Fringe field distortions

Figure 5. Three-terminal parallel-plate capacitor showing uniform field lines (dashed lines) between the high-voltage (H) and low-voltage (L) electrodes. Fringing fields (distorted dashed lines) are present only between the electrode H and the guard electrode, C. The ensemble is enclosed by a metal screen connected to ground (detailed scheme in the Supplemental Material of reference [28]).

The equations of motion used to describe the trajectory of an ion in a linear quadmpole (Equation [6.12], Section 6.4.2) are strictly valid only well inside the rod assembly, well removed from the entrance and exit. At each of these ends the ideal quadmpole field (Equation [6.11]) terminates abmptly, but in any real device is affected not only by the RF and DC potentials applied to the rods but also by the potentials applied to nearby ion optical elements (lenses etc.). Moreover, the field lines created by the potentials applied to the rods spill out for some distance outside the theoretical boundaries. These curved fringe fields (Section 6.4.2a) distort the ideal quadmpole field such that the ion motions in the x- and y-directions that are independent of one another in the main quadmpole field (Equation [6.11]) become coupled as a consequence of mixing radial and axial potentials, i.e. the electrical force exerted on an ion in the z-direction can be a function of the time dependent potentials applied in the X- and y-directions (but now curved in three-dimensions), and vice versa. These effects of fringe fields are important in the following discussion. 

We have recently shown that the presence of phase-separated structures in polymer-blend microparticles can be indicated qualitatively by a distortion in the two-dimensional diffraction pattern. The origin of fringe distortion from a multi-phase composite particle can be understood as a result of refraction at the boundary between domains of different polymers, which typically exhibit large differences in refractive index. Thus, the presence of separate sub-domains introduces optical phase shifts and refraction resulting in a randomization (distortion) in the internal electric field intensity distribution that is manifested as a distortion in the far-field diffraction pattern. 

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