopy analysis method (HAM) is applied to study the behavior of a hyperbolic rods of quadrupole mass filter and a sinusoidal potential form V(ac) cos(Ωt). Numerical computation method of a 20th-order HAM is employed to compare the physical properties of the confined ions with fifth-order Runge-Kutta method. Also, comparison is made for the first stability region, the ion trajectories in real time, the polar plots, and the ion trajectory in x - y plan. The results show that the two methods are fairly similar; therefore, the HAM method has potential application to solve linear and nonlinear equations of the charge particle confinement in quadrupole field.
The capabilities and performances of a quadrupole ion trap under damping force based on collisional cooling is of particular importance in high-resolution mass spectrometry and should be analyzed by Mathieu's differential solutions. These solutions describe the stability and instability of the ion's trajectories confined in quadrupole devices. One of the methods for solving Mathieu's differential equation is a two-point one block method. In this case, Mathieu's stability diagram, trapping parameters a(z) and q(z) and the secular frequency of the ion motion w(z), can be derived in a precise manner. The two-point one block method (TPOBM) of Adams Moulton type is presented to study these parameters with and without the effect of damping force and compared to the 5th-order Runge-Kutta method (RKM5). The simulated results show that the TPOBM is more accurate and 10 times faster than the RKM5. The physical properties of the confined ions in the r and z axes are illustrated and the fractional mass resolutions m/Δm of the confined ions in the first stability region were analyzed by the RKM5 and the TPOBM.