By Harald Rose
This moment version is a longer model of the 1st variation of Geometrical Charged-Particle Optics. The up to date reference monograph is meant as a consultant for researchers and graduate scholars who're looking a complete remedy of the layout of tools and beam-guiding platforms of charged debris and their propagation in electromagnetic fields. Wave facets are integrated during this variation for explaining electron holography, the Aharanov-Bohm impression and the solution of electron microscopes constrained through diffraction. numerous equipment for calculating the electromagnetic box are offered and tactics are defined for calculating the homes of platforms with arbitrarily curved axis. distinct tools are offered for designing and optimizing exact parts reminiscent of aberration correctors, spectrometers, power filters monochromators, ion traps, electron mirrors and cathode lenses. particularly, the optics of rotationally symmetric lenses, quadrupoles, and structures composed of those components are mentioned largely. Beam homes comparable to emittance, brightness, transmissivity and the formation of caustics are defined. Relativistic movement and spin precession of the electron are taken care of in a covariant method by means of introducing the Lorentz-invariant common time and through extending Hamilton’s precept from 3 to 4 spatial dimensions the place the laboratory time is taken into account because the fourth pseudo-spatial coordinate. utilizing this process and introducing the self motion of the electron, its accompanying electromagnetic box and its radiation box are calculated for arbitrary movement. additionally, the Stern-Gerlach impact is revisited for atomic and unfastened electrons.
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Extra info for Geometrical Charged-Particle Optics
83) along the optic axis is real resulting in Im Π = Az = 0. (λ + 1)! 4 Magnetic Vector Potential 49 Fig. 7. Arrangement of the conductors and the direction of the currents in a magnetic cylinder lens eθ = −ex sin θ + ey cos θ → − sin θ + i cos θ = iw/|w|. 85) We realize the antisymmetric potential approximately in the fringing-ﬁeld domains of sector magnets with plane entrance and exit faces. The potential of magnetic cylinder lenses represents the symmetric type. In the simplest case, such a lens is formed by two parallel inﬁnite wires located at the same distance a above and beneath the symmetry plane, respectively, as illustrated in Fig.
We can realize ﬁelds of this type approximately in the case of slit lenses and extended multipoles such that their extension along the axis of symmetry is large compared with the distance of their pole faces from this axis. In this case, we can approximate the ﬁeld within the multipoles with a suﬃcient degree of accuracy by that of a plane (two-dimensional) multipole. Without loss of generality, we can choose any of the three coordinates as the coordinate, which does not aﬀect the potential. However, to stay within the convention of charged-particle optics, the z-axis always represents the optic axis, which coincides with the axis of symmetry in the case of multipoles.
3 Ray Properties Associated with the Eikonal r ϑL = r0 eB ds. 69) It is important to note that the Larmor rotation does not aﬀect the location of the center of curvature. Hence, to guarantee that the normal unit vector en of the accompanying triad always points in the direction of the center of curvature K, we must rotate the triad back by the angle ϑL . 62) for the circulation, this component does not aﬀect the curvature of the trajectory. 3 Multipole Expansion of the Stationary Electromagnetic Field Constant currents form stationary magnetic ﬁelds.
Geometrical Charged-Particle Optics by Harald Rose