The area inside the boundaries characterizes voltages with stable trajectories, while the the area outside the boundaries characterizes unstable trajectories for that stability region.įigure 3. The r 0 is computed based on a round quadrupole rod diameter of 9.5mm and an operating frequency of 1.2MHz. The amplified view of this First Stability Region is illustrated in Figure 3, showing suitable substitutions for the Mathieu parameters a and q to translate the axes into RF-DC voltage space for m/z 219. Regions of simultaneous overlap are labeled A, B, C, and D. The Mathieu stability diagram in two dimensions (x and y). The traditional operating region for quadrupole mass filters is represented by the Region A in Figure 2.įigure 2. The families of solution boundaries for the Mathieu equation that lie near the origin are depicted in Figure 2, showing four distinct regions of stable trajectories for ions passing through the quadrupole, utilizing the Mathieu a and q parameters. Graphical treatment can answer the questions such as ‘Does the ion have a stable trajectory at the voltages applied? Will the ion pass through the quadrupole?. This represents that in each of the x and y direction, the motion is sinusoidal, comprising micromotion at the harmonic frequencies added in and macromotion at the fundamental frequency (ξ 0). Considering ion trajectories as infinite sums of sine and cosine functions, with each succeeding term comprising higher frequency and smaller amplitude, is acceptable. The aforementioned equation is intuitively reduced to a similar infinite sum of sine and cosine functions. The solution to this second order linear differential equation is as follows: In the above equations, u= Position along the coordinate axes (x or y) and is represented as Ωt/2, in which t is time and Ω is the applied RF frequency e = the charge on an electron U = Applied DC voltage V = Applied zero-to-peak RF voltage m = Mass of the ion and r 0= The effective radius between electrodes. When discussing quadrupole theory, it is customary to mention the Mathieu Equation: Schematic of a typical quadrupole power supply connections is illustrated in Figure 1. Two electrical connections are required for the quadrupole. Striking the quadrupole electrodes neutralizes the ions with unstable trajectories. For a specific system, the amplitude of the voltages identifies the mass or range of masses that have stable trajectories through the quadrupole. The application of a combination of precise DC and RF voltages to the quadrupole rods helps focusing the ions to be mass analyzed down the quadrupole center. Schematic of typical quadrupole power supply connections The common quadrupole fabrication technique involves positioning the four round poles in such a fashion that the centers of the poles coincide with the corners of an imaginary square.įigure 1. The orientation of the electrodes is such that there is a hyperbolic (quadrupolar) electric field between them. A quadrupole mass filter is composed of four mutually parallel, highly precise, electrically-isolated electrodes.
0 kommentar(er)
