Quadrupole field

If an ion has to travel from one end of a quadmpole to the other, it must have some kinetic energy in the z-direction. This kinetic energy can be induced by application of an accelerating potential to the ions before they enter the quadrupole field. 

Ion trap analyzer. A mass-resonance analyzer that produces a three-dimensional rotationally symmetric quadrupole field capable of storing ions at selected mass-to-charge (m/z) ratios. 

Py/GC/MS. pyrolysis, gas chromatography, and mass spectrometry used as a combined technique Py/MS. pyrolysis and mass spectrometry used as a combined technique oa-TOF. orthogonally accelerated time of flight Q. quadrupole field or instrument... 

Quadrupole analyzer A mass filter that creates a quadrupole field with dc and rf components so that only ions of a selected mass-to-charge are transmitted to the detector. 

The operation of this type of device is fundamentally different to those described previously in which ions of one m/z ratio at a time enter the mass analyser. By varying the conditions in the mass analyser, e.g. magnetic field, quadrupole field, etc., ions of different m/z values are brought to the detector and a corresponding mass spectrum obtained. 

For polarizable charge distributions, additional classical-type interactions arise from the induced dipole, quadrupole, and higher moments on each monomer, which are proportional to the fields created by the asymmetric charge distribution on the other monomer. The proportionality constants for each multipole field are the monomer polarizabilities aa and ah (a111 for dipole fields, a(Q) for quadrupole fields, etc.). The leading two induction interactions are ... 

The helium gas in the trap not only helps in trapping the ions but also cools them (i.e., the kinetic energy of a trapped ion is dissipated through repeated collisions with the He gas), thus forcing the ions to the center of the trap where the quadrupole field is best defined. Both sensitivity and mass resolution are significantly enhanced by the presence of the He gas. Moreover, the same He can also be used to induce fragmentation when working in the MS" mode (see below). 

JJor chemists interested in modem theories of chemical bonding, the most useful data obtainable by the Mossbauer technique are the magnitude and sign of the electric quadrupole field gradient tensor and the magnitude of the shift, 8, (which we prefer to call the chemical isomeric. Cl, shift), of the center of the Mossbauer spectrum relative to some standard absorber. Although a considerable amount of chemical and structural information is potentially available from quadrupole data on iron compounds, relatively little use has been made of such data in the literature, and we will not discuss this parameter here. We will instead restrict ourselves to two main points review of the explanations put forth to explain Cl shift data in iron compounds, and a survey of some of the correlations and generalizations which have been found. 

In case of an inhomogenous periodic field such as the above quadrupole field, there is a small average force which is always in the direction of the lower field. The electric field is zero along the dotted lines in Fig. 4.31, i.e., along the asymptotes in case of the hyperbolic electrodes. It is therefore possible that an ion may traverse the quadrupole without hitting the rods, provided its motion around the z-axis is stable with limited amplitudes in the xy-plane. Such conditions can be derived from the theory of the Mathieu equations, as this type of differential equations is called. Writing Eq. 4.24 dimensionless yields... 

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. 

The quadrupole ion trap (QIT) creates a three-dimensional RF quadrupole field to store ions within defined boundaries. Its invention goes back to 1953, [103-105] however, it took until the mid-1980s to access the full analytical potential of quad-mpole ion traps. [137-140] The first commercial quadmpole ion traps were incorporated in GC-MS benchtop instruments (Finnigan MAT ITD and ITMS). Electron ionization was effected inside the trap by admitting the GC effluent and a beam of electrons directly into the storage volume of the trap. Later, external ion sources became available, and soon a large number of ionization methods could be... 

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 (RE) 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 ion trap is a device that utilizes ion path stability of ions for separating them by their m/z [53]. The quadrupole ion trap and the related quadrupole mass filter tvere invented by Paul and Steinwedel [57]. A quadrupole ion trap (QITor 3D-IT) mass spectrometer operates with a three-dimensional quadrupole field. The QIT is formed by three electrodes a ring electrode with a donut shape placed symmetrically between two end cap electrodes (Fig. 1.20). 

We may arrive at this conclusion another way. In Table 13.6 the components xx —yy)/2, xy, xz, and yz are zero indicating that the quadrupole field is cylindrically symmetric about the z-axis. The axial moment around the x- or j-axis is... 

Quadrupole mass analyzers consist of four rods that produce a radio frequency quadrupole field. Only a single mass-to-charge ratio has a stable trajectory through the mass analyzer, but the electric potentials can be swept rapidly, either continuously or in discrete steps to measure a variety of masses. Quadrupole mass spectrometers are used in a wide variety of applications, but are not widely used in cosmochemistry. 

Resolution versus Sensitivity. A quadrupole mass filter can be programmed to move through a series of RF and dc combinations. The Mathieu equation, which is used in higher mathematics, can be used to predict what parameters are necessary for ions to be stable in a quadrupole field. The Mathieu equations are solved for the acceleration of the ions in the X, Y, and Z planes. A selected mass is proportional to (dc x RF x inner radius)/(RF frequency). For a given internal quadrupole radius and radio frequency, a plot can be made of RF and dc values that predict when a given mass will be stable in a quadrupole field. This is called a stability diagram (Figure 13.3). RF and dc combinations follow the value shown... 

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. 

The principles behind an ion trap mass spectrometer are similar to those of the quadrupole mass filter, except that the quadrupole field is generated within a three-dimensional cell using a ring electrode and no filtering of the ions occurs. All of the steps involved in the generation and analysis of the ions take place within the cell, and in order to detect the ions they must be destabilized from their orbits, by altering the electric fields, so... 

An ideal quadrupole field can be generated using four parallel electrodes (Z, = 5 to 20 cm) which have a hyperbolic cross-sectional field at their interior (Fig. 16.9). The electrodes are coupled in pairs and a potential difference U is applied across the pairs. If the distance between two opposite electrodes is 2 r0, then the potential d> within the xy plane of the quadrupole will be given by ... 

Welsh suggested correctly that similar transitions take place even if the molecular pair is not bound. The energy of relative motion of the pair is a continuum. Its width is of the order of the thermal energy, Efree 3kT/2. Radiative transitions between free states occur (marked free-free in the figure) which are quite diffuse, reflecting the short lifetime of the supermolecule. In dense gases, such diffuse collision-induced transitions are often found at the various rotovibrational transition frequencies, or at sums or differences of these, even if these are dipole forbidden in the individual molecules. The dipole that interacts with the radiation field arises primarily by polarization of the collisional partner in the quadrupole field of one molecule the free-free and bound-bound transitions originate from the same basic induction mechanism. 

As mentioned above, for the H2-He pair two principal induction mechanisms exist multipole and overlap induction. Multipolar induction occurs mainly in the electric quadrupole field of H2 which polarizes the colli-sional partner (He). Qualitatively, the nature of the partner X is of little significance as long as it is polarizable. Quantitatively, one expects highly polarizable species (like Xe) to give rise to much stronger rotational lines than more weakly polarizable atoms (like He). Mainly for that reason, the rotational lines of H2-He are much weaker than those of H2-H2. (Another reason is that for H2-H2, molecule 1 induces a dipole in 2 and 2 induces one in 1, thereby doubling the intensities.)... 

Further mathematical operations allow the equation of motion of an ion in the x-plane of a quadrupole field (Eq. (6)) to be determined as follows. 

PENNING TRAP A different approach to mass measurements was developed at Mainz. Thermal ions can be confined in a static homogenous magnetic field and a superimposed electrostatic quadrupole field. A measurement of the cyclotron frequency enables the measurement of the mass of the stored ion. A resolving 6 8 -7 -8... 

The muon g — 2 value has been determined in a series of experiments at CERN [45,46]. The primary purpose of the new muon g — 2 experiment at Brookhaven National Laboratory is to improve the precision of the experiment by about a factor 20 and verify the presence of the electroweak effect which has been evaluated to two loop orders in the Standard Model. In this experiment, polarized muons from pion decays are captured in a storage ring with a uniform magnetic field and a weak-focusing electric quadrupole field. For a muon momentum of 3.09 GeV/c and 7 = 29.3 the muon spin motion is unaffected by the electric quadrupole field and the difference frequency uia is given by... 

The trapping field is similar to that discussed by Pritchard [18] and Hess[7] and is generated by a superconducting coil system operated during the measurements in persistent mode. For radial confinement we use four racetrack shaped coils which provide a quadrupole field. At maximum current (36 A) the quadrupole field reaches 1.4-1.5 Tesla at r-6.5mm, the surface of the sample cell. Two dipole fields are used for axial confinement. They are located near the ends of the racetracks at z- +50mm and z--50mm with respect to the center of the trap. 

Ion lifetimes as long as milliseconds have been measured in a number of different ways. One of the earliest methods involved flight tubes some metres long along which the ions were passed at relatively low velocities and within which the decompositions studied occurred [817, 818, 878]. The trajectories were stabilized by electric radio frequency quadrupole fields. Ionization was by electron impact and decompositions of carbonium ions derived from alkanes were observed over the time range 1/is to 1 ms. 

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