Ideal Quadrupole Field Research Articles

Transmission for a Quadrupole Mass Filter with Dipolar Excitation

Mass peaks are calculated using the numerical simulation of ion trajectories in the linear quadrupole with the dipole excitation(s). Using this data, diagrams for transmission versus resolution are calculated both for the ideal quadrupole field and for the quadrupole field with round rods. It is shown that, using the dipole excitation mode, resolution may be increased from R0.1 = 1000 to R0.1 = 2200 with 20% QMF transmission in an ideal case, and, for the round rods, the dipole excitation along the isoline βy = 0.01 enables an increase in resolution R0.1 from 500 to 800 at a 20% level of transmission.

On loading of a magneto-optical trap on an atom-chip with U-wire quadrupole field

ABSTRACTThe role of U-wire generated quadrupole-like magnetic field profile on loading of cold atoms in a magneto-optical trap (MOT) on atom-chip has been investigated. It is shown by simulations that the quadrupole field profile and the centre of the quadrupole field vary depending upon the U-wire current and bias field values. Moreover, the resemblance of generated field profile to the ideal quadrupole field critically depends on the values of current in U-wire and bias magnetic field. The observed number of trapped atoms in the MOT and its position has also been found to depend on the quadrupole field profile. The number of trapped atoms in the MOT reaches maximum when the field profile approaches close to an ideal quadrupole field. These studies are, in general, useful in optimizing the number in the MOT before transfer of these cold atoms to the microtraps of an atom-chip.

Dipole Excitation: A New Method for Mass Analysis with a Quadrupole Mass Filter.

Trajectory calculations are used to investigate peak shapes and ion transmission with a proposed new method of mass analysis with a quadrupole mass filter. Dipole excitation is applied to either the x or the y electrodes, or both, to create bands of instability within the first stability region. With excitation between the y electrodes (near β y = 0), ions are removed from the low mass side of a peak, and with ion excitation in x (near β x = 1), ions are removed from the high mass side. The mass resolution can be approximately doubled with comparatively little loss in ion transmission. Ion motion in an ideal quadrupole field and in the field of a quadrupole constructed with round rods has been studied. With an ideal quadrupole field, excitation in y is found to give better peak shape and resolution than excitation in x. With quadrupoles constructed with round rods, excitation in y is found to remove ions from both the low and high mass sides of a peak. The additional higher order multipoles introduced to the quadrupole potential by the use of round rods couple the x motion to the y motion so that exciting the y motion also excites ions in x. Thus, only excitation in y is necessary. Both with an ideal quadrupole field and quadrupoles constructed with round rods, the resolution can be increased ca. ×2 with little loss of transmission. Graphical Abstract ᅟ.

Mass resolution of linear quadrupole ion traps with round rods.

Auxiliary dipole excitation is widely used to eject ions from linear radio-frequency quadrupole ion traps for mass analysis. Linear quadrupoles are often constructed with round rod electrodes. The higher multipoles introduced to the electric potential by round rods might be expected to change the ion ejection process. We have therefore investigated the optimum ratio of rod radius, r, to field radius, r0, for excitation and ejection of ions. Trajectory calculations are used to determine the excitation contour, S(q), the fraction of ions ejected when trapped at q values close to the ejection (or excitation) q. Initial conditions are randomly selected from Gaussian distributions of the x and y coordinates and a thermal distribution of velocities. The N = 6 (12 pole) and N = 10 (20 pole) multipoles are added to the quadrupole potential. Peak shapes and resolution were calculated for ratios r/r0 from 1.09 to 1.20 with an excitation time of 1000 cycles of the trapping radio-frequency. Ratios r/r0 in the range 1.140 to 1.160 give the highest resolution and peaks with little tailing. Ratios outside this range give lower resolution and peaks with tails on either the low-mass side or the high-mass side of the peaks. This contrasts with the optimum ratio of 1.126-1.130 for a quadrupole mass filter operated conventionally at the tip of the first stability region. With the optimum geometry the resolution is 2.7 times greater than with an ideal quadrupole field. Adding only a 2.0% hexapole field to a quadrupole field increases the resolution by a factor of 1.6 compared with an ideal quadrupole field. Addition of a 2.0% octopole lowers resolution and degrades peak shape. With the optimum value of r/r0 , the resolution increases with the ejection time (measured in cycles of the trapping rf, n) approximately as R0.5 = 6.64n, in contrast to a pure quadrupole field where R0.5 = 1.94n. Adding weak nonlinear fields to a quadrupole field can improve the resolution with mass-selective ejection of ions by up to a factor of 2.7. The optimum ratio r/r0 is 1.14 to 1.16, which differs from the optimum ratio for a mass filter of 1.128-1.130.

Coil shape of a two-fold symmetric perfect superconducting quadrupole for use in common-coil twin magnets

A four-fold symmetric superconducting quadrupole with a coil shape generated by two perpendicular intersecting ellipses, produces the perfect quadrupole field. We have shown that a two-fold symmetric coil generated by two perpendicular ellipses of dissimilar sizes also can produce ideal quadrupole field. Two non-intersecting elliptic current distributions (one inside the other) also can generate quadrupole field. Such coil geometries can find application in common-coil twin quadrupole magnets.

General coil-shape in superconducting quadrupole magnets for generating the perfect field

It is well-known that a constant current in a coil configuration generated by two perpendicular intersecting ellipses produces the perfect quadrupole field. We have found that an ideal quadrupole field can be obtained with a variety of coil shapes and the intersecting ellipse shape is only a special form in that class. We have given the general form of the coil shape for generating the ideal quadrupole field. The shape parameters of the coil can be optimized to obtain the maximum possible gradient for a given coil cross-section and aperture.

A coil shape in superconducting quadrupole magnets for obtaining the perfect field

A cos(2θ) current distribution over a cylindrical surface gives an ideal quadrupolar field in so-called cos(2θ) quadrupoles. A constant current in a coil configuration generated by two perpendicular intersecting ellipses also produces the perfect quadrupole field. We have found that an ideal quadrupole field can be obtained with a coil shape, different from the intersecting ellipses. Block-coil quadrupoles have been designed based on the coil shape as well as the intersecting ellipse shape.

A new concave electrostatic lens with periodic electrode configuration

To obtain a large aperture lens with outstanding focal length homogeneity, a concave electrostatic quadrupole lens with a periodic configuration of the electrodes was developed and its performance was numerically studied. By adjusting the azimuthal angle (θc) of the electrode to an adequate periodic function along the lens axis, the integration of the field gradient along the axis, for a period (∫φdz/∫dz), becomes equal to an ideal quadrupole field distribution. To verify the usefulness of the lens, the beam spot distortion of the paraxial beam, which had an initial beam diameter of 90% of the lens radius, was calculated. The results revealed that the error of the focal length inside 90% of the lens radius was only 0.012% when the lens has nine period per unit length. Also, by considering the characteristics of the modified Bessel function, a simple formula for the uniformity of the focal length was obtained, and this expression agreed well with the simulation results.

Computer simulation of the quadrupole mass filter

The quadrupole mass filter is currently used in the most popular type of mass spectrometer, but its characteristics are not fully understood. A simple iterative method of numerical computation has been used to simulate ion trajectories in an ideal quadrupole field. The method is based on elementary equations of classical physics. Comparisons have been made with numerical integration techniques and matrix methods. A preliminary study of the quadrupole mass filter including an investigation of ion exit distributions with this iterative approach is presented. The distributions of ensembles of ions at the exit of the quadrupole field are presented with the aid of computer graphics.

Quadrupole fields in circular concave electrodes and poles

Two-dimensional equipotential models of circular concave quadrupole lenses are investigated. Exact solutions are carried out by the method of conformal mapping and expanded in series of multipoles. Conditions for approximating the ideal quadrupole field are obtained. Slight errors in an earlier, approximate treatment are detected.

Determination of multipole admixtures in quadrupole fields by incremental field measurement by means of a Hall probe

The field strength in an ideal quadrupole field is B( r) = g· r, where g is the gradient and r the distance from the neutral axis. It is possible to check the constancy of the field value at the distance r from the axis by means of a Hall probe, if the probe, which is led on a circle around the neutral axis, follows the given direction of the field also by rotation around its own axis. The two movements are coupled in a program-controlled measuring machine in which an adjusting device aligns the sensitive axis of the probe with its axis of rotation. The respective admixtures of higher multipole orders can be analysed from the fluctuation of the field value along the circle traversed.

Quadrupole Mass Filter: Circular Rods and Peak Shapes

A frequently observed characteristic of quadrupole mass filters is the appearance, at high resolution, of a separate “precursor” peak on the low mass side of each mass peak. The present report shows that such false precursor peaks can result from the use of round rods (rather than hyperbolic rods) that are common in all commercial instruments. Round rods introdnce sixth- and tenth-order terms to the ideal quadrupole field. We have computed the amount of sixth-order distortion introduced by the use of circular rods. The equipotential line produced at the surface of a round rod can be represented quite well by a quadrupole field with a large amount of sixth-order distortion. This distortion introduces a resonance line in the Mathieu stability diagram that at high resolution is near the edge of the peak on the low mass side. The resonance line can distort the peak to produce an apparent precursor peak.

Quadrupole Field in Circular Concave Electrodes

The fields in circular concave electrodes with both infinitesimal and infinite thickness are analyzed by giving appropriate boundary conditions, and the optimum electrode angles for approximating the ideal quadrupole field best are obtained. These angles are 44° for infinitesimal thickness and 37° for infinite thickness. These results are verified by field plotting method. The realization of these electrodes is also discussed.