Hyperbolic rods

Theoretically, each electrode should have a hyperbolic cross section for optimized geometry of the resulting quadrupole field, and thus for optimized performance. [103,104] However, cyclindrical rods are often employed instead, for ease of manufacture. By adjusting the radius of the rods carefully (r = 1.1468ro), a hyperbolic field may be approximated. [113] However, even slight distortions of the ideal quadrupole field either from interference with external fields or due to low mechanical precision or inadequate shape of the device cause severe losses of transmission and resolution. [114] The expected advantages of hyperbolic rods [115] have been demonstrated by ion trajectory calculations [110,116] circular rods cause a reduction in macromotion frequency because of an increased residence time of the ions in close vicinity to the rods this in turn means reduced resolution. 

Brubaker, W.M. Comparison of Quadrupole Mass Spectrometers With Round and Hyperbolic Rods. J. Vac. Sci. Technol 1967,4, 326. 

Fig. 1.17 The quadrupole mass analyzer is formed by four circular or hyperbolic rods placed in parallel. O Quadrupolar potential.

An ideal hexapole field consists of six alternately charged hyperbolic rods, and the electrostatic potential inside this array is given by,... 

Improved separation behaviour is observed in quadrupole analyzers with hyperbolic rods (see Figure 3.9). The quadrupole field is produced by four parallel hyperbolic electrodes, whereby Equations 3.16-3.17 can be applied. 

Quadrupole with hyperbolic rods and applied potentials. The equipotendal lines are represented above, on the left. 

A quadrupole mass filter consists of four hyperbolic rods on which a potential U F0cos cot is applied (see Fig. 2.6). The hyperbolic shape lead to the production of a quadrupolar field, where the field intensity is linearly dependent on space. However, these conditions can be validly approximated by the use of cylindrical rods (see Fig. 2.7). The ions are injected in the z direction and experience a field due to the direct current (dc) and radio frequency (rf) potentials applied on... 

The quadrupole mass filter consists of four parallel hyperbolic rods in a square array (Figure 4.17). Cylindrical rods are in current use. The inside radius (field radius) is equal to the smallest radius curvature of the hyperbola. Diagonally opposite rods are electrically connected to radio frequency/ direct current voltages, which create a hyperbolic field within the rods. For a given radio frequency/ current voltage ratio, only ions of a dedicated m/z value are transmitted to the filter and reach the detector. Ions with a different m/z ratio are deflected away from the principal axis and strike the rods. To scan the mass spectrum, the frequency of the radio frequency voltage and the ratio of... 

Quadrupole Mass Filters Quadrupole mass analyzers consist of four electrodes, ideally of hyperbolic rods, that are accurately positioned in a radial array. For practical as well as economic reasons, most quadrupole mass filters have employed electrodes of circular cross section. A potential is applied to one pair of diagonally opposite rods consisting of a DC voltage and an rf voltage. To the other pair of rods, a DC voltage of opposite polarity and an rf voltage with a 180° phase shift are applied. The ion motion under the influence of this two-dimensional (2D) field can be described mathematically by the solutions to the second-order linear differential equation, known as Mathieu equation, from which the Mathieu parameters, and can be derived as... 

Quadrupole mass analyzers consist of four parallel circular or hyperbolic rods (Figure 1.17). Each pair of opposite rods are electrically connected and supplied voltages of the same magnitude but different polarity. The voltage applied to each pair consists of a direct current (DC), U, and a radiofrequency (rf) component, Vcosot. Typical values are several himdred volts for U, several ttiousand volts for V, and megahertz for m. Since the total potential of each rod is -i-(U + V cos tot) or -(U + Vcostot), the rf field periodically alternates the rods polarity. ... 

Thermo Einnigan linear ion trap In the Thermo Einnigan instrument shown in Figure 3, an ion beam from an electrospray source is directed through a heated capillary, two successive rod arrays, a front lens, and into a linear ion trap composed of three sections of quadrupole hyperbolic rod arrays with Zo = 4 mm. Radial confinement of ions is effected by the trapping potential well in the center section and axial confinement by dc potentials applied to the front and rear lenses. The basic design of the linear... 

The quadrupole mass analyzer consists of four hyperbolic rods at right angles to each other (see Fig. 10.6). A DC voltage is applied to all rods (adjacent rods have opposite signs) and the signs of the voltage are rapidly... 

The QIT consists of two hyperbolic electrodes serving as end caps along with a ring electrode that replaces two of the linear quadmpole rods, i.e., it could theoretically be obtained by rotating a linear quadmpole with hyperbolic rods by 360° (Fig. 4.43, 4.44). Thus, a section through the rz-plane of the QIT closely resem-... 

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