By Helmut Liebl
Authored by means of a pioneer of the sphere, this review of charged particle optics offers an excellent creation to the sphere for all physicists wishing to layout their very own gear or larger comprehend the tools with which they paintings. utilized Charged Particle Optics starts off through introducing electrostatic lenses and fields used for acceleration, focussing and deflection of ions or electrons. next chapters provide specified descriptions of electrostatic deflection components, uniform and non-uniform magnetic zone fields, snapshot aberrations, and, eventually, fringe box confinement. A bankruptcy on purposes is extra.
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In the x2 , y2 coordinate system the equation of a trajectory leaving the sector ﬁeld can be written y2 = L1 α1 + x2 1− L1 f α1 + λδ . 18) It is the equation of a lens plus the dispersion term λδ. 19) δ2 δ1 δ2 = δ1 = δ, 0 01 with L1 α1 = y1 , α1 = y1 . 2 Cylindrical Condenser 51 energy dispersion factor λ= sin √ √ 2φ 2 , focal distance (distance of focus from ﬁeld boundary) √ re cot 2φ √ , g= 2 distance of principal planes from ﬁeld boundary √ re tan φ/ 2 √ . 23) For small sector angles φ the sector ﬁeld can be considered a parallel plate condenser, and indeed, the dispersion factor becomes (with √ √ sin( 2φ) ≈ 2φ) λ = φ (comp.
25) is used the symmetric imaging √ case,√one obtains, with √ for √ L1 = 2f = re 2/ sin 2φ and λ = sin 2φ / 2, the theoretical energy resolution s1 ∆V = . 28) V0 th re Note that this does not depend on the sector angle φ. One important aspect in designing a sector ﬁeld energy analyzer is the choice of the gap width d. It should be wide enough so that the selected beam does not hit the plates somewhere in the ﬁeld. The plate spacing must therefore be wider than the largest beam width occurring in the ﬁeld.
Secondly, a high refractive power (=short focal length) can be achieved with a center electrode voltage comparable to the source voltage. In the accel–decel mode, a separate voltage supply with the opposite polarity as the source voltage supply is required, and much higher voltages are required for the same refractive power. In spite of this, the accel–decel mode is advantageous when the focal length required is not too short. The reason is that in this mode both the spherical and the chromatic image aberrations are smaller than in the decel–accel mode.