Trapping region

Fig. 1. Schematics of an electrospray ion trap mass spectrometer. The ions produced from the electrospray ion source are transferred into the vacuum system of the mass spectrometer and guided into the trapping region where they are stored. After storage they can be scanned toward the detector to generate a mass spectrum. Alternatively, ions of a single m/z can be stored inside the trap, accelerated so that they fragment on collision with restgas molecules, and the fragments can be scanned toward the detector to determine their mass.

Stratographic trap Regions of the seabed where steep gradients in porosity retard the migration of petroleum and hence cause large pools of oil, gas and tar to accumulate. 

In the cement industry, the term hydration is used to describe a range of reactions between cement and water to produce a hardened product. A cement clinker particle is a multiphase solid having massive calcium silicate grains (50-100 pm) in a matrix of interstitial aluminate and ferrite. This is described as analogous to a distorted clay sequence, which traps regions of porosity-pore size distribution from nanometer to micrometer. 

The H atoms will not be confined by the constant solenoid field and therefore leave the trap region with an energy distribution given by the temperature of the e+-plasma and its rotation speed. 

Typical trajectories calculated by this Monte Carlo method are shown in Fig. 8. The overall result is that about 7 x 10-5 of all antihydrogen atoms initially formed in the trap region can be transported to the H detector after S2. At expected formation rates of about 200/s [32] this would result in a count rate of 1 event per 2 minutes on resonance. This seems rather small, but is feasible since the antihydrogen atoms can be easily detected with unity efficiency from the annihilation of their constituents. 

The experimental configuration is shown in Fig. 1. The EBIT uses an intense and mono-energetic electron beam which is magnetically confined to trap and ionize charged ions. Metal ion species such as vanadium are created by a metal vapour vacuum arc (MEVVA) and are sequentially ionized as they enter the trap region of the electron beam. The NIST EBIT and spectra are described in further detail elsewhere [13,14]. 

When applying the Poincare-Ben-dixson theorem, it s easy to satisfy conditions (1)—(3) condition (4) is the tough one. How can we be sure that a confined trajectory C exists The standard trick is to construct a trapping region R, i.e., a closed connected set such that the vector field points inward everywhere on the boundary of R (Figure 7.3.2). Then all trajectories... 

When polar coordinates are inconvenient, we may still be able to find an appropriate trapping region by examining the system s nullclines, as in the next example. 

Now consider the region bounded by the dashed line shown in Figure 7.3.5. We claim that it s a trapping region. To verify this, we have to show that all the vectors on the boundary point into the box. On the horizontal and vertical sides, there s no problem the claim follows from Figure 7.3.4. The tricky part of the construction is the diagonal line of slope —1 extending from the point b, b/a to the nullcline y = x/(a + x ). Where did this come from ... 

This inequality implies that the vector field points inward on the diagonal line in Figure 7.3.5, because dy/dx is more negative than -1, and therefore the vectors are steeper than the diagonal line. Thus the region is a trapping region, as claimed. ... 

Can we conclude that there is a closed orbit inside the trapping region No There is a fixed point in the region (at the intersection of the nullclines), and so the conditions of the Poincard-Bendixson theorem are not satisfied. But if this fi xed point is a repeller, then we can prove the existence of a closed orbit by considering... 

Using numerical integration, compute the limit cycle of Exercise 7.3.1 and verify that it lies in the trapping region you constructed. 

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