Wiley-McLaren space focusing

When reaction products are formed in a finite region, rather than a point source, it is best to extract the ions with a combination of acceleration and drift regions which are consistent with the Wiley-McLaren space focusing condition (Wiley and McLaren, 1955). Specific ratios of acceleration and drift distances for given electric fields are imposed so that the ion TOP is independent of the precise initial position of ionization. This is easily explained as follows. Suppose that two ions (with initially zero kinetic energy) are formed at positions Uj + 8 and tij — 8 as measured from the second acceleration, or drift region. Clearly the ion closer to the drift region will reach this... 

Figure 5.25 Ion TOP distributions for isotropic angular distribution of dissociation products. The mass of the fragment ion is 30 amu, the electric fields in the first two acceleration regions are 10 and 100 V/cm and the acceleration distances are 2 and 1 cm, respectively. The drift distances are indicated in the figure. The d = 55 cm corresponds to the Wiley-McLaren space focusing condition. For each drift distance, the ion TOF was calculated for three product translational energies of 0, 0.5, and 1.0 eV.

Today, the modern version of time-lag focusing, or delayed extraction,14 16 is used in almost all MALDI-TOF mass spectrometers. It is in fact a special case of the Wiley and McLaren method, in which the initial spatial distribution (usually a very thin sample and matrix mixture dried on a stainless steel plate) is assumed to be zero. Therefore, after the delay time the velocity and spatial distributions are correlated, i.e. ions of highest velocity have moved the greatest distance. This space velocity correlated focusing has been described by Colby and Riley,17 and provides considerably better focusing than can be obtained from two independent and uncorrelated initial distributions in space and velocity/energy that comprise the general Wiley-McLaren case. 

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