Abstract. The dynamics of sa'turated two-dimensional superfluid 4He films is shown to be gO,verned by the Kadomtsev-Petviashvili equation with negative dispersion. It is established that the phenomena of soliton resonance could be observed in such films. Under the .lowest order nonjinearity, such resonance would happen only if two dimensional effects arc taken into ,account. The amplitude and velocity of the resonant soliton are obtained.

We consider the case of a quadrupole mass spectrometer (QMS) in which a static magnetic field is applied axially in the z-direction along the length of the mass filter. The theoretical approach assumed in the model is that the QMS contains hyperbolic rods as electrodes and that the magnetic field acts over the full length of the mass filter assembly. Initial experimental results with argon and helium for a low-resolution instrument confirm the predicted theoretical trends. The analysis also predicts for which values of operating parameters an enhancement of the instrument resolution is achieved when an axial magnetic field is applied. The model predicts instrument resolution R Ͼ3000 for a QMS with a 200 mm long mass filter via application of an axial magnetic field. Attributes of the QMS such as versatility, accuracy, low cost, mass range, and sensitivity have ensured that it has been deployed in a wide range of applications, varying considerably from the modest residual gas analyzer to high-performance mass spectrometer for chemical analysis of simple and complex molecules, e.g., when used in conjunction with gas chromatography [7,8]. Different applications have different requirements for resolution, sensitivity, and stability.There have been many analytical predictions of the behavior of QMS. Dawson used matrix methods to calculate ion transmission for various scan lines and various apertures both with and without fringing fields, based on maximum ion displacements for mass filters [9]. Later research describes the performance of the QMS more comprehensively by solving the Mathieu equation in two dimensions for an infinitely long mass filter [2]. Batey showed that some features of the behavior of the QMS could be predicted by tracing the motion of ion through the mass filter [10]. Muntean used the matrix method to develop a computer simulation program to model ion transmission through the filter by calculating ion trajectories in radio frequency (rf) only quadrupoles [11]. More examples of such types of analytical work include the modeling of ion transmission through the filter by calculating ion trajectories in exactly determined hyperbolic quadrupole fields [12], the effects of rf frequency, phase and magnitude on the performance of QMS [13], and the effects of initial ion energy and quadrupole rod length on transmission percentage of ions through the mass filter along with the effects of aperture parameters [14]. Some workers have developed computational methods to determine the trajectories of large number of ions in QMS; their computer program generates large number of ions (at least 10 5 ions injected into the quadrupole model at each point on the mass scale), thus providing a detailed computer simulation for both hyperbolic and circular rods [15,16]. Douglas and Konenkov have used numerical calculations to investigate the influence of electrode radius r to field radius r 0 , which is referred to as (r/ r 0 ) on the peak shape for a linear QMF constructed with round rods [17]. Other workers have used com...

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The qualitative and quantitative identification of low mass isotopes in the mass range 1-6 u poses certain difficulties when attempting to achieve the required resolution with an instrument suitable for deployment within a process environment. Certain adjacent species present in the process sample (HT and D 2 ) require a resolution greater than 930 to achieve an accurate measurement. We demonstrate here through simulation techniques that this level of performance required is unachievable using commercially available instruments. Using previously reported simulation techniques, this article demonstrates how the required performance for resolving the low mass isotopes can be achieved by a quadrupole mass spectrometer (QMS), which incorporates a quadrupole mass filter (QMF) constructed from hyperbolic electrodes and operated in zone 3 of the Mathieu stability diagram. (J Am Soc Mass Spectrom 2010, 21, 1364 -1370

The phenomenon of two-solilon resonances of the Kadomtsev-Petviashvilli equation for the superfluid surface density OUl:tuation in He films is studied. The velocity of [he resonant wliton is obtained.Recently the study of soHton propagation in helium ftlms has received much attention. The intrinsic nonlinearity in this system arising from the van der Waals potential due to the substrate suggests the existence of solitonic behaviour. Several experiments r I] in 4He films indicate the propagation of undistorted waves at very low temperatures. These finite amplitude effects are not explained in terms of a linearized theory.