A quadrupole mass analyzer is made of four hyperbolic or circular rods placed in parallel with identical diagonal distances from each other. The rods are electrically connected in diagonal. In addition to an alternating radiofrequency (RF) potential (V), a positive direct current (DC) potential (U) is applied on one pair of rods while a negative potential is applied to the other pair (Fig. 1.17). The ion trajectory is affected in x and y directions by the total electric field composed by a quadrupolar alternating field and a constant field. Because there is only a two-dimensional quadrupole field the ions, accelerated after ionization, maintain their velocity along the z axis.
The motion of ions in the quadrupole (x, y) is quite complex and can be described by the Matthieu equations. The solution of the Matthieu equations generate two terms, a and q, which are proportional to the RF and DC potentials, respectively. For a detailed description of Matthieu equations, please see reference . The trajectories of ions are stable when the ions never reach the rods of the quadrupole. To reach the detector an ion must have a stable trajectory in the x and y directions. With a quadrupole mass analyzer a mass spectrum is obtained by increasing the magnitude of U (DC) and V (RF) at a constant ratio. In a quadrupole mass analyzer when the DC voltage of a quadrupole is set to zero and
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