Electromagnetism

Applied Charged Particle Optics by Helmut Liebl

By Helmut Liebl

Authored via a pioneer of the sector, this evaluation of charged particle optics presents a superb advent to the sphere for all physicists wishing to layout their very own equipment or greater comprehend the tools with which they paintings. utilized Charged Particle Optics starts via introducing electrostatic lenses and fields used for acceleration, focussing and deflection of ions or electrons. next chapters supply certain descriptions of electrostatic deflection components, uniform and non-uniform magnetic region fields, picture aberrations, and, eventually, fringe box confinement. A bankruptcy on purposes is further.

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62) 36 1 Lenses: Basic Optics Since both V1 and V2 have to be positive to let particles pass through the apertures, the focal length f is always positive for any ratio V1 /V2 (except the trivial case V2 = V1 ). 62) for either V1 /V2 < 1 or V1 /V2 > 1. Thus, it is not possible to operate such a lens with telescopic imaging as the emission lens shown in Fig. 30 (acceleration field plus immersion lens). This means that any change of beam energy is linked with focusing of the beam by the accelerating or decelerating field.

Fig. 39 shows an example of a symmetric einzel lens constructed of apertured electrodes. The potential distribution resembles a saddle surface when the equipotential lines are considered as topographic level lines. Two modes of lens operation are possible: decel– accel and accel–decel, represented by the axial potential distribution shown in the figure. The “lens strength” D/f of the lens (Fig. 40) 40 1 Lenses: Basic Optics Fig. 40. Typical dependency of refractive power of einzel lens on the potential of the middle electrode VL for a beam energy eVB has two branches for the two modes.

25) has its opti◦ mum for √ a given ratio s1 /L1 with φ = 90 → λ = 1. It is better by a factor 2 than with the cylindrical condenser. With this sector angle, the object distance can be up to infinity before the image position is at the sector field exit. In case of symmetric imaging, we have here l1 = l2 = g + f = re cot (φ/2) (Figs. 13). These distances become zero for φ = 180◦ . 25) and L1 = 2fr = 2re , sin φ λ = sin φ, ∆V V0 = th s1 . 40) 58 2 Electrostatic Deflection Fig. 11. Lens action of spherical condenser, radially and axially.

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